THE RADIAL DISTRIBUTION OF STAR FORMATION IN GALAXIES AT z ∼ 1 FROM THE 3D-HST SURVEY

Galaxy formation is a complex process involving starbursts, mergers, and strong gas flows (e.g., Hopkins et al. 2006; Brooks et al. 2009; Dekel et al. 2009). Furthermore, stellar migration and secular processes can change the structure of galaxies at late times (e.g., Roškar et al. 2008; Grand et al. 2012). Therefore, even if we could perfectly locate and age date every star in the Milky Way, we still could not say where and with what structural and kinematic properties those stars formed. The only way to establish where a galaxy's stars formed, and hence how it was assembled, is to map the star formation while those stars were forming.

Obtaining Hα and stellar continuum maps of z ⩾ 1 galaxies, with the ∼1 kpc resolution necessary to put constraints on the spatial distribution of star formation, is challenging and has so far only been possible using a combination of adaptive optics and integral field units on 8–10 m class telescopes. These studies paint a complex picture: they find that star-forming galaxies at z ∼ 2 are a mix of "puffy" and often clumpy rotating disks, mergers, and more compact dispersion-dominated objects (e.g., Genzel et al. 2008; Shapiro et al. 2008; Cresci et al. 2009; Förster Schreiber et al. 2009, 2011; Law et al. 2009; Jones et al. 2010; Mancini et al. 2011).

Some studies claim that there are trends in the structural properties of Hα as a function of redshift, implying that the way galaxies assemble their stars varies fundamentally as a function of cosmic time. In particular, Epinat et al. (2009) and Kassin et al. (2012) suggest that galaxies become cooler and more rotation-dominated with time, z ∼ 1–0 being the epoch of "disk settling." This is interesting because most of the stars in the disks of galaxies like the Milky Way were formed in this epoch.

It is now possible to obtain high spatial resolution (≲ 1 kpc) information on Hα emission at z ∼ 1 with a high Strehl ratio, owing to the near-IR slitless spectroscopic capabilities provided by the WFC3 camera on the Hubble Space Telescope (HST). In Nelson et al. (2012), we used data taken as part of the 3D-HST survey to build on previous ground-based studies by mapping the Hα and stellar continuum with high resolution for a sample of 57 galaxies at z ∼ 1 and showed that star formation broadly follows the rest-frame optical light, but is slightly more extended. Here we stack the Hα maps of these galaxies to construct high signal-to-noise ratio (S/N) radial profiles and measure structural parameters of stellar continuum emission and star formation. These unique, high spatial resolution data from 3D-HST are combined with kinematics from the Near Infrared Spectrometer (NIRSPEC) on the W. M. Keck telescope (McLean et al. 1998). We assume H₀ = 70 km s⁻¹ Mpc⁻¹, Ω_M = 0.3, and Ω_Λ = 0.7.

The 3D-HST survey, a 248-orbit Treasury program on the HST, supplies the two-dimensional emission line maps needed to measure the spatial distribution of star formation. The WFC3 G141 grism provides spatially resolved spectra of all sources in the field. The wavelength range of the G141 grism, 1.15 μm < λ < 1.65 μm, covers the Hα emission line for galaxies in the redshift range 0.7 < z < 1.5. The survey also provides broadband near-infrared imaging in the F140W filter, which samples the rest-frame R band for z ∼ 1. Using the same camera under the same conditions to map both Hα and continuum emission allows us to compare their distributions directly, a crucial advantage of this strategy. The maps have a spatial sampling of ∼0.5 kpc at z ∼ 1 (006 pixels). The data presented in this Letter are based on the ∼70 pointings, roughly half of the full data set, that were obtained prior to 2011 June (see Nelson et al. 2012). The survey, data reduction, and determination of derived quantities (e.g., redshifts and masses) are described in Brammer et al. (2012) and van Dokkum et al. (2011).

