COSMOS-DASH: The Evolution of the Galaxy Size–Mass Relation since z ∼ 3 from New Wide-field WFC3 Imaging Combined with CANDELS/3D-HST

DASH is a new technique for efficient large-area observations using the near-IR channel of WFC3 on the HST (Momcheva et al. 2017). In standard HST observations guide stars are acquired for each new pointing. Acquiring a guide star takes approximately 10 minutes, which means that short exposures are only possible with very large overheads and the total number of pointings that can be obtained within an orbit’s visibility window is small.¹⁴ This limitation can be circumvented by acquiring guide stars for only the first pointing and guiding with the three HST gyros for the rest of the pointings. This makes it possible to observe up to eight WFC3 pointings in a single orbit, greatly increasing HST’s large-scale mapping capabilities.

During a standard guided exposure, the three HST gyros receive continuous corrections from the Fine Guidance Sensors (FGS). Turning off guiding stops the stream of corrections from the FGS, and the telescope begins to drift with an expected rate of 0001–0002 s^–1. In CCDs this would lead to detrimental smearing of the image in a typical 5-minute exposure. However, the WFC3/IR detector can perform multiple nondestructive, zero-overhead reads throughout the exposure. By setting the time between reads to 25 s or less, the drift in between reads is ≤005—less than half a pixel (pixel scale = 0129). The data obtained in between the reads can be treated as independent 25 s exposures, which can be drizzled to restore the full resolution of WFC3. In Momcheva et al. (2017) we demonstrated that the resolution of the WFC3 camera is preserved in this process and that structural parameters of the galaxies are consistent with those measured in guided observations.

The DASH method was used in the Cycle 23 COSMOS-DASH program (Program ID: GO-14114) to obtain 456 WFC3 H₁₆₀ pointings in 57 orbits, covering an area of 0.49 deg² in the COSMOS field. The data were obtained between 2016 November and 2017 June. The data were reduced by constructing 11 or 12 individual 25 s exposures from the differences between subsequent reads within each science exposure. The full set of ∼5000 exposures, together with all other existing H₁₆₀ data in the COSMOS field, was then drizzled into a single, large mosaic. The details of the reduction procedure are described in Momcheva et al. (2017) and in Appendix A.1.

The final mosaic of the COSMOS-DASH image is 50,000 × 50,000 pixels (with 01 pixel⁻¹), centered at R.A. = 10:00:28.6, decl. = +02:12:21.0. It is shown in Figure 1 and is available from the COSMOS-DASH website.¹⁵ The total area of the H₁₆₀ imaging is 0.66 deg², with COSMOS-DASH contributing 0.49 deg² and the remaining archival data taken in a variety of programs (list given in Table 4). This roughly triples the area of extragalactic blank survey fields that have been imaged in the near-IR with HST. We note that of these additional programs, our mosaic subsumes the data from GO-12990 (PI: Muzzin), which obtained targeted imaging of 12 galaxies with log M_* > 11.6 at 1.5 < z < 3.0 in COSMOS with ∼1000 s integration time.

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We use the UitraVISTA catalog of Muzzin et al. (2013) for our sample selection in the COSMOS field. Objects are selected from UltraVISTA K_s-band imaging that reaches a depth of AB at 90% completeness. The catalog contains point-spread function (PSF) matched photometry in 30 photometric bands covering the wavelength range 0.1–24 μm and includes the available Galaxy Evolution Explorer, CFHT/Subaru, UltraVISTA, and S-COSMOS data set. Each galaxy in the catalog has a photometric redshift determined by fitting the photometry in the 0.1–8.0 μm bands to template spectral energy distribution (SEDs) using the EAZY code (Brammer et al. 2008). EAZY also provides rest-frame U, V, and J colors, which we used to separate the star-forming and quiescent galaxies. We note that Muzzin et al. (2013) used the default EAZY template set and did not include the “old and dusty” template used in Skelton et al. (2014). This template was designed to extend the red boundary in the UVJ color–color space (see Figure 5). Without spectroscopic redshifts for the reddest galaxies at the highest redshifts, it is difficult to determine which template set provides the most accurate description of the galaxy population. Stellar masses for all galaxies in the catalog were determined by fitting the SEDs of galaxies to stellar population synthesis models using the FAST code (Kriek et al. 2009) using Bruzual & Charlot (2003) templates with solar metallicity, a wide range in age, an exponentially declining star formation history, a Chabrier (2003) initial mass function, and a Calzetti et al. (2000) dust extinction function. Details of the catalog can be found in Muzzin et al. (2013).

