Multi-Epoch Spectropolarimetry for a Sample of Type IIn Supernovae: Persistent Asymmetry in Dusty Circumstellar Material

We present multi-epoch spectropolarimetry and spectra for a sample of 14 Type IIn supernovae (SNe IIn). We find that after correcting for likely interstellar polarization, SNe IIn commonly show intrinsic continuum polarization of 1--3% at the time of peak optical luminosity, although a few show weaker or negligible polarization. While some SNe IIn have even stronger polarization at early times, their polarization tends to drop smoothly over several hundred days after peak. We find a tendency for the intrinsic polarization to be stronger at bluer wavelengths, especially at early times. While polarization from an electron scattering region is expected to be grey, scattering of SN light by dusty circumstellar material (CSM) may induce such a wavelength-dependent polarization. For most SNe IIn, changes in polarization degree and wavelength dependence are not accompanied by changes in the position angle, requiring that asymmetric pre-SN mass loss had a persistent geometry. While 2--3% polarization is typical, about 30% of SNe IIn have very low or undetected polarization. Under the simplifying assumption that all SN IIn progenitors have axisymmetric CSM (i.e. disk/torus/bipolar), then the distribution of polarization values we observe is consistent with similarly asymmetric CSM seen from a distribution of random viewing angles. This asymmetry has very important implications for understanding the origin of pre-SN mass loss in SNe IIn, suggesting that it was shaped by binary interaction.


INTRODUCTION
The environment into which a supernova (SN) explodes may substantially influence what we observe, and that surrounding environment is the product of immediate pre-SN mass loss. While a range of densities are inferred around various types of SNe, the highest density circumstellar material (CSM) is inferred for Type IIn events (SNe IIn), which show strong narrow emission lines in their spectra. The origin of this dense CSM remains uncertain, but it cannot be produced by any normal winds observed in massive stars (Smith 2017). Luminous blue variables (LBVs) such as η Car -which shows substantial axisymmetric CSM in the Homunculus Nebula (Thackeray 1949;Gaviola 1950) -are often suggested as progenitors of SNe IIn (Smith 2005;Smith & Owocki 2006;Smith et al. , 2011bSmith 2014;Gal-Yam et al. 2007;Trundle E-mail: cgbilinsk@gmail.com et al. 2008). Studying the geometry of the SN environment at the time of death may help connect progenitor types to various SNe, since some scenarios for mass loss (binary interaction, mergers, rapid rotation) are expected to produce strong asymmetry in the CSM.
SNe IIn are thought to be the result of fast SN ejecta colliding with dense CSM that was expelled just prior to the death of the progenitor (see Smith 2014 or Smith 2017 for reviews). This slow, pre-shock CSM is seen spectroscopically as narrow (100-500 km s −1 ) and intermediate-width (1000-3000 km s −1 ) Balmer-series emission lines that dominate the optical spectrum, and the shock interacting with CSM generally causes enhanced luminosity with a smooth blue continuum at early times (Schlegel 1990;Filippenko 1997;Smith 2017). Although CSM interaction produces most of the luminosity for typical SNe IIn, the underlying SN ejecta may also be detected as broad emission and absorption features at later times.
A common tool used in studying the shape of SNe IIn is that of spectroscopy. Spectroscopic line profiles can reveal expansion asymmetries along our line of sight, and how they evolve with time. Indeed, numerous observations imply asphericity in SNe IIn in both their CSM and SN ejecta (for example, SN 1988Z: Chugai & Danziger 1994;SN 1995N: Fransson et al. 2002SN 1997eg: Hoffman et al. 2008SN 1998S: Leonard et al. 2000Wang et al. 2001;Fransson et al. 2005;SN 2005ip: Smith et al. 2009Katsuda et al. 2014;SN 2006jd: Stritzinger et al. 2012SN 2006tf: Smith et al. 2008SN 2009ip: Mauerhan et al. 2014Reilly et al. 2017;SN 2010jl: Smith et al. 2012Fransson et al. 2014;PTF11iqb: Smith et al. 2015;SN 2012ab: Bilinski et al. 2018SN 2013L: Andrews et al. 2017SN 2014ab: Bilinski et al. 2020iPTF14hls: Andrews & Smith 2018;SN 2017hcc: Smith & Andrews 2020. A less commonly used tool, though powerful for constraining the geometry of the continuum photosphere, is that of spectropolarimetry. Several studies have been published using spectropolarimetry to study the nature of SNe II-P (see Leonard et al. , 2006Chornock et al. 2010;Dessart et al. 2021). Generally, in SNe II the polarization signal is initially small, increases throughout the photospheric phase, reaches a maximum at the beginning of the nebular phase, and then drops as the inverse of time squared. In SNe II-P, the emission arises from freely expanding SN ejecta, and so polarization points to asymmetry in the ejecta, and therefore, asymmetry in the explosion itself. In SNe IIn, on the other hand, emission arises from the CSM, the shock interaction between the ejecta and CSM, and possibly the freely expanding SN ejecta. As such, observed polarization in SNe IIn may trace the geometry of the CSM more than that of the SN explosion, making the interpretation complicated. Spectropolarimetric results have been published for only a handful of SNe IIn (SN 1997eg: Hoffman et al. 2008SN 1998S: Leonard et al. 2000SN 2006tf: Smith et al. 2008SN 2010jl: Patat et al. 2011SN 2009ip: Mauerhan et al. 2014Reilly et al. 2017;SN 2012ab: Bilinski et al. 2018SN 2013fs: Bullivant et al. 2018SN 2014ab: Bilinski et al. 2020SN 2017hcc: Kumar et al. 2019. The majority of SNe IIn with published spectropolarimetric data exhibit continuum polarization signals on the order of 1-3%. These data do not yet provide a unified picture, however, as the timing of this polarization signal, variations in the position angle, diverse polarization changes across line profiles, and uncertain interstellar polarization (ISP) estimates make the overall picture complicated. It is difficult in the case of SNe IIn to disentangle the underlying SN ejecta and their geometry from that of the bright and spatially more extended CSM interaction regions. Unlike in normal core-collapse SNe, where the polarization arises from centrosymmetric scattering in homologously expanding ejecta, in SNe IIn, the main source of luminosity (the shock running into CSM) is itself spatially extended and likely asymmetric. Furthermore, at least one SN IIn (SN 2014ab) exhibits relatively low levels of continuum polarization but shows signs of significant asymmetry spectroscopically, suggesting that the viewing angle may substantially impact the continuum polarization measurements of SNe IIn (Bilinski et al. 2020). If this is the case, then more SNe IIn with relatively low intrinsic continuum polarization are likely to have been detected, but perhaps the data remain unpublished because of a bias toward publishing significantly polarized events.
A further dilemma in SN IIn polarization studies is the mismatch between the very few models that have been created for these particular type of objects and the observations. Dessart, Audit, & Hillier (2015); Vlasis, Dessart, & Audit (2016); Kurfürst, Pejcha, & Krtička (2020); Williams et al. (2023, in prep.) obtain polarization signals of up to ∼ 2% when modelling various geometries with both symmetric and asymmetric SN ejecta and diverse surrounding environments. These models do not account for the polarization signals seen for recent objects such as SN 2017hcc with polarization as high as ∼ 6%. We present spectropolarimetric data obtained for a sample of 14 SNe IIn: SN 2010jl, SN 2011cc, PTF11iqb, SN 2011ht, SN 2012ab, SN 2009ip, SN 2014ab, Master OT J044212.20+230616.7 (M04421), ASASSN-14il, SN 2015da, SN 2015bh, PS15cwt, SN 2017gas, and SN 2017hcc, obtained over the course of ∼ 8 yr by the Supernova Spectropolarimetry (SNSPOL) project. 1 Some objects have only 1 epoch of spectropolarimetry (SN 2011cc, SN 2011ht, PTF11iqb, M04421, andPS15cwt), while others have multiple epochs (as many as 11 epochs in the case of SN 2010jl). Although the population of SNe IIn has proven itself to be polarimetrically diverse, we attempt to form a more unified picture for SNe IIn using this large spectropolarimetric data sample.

Photometry
We reference photometry for objects available on the Open SN catalog (Guillochon et al. 2017) or from the Super-LOTIS (Livermore Optical Transient Imaging System; Williams et al. 2008) telescope to constrain the approximate date of peak absolute magnitude for all of the SNe IIn we study herein. Table 1 shows the peak dates and peak absolute magnitudes (including the filter they were taken with) for each of our objects. We use these peak dates as a reference point for every object throughout the paper. In general, the SNe IIn within our sample show a wide diversity of peak absolute magnitudes and light curve durations.

Spectropolarimetry
Our spectropolarimetric observations were obtained using the CCD Imaging/Spectropolarimeter (SPOL; Schmidt, Stockman, & Smith 1992) on the 61" Kuiper, 90" Bok, and 6.5 m MMT telescopes. We enumerate all of our observations in detail in Table 2. Observations often spanned multiple nights within a single observing run, so we combined these data into a single epoch to improve the signal-to-noise ratio in the data.
All spectropolarimetric observations were obtained using a rotatable semi-achromatic half-wave plate to modulate incident polarization and a Wollaston prism in the collimated beam to separate the orthogonally polarized spectra onto a thinned antireflection-coated pixel 800 × 1,200 SITe CCD. In order to account for detector quantum efficiency differences and pixel-to-pixel variations, we took a series of four separate exposures that sample a total of 16 different orientations of the waveplate. Although only four waveplate positions are necessary to isolate the ordinary and extraordinary beams  (Stoll et al. 2011), b , c , d (Brown et al. 2014), e , f , g (Bilinski et al. 2020), h (Goranskij et al. 2016).
a This peak date is also either the discovery date or very close to the discovery date for the object, implying that the estimate of the peak date is highly uncertain and was likely sometime before this date.
into Stokes Q1, Q2, U1, and U2, which accounts for variations in detector efficiency, we use a redundant set of 16 orientations to minimize instrumental variation associated with waveplate orientation. The data are then combined using the prescription in Miller et al. (1988). We used the 964 lines mm −1 grating blazed at 14.6°( 4639Å) on the MMT telescope. In this configuration, we obtain a slit demagnification of 0.76, a dispersion of 2.62Å per pixel, and a spectral coverage of 3140Å. We used 600 lines mm −1 grating blazed at 11.35°(5819Å) on the Kuiper and Bok telescopes. In this configuration, we obtain a slit demagnification of 0.81, a dispersion of 4.14Å per pixel, and a spectral coverage of 4970Å. A variety of slit widths were used at each telescope, depending on weather conditions. These exact settings can be found in Table 2 for each specific observation. A typical slit width (4.1 ) at the Bok and Kuiper thus provides spectral resolution of ∼26Å, while a typical slit width (1.5 ) at the MMT provides spectral resolution of ∼16Å. Our analysis is restricted to a wavelength range of 4400-7000Å to avoid spurious detections and fluctuations at the edge of our detector. Observations at the MMT were made at the parallactic angle except in cases where this would result in significant background contamination. Observations made at the Bok and Kuiper telescopes relied on another program using SPOL to observe active galactic nuclei, in which the rotation angle was fixed, so observations were made without regard to the parallactic angle.
A number of polarized stars (Hiltner 960, VI Cyg 12, BD +64 106, BD +59 389, HD 245310, and HD 155528) were used to calibrate the position angle (Schmidt, Elston, & Lupie 1992). We found the discrepancy between the measured and the expected position angle to be < 0.2°between multiple polarimetric standard stars. We also observed a number of unpolarized standard stars (BD +29 4211, G191B2B, and Table 2. Spectropolarimetric observations taken with the 61" Kuiper, 90" Bok, and 6.5 m MMT telescopes. Days are measured relative to the date of the peak observed magnitude for each SN. Ap. indicates the slit width size in arcseconds for the aperture used. Multiple slit widths are listed if multiple images were taken on the same day using different slit widths for the different exposures. Exp. indicates exposure times for each full Q or U sequence at every waveplate position, so the total exposure time on the target is twice this value.      HD 212311) to verify that we had low instrumental polarization (typically < 0.1%) for each set of observations (Oke 1990). The data were then also flux calibrated using the unpolarized standard stars. Spectropolarimetric data reduction was performed using IRAF 2 . Specifically, each observation was bias subtracted, flat fielded, and wavelength calibrated (typically using He, Ne, and Ar lamp spectra). We used a fully-polarizing Nicol prism placed in the beam above the slit to correct for the efficiency of the waveplate as a function of wavelength. When binning our data, we bin the data in q and u weighted by photon count first (though flux-weighting provides nearly identical results), then compute derivative properties, such as the polarization or position angle. Throughout the paper we use two continuum wavelength bins: 5100-5700Å and 6000-6300Å.