The 3D-HST grism spectra have high spatial resolution and low spectral resolution (R ∼ 130), meaning that emission line structure reflects almost exclusively spatial structure (morphology) in contrast to data with high spectral resolution where structure reflects velocity (rotation or dispersion). Emission line maps of galaxies are made by subtracting the continuum emission from the two-dimensional spectrum. The details of the procedure are described in Nelson et al. (2012), Lundgren et al. (2012), and K. B. Schmidt et al. (2013, submitted).

We selected galaxies with redshifts 0.8 < z < 1.3, total F140W AB magnitude <21.9, and rest-frame EW(Hα) >100 Å. We also limited the sample to galaxies with effectively no contaminating flux from the spectra of other nearby objects. The position of the sample in the 0.8 < z < 1.3 star formation rate (SFR)–stellar mass plane is shown in Figure 1. SFRs were derived from the IR + UV luminosities as described in Whitaker et al. (2012). The selected galaxies lie predominantly on the upper half of the "star-forming main sequence" (as shown in the histogram of Figure 1; e.g., Noeske et al. 2007; Daddi et al. 2007; Whitaker et al. 2012). These galaxies were selected in Hα not IR; while this selection may bias the sample, it may possibly also have the advantage that it adds less uncertainty to interpreting the spatial distribution of star formation due to dust extinction.

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3.1. Stacked Hα and Stellar Continuum Emission

We stack the high spatial resolution Hα maps from 3D-HST to create average Hα maps—increasing the S/N and providing for a reliable measurement of the structural properties of Hα to large radii for this sample at z ∼ 1. We divide the sample in three bins based on their Hα size¹⁰ in order to homogenize the sample and investigate trends with size.¹¹ The median stellar masses of the stacks are log (M_*) = 10.0, 10.2, 10.2. The galaxies are normalized by their F140W flux and centered according to their luminosity-weighted F140W image centers. We masked the [S ii] λλ6716, 6731 Å emission in the fit. At our spectral resolution, the FWHM of a line is ∼100 Å, meaning that Hα λ6563 Å and [N ii] λ6583 Å are unresolved but Hα and [S ii] are separated by ∼3 resolution elements. We rotated the images based on their GALFIT-derived F140W position angles to align them along their major axes, summed them, and divided the resulting stack by the summed masks. Finally, in order to correct for the effects of the point-spread function (PSF), the stacks were deconvolved by adding the GALFIT-derived PSF-deconvolved model to the residuals of the fit, a method developed in Szomoru et al. (2010).

Figures 2 and 3 show the stacked, PSF-corrected Hα emission. The S/N in the stacks is high, and the emission is clearly spatially extended. Furthermore, both the rest-frame R band and Hα maps are clearly elongated. We quantified the structural properties of the stacks with GALFIT (Peng et al. 2002) using empirical PSFs. For the continuum and Hα, we find weighted mean axis ratios of b/a(R) = 0.55 ± 0.07 and b/a(Hα) = 0.58 ± 0.09, respectively, consistent with expectations for randomly oriented disks with thickness c/a = 0.26, 0.33. This thickness could be attributed to disks being intrinsically thick at z ∼ 1, heterogeneous properties of the galaxies being stacked, the effect of bulges, and a selection biased toward face-on galaxies, or noise.

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3.2. Radial Profiles are Nearly Exponential

3.3. Effects of Dust

A major uncertainty in the interpretation of the radial Hα profile is the effect of differential dust extinction: if some parts of the galaxies are more obscured than others (see e.g., Wuyts et al. 2012), the derived radial profile of Hα would not reflect the radial profile of star formation. To assess the importance of this effect, we estimate the extinction as a function of radius. We determine the extinction from the radial color profile.