Although this catalog is based on an early release of the near-IR data in this field (UltraVISTA-DR1), it is easily deep enough for the relatively bright galaxies analyzed in this paper. In Appendix B.1 we describe two corrections that are applied to the masses. We first correct them for flux that is missing in the catalog aperture, using the GALFIT total magnitudes. Next, we determine whether any systematic offsets need to be applied. We show that the stellar masses (and photometric redshifts) are in very good agreement with the recent COSMOS2015 catalog (based on DR2; Laigle et al. 2016). However, the masses are 0.1 dex lower than those in van der Wel et al. (2014), for the same galaxies. The same offset is obtained when matching the number density of galaxies with masses M_* > 10¹¹ M_⊙ in the two catalogs. As discussed in Section B.1, we apply a 0.1 dex offset to all the masses, for consistency with van der Wel et al. (2014).

In this paper we study the most massive galaxies at 0.1 ≤ z_phot ≤ 3.0 with . The existing 3D-HST/CANDELS samples are sufficiently large for determining the size–mass relation below this limit (van der Wel et al. 2014); furthermore, at lower masses the COSMOS-DASH imaging is too shallow for accurate measurements of structural parameters at the highest redshifts. Figure 3 shows all galaxies in UltraVISTA in the plane of mass versus redshift, before the corrections are applied. Our sample is well above the completeness limits of the catalog, even at z = 3. We find 918 galaxies in the catalog with , of which 749 galaxies are at 0.1 < z < 1.5 and 169 galaxies are at 1.5 < z < 3.0. Figure 6 shows the images (H₁₆₀ + I₈₁₄) of a few example galaxies, in six bins of redshifts, while Figure 7 shows their corresponding SEDs.

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The 0.66 deg² COSMOS-DASH mosaic does not cover the entire UltraVISTA area. Furthermore, at z ∼ 2 the H₁₆₀ filter samples the rest-frame V band, but at z ∼ 1 it samples the rest-frame I band. Because of these considerations, we use the COSMOS-DASH data only in the redshift range 1.5 < z < 3.0. For galaxies at 0.1 < z < 1.5 we use the HST ACS I₈₁₄ observations of the COSMOS field (Koekemoer et al. 2007). The ACS mosaic spans 1.66 deg² and covers the entire UltraVISTA area. By combining the ACS and WFC3 imaging, we ensure that the volumes at z ∼ 1 and z ∼ 2 are roughly matched and that we measure sizes at approximately the same rest-frame wavelengths. As discussed in Appendix B.2, we correct for residual wavelength-dependent effects using previously measured color gradients of galaxies.

We obtained the reduced ACS v2.0 mosaic from the NASA/IPAC Infrared Science Research Archive.¹⁶ The image mosaic software Montage v5.0¹⁷ was used to create square cutouts of centered on the galaxies. We visually inspected all galaxies that are covered by the images and remove those that are on an edge. A total of 203 galaxies at 1.5 < z < 3.0 are covered by the 0.66 deg² COSMOS-DASH mosaic (308 galaxies deg⁻²), while 788 galaxies at 0.1 < z < 1.5 are covered by the 1.64 deg² ACS-COSMOS (493 galaxies deg⁻²). These 991 galaxies at 0.1 < z < 3.0 form our sample for the structural study.

As part of the analysis we split the sample into star-forming and quiescent subpopulations of galaxies. Observationally, for intermediate to massive galaxies, the sizes at a fixed stellar mass and redshift are dependent on their colors, with the bluer galaxies being larger than redder galaxies. We want to test whether this relation holds at the highest masses and redshifts.