Non-Polarization Spectroscopy
In order to better constrain the ISP by using interstellar Na i D absorption line equivalent widths, we also obtained higher resolution spectra than SPOL provides. We obtained moderate-resolution (R ∼ 4000) spectra using the A detailed summary of each of these basic parameters and the sources from which they are derived is discussed in § 3.
1200 lines mm −1 grating in the Blue Channel (BC) spectrograph mounted on the MMT. We obtained these spectra for SN 2011cc, PTF11iqb, SN 2011ht, SN 2009ip, M04421, ASASSN-14il, PS15cwt, and SN 2017gas at times while the SNe were still bright. All spectra were taken with the long slit at the parallactic angle. Standard spectral reduction procedures were followed for all of the spectra. As discussed in more detail in § 4.1, these spectra are used for the purpose of estimating Na i D absorption line equivalent widths since these objects did not have previously determined values in the literature (or had such low estimates that previous authors chose to neglect the implied host-galaxy reddening).

BACKGROUND INFORMATION ON TARGETS
We list basic parameters for each of the SNe IIn in our sample in Table 3 and discuss them in more detail below. Additionally, we summarize key published results for each object.  (Riess et al. 2005) and taking into account influences from the Virgo cluster, the Great Attractor, and the Shapley supercluster, as we do for all of our targets]. We use a host-galaxy reddening of AV = 0.093 mag (EB−V = 0.030 mag), taken from Patat et al. (2011) as shown in Table 4. The total extinction (host-galaxy and Milky Way) for SN 2010jl is AV = 0.168. SN 2010jl shows many similarities to the bipolar geometry of η Car-it likely arose from a luminous blue variable (LBV) detonating as a SN into a dense bipolar CSM (Smith et al. 2011aFransson et al. 2014). Smith et al. (2011a) identified a candidate massive (> 30M ) progenitor to SN 2010jl in archival Hubble Space Telescope imaging, consistent with the LBV progenitor scenario. However, with a more precise position from post-exposion HST imaging, Fox et al. (2017) find that this source is somewhat offset from the SN position and instead suggest that the progenitor was fully obscured. A diversity of interpretations of the dust properties of SN 2010jl have emerged, some claiming it has pre-existing dust (Andrews et al. 2011), some invoking post-shock dust formation Maeda et al. 2013;Gall et al. 2014), and some positing no dust (Zhang et al. 2012;Fransson et al. 2014). Spectropolarimetric data obtained by Patat et al. (2011);Quirola-Vásquez et al. (2019) show continuum polarization at ∼ 1.7-2% with strong line depolarization, suggesting very low levels of ISP (<0.3%), substantial asphericity, and a line forming region external to the photosphere.

SN 2011cc
SN 2011cc was discovered by the Lick Observatory Supernova Search on 2011 Mar. 17.52 at an unfiltered apparent magnitude of 17.7 (Mason et al. 2011). SN 2011cc is located in the galaxy IC 4612 (redshift z = 0.031895; Rines et al. 2002). We adopt a Milky Way extinction along the line of sight of AV = 0.028 mag (EB−V = 0.0090 mag; Schlafly & Finkbeiner 2011) and a redshift-based distance of 137.5 ± 9.6 Mpc from the NASA/IPAC Extragalactic Database. We estimate a hostgalaxy reddening of AV = 0.22 mag (EB−V = 0.070 mag) from Na i D absorption line equivalent widths (see § 4.1 for a detailed discussion on how we estimate this) in spectra taken on day −66 with the BC on the MMT as shown in Table  4. Only brief Astronomer's Telegrams discovering and then identifying SN 2011cc as a SN IIn have been published so far . The total extinction (host-galaxy and Milky Way) for SN 2011cc is AV = 0.246.

PTF11iqb
PTF11iqb was discovered by the Palomar Transient Factory on 2011 Jul. 23.41 at an unfiltered apparent magnitude of 16.8 (Parrent et al. 2011). PTF11iqb is located in the galaxy NGC 151 (redshift z = 0.012499; van Driel et al. 2016). We adopt a Milky Way extinction along the line of sight of AV = 0.088 mag (EB−V = 0.028 mag; Schlafly & Finkbeiner 2011) and a redshift-based distance of 50.2±3.5 Mpc from the NASA/IPAC Extragalactic Database. We estimate a hostgalaxy reddening of AV = 0.06 mag (EB−V = 0.019 mag) from the Na i D absorption line equivalent widths in spectra taken on day 57 with the BC on the MMT as shown in Table 4. The total extinction (host-galaxy and Milky Way) for PTF11iqb is AV = 0.147.
PTF11iqb was spectroscopically very similar to SN 1998S . Although it initially appeared as a SNe IIn, it quickly transformed into something more like a Type II-L or Type II-P SN, but with additional evidence of interaction again at late times . The progenitor for this object may have been a cool giant with an extended envelope, and the early spectra showed Wolf-Rayet-like features indicative of dense slow CSM heated by a shock . PTF11iqb showed extremely asymmetric line profiles at late times after ∼100 days, and  proposed that the progenitor was surrounded by an inner disk that was overrun by the SN photosphere. The expanding photosphere engulfed the disk and temporarily masked signs of CSM interaction, which were then revealed again at late times as the SN photosphere receded. We estimate a host-galaxy reddening of AV = 0.09 mag (EB−V = 0.029 mag) from the Na i D1 absorption line equivalent width in spectra taken on day 57 with the BC on the MMT as shown in Table 4. The total extinction (host-galaxy and Milky Way) for SN 2011ht is AV = 0.118.

SN 2011ht
Some initial studies of SN 2011ht suggested that it may have been a SN impostor ). However, more extensive studies ) and UV observations (Roming et al. 2012) suggested instead that SN 2011ht was indeed a core-collapse SN IIn, though subluminous due to a low 56 Ni yield. SN 2011ht serves as a prototype for a subclass of objects known as Type IIn-P that could arise from electron capture SNe or massive stars experiencing fallback of the SN ejecta . SNe IIn with a low 56 Ni yield might be similar to the event that originated the Crab Nebula (Smith 2013). A progenitor outburst was detected at the location of SN 2011ht between 287 and 170 days prior to the discovery date, further supporting the idea that the later explosion likely ran into previously ejected CSM (Fraser et al. 2013).

SN 2012ab
SN 2012ab was discovered by the Robotic Optical Transient Search Experiment on Jan. 31.35 at an unfiltered apparent magnitude of 15.8 (Vinko et al. 2012). SN 2012ab is located in the galaxy 2MASX J12224762+0536247 (redshift z = 0.018; Bilicki et al. 2014). We adopt a Milky Way extinction along the line of sight of AV = 0.057 mag (EB−V = 0.018 mag; Schlafly & Finkbeiner 2011) and a redshift-based distance of 82.3±5.8 Mpc from the NASA/IPAC Extragalactic Database. We use a host-galaxy reddening of AV = 0.19 mag (EB−V = 0.060 mag), taken from Bilinski et al. (2018) as shown in Table 4. The total extinction (host-galaxy and Milky Way) for SN 2012ab is AV = 0.243.
Spectroscopy of SN 2012ab suggests that the SN ejecta interact mostly with bluesifted CSM on the near side of the SN at early times, but then transition to having increased shock interaction with redshifted CSM on the far side of the SN at later times Gangopadhyay et al. 2020). Spectropolarimetry of SN 2012ab shows an initial polarization of 1.7% at early times that rises to 3.5% about 24 days later, which is around the same time that the receding CSM interaction began.

SN 2009ip
After already being known as a SN impostor transient since 2009   Table 4. The total extinction (host-galaxy and Milky Way) for SN 2009ip is AV = 0.100. SN 2009ip is a unique SN in that it was studied extensively before explosion. The initial event from 2009 was quickly categorized as an outburst from an LBV showing variability in the prior decade . A detection in archival HST images also revealed the presence of a quiescent progenitor star Foley et al. 2011). Then, in 2012, SN 2009ip garnered much more attention when it resurfaced with two connected brigthening events (Drake et al. 2012;Brimacombe 2012;Prieto et al. 2013). Although the terminal nature of these rebrightening events was contested (Pastorello et al. 2013), SN 2009ip has since faded to levels below that of the progenitor, confirming that it was a true core-collapse SN (Smith et al. 2022). Smith et al. (2013) found evidence for pre-SN CSM dust in early near-infrared spectroscopy of SN 2009ip, while comparing the observed evolution of the light curve and spectra to models suggested that SN 2009ip was the initially faint explosion of a blue supergiant much like SN 1987A, except with much stronger CSM interaction at peak (Smith, Mauerhan, & Prieto 2014).
The polarization of SN 2009ip has been studied in detail. Mauerhan et al. (2014) measured a V -band polarization of ∼ 0.9% at a position angle of θ ∼ 166°during the 2012a event, transitioning to a polarization of ∼ 1.7% at a position angle of θ ∼ 72°during the 2012b event, and then fading thereafter with further changes in the position angle. The evolution for SN 2009ip was interpreted to have arisen from an initially prolate explosion seen in the 2012a event colliding with an oblate CSM distribution during the 2012b event . Reilly et al. (2017) looked at the spectropolarimetric evolution of specific line features observed for SN 2009ip and found that an inclined disk-like CSM best explained the absorption features along with evolution of the position angle seen in SN 2009ip.
3.0.7 SN 2014ab SN 2014ab was discovered by the Catalina Sky Survey on 2014 Mar. 9.43 at an apparent V -band magnitude of 16.4 (MV = −19.0 mag) (Howerton et al. 2014). SN 2014ab is located in the galaxy VV 306c (redshift z = 0.023203; Vorontsov-Velyaminov 1959;Falco et al. 1999). We adopt a Milky Way extinction along the line of sight of AV = 0.083 mag (EB−V = 0.027 mag; Schlafly & Finkbeiner 2011) and a redshift-based distance of 104.4 ± 7.3 Mpc from the NASA/IPAC Extragalactic Database. We use a host-galaxy reddening of AV = 0.18 mag (EB−V = 0.057 mag), taken from Bilinski et al. (2018) as shown in Table 4. The total extinction (host-galaxy and Milky Way) for SN 2014ab is AV = 0.259. SN 2014ab was found to exhibit many spectral properties similar to that of SN 2010jl (Moriya et al. 2020;Bilinski et al. 2020). In particular, spectra of SN 2014ab showed blueshifted intermediate-width components indicative of either an optically thick CSM occulting the far side, obscuration by large dust grains, or inherent asymmetry along our line of sight. Moriya et al. (2020) found evidence of preexisting dust within the CSM around SN 2014ab. Spectropolarimetric data presented in Bilinski et al. (2020), which are also presented in this work, reveal small levels of instrinsic polarization for SN 2014ab, suggesting a mostly symmetric photosphere in the plane of the sky.

