The SAMI Galaxy Survey: $\Sigma_{\rm SFR}$ drives the presence of complex emission line profiles in star-forming galaxies

Galactic fountains driven by star formation result in a variety of kinematic structures such as ionised winds and thick gas disks, both of which manifest as complex emission line profiles that can be parametrised by multiple Gaussian components. We use integral field spectroscopy (IFS) from the SAMI Galaxy Survey to spectrally resolve these features, traced by broad H$\alpha$ components, and distinguish them from the star-forming thin disk, traced by narrow components, in 3068 galaxies in the local Universe. Using a matched sample analysis technique, we demonstrate that the presence of complex emission line profiles in star-forming galaxies is most strongly correlated with the global star formation rate (SFR) surface density of the host galaxy measured within $1R_{\rm e}$ ($\Sigma_{{\rm SFR},R_{\rm e}}$), even when controlling for both observational biases, including inclination, amplitude-to-noise and angular scale, and sample biases in parameters such as stellar mass and SFR. Leveraging the spatially resolved nature of the dataset, we determine that the presence of complex emission line profiles within individual spaxels is driven not only by the local $\Sigma_{\rm SFR}$, but by the $\Sigma_{{\rm SFR},R_{\rm e}}$ of the host galaxy. We also parametrise the clumpiness of the SFR within individual galaxies, and find that $\Sigma_{{\rm SFR},R_{\rm e}}$ is a stronger predictor of the presence of complex emission line profiles than clumpiness. We conclude that, with a careful treatment of observational effects, it is possible to identify structures traced by complex emission line profiles, including winds and thick ionised gas disks, at the spatial and spectral resolution of SAMI using the Gaussian decomposition technique.


INTRODUCTION
The cycling of baryons within and around galaxies plays a critical role in shaping the star formation histories, chemical enrichment, and gas dynamics of present-day galaxies (e.g., Veilleux, Cecil & Bland-Hawthorn 2005;Tumlinson, Peeples & Werk 2017).In its most basic form, the baryon cycle begins with a galaxy accreting ★ E-mail: henry.zovaro@anu.edu.augas from its surroundings-either in the form of a gas-rich merger or directly from the circumgalactic medium-which in turn triggers star formation in the disk, enriching the local interstellar medium with metals.Ensuing stellar winds and supernovae (SNe) explosions may then expel gas and dust from the disk, creating biconical structures filled with Hα-emitting filaments of disk material (Cooper et al. 2008(Cooper et al. , 2009)).Gas entrained by particularly powerful winds can escape the galaxy's gravitational potential, and enrich the intergalactic medium, potentially solving the "missing baryons" problem (e.g., Shull et al. 2012).However, in most cases it is expected that the bulk of this material will eventually return to the disk in the form of a "galactic fountain" (Shapiro & Field 1976;Bregman 1980), redistributing metals throughout the disk and providing fuel from which new generations of stars may form.
Powerful winds launched by vigorous star formation manifest as fast outflows of ionised, neutral, and molecular gas (for a comprehensive overview, see Veilleux, Cecil & Bland-Hawthorn 2005).In nearby galaxies such as M82, powerful outflows can be identified by bright, filamentary Hα emission in the form of conical structures above and below the disk plane (Lynds & Sandage 1963;Bland & Tully 1988;Shopbell & Bland-Hawthorn 1998;Sharp & Bland-Hawthorn 2010).The emission line profiles indicate strong noncircular motions, comprising multiple distinct kinematic components in addition to broad line widths (McKeith et al. 1995;Westmoquette et al. 2009).Studies of large samples of local galaxies have shown that winds are associated with higher stellar masses and star formation rates (SFRs; Avery et al. 2021), and most strongly with high SFR surface densities (Σ SFR ; Heckman et al. 2002;Roberts-Borsani et al. 2020).More recently, Law et al. (2022) found a strong correlation between the spatially resolved Hα velocity dispersion and SFR in local star-forming galaxies, which may be due to increased localised gas turbulence or unresolved broad emission line components at high SFRs.
Many star-forming galaxies do not exhibit winds, but rather thick gas disks that are kinematically distinct from the thin gas disk, which comprises the H ii regions.Present in the majority of disk galaxies (Haffner et al. 2009;Levy et al. 2018;Marasco et al. 2019) including our own Milky Way (Reynolds 1991), these thick gas disks-referred to in the literature by a variety of terms, including extraplanar gas or diffuse ionised gas (DIG)-exhibit scale heights of up to a few kpc (Levy et al. 2018(Levy et al. , 2019;;Marasco et al. 2019;den Brok et al. 2020), and are therefore substantially thicker than the thin gas disk, but typically have a much lower surface brightness than H ii regions.They also exhibit vertical velocity gradients of between −10 and −30 km s −1 kpc −1 (Swaters et al. 1997;Levy et al. 2018Levy et al. , 2019;;Marasco et al. 2019), and therefore exhibit a substantial "lag" in rotational velocity with respect to the thin disk.Thick disks have been observed in both H i and Hα, with the two phases sharing similar kinematics (e.g., Spitzer & Fitzpatrick 1993;Reynolds et al. 1995;Swaters et al. 1997;Howk et al. 2003;Fraternali et al. 2004), suggesting they represent the same structure.Similarly to winds, the presence of thick disks is linked to Σ SFR (Rossa & Dettmar 2003;Rueff et al. 2013;Levy et al. 2018).Fraternali & Binney (2006) proposed that thick ionised gas disks may form via gas return from galactic fountains.Indeed, the kinematics of the thick disk are incompatible with simple hydrostatic equilibrium (Barnabè et al. 2006;Marinacci et al. 2010), and require continuous injection of turbulence to remain stable.Furthermore, recent hydrodynamical simulations suggest that these thick disks may form due to fountains powered by star formation evenly distributed within the disk, whereas centrally concentrated star formation is more likely to produce powerful outflows (Vĳayan et al. 2018).Accretion has also been proposed as a mechanism for the formation of thick disks, although this probably only contributes in a small fraction of galaxies at low redshift (Marasco et al. 2019).Understanding the origins of these thick disks, and their relation to winds, therefore provides insight into how gas is cycled in and out of star-forming galaxies.
In high-resolution spectroscopy, winds and thick disks can be identified by the presence of complex emission line profiles.Whilst winds will regularly produce clear "line splitting" and broad emis-sion line components (e.g., Westmoquette et al. 2009), thick disks present as subtle wings tracing gas at lower rotational speeds than the thin disk (e.g., Marasco et al. 2019).Indeed, Belfiore et al. (2022) proposed that thin and thick disk Hα emission can be separated via fitting multiple Gaussian emission line components; this was demonstrated earlier by den Brok et al. (2020), who distinguished thick disk emission in a small sample of local galaxies by fitting multiple Gaussian line profiles to the Hα line profiles in low-spectral resolution MUSE observations.
The Sydney-Australian Astronomical Observatory (AAO) Multiobject Integral field spectrograph (SAMI) Galaxy Survey (Bryant et al. 2015;Croom et al. 2021) provides optical integral field spectroscopy (IFS) for 3068 local galaxies.Crucially, the spectral resolution of the red arm of AAOmega ( inst = 29.6 km s −1 ; van de Sande et al. 2017;Scott et al. 2018) is sufficient to resolve individual Gaussian components in the emission lines from ionised gas (e.g., Ho et al. 2014), thereby enabling detailed studies of spectrally resolved winds and thick disks in a large sample of galaxies.
In this work, we use the SAMI Galaxy Survey to determine the underlying galaxy properties associated with complex emission profiles in star-forming galaxies, and therefore the processes that lead to the formation of galactic fountains, winds and thick ionised gas disks.In Section 2 we introduce the sample, and in Section 3 we detail how we identify galaxies with and without complex emission line profiles.In Section 4 we conduct a matched sample analysis to determine the underlying galaxy properties most strongly associated with complex emission line profiles, and in Section 6 we investigate the roles of star formation on both local and global scales.Finally, we discuss our results plus the influence of observational biases in Section 7.For the remainder of this work we assume a flat ΛCDM cosmology with  0 = 70 km s −1 Mpc −1 , Ω M = 0.3 and Ω Λ = 0.7.

