Integral field spectroscopy of luminous infrared main-sequence galaxies at cosmic noon


 We present the results of an integral field spectroscopy survey of a sample of dusty (ultra) luminous infrared galaxies (U/LIRGs) at 2 < z < 2.5 using KMOS on the Very Large Telescope. The sample has been drawn from Herschel deep field surveys and benefits from ancillary multiwavelength data. Our goal is to investigate the physical characteristics, kinematics, and the drivers of star formation in the galaxies whose contribution dominates the peak of the cosmic star formation density. Two-thirds of the sample are main-sequence galaxies in contrast to the starburst nature of local U/LIRGs. Our kinematic study, unique in its focus on z ∼ 2 dusty star-forming galaxies, uses the H α emission line to find that ∼40 per cent appear to be isolated discs based on the ratio of rotational velocity to the velocity dispersion, suggesting steady-state mechanisms are sufficient to power the large star formation rates (SFRs). The ratio of obscured to unobscured star formation indicates the sample of galaxies experiences less dust obscuration compared to intermediate and local counterparts, while also hosting cooler dust than local U/LIRGs. In addition to H α we detect [N ii] 6583 Å in our targets and show the gas-phase metallicities do not exhibit the metal deficiency of local U/LIRGs. These results indicate that, despite their extreme IR luminosity, the underlying mechanisms driving the massive SFRs found at cosmic noon are due to scaled up disc galaxies as opposed to mergers.

). It has also been found that the cosmic SFRD gradually rises from z = 8 to peak around z ≈ 2, known as cosmic noon, and then declines by an order of magnitude to the current epoch (e.g. Madau & Dickinson 2014). To understand the underlying mechanisms driving these large SFRs, we need to understand how U/LIRGs at this epoch form their stars.
In the past couple of decades multiwavelength studies have provided much insight into star formation and its interplay with gas, dust, and existing stellar mass. Observations have found a tight correlation between the SFR and stellar mass (M ) of a galaxy, known as the main sequence (MS) of star-forming galaxies (e.g. Daddi et al. 2007;Noeske et al. 2007). From this relation the specific SFR (sSFR = SFR/M ) is defined, which can be viewed as the fractional growth of the stellar mass within a galaxy. The MS and sSFR can be used to categorize two populations of star-forming galaxies: steadystate secularly evolving galaxies fuelled from continuous in-falling gas from the intergalactic medium (e.g. Dekel, Sari & Ceverino 2009) and short-lived starbursts, which are periods of heightened star formation driven by mergers (e.g. Tacconi et al. 2008;Daddi et al. 2010b;Genzel et al. 2010). Secular star-forming galaxies lie within a scatter of 0.3 dex of the MS, whereas starbursts fall in the region above, often defined as galaxies whose SFR is a factor of 4 or more above the MS correlation (e.g. Whitaker et al. 2012). As would be expected from the evolution of the cosmic SFRD the normalization of the correlation increases with redshift, i.e. for a given stellar mass the SFR of an MS galaxy at z = 2 is ∼20 times greater than an MS galaxy at z = 0 (e.g. Speagle et al. 2014), so secular evolving galaxies at high-z can have SFRs greatly exceeding local starbursts. A similar scaling relation exists between the gas within a galaxy and the SFR, known as the Kennicutt-Schmidtt law (Schmidt 1959;Kennicutt 1998). This correlation gives the star formation efficiency (SFE) of galaxies, i.e. how quick a galaxy can convert the molecular gas reservoirs into stars, and is one of the main mechanisms that determines a galaxies distance from the MS (e.g. Tacconi, Genzel & Sternberg 2020). As in the SFR-stellar mass plane, the Kennicutt-Schmidtt law is bimodal with starbursts appearing to have a higher SFE per stellar mass than MS galaxies (e.g. Daddi et al. 2010b).
Locally (z < 0.2) ULIRGs appear to be undergoing a transient starburst phase, fuelled by interactions and mergers, with a more diverse range of morphological types, such as isolated discs and minor mergers, appearing as the luminosity decreases down to the lowest luminosity LIRGs, which are dominated by secular processes (e.g. Bellocchi, Arribas & Colina 2016;Larson et al. 2016). Their IR spectral energy distributions (SED) are dominated by thermal emission from dust and have dust temperatures in the range 30-55 K (Clements et al. 2018 and references therein). They are very efficient at converting their molecular gas into stars (e.g. Gao & Solomon 2004) with depletion times (τ dep ≡ 1/SFE) of the order of 150 Myr (e.g. Elbaz et al. 2018). Although matched in luminosity, observations have shown that high-redshift (z > 1) U/LIRGs are very different from their local counterparts. Many authors have noted differences in their SEDs (e.g. Farrah et al. 2008;Muzzin et al. 2010), physical properties, and morphologies (e.g. Kartaltepe et al. 2012). High-resolution studies have revealed that the star-forming regions of high-z U/LIRGs are relatively extended with effective radii of order 3-16 kpc (e.g. Iono et al. 2009;Tacconi et al. 2013), while the extent of star formation in local U/LIRGs are much more compact with sizes of 0.3-2 kpc (e.g. . Dynamically, high-redshift U/LIRGs appear to be a mixture of mergers and disc galaxies, with spatially resolved observations revealing large rotating discs at z ∼ 2 with SFRs in the hundreds of M yr −1 without any sign of ongoing major merging (e.g. Förster Schreiber et al. 2009;Wisnioski et al. 2015). There also appears to be difference in the strength of far-infrared (FIR) fine-structure cooling lines arising from the interstellar medium (ISM). Local U/LIRGs are 'deficient' in the luminosity of these FIR metal lines, such as [C II] 158 μm and [N II] 122 and 205 μm, when compared to regular star-forming galaxies and high-z U/LIRGs (e.g. Graciá-Carpio et al. 2011;Rigopoulou et al. 2014;Díaz-Santos et al. 2017).
Intermediate-redshift U/LIRGs (0.2 < z < 0.7) straddle the region of high-z and local galaxies. Pereira-Santaella et al. (2019) found that intermediate-z U/LIRGs seem to be at an earlier stage of interaction and have a lower dust temperature than local U/LIRGs, but have a similar level of dust obscuration. Rigopoulou et al. (2014) and Magdis et al. (2014) showed that the SFE, dust, and [C II] emission lines in the ISM all exhibit characteristics that more closely resemble star-forming MS galaxies than local U/LIRGs. This hints at a gradual evolution in the properties U/LIRGs from high-z to low-z, where by z ∼ 1 the equivalent of local disc galaxies are LIRGs and by z ∼ 2 the equivalent are ULIRGs.
The latest generation near-IR spectrographs, such as the K-band Multi Object Spectrograph (KMOS) and Multi-Object Spectrometer For Infra-Red Exploration (MOSFIRE), have enabled large-scale kinematic studies of galaxies at high z. The KMOS 3D survey (Wisnioski et al. 2015), KMOS Deep Survey (Turner et al. 2017), MOSFIRE Deep Evolution Field (MOSDEF Kriek et al. 2015), KMOS Redshift One Spectroscopic Survey (KROSS Stott et al. 2016), and Survey in the near-Infrared of Galaxies with Multiple position Angles (SIGMA Simons et al. 2016) provide hundreds of galaxies up to z ∼ 4 and spanning 10 9 M < M < 10 11.5 M . These show that up to 80 per cent of the high-mass end appear to be rotation dominated and have baryon to dark matter ratios greater than one within their effective radii, with this baryonic-dark matter ratio increasing with redshift (e.g. Wuyts et al. 2016;Genzel et al. 2017;Price et al. 2020). The discs appear to be thicker (e.g. Elmegreen & Elmegreen 2006) and have a larger velocity dispersion suggestive of a more turbulent ISM (e.g.Übler et al. 2019). As of yet, no kinematic studies have focused solely on the massive high-z dusty star-forming galaxies so it is unclear how z ∼ 2 luminous IR galaxies fit into this picture. It remains to be determined whether the proportion of luminous IR galaxies that are rotation dominated matches that of the general star-forming population or whether large dusty galaxies deviate from the general population.
Observations show that the SFE and gas fraction increase with both distance above the MS and lookback time, although broadly remains constant along the MS in a given epoch and is independent of M (e.g. Magdis et al. 2012;Genzel et al. 2015;Scoville et al. 2017;Tacconi et al. 2018;Piotrowska et al. 2019). It also appears that MS galaxies are responsible for up to 90 per cent of the cosmic SFRD (e.g. Rodighiero et al. 2011;Sargent et al. 2012) and the density of large dust-obscured galaxies increasing with redshift (e.g. Floc'h et al. 2005). This is suggestive that a substantial fraction of high-z luminous IR galaxies should be scaled up versions of local star-forming disc galaxies with their increased SFRs due to the comparatively larger reservoirs of molecular gas at high redshift (e.g. Daddi et al. 2010a;Tacconi et al. 2013;Combes 2018).
Simulations show that since z ∼ 6 merger-driven star formation accounts for only 25 per cent of today's stellar mass (Martin et al. 2017) and may be responsible for as little as 1 per cent of the SFRD at z = 2 (Rodríguez Montero et al. 2019). As U/LIRGs account for as much as 50 per cent of the SFRD at cosmic noon, they act as useful test cases for these simulations.
To fully understand the evolution of U/LIRGs and how they fit into the cosmic star formation history (SFH) it is necessary to study the underlying mechanisms driving the high SFRs in the U/LIRG population at cosmic noon. We need to investigate the properties of IR luminous galaxies and compare these properties to the general star-forming population at this epoch in order to understand U/LIRGs contribution to the SFRD and to track the evolution of U/LIRGs in the range 0 < z < 2.
In this paper, we present integral field spectroscopy (IFS) with KMOS on the Very Large Telescope (VLT) of a sample of dusty starforming galaxies at cosmic noon. In Section 2, we define our sample selection and how we undertook our observations. In Section 3, we show how we analysed the data to find the spectra, SFRs, and kinematics. Section 4 examines the mechanisms driving the huge SFRs of our sample and discusses their evolution across cosmic time. In Section 5, we sum up our results. When required, values of H 0 = 70 km s −1 Mpc −1 , m = 0.3, and = 0.7 were used in this paper. When required the initial mass function (IMF) was assumed to be a Chabrier (2003) form.