M04421
M04421 was discovered by the MASTER Global Robotic Net on 2014 Sep. 20.81259 at an unfiltered apparent magnitude 15.4 (Tiurina et al. 2014). We estimate a redshift of z = 0.01717 from the narrow component of Hα emission detected in day -9 spectra taken with the BC on the MMT. We adopt a Milky Way extinction along the line of sight of AV = 1.091 mag (EB−V = 0.352 mag; Schlafly & Finkbeiner 2011). Since the estimated redshift is very different from that of the claimed host galaxy, 2MASX J04421256+2306209, we instead estimate a redshift-based distance of 71.5 Mpc using our estimate of the redshift. We estimate a host-galaxy reddening of AV < 0.10 mag (EB−V < 0.032 mag) from an upper limit on the Na i D absorption line equivalent widths in spectra taken on day -9 with the BC on the MMT as shown in Table 4. Although we do not correct the data using this reddening estimate, we do use it to set a rough limit on the ISP inferred from Na i D as discussed in § 4.1. The total extinction (host-galaxy and Milky Way) for M04421 is AV = 1.091. Only brief Astronomer's Telegrams discovering and then identifying M04421 as a SN IIn have been published so far (Tiurina et al. 2014;Shivvers et al. 2014).

ASASSN-14il
ASASSN-14il was discovered by the All Sky Automated Survey for SuperNovae on 2014 Oct. 1.11 at an apparent V -band magnitude of 16.5 (Brimacombe et al. 2014). ASASSN-14il is located in the galaxy 2MASX J00453260-1415328 (redshift z = 0.021989; Jones et al. 2009). We adopt a Milky Way extinction along the line of sight of AV = 0.061 mag (EB−V = 0.020 mag; Schlafly & Finkbeiner 2011) and a redshift-based distance of 88.5 ± 6.2 Mpc from the NASA/IPAC Extragalactic Database. We estimate a host-galaxy reddening of AV = 1.40 mag (EB−V = 0.453 mag) from the Na i D absorption line equivalent widths in spectra taken on day -26 with the BC on the MMT as shown in Table 4. The total extinction (host-galaxy and Milky Way) for ASASSN-14il is AV = 1.466. Only brief Astronomer's Telegrams discovering and then identifying ASASSN-14il as a SN IIn have been published so far (Brimacombe et al. 2014;Childress et al. 2014), but a more in-depth study of this super-luminous SN IIn is forthcoming in Dickinson et. al. (2023).
3.0.10 SN 2015da SN 2015da was discovered by the Xingming Sky Survey on 2015 Jan. 9.89694 at an unfiltered apparent magnitude of 16.9 4 . SN 2015da is located near the galaxy NGC 5337 (redshift z = 0.007222; Falco et al. 1999). We adopt a Milky Way extinction along the line of sight of AV = 0.039 mag (EB−V = 0.013 mag; Schlafly & Finkbeiner 2011) and a redshift-based distance of 37.0 ± 2.6 Mpc from the NASA/IPAC Extragalactic Database. We use a host-galaxy reddening of AV = 3.01 mag (EB−V = 0.97 mag), taken from Tartaglia et al. (2020) as shown in Table 4. The total extinction (host-galaxy and Milky Way) for SN 2015da is AV = 3.046. Tartaglia et al. (2020) observe narrow Balmer lines indicative of SN ejecta interacting with CSM continuously over the course of 4 years. SN 2015bh shows many similarities to SN 2009ip. Initially, SN 2015bh was classified as an SN impostor. Spectroscopic studies showed that SN 2015bh began to interact with CSM not long after its first brightening event in 2015 (Ofek et al. 2016;Goranskij et al. 2016;Elias-Rosa et al. 2016;Boian & Groh 2018). The initial brightening in 2015 may have been an actual faint SN core collapse event with the second brightening being due to the onset of CSM interaction (Elias-Rosa et al. 2016), much as is hypothesized for SN 2009ip (Smith, Mauerhan, & Prieto 2014). Pre-explosion observations reveal an LBV undergoing outbursts over the last ∼ 20 yr prior to explosion (Ofek et al. 2016;Elias-Rosa et al. 2016;Thöne et al. 2017  We estimate a host-galaxy reddening of AV < 0.08 mag (EB−V < 0.026 mag) from an upper limit on the Na i D absorption line equivalent widths in spectra taken on day 73 with SPOL on the Bok telescope as shown in Table 4. Although we do not correct the data using this reddening estimate, we do use it to set a rough limit on the ISP inferred from Na i D as discussed in § 4.1. The total extinction (hostgalaxy and Milky Way) for PS15cwt is AV = 0.281. Only brief Astronomer's Telegrams discovering and then identifying PS15cwt as a SN IIn have been published so far .  Table 4. The total extinction (host-galaxy and Milky Way) for SN 2017gas is AV = 2.462. Only brief Astronomer's Telegrams discovering and then identifying SN 2017gas as a SN IIn have been published so far (Brimacombe et al. 2017;Bose et al. 2017).

SN 2017gas
3.0.14 SN 2017hcc  Table 4. The total extinction (host-galaxy and Milky Way) for SN 2017hcc is AV = 0.141. SN 2017hcc is of particular interest because it shattered records for polarization measurements of all types of SNe, not just SNe IIn.  measured an integrated V -band continuum polarization of 4.84%. They also estimated a low contribution from the ISP based on a high Galactic latitude, small extinction in both the Milky Way and the host galaxy, and strong line depolarization in the core of Hα and Hβ. Kumar et al. (2019) also find low host-galaxy extinction and measure a decline of the intrinsic polarization of SN 2017hcc of ∼ 3.5% over ∼ 2 months. Both studies suggest an origin of the continuum polarization in a region with significant asymmetry, such as a toroidal or disk-like CSM Kumar et al. 2019).  suggest that unpolarized line emission arises in the photoionized pre-shock CSM, consistent with narrow line components seen at early times in spectra reported by . Smith & Andrews (2020) also found evidence of dust formation in the post-shock shell and within the SN ejecta for SN 2017hcc. The very high early polarization and the polarization evolution will be discussed in more detail in a separate paper (Mauerhan et al. 2023, in prep.).

Extinction and Reddening
When available, we reference past studies on individual SNe to obtain an estimate of the host-galaxy extinction along our line of sight. Individual results are mentioned in the sections corresponding to that object within § 3 and are summarized in Table 4. We assume a total to selective absorption ratio of RV = 3.1 (O'Donnell 1994), though this may not be true everywhere within the Milky Way Galaxy, nor in other host galaxies. Reddening estimates often utilize the correlation found between the narrow Na i D absorption lines λλ5890 (D2), 5896 (D1) and the interstellar dust extinction along a particular line of sight, though the correlation requires that the lines are not saturated and not blended in moderateresolution spectra (Poznanski, Prochaska, & Bloom 2012). A number of studies have examined the correlation between the equivalent width of the Na i D doublet absorption lines and interstellar extinction (Richmond et al. 1994;Munari & Zwitter 1997;Turatto, Benetti, & Cappellaro 2003;Poznanski, Prochaska, & Bloom 2012). We use the relations provided by Poznanski, Prochaska, & Bloom (2012) in all of our estimations in § 3. Phillips et al. (2013) found that the dustextinction values estimated from the Na i D doublet absorption for one-fourth of their sample of SNe Ia was stronger than expected when compared to those derived from SN colour.
For several objects, either no literature estimate of the host-galaxy extinction existed (SN 2011cc, PTF11iqb, M04421, ASASSN-14il, PS15cwt, and SN 2017gas) or the host-galaxy extinction was deemed from Na i D upper limits to be low enough that it could be neglected (SN 2009ip: Mauerhan et al. 2014and SN 2011ht: Roming et al. 2012). In the cases that moderate-resolution spectra were available from the BC on the MMT (SN 2011cc, SN 2011ht, PTF11iqb, SN 2009ip, M04421, ASASSN-14il, and SN 2017gas), we measured the equivalent width of the Na i D absorption lines in order to estimate the dust-extinction values using the relations described above. When absorption was not detectable, we used the 1σ noise level to derive an upper limit  to the strength of the Na i D absorption doublet. Figure 1 shows one of our moderate-resolution spectra used to estimate the equivalent width of the Na i D absorption lines.
No moderate-resolution spectra were available for PS15cwt, so we attempted to estimate the host-galaxy extinction using our relatively low-resolution Bok SPOL data. Since no absorption lines were clearly present in this data, we instead set an upper limit to the equivalent width of the Na i D absorption doublet. All of these spectroscopic observations are detailed in Table 4.

Spectropolarimetry Parameters
Our spectropolarimetric analysis is performed primarily using the linear Stokes parameters, q = Q/I and u = U/I, which are rotated 45°with respect to each other, allowing us to decompose the polarization signal into orthogonal components in position angle space. Typically, one can combine the Stokes parameters to obtain the polarization level, p = q 2 + u 2 , and the position angle on the sky, θ = (1/2) tan −1 (u/q). However, since the definition of the polarization makes it a positive-definite value, it may seem artificially high in cases where we have a low signal-to-noise ratio because fluctuations will raise the mean polarization level significantly. In this section, we discuss alternatives for the traditional definition of polarization.
Given the issue of the positively-based nature of the traditional definition of polarization when the signal-to-noise ratio is low, we instead consider a few alternative formulations to describe the polarization. First, the debiased polarization (Stockman & Angel 1978): where σq and σu are the statistical errors in the measurements of q and u, respectively, and the sign of p db is chosen to match the sign of [q 2 +u 2 −(σ 2 q +σ 2 u )]. Next, we consider the optimal polarization (Wang, Wheeler, & Höflich 1997): where σp is the statistical error on the polarization propagated from σq and σu. Lastly, we consider the rotated stokes parameters (RSP; Trammell, Dinerstein, & Goodrich 1993): where θ smooth is chosen such that the majority of the polarization signal is rotated onto qRSP .
As discussed in detail in , each estimation of polarization has its limitations, but the traditional definition of polarization and the debiased definition perform worse than the optimal polarization at estimating the true polarization in a simulation of low signal-to-noise ratio polarization spectra across emission lines. In particular, the traditional polarization fails to detect an unpolarized line feature in the simulation, as is expected when the signal-tonoise ratio drops low. The debiased polarization contains a double-peaked probability distribution and results in negative polarization spikes when the signal-to-noise ratio is low (Miller et al. 1988). While the optimal polarization is formally undefined for values where p trad < σp trad , this formulation still results in less negative polarization spikes than the debiased polarization if this restriction on the formal definition is neglected (as we choose to do throughout our paper) and also matches the true polarization signal in the simulation of  more accurately. For these reasons, when determining the average polarization over a large bandwidth (see  for a detailed discussion of the advantages of popt when binning data over large wavelengths), we take the photon-count weighted average of our data and then compute popt. We also make use of popt when comparing our maximal polarization spectra in Figure 11 because qRSP might fail to represent changes in polarization across lines accurately. However, when studying the evolution of spectral features in one object from epoch to epoch, we prefer to study the RSP because they yield the most accurate representation of the true polarization when the signal-to-noise ratio is low, as is often the case in our later epochs. In the case that we are studying the evolution of the polarization of one object epoch by epoch, we are also able to inspect uRSP at the same time, as seen in all of our individual object spectropolarimetry figures in Appendix A, so the choice of inspecting the RSP does not risk overlooking polarization signal that was rotated out of qRSP across line changes. We show an example of one of such figures with q, u, qRSP , uRSP , and θ in Figure 2. We also show a comparison of a q − u plot with that of a qRSP − uRSP plot in Figure  3 to illustrate what the process of generating the RSP looks like.