We use the rest-frame U − V and V − J color space to separate galaxies into star-forming (SF) and quiescent (Q) candidates. Galaxies occupy distinct regions in the U − V versus V − J plane depending on their specific star formation rate and dust content, as demonstrated by Labbé et al. (2003) and Whitaker et al. (2012). Young galaxies with high star formation rates that are red owing to high dust content occupy a different region in the UVJ diagram than old quenched galaxies. In this paper we use a redshift-dependent separation line in the UVJ diagram to identify our SF and Q galaxy candidates (Muzzin et al. 2013). Quiescent galaxies are defined as

This separation was originally defined by Williams et al. (2009) to maximize the difference in specific star formation rates between the two distinct subpopulations on the UVJ diagram. The separation was adjusted by Muzzin et al. (2013) to fit the UVISTA sample since the rest-frame color distribution is different from the Williams et al. (2009) sample, presumably due to small differences in photometric methods. The distribution of our sample of galaxies in the U − V versus V − J plane is shown in Figure 5. At low redshift, the galaxy samples separate into distinct subpopulations in the UVJ parameter space. However, at high redshift the galaxies tend to move closer to the separation line. This may indicate that there are more transition galaxies at z ∼ 2 than at other epochs.

There are more galaxies at 0.1 < z < 1.5 than at 1.5 < z < 3.0, both because the area of ACS-COSMOS is 2.5 times larger than the area of the COSMOS-DASH mosaic and because the density of massive galaxies per square degree in the low redshift bin is more than double that in the higher-redshift bin. This is demonstrated in Figure 4, which shows the number of galaxies per square degree in six redshift bins. The higher number of more massive galaxies at low redshift is expected from the evolution of stellar mass function of galaxies.

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Figure 4 also shows the number of SF and Q galaxies per degree² at 0.1 < z < 3.0. At z < 0.5 less than 10% of the total galaxies are SF, whereas at 2.5 < z < 3.0 more than 85% of the galaxies are SF (see also Marchesini et al. 2014). We will return to this in Section 7.2. In all the plots in this paper, “all” galaxies are represented by gray squares and solid lines, “quiescent” galaxies are presented by red circles and dashed lines, and “star-forming” galaxies are represented by blue circles and dotted lines, unless stated otherwise.

The galaxy images are prepared for fitting in the following way. First, image cutouts are created from the mosaic that is appropriate for its redshift (ACS for z < 1.5, WFC3 for z > 1.5). The size of the square cutout is determined in two stages. In stage 1, for each individual galaxy the image mosaic software Montage v5.0 is used to create square cutouts of sides 18″, centered on the galaxy. We use SExtractor (Bertin & Arnouts 1996) v2.19.5 to identify all sources in the cutouts. SExtractor is run on the individual cutouts with a fixed detection threshold of 1.5 times the standard deviation above the background rms level, 32 deblending subthresholds, and a minimum contrast parameter of 0.005. The size of the central object of interest is determined from the Kron radius measured by SExtractor. In stage 2, square cutouts are created with sides of length equal to 7 times the semimajor axis Kron radius (7 × A_IMAGE × KRON_RADIUS, as expressed in SExtractor outputs).

SExtractor is run again on the individual final cutouts with the same setup as described above. We use the SExtractor segmentation map to create a mask that contains all detected objects except the galaxy of interest. Noise maps are made for individual galaxies with the same size as the final cutouts, assuming that the sky background is the dominant noise component.