The sample
The galaxies studied here were drawn from Herschel observations of the Great Observatories Origins Deep Survey South field (GOODS-S, Elbaz et al. 2011). GOODS-S benefits from the availability of excellent multiwavelength ancillary data (e.g. ZFOURGE, Straatman et al. 2016) including multiple photometric bands, stellar masses etc. The present sample (hereafter our KMOS sample) comprises 18 targets which were selected according to the following criteria: (i) Detection in at least one of the Herschel bands to ensure the U/LIRG-like infrared luminosity of the galaxies and therefore high SFR.
(ii) Spectroscopic redshift or very robust photometric redshift based on at least 10 data points from broad-band photometry.
(iii) Galaxies located in the 2 < z < 2.5 regime -this redshift is chosen to allow the H α spectral line (6563 Å) and the [N II] finestructure doublet (6549 and 6583 Å) to be observed by KMOS.
(v) All targets could be simultaneously observed in one KMOS pointing.

Integral field spectroscopy
KMOS is an Integral Field Spectrograph in operation on the VLT that can simultaneously target up to 24 objects within a patrol field of 7.2 arcmin in diameter (Sharples et al. 2013). Each integral field unit (IFU) has a square field of view of 2.8 arcsec × 2.8 arcsec. This field of view is divided into 14 × 14 pixels giving a seeing limited spatial sampling of 0.2 arcsec. The typical spectral resolution within the K band is 4200 with a 2 channel full width at half-maximum (FWHM).
All of our 18 objects were prepared using the KMOS Arm Allocator (KARMA, Wegner & Muschielok 2008), with each galaxy assigned to an IFU allowing all targets to be observed in a single pointing, ensuring atmospheric conditions are the same across the sample. Observations were taken in the K band which has coverage of 1.934-2.460 μm and a resolution of approximately 3 Å.
The data are made up of 12 separate observation blocks (OBs): six on 2013 November 22/23 and six on 2016 October 9/10. 1 We used the 'stare' observation mode, with eight exposures per OB with an integration time of 600 s per exposure. One IFU was dedicated to a star so we could measure the point-spread function (PSF) for each OB. The seeing varied from 0.3 to 1.3 arcsec over the two nights and the average seeing conditions were approximately 0.6 arcsec.
The raw data were reduced using the standard KMOS pipeline, part of the EsoReflex package (Davies et al. 2013;Freudling et al. 2013). The pipeline carries out dark current correction, flat-field correction, wavelength calibration, telluric correction, sky subtraction, and flux calibration to produce a final data cube and an associated noise cube for each target in each OB. We took the reduced cube from each OB and combined them together to produce a final data cube per target, including the star used to measure the PSF. To account for spatial offsets across the OBs, we found the centre of the PSF via fitting 2D Gaussian to the star and shifted each cube so that the centres aligned for all 12 OBs. This gives our final cubes a spatial dimension of 17 × 16 pixels. We used a weighted average rather than a simple average to account for the observations being carried out under varying seeing conditions. This weighting was calculated by finding the area in arcseconds enclosed by each of the 12 PSFs and summing these together to get a total area. We then found the fractional contribution to the total area by each OB's PSF. The reciprocal of these fractions was then used to assign a weighting for each OB with the sum of all 12 weightings equalling one, i.e. an OB with worse than average seeing has a larger than average fractional contribution to the total area and is thus proportionally down-weighted and vice-versa for an OB with above average seeing. The PSF for the final stacked cubes was found by fitting a Gaussian to the stacked observation of the star, combined using the same weighted average, which gave a PSF FWHM of 0.57 × 0.44 arcsec.