Choosing the Interstellar Polarization
In order to study the polarization signal intrinsic to our targets, we first must deal with the complicated issue of the ISP. After the light from our target leaves its location (with some intrinsic polarization signature), it must then pass through the interstellar medium of its host galaxy that lies along our line of sight, which can impart changes to its polarization signal due to magnetically aligned dust grains. Changes to the polarization signal may also be imparted by dust grains along the line of sight within the Milky Way. Since each change to the polarization signal acts as a vectorial change in the q − u plane, it can be difficult to pin down separate contributions to the ISP, but estimating the bulk ISP effect is more tractable. We first attempt to use relations discovered by Serkowski, Mathewson, & Ford (1975) relating extinction to an upper limit on ISP in an attempt to constrain the influence of the ISP on our intrinsic polarization signals. Since this only sets an upper limit on the magnitude of the ISP with no constraint on the position angle of the ISP in the q − u plane, we further attempt to estimate the ISP from depolarization at the wavelengths of strong Hα emission seen in some of our targets. Each of these approaches is explained in further detail in the following sections. Serkowski, Mathewson, & Ford (1975) suggest that an upper limit on the ISP can be set from the reddening along the line of sight according to:

ISP constraint based on reddening measurements
where E (B−V ) is given in magnitudes and p is the per cent polarization. Estimates of the reddening along various lines of sight within the Milky Way are available (Schlafly & Finkbeiner 2011). In order to estimate the reddening along the line of sight within the host galaxy for our targets, we use Na i D relations discussed in § 4.1. Combining both of these estimates of the reddening, we then place an upper limit on the ISP for each target, as shown by a blue circle of asterisks in all of our q − u plots in Appendix A. Keep in mind that this is an upper limit, not a statement of equality. Many of the targets in the sample within Serkowski, Mathewson, Horizontal dashed lines are included in the q RSP and u RSP plots for clarity. Black dotted circles demark each integer value of polarization in the q − u plot for clarity. Colours, bins, and error bars in the q − u plot on the left correspond to those on the right, with the colors mapped to the wavelength axis labeled on the right. We estimate an ISP magnitude < 0.14 (shown as a circle of blue asterisks) based on Na i D absorption-line measurements (see § 4.1). We mark our estimate of the actual ISP derived from depolarization of Hα narrow emission with a black circle in the q − u plot (see § 4.3.2). The data are grouped into ∼28Å bins.
& Ford (1975) found the ISP to be far below the relation that they use for an upper limit. Additionally, this relation assumes dust properties in the host galaxies are similar to those of the Milky Way, which may not be the case (Leonard et al. 2000;Porter et al. 2016).
In many cases, the ISP upper limit inferred from Na i D is not very restrictive, corresponding to ISP levels larger than the signals we detect. We reiterate that the ISP polarization degree inferred from E (B−V ) (which is, in turn, inferred from Na i D) is only an upper limit; the original empirical relation is derived from an upper threshold, not a fit to a correlation. Physically, it is an upper limit because multiple interstellar medium (ISM) clouds along the line of sight might produce Na i D absorption and dust reddening that add together, but the magnetically aligned dust grains in these multiple clouds might not have the same orientation, and so their induced polarization may therefore cancel. Thus, when the Na i D equivalent width and reddening are very low, this upper limit is useful, but when the ISM reddening has a higher value, the upper limit is not meaningful. Table 5. Fits to the q and u values at the location of depolarized Hα emission lines using λmax = 6521Å (see § 4.3.2 for a detailed discussion on the fitting process). The scale factor was used to make the estimate more consistent with the ISP constraint from reddening, as discussed in § 4.1.

ISP estimate from depolarization in strong emission lines
For a handful of our objects (SN 2010jl, SN 2009ip, SN 2012ab, SN 2015bh, SN 2017gas, and SN 2017hcc), strong depolarization of Hα is seen early on. Because recombination line emission that comes from regions outside the electron scattering photosphere can be assumed to reach us without scattering, we can treat its light as unpolarized. Since the line flux dominates that of the continuum, we expect that the overall polarization signal in the Hα line will approach that of the ISP (although we note that an external polarizing source such as CSM dust can scatter line emission even if it is external to the electron scattering photosphere). The narrow component of the Hα line is not resolved in our spectropolarimetric data, so we attempt to estimate the qISP and uISP values based on the three pixels closest to the narrow Hα emission-line peak. We estimate the continuum flux by fitting the continuum level on either side of the Hα emission line. We then assume that the continuum at the center of the narrow Hα line has similiar polarization to that measured in the 6000-6300Å regions (although there is evidence for a wavelength-dependent polarization in our data, the wavelength dependence is not steep enough to compromise this assumption). After removing the polarization from this continuum flux, we then assume that the remaining polarization signal is associated with unpolarized Hα emission-line flux, and thus is a reasonable estimate of the ISP at the wavelength of the narrow component of Hα emission. The more intrinsically polarized the Hα lines are, or the more polarization that external CSM dust contributes to the overall signal, the worse this correction of the ISP becomes.
In order to estimate the ISP as a function of wavelength, we fit a Serkowski law (Serkowski, Mathewson, & Ford 1975): where λ is the wavelength inÅ, pmax is the maximum polarization across all wavelengths, and K is the Serkowski parameter, through the q depol and u depol values we estimated from the narrow Hα emission line. Specifically, we minimize the errors on a simultaneous fit to (where θ is the position angle) in order to obtain λmax, qmax, and umax. A similar procedure was previously performed in Dessart et al. (2021), where the ISP curve was fit to a number of depolarized lines in one epoch. Cikota et al. (2018) found that the K − λmax relation is an instrinsic property of polarization in the ISM, with KISP = −1.13 + 0.000405λmax,ISP, so we use this relation.
In order to estimate qmax and umax for each of our objects exhibiting strong depolarization, we first estimate a reasonable value for λmax from a late-time (day 113) measurement of SN 2017gas when the continuum is still bright but the polarization signal has significantly faded. We also prefer this epoch of SN 2017gas spectropolarimetry since reddening constraints (see § 4.3.1) suggest that extensive ISP may be contributing to SN 2017gas. Additionally, since this estimate of the ISP may be convoluted by distant CSM dust as is discussed in greater detail in § 5.4, we chose an epoch that did not show polarization stronger at blue wavelengths than red ones. Although this may bias our choice of λmax towards redder wavelengths, we continued with this route because it placed our estimate of λmax closer to those found in past literature estimates of ISP dependence on wavelength (λmax ∼ 5500Å: Voshchinnikov 2012, though Patat et al. 2015;Cotton et al. 2019 have found bluer values for λmax in the ISP) and it allowed us to more confidently avoid fitting distant CSM dust polarization that we find very likely in our targets.
The epoch 5 (day 113) data for SN 2017gas with the ISP fit overplotted on the qRSP is shown in Figure 4. The best-fit value for λmax = 6521Å. Using this λmax value from our fit to the late-time SN 2017gas data along with q depol and u depol from the estimate of the ISP at the wavelength of the narrow component of Hα emission for each of our objects that show strong depolarization, we estimate a wavelength-dependent ISP for each target with significant Hα depolarization. However, the assumption that the ISP along the line of sight to each of the SNe IIn in our sample is well-represented by a similar λmax value has limitations-λmax values for MW dust vary with position on the sky. A summary of the qmax and umax values that resulted from our fits is shown in Table 5.
The above estimate of the wavelength-dependent ISP assumes that the Hα narrow-line flux is completely depolarized. However, careful inspection of the polarized flux across the Hα emission lines reveals that the lines are not completely depolarized. Figure  ized flux would trace the continuum flux if the line emission were completely unpolarized. However, even polarized lines could cause the polarized flux to trace the continuum flux if the lines are polarized at a similar magnitude as the continuum, but at a different angle (this would be seen as a rotation in the q − u plane, but not a change in the magnitude of the polarization). In our case, both polarized flux signals show increases at wavelengths of emission lines compared to the continuum, which cannot arise from unpolarized emission lines. Additionally, it is worth noting that polarization is relatively stronger at blue wavelengths, which we discuss in more detail in § 4.6. Because the line emission is likely polarized to some extent in many of our targets (especially at early times when the optical depth is highest in the CSM interaction region such that the line forming region is beneath the electron scattering photosphere), our estimates of the depolarization correction only go a portion of the way from the continuum polarization to the true ISP location in the q − u plane. 7 Given the generally Lorentzian shape in early-time Hα emission lines for our targets and the lack of significant changes in the position angle across emission lines, we find it most likely that the emission-line region shares a geometry with that of the continuum photosphere (Dessart, Audit, & Hillier 2015). Thus, 7 In principle, the line emission could be polarized opposite to the continuum in the q − u plane, so that when it is combined vectorially it actually causes our estimates to overestimate the displacement between the continuum polarization and the ISP in the q − u plane. However, since the Hα emission-line profiles at early times when strong depolarization is seen often exhibit broad Lorentzian profiles (see § 4.5 for more discussion on the Hα emission line profiles), we expect that the broad emission-line flux, which appears polarized, originates in a region coincident with the electron-scattering continuum photosphere (when electron scattering dominates, it imparts a symmetric broadening around zero velocity with a Lorenztian shape; Chugai 2001; Smith 2017). our estimate of the displacement between the continuum polarization and the ISP derived from depolarization is likely an underestimate of the true offset. When our constraint on the ISP from reddening suggests an ISP value further from the continuum than that estimated from depolarized Hα emission, we adjust the wavelengthdependent ISP estimate from depolarization to be closer to being consistent with the reddening constraint. In cases where the reddening constraint is less stringent on the ISP (keep in mind that this constraint just sets an upper limit on the magnitude of the ISP, not an actual estimate of it), we instead adjust the ISP estimate from depolarization by a factor of 0.5 to reflect the possibility that a significant fraction of the line emission is polarized. We list the scale factors used for our sample in Table 5. Larger data sets or a more in-depth study of line polarization at early times in SNe IIn may lead to a better estimate of this scale factor.
We then correct the q and u data for each SN that exhibits strong depolarization using this wavelength-dependent ISP estimate. As an example, we compare the spectropolarimetric data for SN 2017gas with the ISP signal included and removed side-by-side in Figure 3. In all cases where we have adjusted our data using an estimate of the wavelengthdependent ISP, the variation of the polarization signal from epoch to epoch is significantly greater than the ISP estimate. This implies that even if our estimate of the ISP was made incorrectly, our targets still exhibit significant intrinsic polarization through the changes in their polarization signal from epoch to epoch.