The color profile is determined from the combination of the F140W stacks with ACS F814W stacks, which can be converted into rest-frame U − V color profiles. As shown in the left panel of Figure 4, for most of the radial extent of the stacks the color is fairly constant, but it becomes redder inside a radius of 2 kpc (see also Szomoru et al. 2012). To estimate roughly how color translates into missed star formation, we assume that the star formation that is not captured by Hα will be captured by the IR (Kennicutt et al. 2009). Using photometry from R. E. Skelton et al. (2013, in preparation), in addition to rest-frame U − V colors and IR-based SFRs from the NEWFIRM Medium Band Survey (Whitaker et al. 2012), empirical relations were derived for the translation of rest-frame U − V colors into star formation corrections:

$$\begin{equation} \log (\hbox{SFR(IR+H}\alpha))-\log (\hbox{SFR(H}\alpha)) \sim 0.3\times (U-V). \end{equation} \tag{ 1 }$$

The dust-corrected radial profiles are shown in the right panel of Figure 4. The smallest galaxies appear to have star formation that is marginally steeper than exponential. The large galaxies have the largest radial gradients but their implied star formation is still less steep than exponential. Although this analysis assigns the entire observed color gradient to extinction, the centers of the radial color profiles could be red because of dust or age. Importantly, the Sérsic indices of the star formation in these stacks based on the implied dust correction remain close to one: n = 1.4, 1.1, 0.6 for each of the stacks, weighted mean = 1.0 ± 0.4. So, even when accounting for dust, the averaged star formation in these galaxies has a nearly exponential spatial distribution.

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The flattening of the stacks and the exponential Hα profiles suggest that the star formation occurs in rotating disks. To test this, we measured kinematics for a subset of this sample using NIRSPEC on the Keck II telescope on 2012 April 9–10. The sample comprises eight galaxies chosen from the small (1), middle (5), and large (2) stack, which have sizes, masses, Sérsic indices, SFRs, and axis ratios representative of the sample as a whole.

We used the low dispersion mode of NIRSPEC with 05 seeing and a slit width of 07, giving a spectral resolution of σ ∼ 80 km s⁻¹ in the J band (compared to ∼500 km s⁻¹ in the grism spectra). The slit was aligned along the major axis of each galaxy and observations were conducted in a series of four 900 s exposures, dithering along the slit. The data reduction followed standard procedures for long-slit spectroscopy (see, e.g., van Dokkum et al. 2004). We extracted kinematic information from the two-dimensional spectra by fitting a Gaussian to the Hα and [N ii] emission simultaneously at each spatial position along the slit. The median [N ii]/Hα is 0.3. Assuming the velocity shear in the two-dimensional spectra is due to rotation, we take the rotational velocity to be the velocity difference between the geometrical center of the galaxy and the maximum velocity. We correct the rotation velocities for inclination angle using the 3D-HST axis ratios. We calculate one-dimensional velocity dispersions by fitting a Gaussian to the Hα emission in the central row of each spectrum. We calculate the instrumental σ to be ∼80 km s⁻¹ by fitting a Gaussian to the sky lines. The intrinsic velocity dispersion is calculated by subtracting the instrumental dispersion from the measured dispersion in quadrature.

We find that all galaxies show velocity shear in their two-dimensional spectra, with derived rotation velocities of 90–235 km s⁻¹ uncorrected and 110–330 km s⁻¹ corrected for inclination.¹² Figure 5 shows the rotation curves for one example galaxy for each stack. These spectra are of the best quality but appear to be representative of the eight. The velocity profile of the smallest galaxy in Figure 3 does not show evidence for a turnover, which means the measured maximum velocity is a lower limit on the rotation velocity at large radii. We conclude that the kinematics are consistent with the disk interpretation of the structural properties of the Hα emission. Although different classification methods make it difficult to perform a quantitative comparison, our results are qualitatively consistent with the finding that a large fraction of star-forming galaxies at z ∼ 1 appear to be rotating. (e.g., Wisnioski et al. 2011; Epinat et al. 2012; Swinbank et al. 2012).