Spectra
To find the H α and [N II] emission lines, we inspected the cube at the expected H α wavelength based on the redshift of the galaxy. Once the emission lines were identified, individual apertures were applied to each data cube to distinguish between galaxy and sky emission. Two apertures were applied to each cube: the galaxy aperture and the sky aperture. The galaxy aperture was scaled to cover the extent of the galaxy emission. The remaining spaxels were dedicated to the sky aperture, which was normalized to be the same area as the galaxy aperture.
All spaxels within the galaxy apertures were collapsed into a onedimensional spectrum and model spectra were fitted to the observed H α and [N II] emission lines. This model involved simultaneously fitting three Gaussian profiles and a linear function to account for any continuum. The ratio of the [N II] 6583 Å/ [N II] 6549 Å peak flux was preset to 0.34 as predicted theoretically (e.g. Osterbrock & Ferland 2006) and the width of the [N II] Gaussian profiles was forced to equal the width found for the H α emission line. All three lines were also forced to share the same line of sight velocity. The best fit was determined by a χ 2 minimization to the observed flux. For galaxy o13 the [N II] lines are not detected and their expected line centres coincide with a trough in the observed spectra, which affected the fitting of the model spectra. Instead, this was fitted with a single Gaussian curve, centred on the H α line, and a linear function.
To ensure we did not miss any H α flux, we created a sky spectrum by collapsing all spaxels within the sky aperture and compared the sky spectrum to the integrated galaxy spectrum. If any H α emission was found in the sky spectrum, we increased the size of our galaxy aperture and repeated the above analysis. Finally, to calculate the signal-to-noise ratio (S/N) of our spectra we used the mean and rms derived from the sky emission.
Although the pipeline does basic sky subtraction by allocating a sky IFU to the object IFU, there were still some large residual sky emission around the edge of the reduced cubes. To ensure these pixels did not skew the background rms calculations, we clipped any pixels in the sky aperture that were greater than 3σ above or below the mean sky emission.
H α line emission was detected in 14 of the 18 targets,and the spectra shown in Figure 1. We have marginally detected (∼3σ ) the [N II] 6583 Å line in four of our galaxies. The total H α and [N II] fluxes from the galaxies were evaluated by integrating the area under their respective Gaussian curves. The total H α flux for our KMOS sample ranges from 3.07 × 10 −17 to 8.23 × 10 −17 erg s −1 cm −2 and an instrument-corrected FWHM of 75-473 km s −1 ; our results are shown in Table 2. The FWHM of 75 km s −1 for galaxy o2 is a lower limit as a noise spike occurred on the red wing of the H α emission line, which was corrected for in the data reduction, leading to a loss of flux on the red side of the line. Intensity maps of the observed H α for the 14 galaxies were made by summing the intensity in all channels that span the emission line, and these are shown in Fig. 2. For three of the four targets with undetected H α we estimated a 3σ upper limit for the line flux. First, we fitted an aperture of 1 arcsec in radius to each cube and then used the redshift of the target to find the expected peak wavelength of the H α emission line. We found the channel that corresponds to the peak wavelength and extracted a spectrum spanning 12 channels either side (half way between the expected H-alpha and [N II] emission lines). From this we calculated the mean and standard deviation of the spectrum. Assuming the average linewidth of our sample, 267 km s −1 and a peak amplitude equalling the 3σ value, we estimated an upper limit for the H α line flux. We could not get an upper limit for galaxy o11 due to a skyline falling in a couple of the channels of the expected H α emission.
The analysis outlined in Section 2.2 was repeated but instead of the seeing weighted averaging method we recombined the cubes using a noise weighting scheme. The spectra derived from both cubes agree well within error, therefore, the choice of weighting scheme does not have a significant impact on the analysis and the results reported here.

Star formation rates
H α emission is a sensitive tracer of star formation within the past 10 Myr as, in the absence of AGN, it is the O-type star that provides the bulk of the requisite ionizing radiation (see Kennicutt & Evans 2012 review for details on SFR tracers). Although we cannot exclude the presence of an AGN in our sample, the H α/[N II] 6583 Å ratio is below one for the entire sample, which is consistent with the starforming locus of the BPT diagram at z ∼ 2 (Shapley et al. 2015).
However, H α is strongly attenuated by dust so in ULIRGs this provides a lower limit for the ongoing star formation (e.g. Hopkins et al. 2001). The absorption cross-section of galactic dust strongly peaks in the UV so, assuming radiative transfer balance, the IR emission is attributable to reprocessed stellar light from underlying O-type and B-type stars. This makes L IR emission a probe of the SFH within the past 100 Myr (Kennicutt & Evans 2012) and is also a tracer of the galaxy's obscured star formation.
To determine the L IR from our sample of galaxies, we fit the available Herschel and Spitzer photometry (Wang et al., in preparation) by using the dust model of Draine & Li (2007) following the methodology described in Magdis et al. (2013). The L IR for our sample are listed in Table 3, with the fits resulting in six of our galaxies being ULIRGs, eight are LIRGs, and four could not be determined due to poor SED fits.
Taking the L IR and H α emission we can investigate the recent SFH of our sample using the following conversion factors from Murphy et al. (2011b): Although these conversion factors were calibrated using a Kroupa (2001), they yield the same results as a Chabrier IMF (e.g. Chomiuk & Povich 2011, Kennicutt & Evans 2012. The SFR H α for our KMOS sample, uncorrected for attenuation, range from 6 to 21 M yr −1 with the SFR IR having values ranging from 40 to 783 M yr −1 (see Tables 2 and 3).