Intrinsic Spectropolarimetry
Our spectropolarimetric results, after correcting the data using our estimates of the wavelength-dependent ISP for any objects with clear depolarization in Hα emission (as discussed in detail in § 4.3.2), are enumerated in Table 6. Individual q − u figures for every SN IIn in our sample are also included in Appendix A, showing the data both before and after wavelength-dependent ISP correction if it was implemented.
The temporal evolution of the continuum polarization for our sample of SNe IIn is shown in the top panel of Figure 6, where we have aligned the SNe relative to their times of peak brightness (in R-, V -, or i-bands; see Table 1). This shows the per cent polarization when binned across 5100-5700Å, which is the main bin size we use to discuss these results throughout the paper (the numbers are slightly different in the 6000-6300Å bin, but this does not affect our conclusions). The range of polarization degree and the rise/decline rates are diverse. The statisical errors (shown with smaller endcap sizes compared to ISP errors in Figure 6) are generally quite small because we have combined the polarization signal over large wavelength bins. Although we have removed an estimate of the wavelength-dependent ISP for objects that contained strong depolarization of Hα in at least one epoch (SN 2010jl, SN 2012ab, SN 2009ip, SN 2015bh, SN 2017gas, and SN 2017hcc), we still show an uncertainty due to the magnitude of the ISP estimated from reddening on the first data point (using a larger endcap size than for the statistical errors) for each target to reflect this potential uncertainty.
The highest polarization signals observed (3−6%) are only seen at times near peak brightness or before (< 50 days). SN 2017hcc shows the strongest drop in polarization from 5.76% on day −45 to 2.82% on day −15. Between days 0 and 113, SN 2017gas drops from 2.91% to 1.65%, roughly a 0.011% per day decline. SN 2010jl also exhibits a gradual decline from days 25 to 239 of 2.19% to 0.37%, similar to that of SN 2017gas, and flattens out thereafter. The polarization signal generally drops steadily over time for the majority of the targets in our sample with several epochs of spectropolarimetry (SN 2010jl, SN 2009ip, SN 2015da, SN 2017hcc, and SN 2017gas). There are, however, some cases where the continuum polarization instead increases over a short time period (before declining at later times, when data are available). This can be seen clearly in the early data for SN 2012ab, SN 2009ip, ASASSN-14il, and SN 2015bh. We interpret these various changes and trends in continuum polarization in detail in § 5.3.
We also show the continuum polarization measured across 6000-6300Å side by side with that measured across 5100-5700Å in Figure 7. For the most part, the trends across both wavelength bins match each other quite well. However, increases in the polarization that were seen in some objects (SN 2009ip, ASASSN-14il, andSN 2015bh) are generally less pronounced in the 6000-6300Å bin than they are in the 5100-5700Å bin. This is a hint that the polarization has some possible wavelength dependence that is not expected for pure electron scattering, as discussed more below in § 5.4. Figure 8 compares the evolution of the position angle θ with time when binned across the two different bandpasses we chose. The position angle remains roughly constant in both bands for most of our targets. However, there are some pronounced exceptions to this trend in SN 2009ip and SN 2014ab. On day −14, SN 2009ip exhibits a position angle of 176°in the bin centered on 5400Å, progressing to 71.6°on day 7, and continuing to evolve past 60.5°on day 37 all the way back to 105.8°on day 60 (this evolution in θ was discussed in detail previously by Mauerhan et al. 2014). SN 2014ab exhibits a position angle of 13.1°on day 77, but changes to 73°by day 99 with a gradual decrease half of the way back towards the initial value thereafter. In some cases, the significant change in the position angle can be attributed to the polarization being very low and nearly centered on the origin by this time, so slight changes in the polarization can result in large changes in the polarization angle. We discuss the implications for these changes in more detail in § 5.3.

Hα Emission Line Evolution
We measured the Hα equivalent widths and the full velocity widths at 20% maximum (V20) for each of our targets at each epoch (we chose 20% maximum instead of half maximum in order to better sample the broad wings of the Hα line). The results are shown in Figure 9.
The Hα equivalent width generally increases over time past peak for all of our targets, as is typical for SNe IIn (Smith, Mauerhan, & Prieto 2014). There are, however, a few notable cases in which it also decreases with time leading up to the time of peak. In particular, between the first two epochs of data for SN 2017hcc, SN 2017gas, and SN 2009ip, we see a significant drop in the Hα equivalent width, which has been noted previously for some SNe IIn that are discovered well before their peak luminosity phase (e.g.  Table 6. ISP-corrected continuum polarization measurements for our sample of SNe IIn. Day is measured relative to the observed peak shown in Table 1 and often includes data from many nights that have been combined into a single epoch, as detailed in Table 2. popt is the optimal polarization, which alleviates the positive-definite bias of traditional polarization definitions, as discussed in § 4.2. "5400" indicates data binned across 5100-5700Å, while "6150" indicates data binned across 6000-6300Å. θ is the position angle.

Name
Day p opt,5400 (σ) θ 5400 (σ) q 5400 (σ) u 5400 (σ) p opt,6150 (σ) θ 6150 (σ) q 6150 (σ) u 6150 (σ)  The evolution of V20 is similar to that of the Hα equivalent width. For most of our objects, V20 for Hα increases with time, except for the same few outliers as mentioned for Hα equivalent width. We discuss implications for the general trend of increasing Hα equivalent width and V20 (and exceptions) in detail in § 5.3.
Though it is beyond the scope of this paper, it is worth noting that the Hα emission line sometimes has a more complex evolution through time across different velocity components of the line profile. In particular, we note that the position angle in some of our spectropolarimetric results changes across the Balmer-series lines (most prominently for SN 2010jl when the continuum polarization has significantly faded; Williams et al. 2023, in prep.). A more in-depth study into changes across individual emission lines could discover more about the implied geometrical differences between the line-forming region and the electron-scattering continuum photosphere.

Wavelength-Dependent Polarization
Polarization arising from an electron scattering photosphere where Thomson scattering dominates is expected to be wavelength independent. While the polarized flux (shown in Figure 5) is of course wavelength dependent, the polarization degree (p) should be flat for electron scattering. However, the polarization signal for many of our objects shows a general trend of stronger polarization at bluer wavelengths. In order to quantify this trend, we fit a line through the continuum in the polarization data, excluding notable emission and absorption line regions, to estimate a slope parameter.   Figure 7. Same as in Figure 6, but with previously published spectropolarimetric data included and marked by hexagonal stars. Top panel: Polarization measurements across the 5100-5700Å bin. Bottom panel: Polarization measurements across the 6000-6300Å bin.
The intrinsic polarization slope parameter, Sp, for all of our data is shown in the bottom panel of Figure 6. A negative value for Sp indicates that the polarization skews upward at blue wavelengths, while a positive value indicates that the polarization skews upward at red wavelengths. The evolution of this slope parameter does not follow the same trend for each of our targets. In some cases (SN 2009ip, SN 2014ab, SN 2017hcc) it becomes increasingly positive as the polarization signal decreases and the object fades. In other cases (SN 2010jl, ASASSN-14il, SN 2015da), the slope parameter becomes more negative at first and then reverses back toward null or positive values. In other cases (SN 2017gas), the slope parameter begins strongly negative, becomes more positive for a few epochs, and then decreases again. Lastly, in some cases the slope parameter quickly becomes more negative (SN 2015bh) or more positive (SN 2012ab) without any late-time data to constrain how it eventually evolves from this initial trend. We discuss the implications of this wavelengthdependent polarization on the SN environments in § 5.4.
To test whether our ISP correction had contributed significantly to this polarization slope, we fit a line to the polarization signal for each epoch of our data without any ISP correction as well. We show a comparison of the slope parameters before and after ISP correction in Figure 10. Although ISP correction does push the slope parameters to slightly more negative values in general (which is reasonable given the ISP estimates peaking at λmax), even the uncorrected data have slopes that are skewed to the blue. We perform a two-sample Kolmogorov-Smirnov test on the two populations which returns a p-value of 0.951, suggesting that they do indeed arise from similar populations. Therefore, our ISP correction does not introduce a strong bias to artificially produce an inherently blue slope.   (SN 2009ip, SN 2010jl, SN 2012ab, and SN 2014ab) are also included in this study. We list the published values for the continuum polarization for these SNe IIn in Table 7, and we show their continuum polarization values alongside the ones from our sample in Figure 7. Since the continuum polarization was often integrated over a variety of bandwidths in the past literature, we chose the bandwidths that most resembled ours for the purposes of Figure 7 and Table 7. Most SNe IIn with published spectropolarimetric results show high continuum polarization values in the range ∼ 1-3%, suggesting significantly aspherical shapes for their electron scattering regions. Additionally, whenever spectropolarimetry on an object within our sample already had previous data published, we found good agreement between the past data and our results. We summarize the past results and their implications for each SNe IIn target with previously published spectropolarimetric data individually below.

SN 1997eg
Detailed multi-epoch spectropolarimetry of SN 1997eg was interpreted as aspherical SN ejecta misaligned with a surrounding CSM disk (Hoffman et al. 2008). These authors favored a toroidal shell model as was proposed by Kasen et al. (2003) Figure 9. Top panel: Hα equivalent width relative to the peak date for our entire SNe IIn sample. We have cut off the late-time data that shows very little continuum flux and thus strong Hα equivalent widths for clarity in the early-time data we are most interested in. Bottom panel: Velocity of the full-width-at-20%-maximum relative to the peak date for our entire SNe IIn sample.
ization that increased steadily with time (they also discuss alternate choices).

SN 1998S
Spectropolarimetry of SN 1998S showed strong linear polarization (∼3%) indicative of an equatorial CSM disk, similar to that seen for SN 1987A, but much denser and closer to the SN (Leonard et al. 2000;Wang et al. 2001). The high continuum polarization measurement in this scenario is contingent once again on an estimate of the ISP, in which Leonard et al. (2000) favor a model with mostly unpolarized broad lines due to negligible deviations from the continuum seen in the polarized flux. This results in an interpretation where SN 1998S underwent CSM interaction early on (strong polarization in epoch 1), after which the SN ejecta engulfed the closest CSM region (weak polarization in epoch 2), and then eventually ran into another disk of CSM (strong polarization in epoch 3) with which interaction persisted for hundreds of days (Leonard et al. 2000).

SN 2006tf
Although only one epoch of spectropolarimetric data exists for SN 2006tf, it shows relatively strong continuum polarization (∼ 1%) with mild depolarization across many emissionline features . Without an accurate estimate of the ISP it is difficult to assess the intrinsic continuum polarization, but the relatively weak depolarization in emission lines suggests a somewhat less intrinsically polarized SN IIn than other SNe IIn studied spectropolarimetrically prior to SN 2006tf . Note that, like SN 2010jl, SN 2006tf was a super-luminous SN IIn.