THE SAMI GALAXY SURVEY
The SAMI Galaxy Survey (Croom et al. 2012;Bryant et al. 2015) is an IFS survey of 3068 local ( < 0.095) galaxies spanning a stellar mass range 10 7 − 10 12 M ⊙ in field, group and cluster environments.Each target was observed with the Sydney Australian Astronomical Observatory Multi-Object Integral Field Spectrograph (SAMI;Croom et al. 2012) on the 3.9 m Anglo-Australian Telescope at Siding Spring Observatory.SAMI is a multi-object fused-fibre-bundle instrument that feeds the AAOmega spectrograph (Sharp et al. 2006), which has separate blue (3700-5700 Å,  = 1812) and red (6300-7400 Å;  = 4263) arms.Each fibre bundle, or hexabundle (Bland-Hawthorn et al. 2011;Bryant et al. 2014), comprises 61 individual 1.6" diameter optical fibres with a high filling factor of 75 per cent and a total footprint of 14.7".The observations for each target were dithered on-source to account for gaps between fibres in the hexabundle.The final reduced data cubes have 0.5" × 0.5" spaxels (spatial pixels) with an average effective seeing of 2".We used the data products from the third SAMI data release (DR3; Croom et al. 2021) 1 , which includes the original data cubes, plus twodimensional maps of emission line fluxes, gas and stellar kinematics, and other quantities.DR3 also includes tables2 containing measurements of additional physical quantities and data quality flags for each galaxy.Spectroscopic and flow-corrected redshifts () and stellar masses ( * ) were extracted from the InputCatGAMADR3 (Bryant et al. 2015), InputCatClustersDR3 (Owers et al. 2017) and InputCatFiller tables.Effective radii ( e ) and axis ratios (/) were derived from -band SDSS, VST and GAMA photometry were computed using the multi-Gaussian expansion (MGE;Emsellem et al. 1994;Cappellari 2002) fits described in D 'Eugenio et al. (2021).Inclinations () were derived from these axis ratios using eqn. 1 from Poetrodjojo et al. (2021) adopting an intrinsic disk thickness of  0 = 0.2.
To obtain spatially resolved measurements for each galaxy, we used the unbinned ("default") data products, which include emission line profile fits carried out using lzifu (Ho et al. 2016a), which first fits and then subtracts the stellar continuum to more accurately fit the emission lines.In this work we use the "recommended" component fits, in which LZComp (Hampton et al. 2017a,b), an artificial neutral network (ANN), was used to evaluate the best-fitting number of components in each spaxel (i.e., one, two or three components).The components are ordered by velocity dispersion, such that components 1, 2 and 3 refer to the narrow, broad and extra-broad components respectively.For each galaxy, DR3 includes maps of the total emission line fluxes in each spaxel-i.e., summed over all Gaussian emission line components-for [O ii]λλ3726, 9, Hβλ4861, [O iii]λλ4959, 5007, [O i]λ6300, [N ii]λλ6548, 83, Hαλ6563 and [S ii]λλ6716, 31; fluxes for individual components are only provided for Hα due to S/N limitations and the lower spectral resolution of the blue arm of AAOmega.The line-of-sight (LoS) ionised gas velocity ( gas ) and velocity dispersion ( gas , corrected for instrumental resolution by lzifu) are provided for each individual component, however.
We also used the SFR and Σ SFR maps produced by Medling et al. (2018), which were derived using the reddening-corrected Hα fluxes from the recommended-component fits assuming a Chabrier (2003) initial mass function (IMF) and the SFR calibration of Kennicutt et al. (1994).We note that these SFR measurements are based on the total Hα emission line flux, which may lead to over-estimates of the SFR in cases where broad emission line components are associated with emission from other sources such as shocks or DIG.However, Belfiore et al. (2022) argue that in nearby star-forming galaxies, DIG is predominantly ionised by leaky H ii regions, and should therefore be included in SFR estimates; they also concluded that including DIG from evolved stellar populations in these estimates will not lead to a significant over-estimate of the SFR in kpc-resolution data, such as SAMI.None the less, we repeated our analysis using SFR measurements from only the narrow Hα component in each spaxel, and found that it made no meaningful difference to our conclusions.Global SFRs and Σ SFR were measured for each galaxy by summing the SFRs in these maps within nuclear apertures of diameter 3 kpc and 2 e .
Emission line fluxes were corrected for extinction using the Fitzpatrick & Massa (2007) reddening curve with   = 3.1 and assuming an intrinsic Balmer decrement of Hα/Hβ = 2.86 which corresponds to a standard nebular electron temperature and density of 10 4 K and 100 cm −3 respectively (Dopita & Sutherland 2003).To ensure reliable extinction correction, this step was only applied to spaxels in which the total flux S/N of both Hα and Hβ exceeded 5. Hα equivalent widths (EW(Hα)) were computed as the nonextinction-corrected Hα flux divided by the mean continuum level in the rest-frame wavelength range 6500-6540 Å.

Data quality and S/N cuts
Using the DR3 CubeObs table as described in Croom et al. (2021), we identified and removed galaxies with bad sky subtraction residuals (as indicated by WARNSKYR and WARNSKYB), those with flux calibration issues (WARNFCAL and WARNFCBR), and those containing multiple objects in the SAMI field-of-view (FoV) (WARNMULT), leaving 2997 galaxies.
To ensure high-quality kinematics and Hα fluxes of individual components within individual spaxels, we adopted a minimum flux S/N (defined as the flux divided by the formal uncertainty provided by LZIFU) of 5 in Hα in each component, plus a component amplitudeto-noise (A/N) of at least 3, here defined as the Gaussian amplitude of the component divided by the RMS noise in the rest-frame wavelength range 6500 Å-6540 Å.We also required a minimum gas velocity dispersion S/N of 3 in each component as defined by Federrath et al. (2017), which accounts for the uncertainty in measuring the width of individual emission line components that are close to the instrumental resolution.For total emission line fluxes in each spaxel (that is, summed over all emission line components), we required a minimum S/N of 5. Example fits from spaxels meeting these criteria are provided in Appendix A.
We used only the O3 vs. N2 and O3 vs. S2 diagrams due to the relative weakness of the [O i] emission line.To ensure reliable classification, only spaxels with a flux S/N of at least 5 in all of Hβ, Hα, [O iii]λ5007, [N ii]λ6583, and [S ii]λλ6716, 31 lines were classified.Due to the lower spectral resolution of the blue arm ( = 1812) compared to the red arm ( = 4236), blue lines such as [O iii] and Hβ may not have reliable flux measurements for individual components.As a result, DR3 only provides total fluxes for lines other than Hα, rather than those of individual components.Spectral classification was therefore performed using the total emission line fluxes in each spaxel.We note that, in cases where multiple emission line components are present that arise from different excitation mechanisms (e.g., a star-forming component plus a shocked component), the classification is naturally weighted towards the component with the highest luminosity.
Each spaxel was assigned one of the following spectral classification: • Star-forming (SF): lies below the Kauffmann et al. (2003) line in the N2 diagram, and below the Kewley et al. (2001) "extreme starburst" line in the S2 diagram.
• Composite: lies above the Kauffmann et al. (2003) line in the N2 diagram but below the the Kewley et al. (2001) "extreme starburst" line in both the N2 and S2 diagrams.
• LINER: lies above the Kewley et al. (2001) "extreme starburst" line in both the N2 and S2 diagrams but below the Kewley et al. (2006) LINER/Seyfert line in the S2 diagram.
• Seyfert: lies above the Kewley et al. (2001) "extreme starburst" line in both the N2 and S2 diagrams but above the Kewley et al. (2006) LINER/Seyfert line in the S2 diagram.
• Not classified: low S/N in or missing at least one of Hα, Hβ,