Kinematics
To investigate the kinematics of the 14 galaxies in which H α was detected we used GalPak 3D (Bouché et al. 2015) which fits a rotating disc model to the observed flux. GalPak 3D 's Bayesian approach is well suited to recovering kinematic parameters from marginally resolved galaxies with low S/N at increasing disc radius. GalPak 3D 's model galaxy has 10 free parameters: x, y, and z centroid position, flux, half-light radius, turnover radius, position angle, inclination, maximum rotational velocity, and the one-dimensional intrinsic velocity dispersion. The emission from this model galaxy is subsequently convolved with a PSF, specified by the user, and the best fit to the observed data is found via a Bayesian Markov Chain Monte Carlo (MCMC) approach.
For our input cube we cut around the H α emission line to ensure no contamination from the [N II] lines on either side. The PSF was set to the one calculated in Section 2.2 and the KMOS instrument was chosen so that GalPak 3D properly accounted for the appropriate instrumental resolution. For our galaxy model we assumed that the H α emission follows an exponential radial flux profile, the rotation curves have an arctan functional form, and the intrinsic velocity dispersion is isotropic and spatially constant across the disc. We set the aspect ratio (vertical scale height to effective radius) to 0.2, to account for thicker discs at high redshifts (e.g. Förster Schreiber et al. 2009;Wuyts et al. 2016). The spatial and kinematic parameters, listed in the previous paragraph, were left free for the MCMC to fit.
Six of the sample converged in the MCMC to parameters consistent with a rotating disc. The spatial and kinematic parameters found by GalPak 3D are shown in Table 4 and the model for galaxy o3 is shown in Fig. 3. We rejected model discs that converged to unphysical values, e.g. rotational velocities approaching 1000 km s −1 or half light radii/flux far exceeding our emission maps. Likewise, we rejected models that only converged due to a hard boundary being adopted in GalPak 3D , i.e. rotational velocities of 350 km s −1 if the hard boundary is set to 350 km s −1 . We rejected discs if any individual parameter was bimodal or if the model galaxy provided a poor fit to the data upon inspection of residuals between the model and observed galaxies. Galaxy o17 was omitted from this analysis as some noisy channels in the blue wing of the emission line appeared to be affecting the best-fitting parameters.
To test our results sensitivity to the assumed galaxy model, we repeated the analysis with a Gaussian radial flux profile and subsequently rerun the analysis using GalPak 3D 's default aspect ratio of 0.15 and all results agreed within error.

Modes of star formation
The location of a galaxy in the M -SFR plane is strongly linked to its mode of star formation. Although neither the mass nor the SFR relies on knowledge of what the gas is doing, the SFR is implicitly modulated by gas fraction and the SFE within the galaxy (e.g. Tacconi et al. 2018). This, in turn, allows the underlying mechanism driving star formation to be inferred by a galaxy's position with respect to the main sequence. To place our sample on the MS (Fig. 4), we use the SFR IR derived from the L IR and the stellar mass derived from fitting Bruzual & Charlot (2003) models to the BVizYJH photometry and the Infrared Array Camera (IRAC) 3.6, 4.5, 5.8, and 8.0 μm photometric bands.
In summary, for each galaxy SED we generated a set of models using the stellar population synthesis templates of Bruzual & Charlot (2003). We adopted the Padova stellar evolution tracks (Bertelli et al. 1994) and constructed models with solar metallicity and a Chabrier IMF. We used the Calzetti et al. (2000) starburst attenuation law to account for the extinction. For the parametrization of the SFH of each galaxy we considered two simple single-component models: an exponentially declining model of the form SFR(t) ∼ exp (-t/τ ) with efolding times of τ = 0.05, 0.1, 0.5, 2.0, and 5.0 Gyr, and continuous star formation (CSF) models. Finally, we used a χ 2 minimization technique to find the best-fitting model to each galaxy SED.
We can quantify how far each galaxy lies from the MS via where M is the stellar mass and a = −19.99, b = 3.44, and c = −0.13 (taken from Whitaker et al. 2014). The SFR IR confirm all but two of our sample to be MS as seen in Fig. 2 , with the two outliers being galaxy o7, having a distance above the MS ( SFR) of 0.99 dex, and o15, with SFR = 0.78 dex. This suggests that star formation in luminous IR galaxies at cosmic noon is dominated by steady-state processes.
To determine τ dep and thus further explore the mode of star formation in our sample of galaxies, we searched for ancillary CO or Rayleigh Jeans continuum data that would enable us to compute gas masses. Two of our KMOS sample had the requisite observations: galaxies o3 and o7. Galaxy o3 was previously studied in Wiklind et al. (2019) in which they used the same continuum method to estimate a molecular gas mass of 8.57 × 10 10 M . Using this value gives a depletion time of 0.35 Gyr which is approaching that of an MS star-forming galaxy at cosmic noon (e.g. Tacconi et al. 2020).
Galaxy o7 is an interesting case as it clearly falls within the starburst regime, with its SFR of 783 ± 5 M yr −1 It has been previously studied by Elbaz et al. (2018)   optically thin emission and conversion factors based on local galaxies. Although differing ISM conditions at high-z galaxies compared to local ones introduce uncertainty in this method, similar potential sources of error exist in the standard CO to H 2 method of finding molecular gas reservoirs in high-z ULIRGs (e.g. Bolatto, Wolfire & Leroy 2013).
The molecular gas masses and corresponding depletion times for these two galaxies agree well with our finding of one galaxy being a starburst and the other an MS based on their location on the M -SFR plane. Recent studies (e.g. Elbaz et al. 2018;Franco et al. 2020;Valentino et al. 2020) have shown that position on the M -SFR plane may not hold in all cases when categorizing a galaxy's mode of star  formation, with some massive z ∼ 2 MS galaxies exhibiting high SFEs and very short depletion time-scales. Such objects appear to have compact star formation and are gas poor compared to their MS counterparts and it is suggested (e.g. Dekel & Burkert 2014;Popping et al. 2017) that these galaxies are at the end of their starburst phase and are the progenitors of massive elliptical galaxies. Conversely, case studies of starbursting submillimetre galaxies (SMGs) have signatures consistent with rotating discs (e.g. Hodge et al. 2019;Drew et al. 2020), so distance above the main sequence does not always imply a merger. Our analysis indicates that the majority of our sample of galaxies are consistent with being secularly evolving MS galaxies with only o7 and o15 being starbursts. Future observations of the molecular gas content of these galaxies likely confirm this finding.

Obscured versus unobscured star formation
As our luminous IR galaxies emit strongly at FIR wavelengths >100 μm a priori we know these to be dusty star-forming galaxies. H α is strongly attenuated by dust so it is likely to underestimate the true SFR. In compact star-forming galaxies, e.g. mergers, the SFR H α can be orders of magnitude lower than IR estimates of SFR (e.g. Rodríguez-Zaurín et al. 2011). High-redshift U/LIRGs have more extended star formation with lower SFR surface densities so for a given IR luminosity attenuation is expected to be weaker at high-z (e.g. Buat et al. 2015).
As mentioned in Section 3.2, H α and FIR emission arises from stellar populations with different age ranges, 10 and 100 Myr, respectively. If we assume a constant SFH in the past 100 Myr, we can take the ratio of log(SFR H α /SFR IR ) as a proxy for the obscured versus unobscured star formation. This allows us to investigate how dust enshrouded our sample is when compared to intermediate-z The average log(SFR H α / SFR IR ) ratio of our sample is −1.08 ± 0.34 (or −1.06 ± 0.37 when excluding the H α upper bounds), while the value for the intermediate-z U/LIRGs is −2.2 ± 0.4, with values of −2.0 ± 0.5 and −1.6 ± 0.5 for the local ULIRGs and LIRGs, respectively. Our sample has similar log(SFR H α / SFR IR ) to local LIRGs (see Fig. 5) with only galaxy o7, a starburst, falling within the location of local ULIRGs. This demonstrates that for the same L IR , high-z U/LIRGs appear to be less dust obscured than their local and intermediate-redshift counterparts.
Despite our sample size being relatively small there is a statistically significant correlation between the magnitude of obscuration and a galaxy's distance from the MS, as shown in Fig. 6, with a linear fit giving a Pearson's ρ = −0.88 and a P-value <0.001. Followup continuum studies of the dust distribution within our sample of galaxies are needed to further investigate this correlation.