SN 2013fs
Although SN 2013fs was measured spectropolarimetrically, the polarization signal was only constrained by an upper limit of < 1% at all epochs after subtracting off an ISP assumed from the second epoch (Bullivant et al. 2018). Additionally, although SN 2013fs initially appeared as a SNe IIn much like Figure 10. A histogram showing Sp for our sample of SNe IIn that exhibit strong line depolarization with ISP correction (dashed region) and without (blue region). Although Sp becomes more negative in general after ISP correction, ISP correction does not significantly affect the claim that Sp is predominantly negative across our sample.
PTF11iqb, it transitioned to a SNe II-P or II-L as the fleeting SNe IIn signatures faded after a short time (Bullivant et al. 2018). For these reasons, we do not show these polarization constraints in Figure 7.

SN 2010jl, SN 2009ip, and SN 2017hcc
These three objects have previously been studied in the literature but they are also a part of our sample of SNe IIn. Please see § 3.0.1, 3.0.6, and 3.0.14 for a detailed discussion of their key features.

Peak Polarization
Until recently, the highest polarization signals measured for SNe IIn were seen in SN 2010jl (∼ 2%, Patat et al. 2011) and SN 1998S (∼ 3%, Leonard et al. 2000, though this continuum polarization estimate for SN 1998S is contingent on an ISP measurement that is somewhat uncertain, implying that it may never have been detected at an intrinsic polarization of 3%). Recently, however, SN 2017hcc was detected with broadband polarization measurements extending to 4.84% on day −35 (Kumar et al. 2019). We measure the highest instrinsic polarization ever recorded for a SN in SN 2017hcc on day −45 with a continuum polarization measurement of 5.76% (see also Mauerhan et al. 2023, in prep.) Additionally, our sample contains a number of other SNe IIn that exhibit continuum polarization measurements around the 2 − 3% range.
We show a comparison of the peak polarization spectrum for each of our targets with high signal-to-noise ratio in Figure  11. For targets with an average optimal polarization degree above 1% and a standard deviation in the optimal polarization below 1.25%, we selected the spectrum with the highest intrinsic optimal polarization. If the target was not observed to have an optimal polarization above 1%, we instead plot the spectrum closest to the date of peak magnitude that meets our standard deviation cutoff in the continuum of < 1.25%. There is a dearth of SNe with continuum polarization between ∼ 0% to ∼ 2%, but with the small number of objects, it is uncertain whether this gap in intrinsic polarization is real or simply due to stochastic sampling. If we had caught some of our more highly polarized targets at later times, we might have measured their peak polarization spectra in this region.
Thus, we suggest that the gaps in the peak polarization plot shown in Figure 11 may be due to sample size.
Of particular interest here is the peak polarization spectrum of SN 2017hcc, because it reaches almost 6% on day −45. Early models of SN polarization that focused on SN 1987A predicted signals of up to 4% for an oblate ellipsoid with a fattening of E = 0.2, where the fattening is the axis ratio of the elliptical density distribution of the envelope (Hoflich 1991). Later work done on modeling SNe specifically with interaction (Dessart, Audit, & Hillier 2015;Vlasis, Dessart, & Audit 2016;Kurfürst, Pejcha, & Krtička 2020) only predicted polarization signals of up to about 2%. The various models considered included both symmetric and asymmetric SN ejecta interacting with a CSM disk, colliding wind shells in binary stars, bipolar lobes similar to those of the Homunculus nebula in η Car (Smith 2006), and a relic disk similar to that considered for SN 1997eg (Hoffman et al. 2008). One key limitation of these models is perhaps that the full 3-D geometry is not modeled. In general, if the CSM interaction region has a toroidal geometry, the SN ejecta will progress more rapidly into the polar regions where the CSM is less dense, making the photosphere take on a prolate geometry and potentially engulf the disk (see . This can result in a complicated flux source geometry that the models fail to accurately depict when photons are deposited into the interaction regions at various angles in a 3-D consideration. Models are generally unable to reach polarization as high as 6% at early times. Perhaps this is because higher optical depths in the CSM that would be required to reach higher polarization degrees would also result in multiple scatterings that wash out the polarization signal from most viewing angles (Wood et al. 1996). Additionally, the orthogonal geometries of the interaction region and the photosphere end up competing, producing polarization signals that may significantly cancel each other in the models (L. Dessart, private communication). As discussed below in § 5.4, however, an alternative way to easily achieve high polarization levels is with scattering by CSM dust, which is also consistent with the wavelength dependence that we observe.

Continuum Polarization Evolution Through Time
In § 4.4 we summarized the observed temporal evolution of the continuum polarization for our sample of SNe IIn. The strongest polarization signals in our sample exceed previously published values for other SNe IIn as discussed in § 5.2. The temporal evolution we measure has proven to be diverse. There are some emerging trends, however, such as steadily declining continuum polarization at late times.

Declining Polarization at Late Times
In the most strongly polarized objects for which we also have multiple epochs of spectropolarimetry at late times (SN 2010jl, SN 2017gas, SN 2017hcc), a simple drop in optical depth due to lower densities at larger radii may help explain most of the steady drop in polarization. From epoch 2 onward for SN 2017gas and SN 2017hcc, as well as from epoch 1 for SN 2010jl, we generally see a drop in continuum polarization matched with an increase in the Hα equivalent width and an increase in V20. In general, the Hα equivalent width in SNe IIn increases as the continuum optical depth drops and the continuum luminosity fades Smith, Mauerhan, & Prieto 2014;Smith 2017), whereas broad lines from the fast SN ejecta are typically exposed at late times as the optical depth of the CSM interaction region drops (Smith 2017;. Figure 9 shows that V20 typically increases to 6000-10000 km s −1 after day 100, consistent with the emergence of the fast SN ejecta. In the case of other SNe II, we often see the polarization signal increase as the object enters the nebular phase, revealing the central mechanism of the explosion (Leonard et al. , 2006Chornock et al. 2010;Dessart et al. 2021). However, this is not seen in our sample of SNe IIn, likely because the CSM interaction regions are overwhelming the central SN ejecta while they remain bright. After the CSM interaction has faded sufficiently to reveal the central SN ejecta (though in many cases for SNe IIn, CSM interaction still dominates the brightness at late times, thus preventing a nebular phase from truly occurring) the SN ejecta are likely no longer bright enough to produce polarization comparable to that seen at nebular times in SNe II.
Although the drop in polarization for SN 2010jl, SN 2017gas, and SN 2017hcc can generally be attributed to decreasing optical depths, the changes that occur between the first two epochs of spectropolarimetry of SN 2107gas and SN 2017hcc defy this explanation. The continuum polarization drops precipitously, matched instead with a decrease in V20 and a decrease in the Hα equivalent width. Thus, the rapid drop in continuum polarization seen in SN 2017gas and SN 2017hcc between their first two epochs of data may be due to real geometrical changes in the photosphere, increased multiple scattering within the CSM interaction region, or decreased contribution to the luminosity from a light echo originating in CSM dust. An increase in multiple scattering can wash out the polarization signal (Kopparla et al. 2016, though see Hoffman, Whitney, & Nordsieck 2003 for a discussion on multiple scattering and viewing angle). As the optical depth in the continuum likely increased during these epochs, multiple scattering may have begun to play a bigger role. This may be more important in the case of SN 2017gas where the line emission was more significantly polarized at early times than that of SN 2017hcc, suggesting a line-emission region beneath the electron scattering photosphere. Lastly, in both cases (though much more pronunced in SN 2017hcc), Sp becomes less negative between the first two epochs. This is consistent with early CSM dust producing a strong wavelength-dependent polarization in the first epoch, but then being obliterated before the 2nd epoch.

Increasing Polarization at Early Times
Sometimes the continuum polarization increases rather suddenly at early times near peak in our sample of SNe IIn. Since SNe IIn are thought to be the result of SN ejecta interacting with CSM regions that were produced within years or decades prior to the death of the progenitor (Smith 2014(Smith , 2017, it would make sense that multiple CSM shells could exist at a variety of distances from the SN. As the SN ejecta expand and reaches new CSM shells, this interaction could cause the polarization signal to suddenly increase if the newly overtaken shells are asymmetric.  Figure 11. A comparison of the peak observed polarization spectra (unbinned) for most of our SNe IIn sample. In cases where the polarization signal is low, we instead use high signal-to-noise ratio data temporally close to the peak date (see § 5.2 for a detailed discussion on how we choose the spectra plotted here and why the observed gap is likely due to sample size). Targets with spectropolarimetry that do not meet our noise cutoff are excluded from this plot for clarity.
If the external CSM shells have different geometries than each other or the underlying SN ejecta, this might not only result in a change in the magnitude of the polarization, but also the polarization angle, as is seen in the case of SN 2009ip. Indeed, Mauerhan et al. (2014) found that the change in polarization paired with the change in position angle is likely due to a mismatch between the initial SN ejecta photosphere occulted by a disk during the 2012a event and the later interaction with the disk that turns on during the 2012b event. The other SNe IIn for which we observe a sudden increase in the polarization (SN 2012ab and SN 2015bh) do not show a large change in the position angle as in the case of SN 2009ip. Their increase in polarization without a change in the position angle does suggest that any new CSM interaction that began later was still aligned with the previous interaction geometry. This, in turn, suggests that multiple CSM regions may exist around SNe IIn that are aligned along the same axis.
For SN 2012ab, the sudden increase in polarization is paired with only a small change in position angle, suggesting instead a distant CSM region that contains a geometry aligned with that of the earlier source of polarization. Considering the spectral evolution of the line profiles,  found that SN 2012ab's rise in polarization is likely due to interaction beginning on the far side of the SN, which had an axis of symmetry similar to that of the early-time interaction observed on the near side of the SN.
In the case of SN 2015bh, the rise in polarization is paired with a slight but significant change in the position angle, paired with a sudden onset of much stronger depolarization seen in Balmer emission lines. This is likely due to the onset of CSM interaction with a geometric footprint similar to that of the photosphere arising at earlier times. We expect that either the CSM interaction that began by day 18 for SN 2015bh has begun powering the photoionization of a new region of more distant CSM or the earlier line-emitting region has proceeded beyond the electron scattering photosphere, so that less of the line emission is polarized. Figure 12 shows the polarized flux for SN 2015bh between days −3 and 18, where initially the line emission shows significant polarization, but this line polarization decreases dramatically by day 18. This confirms that by day 18 SN 2015bh has a new source of depolarizing line emission, either due to a new photoionized CSM shell or to the pre-existing line emission region now being external to the electron scattering photosphere.
A similar case arises for ASASSN-14il where the polarization increases initially and then remains constant, but in this case we do not observe strong line depolarization. We suggest two possible scenarios in this case. Either ASASSN-14il was initially polarized on day −15 and has become unpolarized by day 17 (with the remaining polarization signal seen on days 17-73 arising due to a strong ISP), or perhaps new CSM interaction began between days −15 and 17 and persisted until at least day 73 without any strong depolarizing line emission. This might imply that the line emission region is still entrenched within the electron scattering photosphere, or that we do not have a good estimate of the ISP. The change between day -15 and 17 does, however, still indicate that ASASSN-14il does have intrinsic polarization, even if it is difficult to tell whether it was instrinsically polarized at the earlier epoch, the later epoch, or perhaps both.
Previously published literature on SN 1997eg and SN 1998S also suggests an increase in the continuum polarization over time (Leonard et al. 2000;Hoffman et al. 2008). In both cases, a diversity of scattering regions is evoked. For SN 1997eg, Hoffman et al. (2008) proposed a dual-axis model with a toroidal CSM misaligned from the asymmetric underlying ejecta. For SN 1998S, the change in polarization is described as interaction with a nearby CSM region that is then encompassed by the SN ejecta, that eventually runs into another disk of CSM at a later date that preserves interaction for a much longer period of time (Leonard et al. 2000). These are both consistent with the results from our sample of SNe IIn, which suggest that these objects have diverse CSM environments around them at the time of explosion which can result in a complicated series of increases and decreases in polarization, though rarely coupled to huge changes in the position angle.