DEFINING 1-AND MULTI-COMPONENT GALAXIES
Our aim is to determine the fundamental differences between starforming galaxies exhibiting large numbers of spaxels with complex emission line profiles-that is, containing multiple componentsand those without, which we refer to as "multi-component galaxies" and "1-component galaxies" respectively.Here, we describe our method for classifying SAMI galaxies into these two categories.
We begin by defining a parent sample.For a galaxy to be included, it must contain at least 50 spaxels that can be spectrally classified after making the data quality and S/N cuts detailed in Section 2.1; this requirement removes galaxies that are poorly resolved and those with overall low emission line S/N and therefore less reliable multicomponent fits.In this work, we are primarily interested in winds and outflows associated with star formation.Because active galactic nuclei (AGN) can also contribute to these phenomena, we remove possible AGN hosts from our sample by requiring at least 80 per cent of spectrally-classified spaxels to be star-forming, and that all but one spaxel within 2" of the nucleus must be star-forming, unclassified, or have EW(Hα) < 3 , where this last criterion allows for spaxels where the dominant photoionisation mechanism is evolved stars (Singh et al. 2013;Belfiore et al. 2016;Byler et al. 2019).We also remove galaxies containing any spaxels classified as Seyfert.Our final parent sample of star-forming galaxies contains 655 objects.
From this parent sample, we select "1-component" and "multicomponent" galaxies according to the following criteria: 1component galaxies are those in which over 99 per cent of all spaxels with emission line components that pass our S/N and data quality cuts contain only 1 component, and multi-component galaxies are those in which at least 15 per cent of all such spaxels contain 2 or more components.Objects in which 1-15 per cent of spaxels contain multiple components are not classified as either 1-or multi-component galaxies.
Figure 1 shows examples of 1-and multi-component galaxies.SDSS images are shown, alongside maps displaying the number of emission line components fitted in each spaxel, spectral classifications, and the LoS velocity of the narrow and broad components.Note that we do not base our classification on the number of 3-component spaxels due to their rarity: of all spaxels containing emission lines exceeding our S/N requirements, approximately 6.8 per cent contain 2 components whereas only 0.7 per cent contain 3 components.That said, our multi-component galaxy sample contains objects with appreciable numbers of spaxels containing 3 components, e.g., galaxy 53770 as shown in Fig. 1.
Although our choice of 15 per cent is somewhat arbitrary, we find that shifting this threshold does not meaningfully change our results; 15 per cent strikes a good balance between having a sufficiently large multi-component galaxy sample to conduct statistical analysis, and having a large enough number of multi-component spaxels within each galaxy to ensure our multi-component sample is not contaminated by spaxels with unreliable 2 or 3-component fits.Our criteria result in 266 1-component galaxies and 133 multi-component galaxies.
Note that our selection criteria for multi-component galaxies do not explicitly take into account the origin of the broad-line emission, and as such includes systems in which the broad component is due to beam smearing, winds/outflows, thick disks and other processes such as mergers and stripping.For example, as shown in Fig. 1, the broad component in galaxy 491457 exhibits smooth rotation similar to that of the narrow component, whereas that in galaxy 53770 is clearly blueshifted, and likely represents a wind.
A drawback of spatially resolved data in comparison with in-tegrated spectra is the lower S/N.We therefore repeated our 1and multi-component classification process using velocity-subtracted 1 e aperture spectra to check whether there are any galaxies with low surface-brightness broad line emission that is not detectable in the spatially resolved data.As detailed in Appendix B, there were no galaxies classified as 1-component using the resolved data that were classified as multi-component in the aperture spectra.In fact, 20 galaxies classified as multi-component using the resolved data were classified as 1-component using the aperture spectra, possibly due to beam smearing effects "washing out" faint broad components in individual spaxels.We therefore rely only upon the resolved classifications for the remainder of this paper.As shown in Fig. 2a, the multi-component galaxies are more massive, and have significantly higher mean SFRs and Σ SFR measured within 1 e (SFR  e and Σ SFR,  e , respectively) as well as higher specific SFRs (sSFRs) than 1-component galaxies.In particular, there is essentially no overlap in the distributions in Σ SFR measured within 3 kpc (Σ SFR, 3 kpc ) of the 1-and multi-component systems; however, Σ SFR, 3 kpc may not reflect the true Σ SFR within the galaxy in systems with  e < 3 kpc, which represents a significant fraction of our galaxies.For this reason, we primarily rely on  e -based measurements for the remainder of this work.The multi-component galaxies also have higher values of log 10 ( * / e ) and log 10 ( * / 2 e ), which are proxies for gravitational potential and stellar surface density respectively, and slightly redder  −  colours than 1-component galaxies.They also have clumpier star formation distributions on average, as evidenced by their higher Gini coefficients (, Gini 1936), which are computed using

General properties of 1-and multi-component galaxies
where   is the Σ SFR (or equivalently SFR) in spaxel ,  is the total number of spaxels where the Σ SFR can be measured and s is the average Σ SFR in the galaxy. = 0 corresponds to perfect equality, i.e., every spaxel has the same Σ SFR , whereas  = 1 corresponds to maximal inequality, i.e., all star formation is concentrated in a single spaxel.Gini coefficients are discussed further in Section 6.
Figure 2b shows the distribution in various observational quantities in the 1-and multi-component samples.
In the leftmost panel we show log 10 ⟨Hα A/N⟩ 3kpc , the mean Hα A/N measured within a 3 kpc aperture.Here, and for the remainder of this paper, Hα A/N is defined within each spaxel as the peak amplitude of the Hα line profile (directly measured from the spectrum, and therefore not corrected for stellar absorption) relative to the mean continuum level in the rest-frame wavelength range 6500 Å-6540 Å divided by the RMS noise measured in the same range.We opt to use A/N rather than flux S/N as the latter is based on the fluxes and formal uncertainties provided by LZIFU, and may not representative of the true S/N in cases of bad fits.The multi-component galaxies exhibit higher mean Hα A/N than the 1-component galaxies.
They also tend to be more distant, although this could result from SAMI's stepped sample selection function, in which all essentially all galaxies with log 10  * < 9 are located at  ≲ 0.03 (see fig. 3 of Croom et al. 2021).Compared to the 1-component galaxies, multicomponent galaxies are slightly over-represented at intermediate inclinations and under-represented at high inclinations, which is contrary to expectations if the presence of multiple components is a consequence of beam smearing alone.Potential explanations for this over-representation are discussed in Section 7.2.
The locations of the 1-and multi-component galaxies on the star-forming main sequence (SFMS) are shown in the upper panel of Fig. 3.At stellar masses below approximately 10 10 M ⊙ , multicomponent galaxies sit along the upper envelope of the SFMS, having elevated SFRs for their mass, whilst at higher masses they exhibit a wider range of SFRs.The bottom panel, which shows Σ SFR,  e as a function of stellar mass, shows that the multi-component galaxies typically have The  e measurements were derived using -band photometry (for details see D 'Eugenio et al. 2021) which includes the Hα emission line for galaxies at  ≲ 0.066, representing the majority of galaxies in our sample (see Fig. 2b).In galaxies with high SFRs,  e may be biased towards smaller values by bright Hα emission in the nuclear regions, thereby no longer representing the stellar extent of the galaxy and in turn elevating Σ SFR,  e .A 10 per cent Hα contribution to the band flux corresponds to an emission line EW(Hα) of approximately 150 Å; within 1 e , the average EW(Hα) exceeds this amount in only 3 and 2 of our 1-and multi-component galaxies respectively, indicating that only a very small fraction of our sample is likely to have biased  e measurements.We therefore conclude that the  e measurements are not significantly biased by this effect and use  eaperture measurements for the remainder of this work.Plots made using the 3 kpc circular ("round") aperture measurements are shown in Appendix C for comparison.

MATCHED SAMPLE ANALYSIS
As shown by Fig. 2, the 1-and multi-component galaxies have statistically significantly different distributions in a number of physical properties, including stellar mass and SFR; they also differ in observational properties such as inclination and S/N.Identifying the processes that cause complex emission line profiles therefore requires careful treatment due to underlying correlations between various parameters.For example, the multi-component galaxies have higher stellar masses and higher SFRs; however, because stellar mass is itself correlated with SFR (Fig. 3), this alone does not indicate whether the presence of complex emission line profiles is driven by stellar mass or SFR.
Observational biases must also be controlled for.For instance, the multi-component galaxies have higher Hα A/N; a scenario in which all galaxies would exhibit multiple emission line components In each panel we show the distribution in the full SAMI sample of 2997 galaxies (thin black line), the 1-component galaxy sample (shaded blue histogram), and multi-component galaxy sample (thick blue line).In (b), the top axis ticks of the bottom right-most panel show the axis ratios / corresponding to the measured inclinations assuming an intrinsic disk thickness  0 = 0.2 (Poetrodjojo et al. 2021).The text in the upper left corner shows the -values of the KS and AD tests applied to the 1-and multi-component samples.In all quantities except for  e , the very low -values indicate that the samples are highly unlikely to be drawn from the same parent sample, suggesting the two samples have fundamentally different distributions in all quantities shown here.
given sufficient A/N could therefore be consistent with these observations.However, the multi-component galaxies also have higher SFRs, meaning that at a fixed redshift they will have brighter Hα emission, and therefore higher A/N.The offset in A/N could therefore also occur if SFR is the fundamental driver of multiple emission line components.
To control for the effects of observational and physical parameters on the presence of multiple emission line components, we perform a matched sample analysis (e.g., Kaasinen et al. 2017) using an adaptive threshold matching technique as follows: (i) For each multi-component galaxy, we identify all unmatched 1-component galaxies within some matching threshold Δ of the quantity  being matched.
(ii) If this is successful, we select the 1-component galaxy from this subset that is closest to the multi-component galaxy in , and subsequently remove both galaxies from the lists of unmatched galaxies.
(iii) Otherwise, if there are no 1-component galaxies within ±Δ of , the multi-component galaxy remains unmatched and we repeat step (i) for the next unmatched multi-component galaxy.
(iv) Once we have attempted to match all multi-component galaxies, we terminate the process if at least 80 per cent of all multicomponent galaxies have been matched.Otherwise, we increment the matching threshold by +Δ and repeat the matching process (step (i)) on all of the unmatched multi-component galaxies.
(v) If necessary, steps (i)-(v) are repeated once more with a match threshold of 3Δ, after which the process is terminated.
Δ was set to the typical uncertainty for quantities in which measurement uncertainties were available; Δ values for other parameters were chosen to provide sufficiently large matched samples to enable Table 1.Match thresholds Δ used for the matched sample analysis (Section 4).