Dust temperature
Dust properties within a galaxy can be inferred from the Rayleigh Jeans regime of the FIR emission (e.g. Casey, Narayanan & Cooray  2011), respectively. The average log ratio of our sample is −1.2 ± 0.4, while the log ratio for the intermediate-z U/LIRGs, local ULIRGs, and LIRGs is −2.2 ± 0.4, −2.0 ± 0.5, and −1.6 ± 0.5, respectively. Galaxy o7 and o15 are marked as both of these galaxies fall above the main sequence, with o7 being the only one of our sample to fall within the range of the local ULIRGs. Figure 6. The relation between extinction, as represented by log(SFR H α / SFR IR ), and a galaxies vertical offset from from the main sequence of Whitaker et al. (2014), in dex, represented by SFR. The linear fit has a Pearson's ρ = −0.88 and shows that the level of obscured star formation increases with distance above the main sequence. 2014). A single modified blackbody fitted to the FIR photometry is sufficient to determine the cold temperature of large dust grains, whereas a mixture of modified blackbodies is required to account for the warm dust of the smaller dust grains (e.g. Draine & Li 2007).
Using our Herschel photometry, and limiting ourselves to wavelengths >100 μm to ensure we are sampling the peak and Rayleigh Jeans slope of the emission, we fit a modified blackbody to evaluate the cold dust temperature (T dust ) for our sample. We assumed a greybody emission model of the form: Figure 7. The modified blackbody, as described in Section 4.3, fitted to the photometry of galaxy o7. The best fit from the MCMC is plotted in blue and the observed flux is given by the red data points.
where F ν is the flux density in Jy, β is the emissivity coefficient, ν 0 is the rest-frame frequency at which the optical depth reaches unity, and B ν (ν obs ,T d ) is the blackbody function. Due to the small number of photometry points we adopted the Markov chain Monte Carlo (MCMC) approach of Dowell et al. (2013) to fit the FIR emission. This MCMC model uses a power law for the Wien side of the peak, F ν ∝ ν −α , giving the model five free parameters in total: α, β, T dust , ν 0 , and a normalization factor (see Dowell et al. 2013 for full details). We assumed that the dust emission is optically thin, has a single dust temperature rather than a multidust temperature model, and the emissivity parameter was set to β = 1.5 (e.g. Casey et al. 2014). We fit a grey-body to galaxies with three or more photometry points >100 μm and relaxed the Wien power law condition, reverting to a standard grey-body, for those galaxies that had only three photometric data points available. Seven of our KMOS sample had the requisite photometry data and we compute a range of temperatures between 23 and 50 K, with an average value of 36 ± 8 K (see Table 3 and Fig. 7). Previous studies have found that the intensity of the radiation field increases with lookback time (e.g. Magdis et al. 2012;Huang et al. 2014;Béthermin et al. 2015) along with a concurrent rise in dust temperatures, within MS galaxies, back to z ∼ 2 (e.g. Magnelli et al. 2014). Local U/LIRGs have T d ∼ 30-55 K (e.g. Clements et al. 2018), while local normal star-forming galaxies detected by the Herschel Space Observatory have colder dust with an average T d ∼ 20 K (Cortese et al. 2014). Dust temperatures for z ∼ 2 ULIRGs have been found in the range 25-60 K (e.g. Magdis et al. 2010;Symeonidis & Page 2018), providing evidence that ULIRGs do not follow the same redshift-T d trend as MS galaxies.
On the other hand, z ∼ 2 galaxies lying above the MS often contain warmer dust than what is found in local ULIRGs, e.g. Miettinen et al. (2017) find T d values up to 79 K. High-z star-forming galaxies hosting an AGN can have a similar range of dust temperatures as their non-AGN counterparts (e.g. Chen et al. 2021), but extremely luminous AGN such as dust-obscured quasars tend to have higher temperatures, with studies showing an average T d > 60 K (e.g. Fan et al. 2017;D'Amato et al. 2020).
Comparing our dust temperatures to previous results, and noting we have no evidence of an AGN within our sample, we reaffirm our findings, in Section 4.1, that the T d is consistent with MS star-forming galaxies and the SFR appear to be driven by secular steady-state processes.