Light Echo from Dusty Distant CSM
In our measurements, the wavelength dependent slope of the polarization -Sp -increases or decreases monotonically, or may change directions during its evolution (see § 4.6 for a summary of the measured evolution of the wavelengthdependent polarization). While we detect a tendency for SNe IIn to have a blue slope in the continuum, especially at early times, there is no clear trend in Sp that unites all the SNe IIn in our sample. Instead, we explore options that might allow for a wavelength-dependent polarization that produces a stronger polarization at blue wavelengths that can also occur at variable times.  showed that wavelengthdependent polarization can arise due to variation in albedo and continuum source function with wavelength and depth. Primarily, bound-bound and bound-free transitions could cause this wavelength-dependent change in polarization. However, the models in  occur at relatively late times when the albedo is low and recombination is occurring. Instead, a majority of our data show strong wavelength-dependent polarization at early times. At these times, the SNe are expected to be hot and ionized, with a high albedo and negligible contribution from recombination. Under these conditions, models considering the albedo show a mostly flat wavelength independent continuum polarization (L. Dessart, private communication), so we look to other options that can explain our early-time wavelength-dependence.
Light echoes included in the unresolved SN light have been observed for a variety of SNe (Gouiffes et al. 1988;Welch et al. 2007;Andrews, Smith, & Mauerhan 2015). In the case of SNe IIn, it is plausible that distant CSM (whose presence is already likely for SNe IIn given their presumed progenitor history of eruptive mass-loss) causes such a light echo, which alters the polarization properties of the light significantly (Nagao, Maeda, & Tanaka 2018). Light from this echo at the extrema tangential to our line of sight will be preferentially scattered at bluer wavelengths. Additionally, because light is a transverse wave, the light from this echo that scatters orthogonally towards us will be highly polarized. Given that the polarization signal we measure is on the order of a few percent, a light echo that does not significantly affect the overall luminosity of the SN could still significantly affect the polarization signal because its light is very strongly polarized. This overall contribution to the light from tangential CSM dust may be why we see a strong predominance of a negative Sp in most of our objects.
Additionally, the light from the CSM dust might arrive at variable times for the objects in our sample depending on the distance from the SN photosphere to the CSM. This is supported by the diversity of the time evolution of Sp. If the neutral and dusty CSM is close to the SN, we may see a light echo soon after explosion causing a wavelength-dependent shift in the overall polarization signal at early times, as is seen in SN 2015da and SN 2015bh. In other cases where Sp becomes more negative at later times (such as in the case of SN 2010jl), the CSM may be more distant and so the echo light arrives later. Although it is beyond the scope of this paper, the time delay between the SN peak and the epoch with the most negative Sp may provide a reasonable measure of the distance to the distant CSM that causes the wavelength-dependent polarization. The magnitude of the wavelength-dependent polarization shift may also help inform the strength of the light echo and thus the scattering properties of the distant CSM. With enough frequently-sampled spectropolarimetry, there might be a way to separate the polarization signal from the light echo and the CSM interaction region. In the past, light echoes have been used as a powerful tool to explore the history of eruptive mass-loss and even separate such eruptions into different phases (Smith et al. 2018a,b).
One of the most interesting objects from our sample that shows heavy wavelength-dependent polarization is SN 2015da. In the 3rd epoch of spectropolarimetric data for SN 2015da, Sp becomes significantly more negative at a time when the continuum polarization is also measured to be high and no line depolarization is seen. Although the ISP constraint on SN 2015da from reddening is not very restrictive (ISP <8.73%) because it is heavily reddened, the wavelengthdependent polarization is projected along the same position angle as the continuum polarization, suggesting that the external CSM dust shares a geometry with the continuum polarization region for SN 2015da. It would be unlikely for the CSM dust that produces the wavelength-dependent polarization to be directly aligned with the ISP, so this suggests that the ISP for SN 2015da may actually be quite small. This reinforces the idea that objects can indeed exist with reddening to ISP relations far below the upper limit set in Serkowski, Mathewson, & Ford (1975).
Overall, we see a diversity of changes in Sp, which is consistent with a variable number of distant CSM shells producing light echoes with variable time delays depending upon their distance to the SN. We find this to be the most plausible explanation for the general predominance of negative Sp values, the diverse trends in Sp, and the numerous CSM-interactionrelated conclusions that are already well-founded for SNe IIn.

Viewing Angle
Our sample of SNe IIn constitutes a diverse population with a variety of peak polarizations, rise times, and decay times, but it still has a few unifying factors like the steady drop in polarization at late times as Hα equivalent widths and V20 rise, and a general preference for showing a blueward slope in the continuum polarization level. Here, we focus on the facts that 1. SNe IIn show strong continuum polarization at early times, 2. a nonnegligble but significant fraction show little polarization at any time, and that 3. almost all SNe IIn have a negative Sp. The combination of these properties suggests that a common axisymmetric geometry with a variety of viewing angles may play an important role in the spread of measured polarization signals for these objects, as already suggested in Bilinski et al. (2020) when studying SN 2014ab.
In Figure 13, we show an updated schematic derived from the work in Bilinski et al. (2020), with a predominantly disklike or toroidal geometry for the densest CSM. We have included the consideration that the distant CSM (shown in green) may be causing wavelength-dependent polarization due to CSM dust scattering. At early times in most SNe IIn, the CSM is optically thick and the emitting photosphere is ahead of the forward shock (Smith 2017), and so we do not see the SN ejecta directly. As such, we are unable to probe the geometry of the SN ejecta with spectropolarimetry unless we observed the SN prior to the start of CSM interaction (as was the case for SN 2009ip; Smith, Mauerhan, & Prieto 2014;Mauerhan et al. 2014). Instead, spectropolarimetry of SNe IIn probes the asymmetry of the SN environment and helps us learn more about the SN progenitor and its final years that otherwise would have remained hidden (though see Khazov et al. 2016 for a discussion on how flash spectroscopy may inform mass loss from core collapse events as well).
Suppose that all SNe IIn have a similar axisymmetric geometry (such as the disk-like/toroidal one shown in Figure  13). In that case, when various SNe IIn are viewed from a random distribution of angles relative to the polar axis, we should see a distribution of polarizations from some upper threshold, corresponding to systems seen nearly edge-on, down to zero. If the CSM is really axisymmetric, nearly poleon views (like that of SN 2014ab, similar to that of panel B in Figure 13) will show very low polarization at all times, whereas viewing directions that are between mid-latitudes and the equatorial plane will see the highest polarization (similar to panel A in Figure 13). If the distant dusty CSM has the same axisymmetric geometry as the inner CSM disk, we would expect to see a strong increase in the polarization for objects viewed from mid-latitudes at early times (explaining how something like SN 2017hcc might have reached a polarization degree of almost 6%). As optical depths fade at late times, the polarization degree will fall for all objects with an electron scattering component in the polarization.
According to Figure 11, 7 of the 10 objects shown there display significant polarization, whereas only 3 maintain low polarization at all epochs (the other 4 objects in our sample were excluded because they did not meet the signal-to-noise ratio cutoffs we set in this analysis). Although it would likely require sophisticated models to predict a detailed relation between viewing angle and polarization degree, we can attempt to estimate the fraction of SNe IIn that we would expect to see with low or high polarization based on a simple statistical model. In our equatorial disk model, we assume that objects viewed between 0°and 45°(0°being edge-on with the disk) would be significantly polarized, while objects viewed nearer the polar axis, with viewing angles between 45°to 90°, would be only weakly polarized. In this axisymmetric model, we would expect that ∼ 71% of objects would be found within the mid-latitudes and ∼ 29% within the polar latitudes. Although our sample is small, our observations are in line with these predictions. Nevertheless, because our sample of SNe IIn is quite small (even though it is the largest spectropolarimetric data set for SNe IIn yet), we do not attempt to empirically constrain the range of viewing angles that might produce low or high polarization signals.

Implications for Pre-SN Mass Loss
Despite the large diversity of polarization properties in the SN IIn sample, there are two key properties that most SNe IIn exhibit. Every object with late-time data shows a steady drop to low levels of polarization at late times. This does not necessarily mean that the more distant CSM hit by the shock at late times is more spherical. Instead, this drop may result because at late times when the optical depth has dropped due to lower CSM densities at large radii, the electron scattering continuum is making a weaker contribution to the total light, even though CSM interaction continues. This is consistent with the observation that the Hα equivalent width rises at late times as the continuum fades away (Figure 9). Additionally, most SNe IIn exhibit a wavelength-dependent polarization at some point in their evolution, but only in rare cases (SN 2009ip) do we see a change in the position angle. This implies that the scattering by distant CSM dust that contributes the wavelength-dependent polarization is asymmetric, but mostly aligned with the inner CSM that gives rise to the electron scattering polarization signal. This provides an important constraint for pre-SN eruptive mass loss: namely, sources of progenitor mass loss must be able to produce highly axisymmetric CSM with a persistent and stable orientation during these eruptive episodes.
Based on the requirement of extremely high mass-loss rates needed to power luminous SNe IIn through CSM interaction, progenitors for SNe IIn have mainly been suggested to be LBVs (Smith 2005;Smith & Owocki 2006;Gal-Yam et al. 2007;Fox et al. 2011; Bilinski et al. (2020). We present key observable features for SNe IIn in this schematic as viewed from two orthogonal locations, viewing points A and B. While we place A and B at two orthogonal extremes, the viewing angles at which we observe targets within our sample likely lie somewhere in between these two points. There may be many CSM shells at a diversity of distances that produce narrow emission and absorption lines as well as potentially scatter light from the SN photosphere as an echo back into our line of sight. These CSM shells may project anywhere in a 3-dimensional shell (into/out of the page). Because the position angle does not typically change significantly when the polarization signal increases for most of our targets, we suggest that these CSM shells may be preferentially aligned with the equatorial CSM interaction regions. The unshocked CSM shown in a brown color likely produces the majority of strong narrow Balmer-series emission and absorption. The equatorial torus of CSM interaction with the interior SN ejecta (shown in black) is likely where the continuum photosphere resides in most of our observations. The narrow/intermediate-width unpolarized line emission and broad Lorentzian polarized line emission likely originate in this CSM interaction region. The SNe ejecta are shown in grey, though we do not actually constrain the geometry of the SN ejecta to be spherical. The magnitude of the polarization from the distant CSM dust echoes may be larger than the polarization from the electron scattering geometry, even though the cartoon depicts it as having smaller polarization. 2017), though extreme red supergiant progenitors have also been proposed (Smith, Hinkle, & Ryde 2009;). Other related clues, such as variable winds, have also pointed to LBVs as potential SN IIn progenitors (Trundle et al. 2008). The mechanism by which LBVs undergo their episodes of eruptive mass loss is uncertain. Explosions resulting in a strong blast wave (Smith 2008) or super-Eddington winds (Shaviv 2000;Owocki, Gayley, & Shaviv 2004;Smith & Owocki 2006) have been suggested, but the source of energy for either mechanism is still unclear. Pulsational pair instabilities (Woosley, Heger, & Weaver 2002;Woosley, Blinnikov, & Heger 2007) and wave-driven mass loss (Meakin & Arnett 2007;Quataert & Shiode 2012;Shiode & Quataert 2014) models might account for this additional needed energy in SN precursors, but these models are studied in 1-D and they do not depend on nor result in axisymmetric geometries. Thus, they drive mass loss without necessarily creating an axisymmetric CSM with a persistent orientation as is suggested by our observations. Instead, repeated binary interactions (Smith & Frew 2011;Smith & Arnett 2014;Smith et al. 2018a) or pre-SN mergers (Podsiadlowski et al. 2010;Smith & Arnett 2014) could supply the energy needed for eruptive mass loss, and they are also consistent with axisymmetric CSM with a persistent orientation.
Bipolar shapes and binary companions appear to be common around evolved massive stars with visible nebulae, including famous examples like η Carinae (Damineli 1996;Damineli, Conti, & Lopes 1997;Smith 2006;Smith, Ginsburg, & Bally 2018) and the progenitor of SN 1987A (Chevalier & Dwarkadas 1995). In particular, a bipolar nebula with rari-fied CSM along the pole and dense CSM along the equator, much like what is seen for η Carinae (Smith 2006;Smith, Ginsburg, & Bally 2018) fits this picture well. The multiple CSM shells at a range of distances from the SN that we predict from our observations are reminiscent of the multiple eruptions that η Carinae has experienced in the recent past (Smith & Morse 2004;Kiminki, Reiter, & Smith 2016;Smith et al. 2018a).  show how this bipolar geometry with dense equatorial CSM can also explain the spectroscopic evolution of SN 2017hcc. Since this bipolar nebula model is also consistent with SNe IIn that exhibit low polarization (such as SN 2014ab) if viewed along the polar axis, we suggest that this is the most promising unified picture for the environments of SNe IIn. Obviously, some individual objects may also deviate from this clean picture; for example, binary systems with eccentric orbits may act to disrupt the axisymmetry of the CSM .