Quantity
Δ fair comparison whilst ensuring reasonable similarity in the matched quantity between 1-and multi-component galaxies.The values of Δ used are given in Table 1.
Validity of the final matched 1-and multi-component galaxy samples was determined using the 2-sample KS and AD tests as in Section 3.1; when matching, we required  > 0.05 in both of these tests to ensure that the matched samples were valid.To ensure stability of our results, we repeated steps (i) to (v) 1000 times for each matched quantity, each time randomly sorting the list of multi-component galaxies, and inspecting the distribution of -values.In all matched quantities the -values exceeded 0.05 in both KS and AD tests over 99 per cent of the time, indicating stable results.

Matched sample analysis results
Figure 4 shows violin plots representing kernel density estimates (KDEs) of the distributions in various parameters for the 1-and multi-component galaxy samples matched in  * SFR  e , Σ SFR,  e and .To control for observational biases, we also show samples simultaneously matched with these physical quantities and in succession with log 10 ⟨Hα A/N⟩ 3 kpc , angular scale and inclination.
To control for observational biases, we also show samples matched with these physical quantities simultaneously in log 10 ⟨Hα A/N⟩ 3 kpc , angular scale and inclination.The results of KS and AD 2-sample tests are indicated for each violin plot; text in red represent  < 0.05, indicating a statistically significant likelihood that the samples are not drawn from the same underlying distribution.Results for matched samples in other combinations of parameters are summarised in Fig. C1.
We first match in  * (first four columns of Fig. 4).When controlling for  * (column 1), the multi-component galaxies have smaller  e and significantly higher SFR  e ; in particular, they exhibit mean Σ SFR,  e and Σ SFR, 3 kpc nearly 1.0 dex higher than those of the matched 1-component galaxies.They also have significantly higher values of , indicating clumpier and/or more centrally-concentrated SFR distributions, much higher average Hα A/N and have distinct distributions in angular scale and inclination.However, when controlling for Hα A/N, angular scale and inclination by matching in these quantities simultaneously with  * (columns 2-4), the multicomponent galaxies still exhibit significantly higher SFR  e , Σ SFR and , and tend to be more compact.
We now consider SFR  e (columns 5-8 of Fig. 4).When matched in SFR  e alone (column 5), the multi-component galaxies have a significantly different distribution in  * , being less massive than the 1-component galaxies; however, when controlling for Hα A/N, angular scale and inclination this difference disappears.Rather, when accounting for these observational effects, the multi-component galaxies are differentiated by being more compact and having higher Σ SFR than 1-component galaxies at the same SFR  e ; they also exhibit higher Gini coefficients.
As shown in Fig. 3, there is some overlap between the 1-and multicomponent galaxies on the SFMS and the Σ SFR main sequence.To determine what distinguishes the two samples in the overlapping regions of these parameter spaces, in the 4th column of Fig. C1 we match in both  * and SFR  e , which yields similar results to matching in SFR  e alone: the matched multi-component galaxies have significantly higher Σ SFR,  e and Σ SFR, 3 kpc , and are more compact than the 1-component galaxies.Note that we do not simultaneously match in observational parameters as the resulting sample sizes become too small to perform statistical analysis; however, this is unlikely to bias our results, having just shown that the multi-component galaxies exhibit elevated Σ SFR when matched in  * and SFR  e even when controlling for Hα A/N, angular scale and inclination.In the 5th column of Fig. C1, we match in both  * and Σ SFR,  e .In this case, the matched 1-component galaxies have similar SFR  e , suggesting that Σ SFR is more fundamental than SFR in determining the presence of complex emission line profiles in these galaxies.
We now match in Σ SFR,  e (columns 9-12 of Fig. 4).Note that the nearly disjoint distributions of the 1-and multi-component galaxies in Σ SFR,  e (as shown in Fig. 2b) results in a relatively small sample size of 18 when matching in this quantity, and that the matched 1component galaxies may not be representative of the overall sample.None the less, at a fixed Σ SFR,  e , the multi-component galaxies are significantly larger, more massive and have higher SFR  e than the 1-component galaxies; these trends persist when controlling for Hα A/N, angular scale and inclination.Although the multi-component galaxies have a median Σ SFR, 3 kpc over 0.5 dex higher than those of the matched 1-component galaxies, this may not be representative of the true Σ SFR within the galaxy itself due to their small size.For this reason, we do not match in Σ SFR, 3 kpc .Rather, we propose that these high-Σ SFR 1-component systems may harbour the same underlying physical phenomena that manifest as complex emission line profiles in more massive systems (e.g., winds) but that it may not be possible to detect them at the spectral resolution of SAMI; these high-Σ SFR 1-component galaxies are discussed further in Section 4.1.1.
As is clear from Fig. 4, the multi-component galaxies exhibit significantly higher Σ SFR than the 1-component values regardless of which quantity is held constant, even when controlling for observational biases.We therefore conclude that Σ SFR is the most important physical parameter in determining the presence of complex emission line profiles in star-forming galaxies.However, Hα A/N, spectral resolution and inclination effects may play a secondary role; these are discussed further in Sections 4.1.1,7.2.2 and 7.2.3.

High-Σ SFR, 𝑅 e 1-component galaxies
As shown in columns 9-12 of Fig. 4, our sample contains a small population of 1-component galaxies with high Σ SFR .
Matching in Σ SFR,  e alone yields 18 compact, low-mass 1component galaxies with high Σ SFR,  e that have significantly lower Σ SFR, 3 kpc than the matched multi-component galaxies.This could indicate that Σ SFR, 3 kpc is fundamentally more important than Σ SFR,  e ; however, it is also possible that Σ SFR, 3 kpc is not a reliable estimate of the true Σ SFR within these galaxies due to their small sizes, as stated in Section 3.1.However, matching in both  * and Σ SFR,  e (5th column of Fig. C1) reveals a sample of 1-component galaxies with similar masses and sizes to the matched multicomponent galaxies.Notably, these galaxies have lower Σ SFR, 3 kpc by around 0.4 dex but have similar sizes to the matched multi-component galaxies, suggesting the offset in Σ SFR, 3 kpc is not an artefact of small galaxy sizes.
The lack of complex emission line profiles in the high-Σ SFR,  e 1component systems may be a spectral resolution effect: as discussed in Section 7.2.2, we may be unable to resolve multiple emission line components in low-mass systems at the spectral resolution of the SAMI instrument.Higher-resolution observations may therefore reveal complex emission line components in these unusual objects.

CORRELATION ANALYSIS
In Fig. 5, we plot   e , the fraction of spaxels within 1 e containing two or three components within an individual galaxy, as a function of global Σ SFR,  e for star-forming SAMI galaxies.Note that although the pixel size of SAMI is 0.5", the effective number of resolution elements across the SAMI FoV is approximately 60, meaning that values of   e < 1/60 may represent artefacts, which may explain the increase in scatter at low values of   e ; this threshold is indicated by the shaded grey region.There is a strong and statistically significant correlation between   e and Σ SFR,  e as indicated by the Spearman's rank correlation coefficient of 0.862 ( ≪ 0.05).Moreover, galaxies with   e = 0 have markedly lower global Σ SFR than those with   e > 0, as indicated by the pink shaded region.A similarly strong correlation is observed between  3 kpc and Σ SFR, 3 kpc (Fig. C2).This trend is consistent with the finding from our matched sample analysis that Σ SFR is the parameter that is most strongly correlated with the presence of complex emission line profiles; however, Figs. 5 and C2 Table 2. Spearman's rank-order correlation coefficients  and associated values computed for correlations between the fraction of multi-component spaxels ( e ) and the quantities given in the leftmost column for the 655 star-forming galaxies in our sample.The strongest correlations, highlighted in bold, are between  e and Σ SFR, e and Σ SFR, 3 kpc .To enable a fair comparison, for quantities indicated by the daggers, the correlation was computed for  3 kpc instead of  e .also reveal that the association between  and Σ SFR is continuous in nature, albeit with significant scatter.