Dynamical ratio
The dynamical ratio is defined as the ratio between the rotational velocity, v rot , and the velocity dispersion, σ 0 , of a galaxy. The mean observed velocity dispersion increases as galaxies go from isolated, to interacting, and finally merging with a subsequent decrease in the amplitude of the rotational velocity (e.g. Bellocchi et al. 2013). Hence, high dynamical ratios correspond to isolated discs with lower ratios signifying mergers and interactions.
Pereira-Santaella et al. (2019) used the dynamical ratio to categorize intermediate-z U/LIRGs into isolated or interacting/merging galaxies by comparing their kinematics to the v rot and σ 0 observed in an isolated sample and an interacting sample of local U/LIRGs. Threshold values of σ 0 < 56 km s −1 and v rot /σ 0 > 3.2 separate the isolated subgroup from the interacting subgroup of local U/LIRGs (for full details see Pereira-Santaella et al. 2019).
To apply this method to our sample, we first need to account for the star-forming ISM at high-z being more turbulent due to an increased molecular gas fraction (e.g. Bauermeister et al. 2013;Saintonge et al. 2013;Übler et al. 2019). Therefore, a σ 0 > 56 km s −1 at high-z can be driven purely by internal dynamic processes and a more turbulent ISM does not always imply a recent merger or interaction. We use the redshift evolution of the intrinsic velocity dispersion to account for this increase in σ 0 as a function of redshift, allowing the thresholds values ascertained in local U/LIRGs to classify our sample. We take the following relation fromÜbler et al. (2019), which holds for ionized gas: σ 0,fit (z)/kms −1 = (23.3 ± 4.9) + (9.8 ± 3.5) × z. (5) By plugging the redshifts of our luminous IR galaxies into this equation, we can find the expected intrinsic velocity dispersion for each galaxy. We then take the ratio of this with the velocity dispersion at z = 0 to find a correction factor (σ 0,fit (z = U/LI RG) / σ 0,fit (z = 0)) which gives us the expected fractional increase in σ 0 between z = 0 and the redshifts of our galaxies. We then rescale the σ 0 found by GalPak 3D by this correction factor to get our redshift-corrected velocity dispersion. E.g. for galaxy o3 the expected σ 0,fit (z = 2.433) is 46.6 km s −1 which is 2.03 times higher than σ 0,fit (z = 0), rescaling the observed σ 0 = 148 km s −1 to the redshift-corrected σ 0 = 73 km s −1 .
To increase the size of our KMOS sample, we supplemented it with targets from the ESO archive (hereafter known as the supplemental sample) which satisfied our criteria, outlined in Section 2.1, with the addition that all archival targets are also in the ZFOURGE database to ensure the supplemental sample occupied the same region of the SFR-M parameter space as our KMOS sample. 28 galaxies (see Table A1 in the Appendix) from the archive satisfied our criteria, with two of these flagged as AGN in ZFOURGE, and the Gaussian FWHM of their PSFs ranged from 0.5 to 0.94 arcsec. The archival galaxies were reduced and modelled following the same procedure as our KMOS sample (see Section 3.3). We note that we have identified a separate observation of our galaxy o17 in the archive (GS4 35056 in Table A1). The reduced cube from this observation did not have the issue of the noisy sky on the blue wing channels of the H α line that was identified in our analysis (see Section 3.3), so we decided to include the archival GS4 35056 cube in the supplemental sample. This cube is used for the kinematic analysis only and to avoid confusion we will continue to refer to it as part of the supplemental sample. 12 of the supplemental sample converged with neither of the two AGNs found to be a disc (see Table A2).
From the entire sample (ours and the ESO supplemental) 15/41 appear to be isolated discs and this fraction increases to 17/41 if we use just the criterion of v rot /σ 0 > 3.2 for the undetermined cases (see Figure 8). The majority of galaxies that converged in GalPak 3D are isolated discs and this is an artefact of fitting a model galaxies to z ∼ 2 observations. The KMOS spectral resolution at 2 < z < 2.5 is ∼40 km s −1 so galaxies with dynamical ratios below unity, i.e. low v rot , may not have the requisite data points to constrain the turnover radius and rotational velocity of a fitted model galaxy. Likewise, galaxies with disturbed morphology (e.g. galaxy o2 in Fig. 2 ) can either prevent the model parameters converging or converge to a poor fit as GalPak 3D assumes a smooth rotating model disc. Factoring in the drop in S/N at increasing radii, GalPak 3D will be biased towards isolated discs with large rotational velocities at z ∼ 2. Therefore, a proportion of the 22 galaxies in which GalPak 3D could not fit a model are likely to be interacting discs, although we cannot quantify this using the above analysis.
Our findings agree with previous result of interacting versus isolated discs at this redshift. Kartaltepe et al. (2012) using HST imagery concluded that ∼50 per cent of galaxies appear to have some form of interaction and Molina et al. (2017) found 3/5 of H α selected MS galaxies from z = <2.23> have signatures of merging based on kinemetry, a method quantifying the asymmetry in the v rot and σ 0 maps allowing galaxies to be classified into ordered rotation or disturbed kinematics (Krajnović et al. 2006).
The KMOS 3D survey (Wisnioski et al. 2019) finds 49-70 per cent of MS galaxies (10.00 < log(M /M ) < 11.75) at z ∼ 2 to be discs. The range corresponds to the exact criteria used for the classification (see Wisnioski et al. 2019 for a detailed description of their criteria). When all five of their criteria are satisfied then the fraction of disc galaxies found is 49 per cent with the value increasing to 70 per cent when considering only the first two criteria. At lower redshifts, the KROSS survey found 83 per cent of star-forming galaxies at z ∼ 0.9 to be rotation dominated (using the definition of v rot /σ 0 > 1; Johnson et al. 2018). Using the same definition, Turner et al. 2017 found that 34 ± 8 per cent of typical star-forming galaxies at z ∼ 3.5 are rotation dominated.
Differences in methodology and classification has been investigated by Rodrigues et al. (2017) where they find a smaller fraction of discs than Wisnioski et al. (2015), from the same KMOS 3D sample of 41 galaxies at z ∼1, by using a different methodology to derive the kinematic parameters, such as the σ -peak or the kinematic centre, and applying the five KMOS 3D survey criteria described above. Rodrigues et al. (2017) also showed that some observations were misclassified as discs when broad-band images were investigated. Where possible we have verified the position angle and inclination, via the Hubble Space Telescope ACS/WFC camera (see Fig. C1). Where adequate S/N was available to fit isophotes to the broadband observations, the position angle for both our KMOS and supplemental samples agrees to within 30 • and the inclination to within 24 • , and corroborate our fraction of isolated discs.
It is instructive to look at how the properties of the z∼2 KMOS sample compares with similar luminosity samples at lower redshifts. Pereira-Santaella et al. (2019) found 10-25 per cent of their intermediate-z sample to be isolated discs, while this fraction goes down to ∼5 per cent for local U/LIRGs with log(L IR /L ) > 11.6 (Bellocchi et al. 2013). Despite differences in sample sizes and systematic errors, the dynamical ratios suggest that the percentage of mergers and interactions in luminous IR systems decreases with lookback time.
The results presented here also agree with the evolution predicted by cosmological simulations. The Horizon-AGN hydrodynamical simulation (Martin et al. 2017) shows that mergers only account for 25 per cent of stellar mass since z ≈ 6 meaning smooth accretion is the dominant driver of star formation through cosmic time. Rodríguez Montero et al. (2019), using the SIMBA simulation, find that mergers contribute only about ∼1 per cent of to the SFR density at z ∼ 2, although they does not include the pre-merger phase in their merging sample.

