Overview of comparison data presented

SUPPLEMENTARY INFORMATION doi:10.1038/nature09452 Overview of comparison data presented In Figure 2, we compare our results with four other data sets chosen to reflect much of the universe in which galaxy evolution has been studied. Three of these cover the redshift range 1.2 to 3.7, when the universe was 5.2 to 1.7 billion years old, respectively. The fourth samples galaxies in the modern universe within 100 megaparsecs of the earth. A short summary of the range of important quantities sampled by each comparison survey is included in Supplementary Table 1, as well as our own data for comparison. Intrinsically lower luminosity galaxies can only be sampled in the local Universe, due to the rapid reduction in apparent brightness with increasing distance. The choice of samples presented is also largely driven by the available data on those samples. The Gassendi HAlpha survey of SPirals 18, 19, 30 (GHASP) includes 203 galaxies observed using Fabry-Perot imaging spectroscopy of the Hα emission line. The instrument used provides a spectral resolution of 10 km/s, and seeing-limited spatial resolution greater than 1.4 kpc. This sample spans a B-band absolute magnitude range of -16 to -22 and galaxy masses of 10 9 to 5 10 11 M (ref 30). Members of this survey were selected to match objects observed in the WHISP 31 survey. Remaining galaxies were selected to be in local, low-density environments, but a few galaxies were selected from clusters. 30 GHASP reports a mean velocity dispersion as a simple mean of the individual spatial locations in the galaxy. As this definition differs slightly from that presented in our letter, we have computed both quantities for our own galaxies, and find these two quantities to be consistent within 10%. Spanning redshift 1.2 <z<1.6 are the first results 4 from MASSIV. These galaxies are drawn from the purely I-band magnitude-limited VVDS survey. 4 VVDS galaxies with the largest [OII] λ3727 emission-line luminosity were selected for this sample. The seeing-limited spatial www.nature.com/nature 1

RESEARCH SUPPLEMENTARY INFORMATION resolution is typically 4.0 to 6.3 kpc and spectral resolution λ/ λ 4000. Because of poor spatial resolution, the authors apply a correction to their measured velocity-dispersion map that accounts for the unresolved velocity gradient. They then compute their velocity dispersion as the error-weighted mean of the individual (corrected) velocity dispersions. As error scales with flux, and they have accounted for their poorer resolution, this quantity is comparable to our σ m parameter. D. Law and collaborators 7 present a sample of 13 galaxies selected from the BM/BX sample. 32 That sample is identified via the U n GR selection method 33 and confirmed via restframe- UV spectroscopy. The 13 galaxies were selected for a variety of reasons, but primarily based on expected Hα emission-line flux sufficient to be detectable with the OSIRIS integral-field spectrograph. We have excluded the one galaxy in their sample at z =3.3 because its Hα luminosity has not been measured. The local velocity dispersion, σ m has been measured in the same way as our own, although their slightly higher spatial resolution further reduces any impact of the local velocity gradient on σ m. Finally, we include a sample 8 of three targets also drawn from the VVDS survey but at z 3.5. Because of the high redshift, these galaxies have their kinematics measured using the [OII] λ5007 emission lines instead of Hα, as Hα falls outside the infra-red atmospheric window. Therefore, we have inferred the Hα luminosity for their sample by inverting 21 their Hβ derived star formation rate. They compute a velocity dispersion in the same way as for the MASSIV data above, and therefore is also comparable to our σ m despite their range in spatial resolution of 1.8 to 4.1 kpc. We have not included other works generally because they have not provided a quantity comparable to our σ m. Most notably is the large SINS sample. 2 Integrated velocity dispersion are reported for the whole sample, and intrinsic velocity dispersions were measured for a subset of the 2 WWW.NATURE.COM/NATURE