Parameter
For completeness, correlation strengths between   e and parameters other than Σ SFR are shown in Table 2; amongst the parameters considered, Σ SFR,  e indeed shows the strongest correlation with   e (with a strength of 0.862), followed by Σ SFR, 3 kpc (0.858).However, there is also a strong correlation between   e and the mean Hα A/N measured within a 3 kpc aperture (0.729).
To determine whether A/N is responsible for the correlation between Σ SFR and   e , we compute partial correlation coefficients (PCCs) in order to examine the influence of confounding variables such as A/N and angular scale upon this correlation.These values are shown in Table 3, and were calculated using the partial_corr function from the python package pingouin (Vallat 2018).In all cases,  ≪ 0.05, indicating statistically a significant correlation between Σ SFR and   e when controlling for all confounding variables considered here.Of all variables, Hα A/N has the strongest impact on the correlation between   e and Σ SFR,  e , confirming that A/N does play a role in determining the fraction of spaxels within any given galaxy that exhibit multiple components.However, when controlling for this effect, the correlation between   e and Σ SFR,  e remains strong at approximately 0.69, indicating that indeed Σ SFR is the variable that is most strongly associated with the presence of complex emission line profiles, and that the higher A/N associated with multicomponent spaxels is most likely due to elevated Hα fluxes resulting from more concentrated star formation.This is consistent with our matched sample analysis, which showed that multi-component galaxies exhibit elevated Σ SFR compared to 1-component galaxies when matched in A/N (Section 4).We therefore conclude that the correlation shown in Fig. 5 is unlikely to be driven purely by A/N.

IS THE PRESENCE OF MULTIPLE EMISSION LINE COMPONENTS DRIVEN BY STAR FORMATION ON LOCAL OR GLOBAL SCALES?
As shown in Sections 4 and 5, galaxies containing complex emission line profiles are associated with higher Σ SFR,  e and Σ SFR, 3 kpc , i.e., global Σ SFR , even after controlling for both physical and observational effects.However, because the global Σ SFR is a measure of the average Σ SFR within individual spaxels, it is unclear whether the presence of complex emission line profiles-and therefore winds, outflows and/or thick ionised gas disks-are associated with star formation on local, or global (i.e., galaxy-wide) scales.We now leverage the spatially resolved nature of the SAMI data set to determine whether star formation on local or global scales is the underlying driver of the presence of multiple emission line components.
In Fig. 6 we show   , or the fraction of star-forming spaxels in the full SAMI data set containing  components, as a function of local Σ SFR (i.e., that measured within individual spaxels), representing the spatially-resolved analogue of Fig. 5. Before continuing, we note that although the spaxel size of SAMI is 0.5", the effective spatial resolution is approximately 2", corresponding to a median physical scale of approximately 1 kpc for the galaxies in our sample (Fig. 2). 1 and  2 increase smoothly as a function of Σ SFR such that 2-and 3-component spaxels begin to dominate at Σ SFR ≳ 10 −1.5 M ⊙ yr kpc −2 .Together, Figs. 5 and 6 indicate that both local and global effects play a role in determining whether or not complex emission line profiles are present.
To further investigate the relationship between   and the roles of local versus global star formation, in Fig. 7 we plot   as a function of local Σ SFR in our sample of star-forming galaxies, but in bins of host galaxy Σ SFR,  e .At a fixed local Σ SFR , spaxels residing in galaxies with higher global Σ SFR are much more likely to exhibit multiple emission line components.This effect is even stronger when Σ SFR, 3 kpc is used as a measure of the global Σ SFR (Fig. C3a).The likelihood of detecting multiple emission line components in any given spaxel is therefore affected not only by the local Σ SFR , but by star formation occurring on scales larger than the spatial resolution of SAMI.This illustrates that care must be taken when studying gas  6, where spaxels have been binned by the Σ SFR, e (i.e., global Σ SFR ) of their host galaxies.Thicker lines indicate spaxels residing in galaxies with higher global Σ SFR, e .Within each bin of local Σ SFR , the points have been slightly shifted in  for clarity.In the legend,  gal refers to the number of galaxies in each Σ SFR, Re bin.Vertical dashed lines indicate bin edges.The likelihood of a spaxel exhibiting complex emission line profiles therefore depends not only upon the local Σ SFR , but on the global Σ SFR of its host galaxy.
kinematics within individual spaxels when divorced from their host galaxy properties.
To investigate the influence of observational biases on this result, in Figs.C3b and C3c we show   vs. Σ SFR in spaxels binned by their host galaxy's inclination and angular scale.At a fixed Σ SFR , the relative enhancement in  2 and  3 in galaxies at different angular scales and inclinations tends to be smaller than that in galaxies with different global Σ SFR , indicating that these observational biases do not primarily drive the splitting between low-and high-Σ SFR galaxies shown in Fig. 7.We do note, however, that spaxels in more face-on galaxies are more likely to exhibit multiple emission line components than those in edge-on systems; this is most likely due to off-planar emission being present as a single emission line component when viewed in a near-edge-on system.The effects of inclination are discussed further in Section 7.2.3.
Under certain circumstances, beam smearing can produce artificial broad emission line components due to smearing of a steep velocity gradient by seeing effects (Marasco et al. 2019;Concas et al. 2022).SFR profiles tend to peak in the nuclei of galaxies, meaning that spaxels with high Σ SFR are more likely to be affected by beam smearing.To determine whether the increase in   with Σ SFR could be partially due to artificial broad line components caused by beam smearing, in Fig. C3d we plot   as a function of local Σ SFR binned by projected spaxel radius.At a fixed local Σ SFR , spaxels located within the seeing disc (approximately 2") are marginally more likely to exhibit multiple emission line components, but this effect is far smaller than the offsets seen between spaxels in galaxies with differ- ent global Σ SFR in Fig. 7.We therefore conclude that the correlation between global Σ SFR and the presence of complex emission line profiles has a physical origin, and that star formation taking place on global scales can affect the kinematics of gas on smaller scales as seen in IFS observations.

How important is clumpiness?
To further investigate the contributions from Σ SFR on local and global scales, we now consider the clumpiness of the star formation distribution within individual galaxies.As shown in Fig. 5, there is considerable vertical scatter in   e versus Σ SFR,  e .If star formation on local, rather than global, scales is the fundamental driver of multiple emission line components, then galaxies with similar global Σ SFR , but clumpier SFR distributions (i.e., containing spaxels with higher local Σ SFR ), should have a larger , whereas if global Σ SFR is more important, then all galaxies should have similar values of  regardless of local variations in Σ SFR .That is, we would expect clumpiness to contribute to the vertical scatter in the relation shown in Fig. 5.
To quantify the clumpiness of star formation we employ the Gini coefficient (Gini 1936), a parameter originally developed to quantify wealth inequality that has previously been applied to parametrise the clumpiness of galaxy morphologies by Lotz et al. (2004) and Bloom et al. (2017).Gini coefficients for each galaxy were computed from the SFR maps using Eqn. 1. Figure 8 shows Σ SFR maps and corresponding Gini coefficients for two SAMI galaxies; galaxy 9403800881 has a much smoother Σ SFR distribution and therefore a much lower Gini coefficient ( = 0.3085) than 47493 ( = 0.7254), which has centrally-concentrated star formation.
As shown in Fig. 2, multi-component galaxies have higher aver-age  than 1-component galaxies, implying clumpier and/or more centrally concentrated star formation, although there is substantial overlap between the two distributions.multi-component galaxies also have higher median  when matched in stellar mass, SFR, and other quantities as shown in Fig. 4.However, as shown in Table 3, the correlation between   e and Σ SFR,  e remains very strong at 0.7578 when controlling for , suggesting that at the spectral and spatial resolution of SAMI, global Σ SFR is more important than local variations in Σ SFR within galaxies in determining the presence of complex emission line profiles.