Dynamical mass
We can infer dynamical masses and dark matter fractions for our sample from the best-fitting kinematics. Using the methodology of Price et al. (2016) the dynamical mass can be calculated from where G is the gravitational constant, k eff (R E ) is the effective virial coefficient, R E is the half light radius, and V c (R E ) is the root mean square velocity, defined as The effective virial coefficient is given by We chose k disp = 5 (e.g. Pettini et al. 2001) and set k rot = 1, (e.g. Miller et al. 2011), which are valid for a spherical potential. The effective virial coefficient term accounts for the existence of a nonnegligible pressure component due to the more turbulent ISM at high-z (e.g. Förster Schreiber et al. 2009;Wuyts et al. 2016), and when V rot (R E )/σ 0 1 equation (6) reverts to the dynamical mass calculated from only rotational support . 2 In the absence of molecular gas observations for most of the galaxies in our sample, we estimate the gas fraction from the following: We approximate τ dep by using the redshift evolution of depletion time from Wisnioski et al. (2015): We assume an α value of −1 to match that of Wisnioski et al. (2015) and Tacconi et al. (2013) and choose a pre-factor of 1.5 Gyr to represent the typical depletion time of a z = 0 MS galaxy (e.g. Saintonge et al. 2013). Rearranging equation (9) and using the fitted M and SFR IR for our KMOS sample and the M and SFR IR from ZFOURGE for the supplementary sample (see Table A1, and Straatman et al. 2016 for methodology), we deduce both a value for the M gas and a value for the total baryonic mass, M bar = M gas + M . We did not calculate a baryonic mass for galaxy o8 as we do not have a fitted SFR IR from which to estimate the gas fraction. By taking the ratio of baryonic mass to the dynamical mass we can subsequently get the dark matter fraction within one R E : To calculate the baryonic mass within one effective radii, we assume that half of the stellar mass is within one R E and a constant 2 M dyn = V rot (R E ) 2 R E /G Figure 8. The dynamical ratio for the two sets of luminous IR galaxies: our sample (red) and the supplemental sample (grey). The dynamical ratio has been corrected for the redshift evolution in velocity dispersion as discussed in Section 4.4 The blue/red boxes represent typical values seen in isolated discs/interactions with threshold values of σ 0 < 56 km s −1 and v rot /σ 0 > 3.2 for isolated discs. 3/6 of our sample appear to be isolated with all 12 of the supplementary sample falling within the boundaries of an isolated galaxy. Galaxies falling within the white areas cannot be determined using this method and can only be categorized by relaxing one of the assumptions.
gas to stellar mass ratio throughout the disc, i.e. half the gas mass is also inside one R E . This is valid as high-z studies have shown gas and H α having a similar spatial extension (e.g. Molina et al. 2019). The baryonic mass within an R E is simply half the total baryonic mass.
It is worth noting that the dark matter fractions are subject to large uncertainties due to various assumptions, including uncertainties in the gas fraction, the assumption of the geometry of the mass distribution, assuming the co-spatial distribution of ionized, molecular and stellar mass, and the accuracy of our kinematic parameters recovered from marginally resolved galaxies; and these assumptions are discussed in detail in the KMOS 3D (Wuyts et al. 2016) and MOSDEF (Price et al. 2016) kinematic surveys. With all these caveats in mind we can attempt to determine whether both samples as a whole are baryon dominated (f D < 0.5) or dark matter dominated (f D > 0.5) within their effective radii.
Both samples span a large range of dark matter to dynamical mass fraction, f D , from baryon-dominated galaxies to unphysical values. The median value across both samples is f D = 0.03 and only three appear to be dark matter dominated within one R E (see Fig. 9), suggesting that high-z luminous IR galaxies are baryon dominated within their effective radii. The ratio of stellar mass to dynamical mass is also plotted in Fig. 9 and contains only two unphysical values, which suggests that the main reason for the unphysical dark matter fractions lies in the estimate for the gas fraction within a galaxy. For example, galaxy o15 lies above the MS so it likely has a lower τ dep than that acquired from equation (10), which gives a τ dep of 0.48 Gyr and a gas fraction of 0.87. The f D becomes physical when the gas fraction falls below 0.61.
In the above analysis we included the three galaxies in our KMOS sample (o3, o14, and o16) that failed one of our criteria for an isolated disc. If their high velocity dispersion is due to a perturbation from an interacting galaxy, and the disc has not yet virialized, then equation (6) does not hold. Whether or not we include these three data points the same conclusion holds: we cannot accurately measure the exact f D for an individual galaxy but we can state the sample as a whole is baryon dominated within one R E . The unphysical values are mainly caused by our estimate of gas fraction, as discussed in Section 4.5, which can be seen when we remove the gas mass and plot stellar mass versus dynamical mass within one R E (right). Further reasons for unphyscial values are discussed in Section 4.5. The three galaxies (o3, o14, and o16) that passed only one of our two kinematic criteria for an isolated disc in Section 4.4 are included as the interacting subsample and these may be an overestimate of the dynamical mass. The left plot only contains five data points for our KMOS sample as we were unable to estimate a baryonic mass for galaxy o8.
This agrees with previous high-z research which showed that galactic discs are baryon dominated inside one R E , displaying a range of median baryon fractions from 70 per cent to unphysical values, i.e. >100 per cent (e.g. Förster Schreiber et al. 2009;Price et al. 2016;Wuyts et al. 2016;Genzel et al. 2017;Lang et al. 2017;Price et al. 2020). Tiley et al. (2019 argued that dark matter fractions of >0.67 are found if f D is calculated within six radial scale lengths, as opposed to on R E . All the results are consistent as probing the dark matter fraction at larger radii probes further out into the halo where baryon fraction decreases, assuming a CDM Universe where the universal baryon, bar , to dark matter, D , fraction is expected to be f b = bar / D ∼0.2 (Aghanim et al. 2019). Our results are also in agreement with IllustrisTNG simulations where f D (<R E ) = 0.29 ± 0.11 (Übler et al. 2021) and NewHorizon simulations (Dubois et al. 2020) in which galaxies, similar in SFR to o5 and o16, are baryon dominated within their R E (Grisdale et al., in preparation).

Drivers of turbulence
The average velocity dispersion values of the two samples agree within error, but our KMOS sample does appear to have a consistently higher σ 0 . Although the supplementary sample satisfy the selection criteria in Section 2.1, these targets were initially selected on their rest-frame optical emission at 2 < z < 2.5 (Wisnioski et al. 2015), which biases the supplementary sample towards less extinguished objects when compared to our KMOS sample. This leads to a greater S/N in the outer disc regions of the supplementary sample, allowing GalPak 3D to probe the kinematics further out into the disc and sample σ 0 away from the central regions of high velocity dispersion.
It is worth investigating potential non-systematic reasons for the range of velocity dispersion within both samples. Previous observational studies (e.g. Johnson et al. 2018;Übler et al. 2019) and semi-analytical modelling (e.g. Krumholz et al. 2018) indicate that turbulence in the high-z Universe is driven primarily by gravitational instability as opposed to feedback from star formation. To check if the σ 0 in our sample is mainly caused by gravitationally unstable discs, we plotted σ 0 versus SFR and versus baryonic mass to try gain insight into the mechanisms driving turbulence. We find weak correlations for σ 0 against baryonic mass with a Pearson's ρ = 0.37 (P-value = 0.13), and for σ 0 versus SFR with Pearson's ρ = 0.30 (P-value = 0.23), as shown in Fig. 10, although neither is statistically significant. The weak correlation of σ 0 versus SFR may be due to the link between the SFR and baryonic mass, via the main sequence, as opposed to any causal link.
It is also possible that the presence of minor mergers is driving the scatter in dispersion. Such minor merger events could not be observed due to the KMOS being a seeing-limited instrument. Simons et al. (2019) showed, via simulations, that under seeing-limited conditions at z ∼ 2, mergers can often be mistaken as discs under a variety of sightlines. Fensch et al. (2017) used simulations to demonstrate that mergers at z ∼ 2 provide an inefficient boost in SFR due to the already turbulent nature of discs at high-z, so being on the MS does not rule out potential mergers. In a forthcoming paper (Hogan et al., in preparation) we will further investigate how minor mergers affect the velocity dispersion within a galaxy and, subsequently, observational signatures such as v rot /σ 0 .