SUPPLEMENTARY INFORMATION RESEARCH Supplementary Table 1. Target Categories Property Our data GHASP MASSIV Law Lemoine-Brusserole Number (with AO) 65 203 9 12 (12) 3 (1) Redshift 0.055 0.151 < 100 Mpc 1.2 1.6 2.0 2.5 3.3 3.7 Hα Luminosity (log erg/s) 40.7 42.6 (41.9) 38.1 41.9 (40.6) 41.8 43.3 (42.5) 42.0 43.2 (42.5) 42.1 42.3 Stellar Mass (log M ) 9.1 10.9 (10.2) 9.0 11.7 9.0 10.8 (10.5) 9.0 10.9 (10.1) 10.1 10.2 Resolution (typical) (kpc) 1.4 6.1 (2.3) 0.03 2.0 (0.4) 4.0 6.3 1.0 2.4 (1.2) 1.8 4.1 sample via dynamical modeling, 34, 35 but both quantities are very different from our σ m. Only the integrated velocity dispersion is measured in two samples of ultraviolet luminous galaxies 36, 37 at z 0.2. The IMAGES survey, 6 which has a spatial resolution of 3 5.5 kpc, computes σ m in a similar fashion. However the central spatial pixel, which includes all the velocity shear for the sample s rotating disks, greatly increases σ m. 38 Therefore, we have not included this sample (and have checked our own sample for this effect elsewhere in this Supplementary Information.) Our sample selection methods The sample of 65 objects presented in the letter is drawn from the Sloan Digital Sky Survey (SDSS) Data Release 4 Graching/JHU value-added catalogue. 13, 14, 39 This catalogue provides emission-line flux measurements, 39 star-formation rates, 13 and stellar masses 14 for galaxies with spectroscopy in the SDSS. In particular, we have choosen from the star-forming sample, 13 which requires galaxies have spectral-line ratios indicative of star formation, not active galactic nuclei, as active galactic nuclei can greatly affect the luminosity of Hα and its correlation with star formation. From this sample of star-forming galaxies, we have applied two selection criteria: (1) galaxies must lie in the redshift range 0.055 < z < 0.084 or 0.129 < z < 0.151, which avoids any contamination from either night sky emission lines or telluric absorption in the atmosphere; www.nature.com/nature 3

RESEARCH SUPPLEMENTARY INFORMATION and (2) galaxies were divided into bins based on their Hα flux (equivalently luminosity), from which galaxies for observation were randomly selected. These criteria and the selected galaxies are summarised in Supplementary Figure 1. No other criteria were explicitly included in our sample selection. However, our sample is subject to the selection criteria of our chosen parent sample. 13 The Hα flux bins were motivated by two facts: (1) in the final selection for integral-field spectroscopic followup at high-redshift, the anticipated flux of the Hα emission line is compared against the limiting sensitivity of the chosen instrument, which typically corresponds to L Hα 10 42.0 erg/s across the galaxy, (2) flux binning allowed the a random selection to still sample the broad range of luminosities desired for our analysis despite large differences in the number of total objects in each flux bin. Of the 395265 galaxies in the Graching/JHU catalogue, 8.7% are star-forming and meet the redshift criteria outlined. Of these, 3.2% have fibre luminosities L Hα > 10 42.0. Of the sample (the 8.7%), 0.20% were observed, and 44% of the observed galaxies had L Hα > 10 42.0. Thus the sampling density of high-luminosity targets is 24 times that of the low-luminosity targets. σ m errors and the effects of beam smearing and resolution In this letter, we have presented velocity dispersions which are averaged across individual spatial pixels of finite size on the galaxy. Statistical errors on the individual velocity dispersions (determined by the errors on the line fits) are propagated through to the (flux weighted) average σ m and are typically 1 2 km/s. The error on the final σ m is smaller than the standard deviation of the individual dispersion measures in each map. This standard deviation is dominated by genuine spatial variations in the location of the turbulent gas, these can be seen in the maps (Figure 1) and are also of astrophysical interest but are beyond the scope of this Letter. We note that the typical values of 4 WWW.NATURE.COM/NATURE