Physical interpretation
In Section 4, we showed that multi-component galaxies have systematically higher Σ SFR,  e than the 1-component galaxies.We also determined in Section 6 that the presence of multiple emission line components is driven by Σ SFR on both global and local scales.Observational biases do not explain these results, indicating an underlying physical mechanism.
Complex emission line profiles in star-forming galaxies are most often interpreted as winds (e.g., McKeith et al. 1995;Westmoquette et al. 2009;Ho et al. 2014) or thick ionised gas disks (also referred to as extraplanar gas, or DIG; e.g., den Brok et al. 2020;Belfiore et al. 2022); both of these phenomena can be interpreted as manifestations of galactic fountains (Fraternali & Binney 2006;Barnabè et al. 2006;Marinacci et al. 2010).Although some SAMI galaxies exhibit complex gas kinematics due to processes such as mergers or ram-pressure stripping (e.g., Quattropani et al., in prep.), visual inspection of SDSS imaging indicates that only approximately 10 per cent of our multicomponent galaxies are undergoing a major merger.We therefore assume that the presence of complex emission line profiles in the star-forming galaxies in our sample indicates the presence of galactic fountains in the form of winds or thick disks.Detailed kinematic analysis of the multi-component galaxies, including consideration of the differences between galaxies harbouring winds and those with thick disks, is deferred to a future work.
Our finding that Σ SFR is the parameter most strongly associated with complex emission line profiles and winds is consistent with previous findings using SAMI data.Ho et al. (2016b) found that edge-on systems with winds have systematically higher Σ SFR than those without.Tescari et al. (2018) additionally found that extraplanar gas in simulated galaxies with higher Σ SFR tend to exhibit high- tails, which the authors interpreted as increased outflow activity due to star formation.More recently, in a sample of star-forming SAMI galaxies, Varidel et al. (2020) found the vertical gas velocity dispersion correlates more strongly with Σ SFR than with SFR.
Recent studies using MaNGA (Bundy et al. 2015) have also found strong links between Σ SFR and winds.Avery et al. (2021) found that galaxies with star formation-driven outflows (as identified by the presence of broad Hα components in aperture spectra) tend to have overall Σ SFR ≳ 10 −2 M ⊙ yr −1 kpc −2 .Earlier, Roberts-Borsani et al. (2020) found that neutral outflows (as traced by interstellar Na D absorption) are only detected in galaxies with Σ SFR ≳ 10 −2 M ⊙ yr −1 kpc −2 .These thresholds are remarkably similar to that we find between the 1-and multi-component galaxies (Fig. 2).
Similar trends have been found between the presence of thick ionised gas disks and Σ SFR .Rossa & Dettmar (2003) detected extraplanar gas only in galaxies above a certain Σ SFR threshold, and using a small sample of galaxies, Rueff et al. (2013) found that DIG becomes brighter and more filamentary as Σ SFR increases.More recently, Belfiore et al. (2022) found that the velocity dispersions of DIG-dominated spaxels (identified by enhanced forbidden line emission) only become significantly larger than the velocity dispersions in H ii region-dominated spaxels in galaxies with high global SFRs.This suggests that at sufficiently low SFRs, it may not be possible to resolve DIG from H ii region emission using our spectral decomposition technique.Together with the correlation between stellar mass and SFR (Fig. 3), this may explain why there are few multi-component galaxies with  * ≲ 10 9 M ⊙ .These and other spectral resolution considerations are discussed in Section 7.2.2.
It is therefore possible that these thick gas disks may be present in most of the star-forming galaxies in our sample, but that they are only detectable with SAMI above a certain Σ SFR and/or stellar mass threshold.Unresolved thick gas disks could explain the population of high-Σ SFR 1-component galaxies as discussed in Section 4.1.1:as shown in Fig. 4, these systems have low stellar masses and low SFRs, but are very compact and so have high Σ SFR,  e .Confirming this scenario would require higher spectral resolution observations.
As shown in Fig. 7, spaxels residing in galaxies with higher Σ SFR,  e are more likely to exhibit multiple emission line components regardless of their local Σ SFR .An analogous effect was found by Law et al. (2022), who found global SFR to correlate more strongly with the Hα velocity dispersion than the local Σ SFR .This trend can be explained by projection effects.A hot wind originating from a high-Σ SFR region of a galaxy will accelerate cloud fragments from the disk outwards in a spherical fashion (Cooper et al. 2008(Cooper et al. , 2009)), forming dramatic biconical structures such as that observed in M82 (Lynds & Sandage 1963;Bland & Tully 1988;Shopbell & Bland-Hawthorn 1998).Due to orientation effects, Hα-emitting filaments in the wind may therefore intersect lines of sight towards lower-Σ SFR regions of the galaxy that are not involved in launching the wind; this would also apply to gas returning to the disk via a galactic fountain, in the process forming a thick ionised gas disk.Evidence for these LoS effects has been observed in the Large Magellanic Cloud, in which highly ionised winds, traced by broad [O vi] absorption, can be seen along lines of sight towards both locations of active star-formation and quiescent regions (Howk et al. 2002;Barger et al. 2016).Our results suggest that spectral decomposition may be a viable way to detect this phenomenon in unresolved systems.

Observational biases
Here, we discuss several sources of observational bias which may be important to consider when carrying out any study relying on multi-component emission line fits.

Reliability of component identification
As detailed in Hampton et al. (2017a), LZComp, the ANN used to classify spaxels as containing 1, 2 or 3 emission line components, is trained using human observers; as such, its reliability as a function of S/N is unclear.Due to our conservative S/N and data quality cuts on the 2nd and 3rd kinematic components within each spaxel (as detailed in Section 2.1), we assume that our sample of 2-and 3component spaxels is unlikely to contain misclassified 1-component spaxels.However, our sample of 1-component spaxels may contain misclassified spaxels that in fact contain 2 (or more) components; here, we perform two tests to determine the degree of contamination within our 1-component spaxel sample.3-component spaxels are not discussed due to their rarity (representing < 1 per cent of all spaxels; see Section 3).
First, we investigate the impact of A/N on the classification process, where A/N is defined as the peak amplitude of the Hα line (measured directly from the spectrum, and therefore not corrected for stellar absorption) relative to the mean continuum level within the rest-frame wavelength range 6500 Å-6540 Å divided by the RMS noise within the same range.We assume that LZComp begins to misclassify multi-component spaxels as 1-component below some A/N threshold, which we define as the 5 per cent confidence interval of the A/N distribution of the 2-component spaxels that pass our S/N and data quality cuts.In Fig. 9 we show distributions in A/N in all 2-component spaxels (red), all 1-component spaxels (black) and SF 1-component spaxels (blue).The vertical dashed line shows the 5% confidence interval for the 2-component spaxels of approximately 19.Whilst over 40% of all 1-component spaxels have A/N below this threshold, fewer than 2% of SF spaxels fail this criterion.Under the assumption that A/N is an important factor influencing the ANN, this implies that the SF 1-component spaxels, which are the focus of this work, are unlikely to be contaminated by a significant amount of low-S/N 2-component spaxels.
We now check the reliability of the ANN classification by inspecting the velocity dispersions of components measured within 1-and 2-component spaxels.When 2-component spaxels are fitted with a single component, the width of the best-fit Gaussian tends to be broader by an average of around 10 km s −1 than that of the narrow component in the 2-component fit, as shown in Fig. 10.We therefore compare the measured velocity dispersions in 1-and 2component spaxels to estimate the contamination of misclassified multi-component spaxels in our sample of 1-component spaxels.
First, we consider all spaxels in the SAMI sample.In the top panel of Fig. 11a, we show  gas distributions for 1-component spaxels (shaded blue),  narrow and  broad of the 2-component spaxels (open purple and open pink respectively), and of  gas from the 1component fits to the 2-component spaxels (shaded orange).The corresponding means, standard deviations, medians and interquartile ranges (IQRs) are reported in Table 4.If there were a significant population of 2-component spaxels contaminating the sample of 1component spaxels, then the blue histogram would be skewed towards values similar to the orange histogram.This is indeed the case: the IQR of the 1-component spaxels is skewed to larger values of  gas compared to the narrow component in 2-component spaxels.However, as shown in the bottom panel of Fig. 11a, among the SF spaxels, which are the focus of this work, the distribution in  gas of the 1-component spaxels is similar to that of  narrow in the 2-component spaxels, whereas the distribution in  gas of the 1-component fits to the 2-component spaxels is markedly offset by approximately 10 km s −1 .The purple histogram is in fact skewed towards higher values of  gas than the blue histogram, and the two distributions are statistically significantly different according to the KS and AD tests with -values ≪ 0.05 for both tests.This would be consistent with there being only minimal contamination by 2-component spaxels amongst the SF 1component spaxels.We also note that among both the 1-component SF spaxels and the narrow component of the 2-component SF spaxels, the average velocity dispersion  gas ≈ 30 ± 10 km s −1 , which is similar to that of the "dynamically cold" ionised gas component associated with SF regions identified by Law et al. (2021); meanwhile, the typical velocity dispersions of the broad component in 2-component SF spaxels is similar to that of their "dynamically hot" component.
We now consider how contamination of misclassified 2component spaxels may affect our galaxy classification (Section 3).In Fig. 11b, we compare the  gas of 1-component spaxels in 1component galaxies (open dashed blue histogram) to  narrow in the 2-component spaxels in multi-component galaxies (open purple).In comparison with Fig. 11a, there is a larger difference between the two distributions, such that the purple histogram is even more skewed towards higher values.This is consistent with our hypothesis that there is only minimal contamination of misclassified 2-component spaxels within the 1-comp.galaxies.Meanwhile, the 1-component spaxels in multi-component galaxies (shaded blue histogram) are much broader than the narrow component in the 2-component spaxels, and have a distribution skewed towards that of the 1-component fits to the 2component spaxels, suggesting that some 1-component spaxels in the 2-component galaxies may represent misclassified 2-component spaxels.
From these two tests, we conclude that our analysis is unlikely to be affected by misclassified multi-component spaxels.Although our multi-component galaxies may contain significant numbers of broad 1-component spaxels that may be misclassified multi-component spaxels, this effect is probably minimal in the 1-component galaxies, indicating that our galaxy classification scheme is robust against contamination of misclassified multi-component spaxels.The inability of SAMI to detect multiple emission line components closely spaced in both velocity and velocity dispersion is demonstrated in Fig. 12, where we plot all 2-component spaxels in the Δ-Δ plane.Again, we do not consider 3-component spaxels here due to their rarity in comparison with 2-component spaxels.There is a "hole" roughly defined by Δ ≲  inst and |Δ| ≲  inst , at which point multiple emission line components can no longer be distinguished at the spectral resolution of SAMI.If Δ ≲  inst but |Δ| ≫  inst , i.e. the two components have similar widths, but are sufficiently separated in LoS velocity, then the two components can be distinguished.Conversely, if |Δ| <  inst but Δ ≫  inst , i.e. the two components have similar LoS velocities but have substantially different widths, then the two components can be distinguished as well.The spaxels lying closest to the "forbidden" region of the parameter space tend to reside in less massive galaxies; we therefore conclude that with SAMI we may be unable to reliably detect DIG/thick ionised gas disks using this method in low-mass systems, as discussed in Section 7.1.
In Fig. 12 we also indicate the spectral resolution of MaNGA (approximately 70 km s −1 ; e.g., Law et al. 2022) by the dotted lines.As shown by the black contours, which trace the distribution of 2component spaxels in the Δ-Δ plane, approximately 53 per cent of 2-component spaxels that can be detected with SAMI have Δ <  inst, MaNGA , indicating that typical broad emission line components in local galaxies cannot be resolved with MaNGA using the standard spectral decomposition technique employed here.This demonstrates the importance of high spectral resolution when conducting detailed studies of gas kinematics.