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The central result of this Letter is that the radial distribution of stacked Hα emission in z ∼ 1 galaxies is close to exponential out to ∼10 kpc. Combined with the axis ratios of the stacks and the kinematics of a subset of the sample, the most straightforward interpretation is that star formation seems typically to occur in disks at z ∼ 1 at least for galaxies with high EW(Hα). The factor of ∼10 increase in the SFRs of galaxies from z = 0 to z = 1 (e.g., Damen et al. 2009; Fumagalli et al. 2012) is apparently driven by increased star formation activity in disks rather than a much greater prevalence of merger-driven central starbursts—consistent with other studies (e.g., Rodighiero et al. 2011; Wuyts et al. 2011, 2012).

This result raises a number of questions. First, it is not clear how these galaxies are related to z ∼ 0 galaxies. An average galaxy in this sample has a distribution of stars with a Sérsic index of n = 1.4. If this average galaxy forms stars with n = 1.0, it will have a lower Sérsic index at later times. Either we are witnessing the build-up of only the latest of late-type galaxies (these galaxies substantially change where their star formation is occurring between z ∼ 1 and z ∼ 0) or their stars, once formed, must migrate into a different configuration. In other words, if these are the ancestors of typical z ∼ 0 spiral galaxies, their bulges need to be built in some way besides the star formation we are seeing. This could be accomplished by mergers or secular evolution (e.g., Bournaud et al. 2009; Ellison et al. 2011). These observations could be understood in the context of the following picture: at z > 1, disks are gas-rich and turbulent. As redshift decreases, the gas fraction decreases, and a bar instability grows, increasing the central concentration and central vertical velocity dispersion. (e.g., van den Bosch 2001; DeBuhr et al. 2012; Forbes et al. 2012).

We also note the somewhat surprising presence of a population of large, rapidly rotating disks with relatively low stellar masses at z ∼ 1. These galaxies have mean r_e(Hα) = 7.3 kpc, v = 240 km s⁻¹, σ = 89 km s⁻¹, and M_* = 2.2 × 10¹⁰ M_☉, meaning they are disks 8 Gyr ago, larger in size than the Milky Way (Drimmel & Spergel 2001), and thicker (Freeman 1987), with ∼1/3 of the stellar mass (McMillan 2011) and similar or higher maximum rotation velocities (Bovy et al. 2009). Both what these galaxies become in the local universe and how such extended star-forming disks were made in an epoch of high disk turbulence are open questions. The small disks on the other end of the size distribution are also of interest. With median r_e(Hα) = 1.9 kpc, r_e(R) = 2.1 kpc, M_* = 8.9 × 10⁹ M_☉, and stacked n(Hα) = 1.2, they more closely resemble compact versions of disky star formers than merger-driven star formation in spheroids (see also van der Wel et al. 2011).

There are several caveats. First, our sample is not complete in mass or in SFR(UV+IR). In future papers (using the full 3D-HST survey) we will study the distribution of star formation as a function of these parameters. Second, the distribution of star formation in the stacks is not necessarily representative of individual galaxies. In individual galaxies the star formation is clumpy (e.g., Genzel et al. 2008, 2011; Förster Schreiber et al. 2009; Nelson et al. 2012; Figure 1) and it is difficult to quantify the structure. Stacking these clumpy objects could be hazardous, but it may also provide more insight than can be gleaned from individual galaxies: assuming that the clumps are transient and "light up" a part of the underlying gas disk for a short time (as in, e.g., Wuyts et al. 2012), our stacking technique effectively produces a time-averaged map of the star formation in the galaxies. Finally, dust attenuation remains a key uncertainty, both in the selection and in the interpretation of the profiles. This can be addressed with maps of the IR emission at the full ALMA resolution, or by measuring (spatially resolved) Balmer decrements.

We thank the referee for a thorough report which improved the Letter. Support from grant HST GO-12177 is gratefully acknowledged.