Metallicity
The metal content of a galaxy can be used to constrain its SFH since gas-phase metallicity is the result of enrichment of the ISM from previous star-forming episodes. The ratio of [N II] 6583 Å and H α, known as the N2 index, can be used to find the gasphase metal content (Z) of galaxies. We converted the N2 index ratios to 12 + log(O/H) using the correlation of Pettini & Pagel (2004) to compare with the metallicity predicted from the massmetallicity relation (MZR) at z ∼ 2. Four of our KMOS sample were marginally detected and their average N2 index is 0.34 ± 0.1. The mean metallicity value derived for our sample is lower than the 1.1 ± 0.8 derived for the intermediate U/LIRG sample (Pereira-Santaella et al. 2019) and the 0.7 ± 0.3 of local U/LIRGs (Rupke, Figure 10. Intrinsic velocity dispersion plotted against SFR (left) and baryonic masses (right) of our galaxies. There is a weak correlation for both σ 0 versus SFR and σ 0 versus baryonic mass with a Pearson's ρ = 0.37 (P-value = 0.23) and ρ = 0.37 (P-value = 0.13) for the SFR and baryonic mass, respectively, although neither is statistically significant. Galaxy o8 could not be fitted with an IR SED so we do not have an SFR IR for this galaxy, giving only five data points in our sample for the left plot.  Maiolino et al. 2008). We can also calculate the expected metallicity of a star-forming galaxy at a given redshift and stellar mass using the following equation from Tacconi et al. (2018): where a = 8.74 ± 0.06, Galaxies o3, o5, and o16 all fall close to the expected value of a star-forming galaxy, with galaxy o7 being much more metal enriched than expected, as shown in Table 5 and Figure 12. The N2 index in galaxy o7 falls in a region of the BPT diagram that could be either in the AGN or starburst regime and without the [O III]/H β we cannot rule out a deeply buried AGN is skewing the N2 index higher (e.g. Kewley et al. 2013). It is also worth noting that o7 has both the highest Z and highest SFR in our sample which goes against the fundamental metallicity relation (FMR) (e.g. Mannucci et al. 2010;Maiolino & Mannucci 2019), in which for a given stellar mass there is an anticorrelation between SFR and metallicity. Assuming it does not contain an AGN, this galaxy may be a genuine outlier from the FMR or its enhanced Z may be due to different conditions in its ISM, such as an elevated N/O to O/H ratio leading to an error in the N2 to metallicity conversion factor (e.g. Shapley et al. 2015;Dopita et al. 2016). Alternative metallicity diagnostics based on IR fine-structure lines (e.g. Pereira-Santaella et al. 2017;Rigopoulou et al. 2018) may be required to shed light in the metal content of starburst galaxies at high redshifts.
Of the nine targets which had H α but no [N II] 6583 Å emission, we stacked eight of these targets to try get a detection from a composite spectrum. Galaxy o13 was left out of this stacking as a skyline fell in the same channel as [N II] 6583 Å. We obtained the composite spectrum by shifting the eight spectra into each galaxy's rest frame and then averaged the flux in each channel, which had a bin size of ∼1 Å. We fit this spectrum the same three-Gaussian model as the individual galaxies giving a marginal 2.5σ detection, as seen in Fig. 11.
The composite spectra gives an N2 index of 0.17 and 12 + log(O/H) = 8.46 ± 0.06, suggesting that on average these galaxies agree with the MZR at their average redshift of 2.26. The disadvantage of using a stacked spectrum is the average behaviour can hide the underlying variance in the sample, so although the average metallicity agrees with the MZR this does not rule out a subsample being metal deficient like the local U/LIRGs.

C O N C L U S I O N
We performed IFS in a sample of 18 luminous IR galaxies in the redshift range 2 < z < 2.5, around the peak of cosmic star formation density. We investigated the mechanisms driving their high rates of star formation and compared their properties to local and intermediate-z U/LIRGs to investigate any differences and evolution in the interplay of dust, gas, and star formation between the high-z Universe and today. The main results are: (i) We detected H α emission in 14 out of 18 galaxies, with a 3σ upper limit calculated in three of the other four. We fitted an IR SED to 14 of our sample and using the SFRs calculated from the H α and IR luminosities we show that obscured star formation is an order of magnitude greater than the unobscured star formation within these galaxies. The average obscuration was less than intermediate and local U/LIRGs with log(SFR H α / SFR IR ) = −1.1 ± 0.1.
(ii) 12 of the sample are main-sequence galaxies with two being a starbursts. We determined the distance of each galaxy from the MS, SFR, and found a statistically significant correlation in which log(SFR H α /SFR IR ) decreases with increasing SFR, demonstrating obscured star formation increases with distance above the MS.
(iii) Six of our H α detections converged to a disc within GalPak 3D . To boost the sample size we choose a supplementary sample of 28 luminous IR galaxies from the ESO archive, and 12 of this supplemental sample were found to be rotating discs. After accounting for the increase in intrinsic velocity dispersion with lookback time the dynamical ratio (V rot / σ 0 ) and redshift-corrected σ 0 suggest 15/41, or 17/41 if only V rot /σ 0 > 3.2 is used, of both samples are isolated discs. This is a higher rate than local and intermediate redshift U/LIRGs, which have ∼5 per cent and ∼25 per cent, respectively. This shows interactions are not necessary to drive the massive SFRs within z ∼ 2 luminous IR galaxies.
(iv) By quantifying the dynamical mass of our galaxies we find them to be baryon dominated inside one R E , similar to previous studies of star-forming galaxies at z ∼ 2.
(v) FIR photometry allowed us to fit a modified blackbody to seven of our luminous IR galaxies. The dust temperatures fall between 23 and 50 K, in line with dust temperatures in steady-state star-forming galaxies.
(vi) We measured the N2 ratio in four galaxies of our sample. The gas-phase metallicity is in broad agreement with the mass-metallicity relation at z = 2-2.5, in contrast to the metal deficiency of local ULIRGs. For the remaining galaxies in our sample we stacked their spectra allowing a marginal detection of [N II] 6583 Å and average gas-phase metallicity follows the mass-metallicity relation.
In summary, our sample of high-z luminous IR galaxies are predominantly main-sequence star-forming galaxies which have very different behaviour to local U/LIRGs. The underlying mechanisms driving the huge SFRs at the peak of cosmic SFRD are consistent with the steady-state processes driving star-forming disc galaxies we see locally as opposed to mergers.