Inclination effects
As discussed in Section 3 and as shown in Fig. 2b, multi-component galaxies are under-represented at near-face-on and near-edge-on inclinations.Additionally, at a fixed local Σ SFR , spaxels residing in galaxies at higher inclinations are less likely to exhibit multiple components (Fig. C3b).There are several possible explanations for this.At higher inclinations, extraplanar gas or winds above and below the disk plane may not share a LoS with gas in the thin disk, and would therefore be visible as a single, but broad, component.In a subset of edge-on SAMI galaxies, Ho et al. (2016b) identified wind-dominated and DIG-dominated systems by assuming that winds should exhibit higher velocity dispersions and greater asymmetry in the velocity field beyond the disk plane compared to DIG.Of their 15 winddominated systems, two are present in our 1-component sample, and two of our multi-component galaxies are found.Meanwhile, their sample of DIG-dominated edge-on systems contains 7 of our 1component galaxies and no multi-component galaxies.This suggests that the presence of multiple emission line components may be an unreliable method for detecting winds and DIG in edge-on systems.However, their sample of edge-on galaxies was chosen to have axis ratios / < 0.26, corresponding to only 23 galaxies in our parent sample of 655 galaxies, indicating that our spectral decomposition technique is unlikely to be missing a large number of wind-and DIG-dominated galaxies in our sample due to edge-on inclination effects.Of the 18 high-Σ SFR 1-component galaxies discussed in Section 4.1.1,only two have / < 0.26, indicating that the lack of observed complex line profiles in these objects is unlikely to result from inclination effects.
The lack of high-inclination multi-component galaxies may also be due to spectral resolution limitations.In Fig. 13 we plot the velocity dispersions of the narrow and broad components ( narrow and  broad respectively), plus Δ, as a function of inclination. narrow is weakly correlated with inclination, most likely due to the artificial broadening of emission lines in more highly-inclined systems due to rotation, whereas  broad is anticorrelated.The observed trends  may arise if the vertical component of the velocity dispersion   is larger than the azimuthal or radial components    and   .Such anisotropy may be expected in the presence of galactic winds (Marinacci et al. 2010) where material is preferentially launched out of the disk plane.However, this explanation contradicts the findings of Law et al. (2022), who found that   <    ,   in a sample of local star-forming galaxies, although their analysis is based upon the Hα velocity dispersion measured from single Gaussian fits to lower-resolution MaNGA data.
Rather, the anticorrelation between  broad and inclination most likely originates from observational effects.Galactic fountains may lead to the formation of a thick ionised gas disk which has a negative vertical velocity gradient resulting in a slower circular velocity than the thin disk (Swaters et al. 1997;Levy et al. 2018Levy et al. , 2019;;Marasco et al. 2019).In this configuration, the LoS velocity separation between the thin and thick disks increases as a function of inclination, whilst in face-on systems Δ ∼ 0 km s −1 .Referring to Fig. 12, SAMI is unable to resolve multiple emission line components when Δ ≲  inst and Δ ≲  inst .Therefore, in face-on systems, we may only spectrally resolve broad emission line components from thick disks if Δ >  inst , whereas in highly inclined systems, spaxels with Δ <  inst may be resolved as long as Δ >  inst .As a re- sult, at low inclinations, we can only detect thick disks in which Δ >  inst , whereas at higher inclinations we may detect thick disks with a wider range of velocity dispersions.Our inability to spectrally resolve face-on thick disks may therefore explain the lack of spaxels with Δ <  inst at inclinations ≲ 20 • .
In wind-dominated systems, we can expect Δ ≫ 0 km s −1 in lowinclination systems, meaning that in principle it would be possible to resolve a broad component with Δ <  inst .However, winds typically have Δ ≫  inst due to large turbulent motions and outflow velocities; this is therefore consistent with the lack of spaxels with Δ <  inst at low inclinations.
Finally, it is also possible that multi-component galaxies are intrinsically "puffier" than their 1-component counterparts, biasing inclination measurements towards lower values due to our assumption of a fixed disk thickness of  0 = 0.2.

CONCLUSIONS
We applied a spectral decomposition technique to distinguish line emission from the star-forming thin disk and winds and/or thick disks in star-forming galaxies from the SAMI Galaxy Survey.Our conclusions are as follows: (i) The presence of complex emission line profiles in star-forming galaxies is strongly correlated with the global Σ SFR of the host galaxy, even when controlling for sample biases in stellar mass and SFR, and observational effects such as inclination, angular scale and A/N.This correlation is consistent with previous studies that have found a strong connection between Σ SFR and both thick ionised gas disks and winds.In fact, virtually all galaxies in our sample that contain a significant fraction of spaxels with complex emission line profiles have Σ SFR ≳ 10 −2 M ⊙ yr −1 kpc −2 , which is remarkably similar to the value found by Roberts-Borsani et al. (2020).
(ii) Whilst global Σ SFR , measured via Σ SFR,  e , is the quantity that is most strongly correlated with the fraction   e of multi-component spaxels within individual galaxies within 1 e , the fraction   of individual spaxels containing multiple components is also strongly dependent on the local Σ SFR measured within individual spaxels.We also find that, at a fixed local Σ SFR , spaxels in galaxies with higher global Σ SFR are more likely to exhibit multiple components.This illustrates the importance of considering global galaxy properties when conducting studies of individual spaxels in IFS surveys.
(iii) There is a strong residual correlation between Σ SFR,  e and   e when controlling for Gini coefficient , suggesting that global Σ SFR is more important than clumpiness in dictating the presence of widespread complex emission line profiles within a galaxy.
(iv) The strong correlation between Σ SFR and the presence of complex emission line profiles is consistent with the findings of previous studies that have employed different techniques to identify winds and thick ionised gas disks.This indicates that the spectral decomposition technique is an effective means of identifying these phenomena in local galaxies.
(v) SAMI is currently the only IFS survey with sufficient spectral resolution to resolve multiple emission line components in local galaxies using the spectral decomposition technique employed here.However, SAMI is likely unable to detect broad emission line components in low-mass galaxies, where the LoS velocity and velocity dispersion offsets between the narrow and broad components are smaller than the instrumental resolution.Hector (Bryant et al. 2020), the successor to SAMI, will have a comparable spectral resolution, enabling similar studies to be carried out on a much larger sample of over 10,000 galaxies.
695671 "QUENCH" and support by the Science and Technology Facilities Council (STFC).L. C. acknowledges support from the Australian Research Council Discovery Project and Future Fellowship funding schemes (DP210100337, FT180100066).