SUMMARY
For the first time, we present multi-epoch spectropolarimetric data for a sample of SNe IIn. This sample includes 14 separate SNe IIn. The continuum polarization measurements exhibit a diversity of trends, which is expected for this class of SNe that already exhibit tremendous heterogeneity Richardson et al. 2014). Below we summarise a few key unifying results discovered across our data set and from past published spectropolarimetric studies of SNe IIn: • Estimating the exact ISP contribution for SNe IIn can be difficult. Reddening constraints (i.e. Na I D) only set upper limits on the ISP without placing it at a particular location in the q − u plane, while depolarization of strong emission lines is uncertain because the lines themselves are often polarized to some extent (especially at early times).
• SNe IIn can exhibit intrinsic polarization in the continuum as high as 5.76%. This is higher than the polarization degree level measured for any other type of SN, and is also beyond the expected polarization from models of SNe IIn that adopt electron scattering as the dominant source of continuum polarization, though modelling the polarization signals of interacting SNe is still in its infancy.
• At late times, the gradual decline in the continuum polarization seen in many of our targets with multi-epoch spectropolarimetric data can be explained effectively by a drop in the optical depth of the CSM interaction region with time.
We generally see an increase in the equivalent width of Hα as the continuum polarization fades and the Hα line profile becomes broader.
• At early times in some objects like SN 2017gas and SN 2017hcc, the continuum polarization drops rapidly as the equivalent width of Hα decreases and the Hα emission lines become narrower. This different behavior at early times could be due to real geometrical changes in the photosphere, increased multiple scattering within the CSM interaction region, or a decreased contribution to the total luminosity from light scattered off CSM dust (perhaps because the dust was destroyed soon after the initial explosion).
• Many SNe IIn show sudden increases in the continuum polarization or changes in their Sp. These can generally be attributed to CSM regions existing at a diversity of distances from each SN IIn. Some experience strong CSM interaction early on, while others experience a delay before the interaction begins. Some SNe IIn even show evidence of multiple CSM shells, which are generally aligned with each other.
• The majority of SNe IIn exhibit wavelength-dependent continuum polarization with a stronger polarization at blue wavelengths. This is not expected for wavelengthindependent electron scattering. We are likely observing the combination of a polarization signal from the continuum electron scattering region found within CSM interaction and additional wavelength-dependent polarization from a light echo scattered towards us by CSM dust. When these two geometries are aligned, they add constructively.
• The diversity of features seen in spectropolarimetric data for SNe IIn can potentially be explained by a combination of diverse environments with multiple CSM shells at various distances combined with a persistent axisymmetric geometry that is seen from a range of different viewing angles.
• Most importantly, SNe IIn require an eruptive pre-SN mass loss mechanism that is highly asymmetric and maintains a persistent, perhaps axisymmetric, geometry. Massloss mechanisms that lead to spherically symmetric ejections prior to death do not adequately match the observed CSM properties of SNe IIn. Binary interactions and eruptive massloss focused within an equatorial disk may provide a plausible explanation for the polarization features we observe, whereas deep seated energy deposition in spherically symmetric stars would seem to be strongly disfavored overall.

FUTURE PROSPECTS
This is the first study of a sample of more than one SN IIn, and it has revealed a number of interesting trends regarding the evolution of the polarization and its wavelength dependence over time. However, there are a few outstanding questions that could be answered with improved temporal coverage with spectropolarimetry at either early or late times, and with other types of observations that may help clarify some outstanding mysteries. Specifically, future studies could benefit the understanding of SNe IIn explosion geometries and their environments in ways that we outline below.

High-cadence early spectropolarimetry
Additional high-cadence early-time spectropolarimetry would help examine the source of the high polarization signal sometimes seen near peak in more detail, and might clarify why other objects do not show this. By following the early-time evolution of both the polarization and the intrinsic slope parameter, one may be able to estimate the distance to the nearest CSM and the extent of the contribution from dusty CSM light echoes. Although we have early-time data for a few objects, only one (SN 2009ip) exhibits a rotation in the polarization consistent with a transition from a SN ejecta photosphere to one located in a CSM interaction region ). There may also be unusual spectropolarimetric signatures at early times due to pre-SN outbursts or double-peaked light curves. For instance, SN 2009ip is unique in having spectropolarimetric data during its first peak in a double-peaked light curve. If one could observe SNe IIn with spectropolarimetry at earlier times, one might be able to constrain the transition from explosion until the onset of CSM interaction. If it is common for SNe IIn to experience a ∼ 90°rotation in their geometry between the time of explosion and first CSM interaction, this would support the bipolar nebula with an equatorial disk picture for SNe IIn.

Improved late-time coverage with spectropolarimetry
Several SNe within our sample lack deep late-time spectropolarimetry, but the ones that do have such data all show a decline in polarization. Acquiring more late-time spectropolarimetry would help confirm that the continuum polarization does fade for all SNe IIn at late times. Additionally, latetime spectropolarimetry (especially using larger telescopes that can still detect a significant signal from the SN as it fades) could provide another estimate of the ISP when the intrinsic polarization of the SN has faded. Spectropolarimetry at late times requires relatively nearby SNe IIn and large telescopes.

Higher resolution spectropolarimetry
SNe IIn are different from other core-collapse SNe in that they have strong narrow lines. At all times, higher resolution spectropolarimetry would be useful in detecting specific differences across emission line features. This would be particularly useful at early times when line emission shows significant polarization, so that estimates of the ISP from depolarization could isolate all polarized flux (both polarized continuum and polarized broad emission-line flux) from the unpolarized flux (the narrow-component of the emission line).

Light curve comparisons and constraints
Although light curves are available for a number of the SNe IIn within our sample, many only have sporadic photometric information. Well-sampled light curves would help confirm whether the general drop in the continuum polarization towards late times occurs alongside a similar drop in the continuum optical depth. Current estimates of the time of peak for many of the SNe IIn within our sample are uncertain, especially when the time of peak is coincident with the time of discovery. Additionally, a well-sampled early-time light curve could help estimate the explosion date for the SN, which would be useful in estimating the distance to the external CSM, especially if a wavelength-dependent light echo is observed. 7.0.5 X-ray, radio, and infrared observations The spectropolarimetry we use is all observed at visual wavelengths. However, studies of X-ray-or radio-wavelength emission could help corroborate the axisymmetric model we present. X-rays generated in the shock interaction region may escape more easily from aspherical environments. In particular, X-rays should escape more easily along the polar caps in the axisymmetric geometry we present. Thus, we would expect to see greater X-ray emission at early times from objects with low continuum polarization like SN 2014ab, SN 2011ht, or ASASSN-14il. Similarly, it would be useful to know if significant emission from dust is present at thermal-infrared wavelengths at the same times that we detect a strong wavelength dependence in the continuum polarization which we have attributed to scattering by CSM dust.

ACKNOWLEDGMENTS
The SNSPOL project is supported by the National Science Foundation under awards AST-1210599 to the University of Arizona, AST-1210372 and AST-2009996 to the University of Denver, and AST-1210311 and AST-2010001 to San Diego State University. N.S. received additional support from NSF grants AST-1312221 and AST-1515559, and by a Scialog grant from the Research Corporation for Science Advancement. Research by D.J.S. is supported by NSF grants AST-1821967, 1821987, 1813708, 1813466, 1908972, and by the Heising-Simons Foundation under grant #2020-1864. P.S. was supported by NASA/Fermi Guest Investigator Program grants NNX09AU10G, NNX12AO93G, and NNX15AU81G. D.C.L. acknowledges support from NSF grants AST-1009571 and AST-1210311, under which part of this research was carried out. J.L.H. acknowledges that the University of Denver resides on the ancestral territories of the Arapaho, Cheyenne, and Ute, and that its history is inextricably linked with the violent displacement of these indigenous peoples. This paper made use of the NASA/IPAC Extragalactic Database (NED), which is operated by the Jet Propulsion Laboratory, California Institute of Technology, under contract with NASA. This paper made use of data from Pan-STARRS1 acquired after May 2014. Operation of the Pan-STARRS1 telescope is supported by the National Aeronautics and Space Administration under Grant No. NNX12AR65G and Grant No. NNX14AM74G issued through the NEO Observation Program.
We thank the staffs at the MMT, Bok, and Kuiper telescopes for their assistance with the observations. Observations using Steward Observatory facilities were obtained as part of the large observing program AZTEC: Arizona Transient Exploration and Characterization. Some observations reported here were obtained at the MMT Observatory, a joint facility of the University of Arizona and the Smithsonian Institution.

DATA AVAILABILITY
The data underlying this article will be shared on reasonable request to the corresponding author.

Appendices APPENDIX A: Q − U PLOTS FOR THE ENTIRE SAMPLE OF SNE IIN
In this appendix we show all 49 epochs of spectropolarimetric data within our sample as q − u plots. If an estimate of the ISP was made from line depolarization for the target, we also show the spectropolarimetric data after ISP correction.