SUPPLEMENTARY INFORMATION RESEARCH this standard deviation range from 4 to 26 km/s across the sample, with a median of 14 km/s. The main possible systematic error arises from finite spatial resolution. The median seeing of 1.3, limits the physical resolution on the galaxy to a median of 2.3 kpc. The resolution of the high-velocity dispersion group (σ m > 50 km/s, as in the letter) ranges between 1.7 kpc to 7 kpc, with median 3.4 kpc, while for the low-velocity dispersion group (σ m > 50 km/s), it ranges between 1.5 and 6.3 kpc with a median of 2.1 kpc. We have checked that there is no correlation between spatial resolution and velocity dispersion across our sample. Because many disk galaxies have a steep inner slope to their rotation curve, the central dispersions can be artificially high due to beam smearing of the true velocity gradient into an apparent measured velocity dispersion. 19 As the central regions of galaxies are also the brightest, a flux-weighted velocity dispersion could be strongly biased by this effect. Consequently, we have investigated how beam smearing impacts our results using a new empirical approach based on the observed velocity map which avoids the necessity to fit complex disk models used in alternative approaches. We construct a velocity-dispersion correction for each spectrum across each galaxy in the following way. First we construct a Hα flux map and a velocity map with five times higher spatial resolution using linear interpolation. We then construct a matched, high-resolution mock data cube observation with a single Gaussian spectrum at each spatial location. The flux and velocity centroid of this spectrum are drawn from the interpolated flux and velocity maps, respectively. The velocity dispersion of the spectrum is set to the instrumental resolution ( 15 km/s). Each wavelength plane of this 3D data cube is then convolved with a 2D Gaussian kernel with FWHM equal to the seeing for each observation. This step smears velocity gradients of neighbouring pixels together, raising the velocity width of each spectrum. This high-resolution data cube is then binned back to the original observational resolution by summing spectra in each spatial bin. The velocity width of each of these spectra is then measured, producing a velocity-dispersion-correction map. www.nature.com/nature 5

RESEARCH SUPPLEMENTARY INFORMATION This correction map is then subtracted from the raw observations in quadrature, and the velocity dispersion recomputed using the same method as before. Measurements of σ m corrected in this way show that beam smearing is less than a 10% effect on the σ m measurements that have not been corrected in this way. We also note that the mean value of the beam smearing correction is 4.1 km/s and 4.5 km/s for the low and high velocity dispersion groups, showing that this is not a significant effect compared to the large trend of velocity dispersion with star-formation rate. Based on this result, we estimate the systematic error in σ m to be 5 10%. A comparison of the beam-smearing-corrected and uncorrected measures of σ m is presented in Supplementary Figure 2. Furthermore, in Supplementary Figure 3, Figure 2 of the letter is reproduced for three different measurements of the local velocity dispersion, and including the effect of a z 2.2 surfacebrightness limit on our own data. Panel d shows more scatter primarily because of the increased scatter in the measure of the total luminosity introduced by the surface brightness limit, particularly for fainter objects. As none of these alternative methods of measuring sigma change our results significantly, we have chosen to use the simple (uncorrected) definition of σ m in this letter. 6 WWW.NATURE.COM/NATURE

SUPPLEMENTARY INFORMATION RESEARCH Supplementary Figure 1 Distribution of SDSS galaxies and selected objects. This shows the number density of all star-forming galaxies in SDSS as a function of redshift and Hα luminosity. Our selection windows are shaded. Galaxies were randomly selected inside each distinct bin in flux and redshift so as to sample the whole range of luminosities in the underlying distribution. The randomly-selected galaxies are marked with the coloured points. www.nature.com/nature 7