Figure 1 .
Figure 1.Example 1-component (top row) and multi-component (bottom two rows) galaxies.The leftmost column shows the SDSS image, where the white circle represents the SAMI FoV.The middle five columns show maps of the number of components, spectral classification, and LoS velocities of the ionised gas in each spaxel, where the white contours represent the logarithmically-scaled stellar continuum, and the black bar shows the angular scale.The minimum and maximum velocity scaling values for each galaxy are shown in the upper-right corner.The rightmost column shows the rest-frame Hα and [N ii]λλ6548, 83 emission line profiles in grey, overlaid with the LZIFU fits, extracted from an individual spaxel in the nucleus of each galaxy.The blue line represents the stellar continuum fit; the purple, pink and orange lines represent the first (narrow), second (broad) and third (extra-broad) Gaussian components respectively, and the black line represents the combined fit.

Figure 2 .
Figure 2. Probability distribution functions (PDFs) in various physical galaxy properties (a) and observational quantities (b) shown for our different sub-samples.In each panel we show the distribution in the full SAMI sample of 2997 galaxies (thin black line), the 1-component galaxy sample (shaded blue histogram), and multi-component galaxy sample (thick blue line).In (b), the top axis ticks of the bottom right-most panel show the axis ratios / corresponding to the measured inclinations assuming an intrinsic disk thickness  0 = 0.2(Poetrodjojo et al. 2021).The text in the upper left corner shows the -values of the KS and AD tests applied to the 1-and multi-component samples.In all quantities except for  e , the very low -values indicate that the samples are highly unlikely to be drawn from the same parent sample, suggesting the two samples have fundamentally different distributions in all quantities shown here.

Figure 3 .
Figure 3. Star-forming main sequence (top) and Σ SFR main sequence (bottom) for the full SAMI sample (grey points), 1-component galaxies (blue filled circles) and multi-component galaxies (blue open circles).Distributions in  * , SFR e and Σ SFR, e for each subsample are shown in the top and righthand panels.

Figure 4 .Figure 5 .
Figure 4. Violin plots showing KDEs representing the distributions in various properties for the 1-component (light blue, left) and multi-component (dark blue, right) matched samples.The full distributions are also shown in grey for reference.Each row shows the distributions in the matched samples in various quantities, and each column shows the distributions matched in the quantity indicated by thick grey outlines around violin plots.The figure is divided into four sub-groups representing samples matched in the quantity shown at the top of the figure:  * SFR e , Σ SFR, e and Gini coefficient .Within each sub-group, the leftmost column of violin plots represents samples matched only in that quantity, and the other three columns represent samples matched in that quantity simultaneously with (from left to right) mean Hα A/N within 3 kpc, angular scale, and inclination.In each violin plot, the circular points and error bars show the mean and interquartile ranges (IQRs) of the 1-and multi-component matched samples, and the number of galaxies in each matched sample is shown in the upper left.The text at the bottom of each plot represents the result of KS and AD 2-sample tests; text in red represents a -value less than 0.05, indicating a statistically significant likelihood that the distributions of the matched sample in that quantity are not drawn from the same parent distribution.

3 NFigure 6 .
Figure 6.Fraction   of star-forming spaxels in the SAMI Galaxy Survey containing 1 (  1 , blue diamonds), 2 (  2 , green squares) and 3 (  3 , purple triangles) emission line components as a function of spaxel-scale (i.e., local) Σ SFR .1 Poisson errors in   are indicated by the vertical black error bars.The log-scaled histogram in the top panel shows the distribution of 1, 2 and 3-component spaxels in Σ SFR .Vertical dashed lines indicate bin edges.

Figure 7 .
Figure 7. Same as Fig.6, where spaxels have been binned by the Σ SFR, e (i.e., global Σ SFR ) of their host galaxies.Thicker lines indicate spaxels residing in galaxies with higher global Σ SFR, e .Within each bin of local Σ SFR , the points have been slightly shifted in  for clarity.In the legend,  gal refers to the number of galaxies in each Σ SFR, Re bin.Vertical dashed lines indicate bin edges.The likelihood of a spaxel exhibiting complex emission line profiles therefore depends not only upon the local Σ SFR , but on the global Σ SFR of its host galaxy.

Figure 8 .
Figure 8. Maps, PDFs and cumulative distribution functions (CDFs) in log 10 Σ SFR for (a) galaxy 9403800881, which has a low Gini coefficient of 0.3085, and (b) 47493, which has a high Gini coefficient of 0.7254.

Figure 10 .
Figure 10.Distribution in the difference between the velocity dispersion of the 1-component fit and the narrow component in the 2-component fit for 2-component spaxels.The median and mean in the distribution are indicated by the white circle and diamond respectively, where the horizontal error bar represents the interquartile range.

Figure 11 .
Figure 11.Velocity dispersion distributions within different subsets of spaxels.Panel (a) shows normalised velocity dispersion distributions for 1component spaxels (pale blue outlined histogram), the narrow component in 2-component spaxels (purple outlined histogram) and that of 1-component fits to 2-component spaxels (shaded orange histogram) for all spaxels (top panel) and for SF spaxels only (bottom panel).Panel (b) shows velocity dispersion distributions for subsets of SF spaxels within 1-and multi-component galaxies.1-component spaxels in 1-and multi-component galaxies are represented by the dashed blue and shaded pale blue histograms respectively.The narrow and broad components in 2-component spaxels in multi-component galaxies are shown in the purple and pink outlined histograms respectively, and the shaded orange histogram represents the 1-component fit to the 2component spaxels.Corresponding medians and means are indicated by the circles and diamonds respectively, and IQRs are shown by the error bars; values are given in Table 4.The SAMI instrumental resolution is indicated by the black dashed line.

Figure 12 .
Figure 12.Δ vs. Δ for individual spaxels with two components, coloured by the stellar mass of their host galaxy.In the upper panel, the data is represented as a 2D histogram, in which the colour of each cell represents the median  * of all spaxels falling within that cell, and the black contours show the number distribution of spaxels on a log scale.The lower panel shows an inset view of the left-hand plot (indicated by the blue rectangle), where spaxels are shown individually as circles.The dashed lines represent the spectral resolution of SAMI (29.6 km s −1 ) and the dotted lines represent the MaNGA spectral resolution (approximately 70 km s −1 ), indicating that MaNGA would be unable to spectrally resolve approximately 53 per cent of the multi-component spaxels identified in this work.

3 NFigure 13 .
Figure 13.Distribution of all 2-component spaxels in  narrow ,  broad and Δ as a function of inclination.The white squares show median values and the error bars represent the standard deviation in different inclination bins.The horizontal dashed lines represent the SAMI instrumental resolution of 29.6 km s −1 .The Spearman's rank-order correlation coefficient and accompanying -value is shown in the upper right-hand corner.

Figure C1 .
Figure C1.Results from the matched sample analysis in Section 4. Each cell compares the distributions in the row quantity between the 1-and multi-component galaxies when matched in the column quantity.The cell colour represents the -value from the two-sample KS applied to the matched samples measured in the row quantity; in dark-coloured cells the distributions are similar, whereas pale colours indicate that the distributions are highly unlikely to be drawn from the same parent sample, i.e., that the 1-and multi-component matched samples are significantly different.The number in each cell represents the difference in the median values of the row quantity between the 1-and multi-component matched samples.Cells in which the -value is below the significance threshold of 0.05 are indicated by coloured text, where red values indicate a lower median value and blue values a higher median value in the multi-component matched sample than the 1-component matched sample.For example, when matched in SFR (2nd column), the stellar mass distributions of the 1-and multi-component galaxies (top row) are significantly different, as indicated by the bold text and pale cell colour, and the matched multi-component galaxies have a median stellar mass 0.35 dex lower than that of the 1-component galaxies.Meanwhile, the matched samples have similar distributions in log 10 (  * / e ) (8th row) as indicated by the dark cell colour.

Table 3 .
Partial Spearman's rank correlation coefficients between log 10 Σ SFR, e and  e when controlling for various parameters.Corresponding -values are not shown as they are ≪ 0.05 in all cases.

Table 4 .
Means, standard deviations, and percentiles for the velocity dispersion distributions shown in Fig. 11.3-component spaxels are not included due to their rarity compared to 2-component spaxels.All values are in units of km s −1 .In general, individual emission line components cannot be resolved by a spectrograph with resolution  inst if the difference between the LoS velocities of the broad and narrow components  broad −  narrow := Δ ≲  inst and the difference in the velocity dispersions  broad −  narrow := Δ ≲  inst .