RESEARCH SUPPLEMENTARY INFORMATION 90 80 70 sm,corr HkmêsL 60 50 40 30 20 30 40 50 60 70 80 90 s m HkmêsL Supplementary Figure 2 Effect of beam smearing on σ m. Here we plot the results of modelling the effect of beam smearing on our measure of velocity dispersion and removing it. The x-axis shows the velocity dispersion as measured using the method outlined in the letter. The y-axis shows the velocity dispersion corrected for beam smearing due to the underlying velocity field. The black line shows the one-to-one relation, and the dashed line shows a fit to the data with a slope of 0.93. Note that the largest outliers are in the low-dispersion regime, where any unresolved velocity shear is likely to be a larger fraction of the dispersion. Correcting for this effect would only further highlight the trend in Figure 2. 8 WWW.NATURE.COM/NATURE

SUPPLEMENTARY INFORMATION RESEARCH a b 80 s HkmêsL 60 40 20 80 40.5 41.0 41.5 42.0 42.5 c 40.5 41.0 41.5 42.0 42.5 d s HkmêsL 60 40 20 40.5 41.0 41.5 42.0 42.5 L Ha Hlog ergêsl 40.5 41.0 41.5 42.0 42.5 L Ha Hlog ergêsl Supplementary Figure 3 Hα luminosity against various measures of velocity dispersion. Panel (a) shows our data on the same L Hα σ m plot presented in Figure 2 for comparison. Panel (b) includes the correction for beam smearing described in the Supplementary Information. Panel (c) shows the simple mean sigma, σ = pix σ pix /N pix, also corrected for beam smearing. Panel (d) shows the result of applying a z 2.2 surface brightness limit to our data, and rerunning the same analysis as presented in Figure 2. All four panels are plotted on the same scale. The correlation between Hα luminosity and dispersion remains in all cases. www.nature.com/nature 9

RESEARCH SUPPLEMENTARY INFORMATION Supplementary References 30. Epinat, B. et al. GHASP: an Hα kinematic survey of spiral and irregular galaxies - VI. New Hα data cubes for 108 galaxies. Mon. Not. R. Astron. Soc. 388, 500 550 (2008). 31. Swaters, R. A., van Albada, T. S., van der Hulst, J. M. & Sancisi, R. The Westerbork HI survey of spiral and irregular galaxies. I. HI imaging of late-type dwarf galaxies. Astron. Astrophys. 390, 829 861 (2002). 32. Steidel, C. C. et al. A Survey of Star-forming Galaxies in the 1.4< Z< 2.5 Redshift Desert: Overview. Astrophys. J. 604, 534 550 (2004). 33. Adelberger, K. L. et al. Optical Selection of Star-forming Galaxies at Redshifts 1 < z < 3. Astrophys. J. 607, 226 240 (2004). 34. Cresci, G. et al. The SINS Survey: Modeling the Dynamics of z 2 Galaxies and the High-z Tully-Fisher Relation. Astrophys. J. 697, 115 132 (2009). 35. Genzel, R. et al. From Rings to Bulges: Evidence for Rapid Secular Galaxy Evolution at z 2 from Integral Field Spectroscopy in the SINS Survey. Astrophys. J. 687, 59 77 (2008). 36. Basu-Zych, A. R. et al. An OSIRIS Study of the Gas Kinematics in a Sample of UV-Selected Galaxies: Evidence of Hot and Bothered Starbursts in the Local Universe. Astrophys. J. L.J 699, L118 L124 (2009). 37. Monreal-Ibero, A. et al. VLT-VIMOS integral field spectroscopy of luminous and ultraluminous infrared galaxies II. Evidence for shock ionization caused by tidal forces in the extranuclear regions of interacting and merging LIRGs. ArXiv e-prints 1004.3933 (2010). 38. Puech, M., Hammer, F., Lehnert, M. D. & Flores, H. 3D spectroscopy with VLT/GIRAFFE. IV. Angular momentum and dynamical support of intermediate redshift galaxies. Astron. Astrophys. 466, 83 92 (2007). 39. Tremonti, C. A. et al. The Origin of the Mass-Metallicity Relation: Insights from 53,000 Star-forming Galaxies in the Sloan Digital Sky Survey. Astrophys. J. 613, 898 913 (2004). 10 WWW.NATURE.COM/NATURE