Detailed knowledge of the image PSF is required for robust modeling of the galaxy morphologies with GALFIT. Many previous studies derive an empirical PSF for a given image mosaic taken from an average of observed images of isolated stars (e.g., van der Wel et al. 2014). The COSMOS-DASH mosaic used here is generated from both the shallow DASH exposures themselves and deeper archival observations taken under the more standard “guided and dithered” observation strategy. To account for the heterogeneous depth and dither/guiding properties of the COSMOS-DASH mosaic, we adopt a new method for generating PSF models by using the WFC3/IR empirical PSF library from Anderson et al. (2015). The WFC3/IR empirical PSFs are provided for all broadband filters and with the spatial variation across the detector sampled on a 3 × 3 grid. Four subpixel center positions are provided at each of these grid points. For each galaxy we wish to model, we first insert the appropriate empirical PSF model at the exact object location in the detector frame of each individual exposure in which that object is found. Then, we drizzle these models to the same pixel grid as the final mosaic using identical parameters (i.e., the relative image weights and pixel scale parameters). In this way, the final model PSFs of each object¹⁸ fully account for the effects of instrument orientation, pixel resampling, and image weighting that together determine the PSF in the science mosaics.

The image cutouts, along with the noise map, the appropriate PSF model, and mask, are provided to GALFIT, which is used to find the best-fitting Sérsic model for each object. The fit parameters are total magnitude (M), half-light radius (r_eff) measured along the semimajor axis, Sèrsic index (n), axis ratio (b/a), position angle (PA), central position (x₀, y₀), and an additive constant (sky). Initial guesses for these parameters are taken from the SExtractor detection catalog that was used to create the masks. A constraints file is constructed so that GALFIT is forced to keep the Sérsic index between 0.2 and 8, the effective radius between 003 and 40″ (0.3 and 400 pixels for COSMOS-DASH, 01 and 1200 pixels for ACS-COSMOS), the axis ratio between 0.0001 and 1, and the magnitude between −3 and +3 mag from the input value (the SExtractor magnitude). We use a wrapper to create the GALFIT feedfiles and to run GALFIT on individual galaxy stamps. Neighboring objects in each image cutout are fit simultaneously or masked out, depending on their proximity and brightness compared to the main object: galaxies are fit simultaneously if they are less than 4 mag fainter and if they are within 1″ from the main target (see Section 4.4 for fitting close pairs of objects).

A number of galaxies that are cataloged as a single object in the UVISTA catalog are split into pairs in the COSMOS-DASH image. Out of the 203 galaxies in our sample at z > 1.5, 18 split into pairs (see examples in Figure 2). For each of the pairs, we fit the two objects simultaneously with GALFIT using the same constraints as those described above. We then estimate the mass of each of the components of the pair by dividing the total mass into two parts weighed by the flux of the components in the H₁₆₀ filter:

where M_⋆,tot is the total stellar mass of the galaxy given in the UVISTA catalog and F_i and F_j are the total model fluxes of the two components from GALFIT. If , then the object is kept in the sample (with the same UVISTA ID number), or else it is rejected from the sample. However, there are no pairs where both the components are above the mass cut. A total 14 out of the 18 have one component above the mass cut and remain in the sample with their revised mass.

After each individual object is fit by the GALFIT wrapper, the χ² value of the fit and the effective radius of the model are checked to ensure that the fits are reasonable. Any fits with χ² > 1.2 or r_eff > 40 kpc are rejected and refit by tweaking the initial conditions. Most of these “failed” fits occur for objects with nearby bright stars, overlapping background/foreground objects or objects that are close to the edge of the mosaic with low signal-to-noise ratio. In those cases the initial GALFIT estimates (based on the SExtractor analysis) may be (too) far from the true values. If a reasonable fit is obtained by changing the initial conditions or by altering the mask, the galaxy is kept in the sample. Otherwise, the galaxy is rejected from our sample.

In the second stage, all objects with n = 0.2 or n = 8, i.e., the boundary conditions given on the GALFIT constraint file, are visually inspected. A third of the galaxies at 0.1 < z < 1.5 from ACS-COSMOS imaging and a quarter of the galaxies at 1.5 < z < 3.0 from COSMOS-DASH imaging required visual inspection. Most of the n = 8 objects are found to have a bright central pixel, in some cases probably due to the presence of an active nucleus. We first refit the objects following the procedure described above. If this does not resolve the problem, the galaxy is refit by fixing the Sèrsic index to the Sèrsic index determined by SExtractor. Even though SExtractor does not incorporate the PSF in its fit and the Sèrsic indices should not be reliable, in practice they correlate quite well with the GALFIT-determined ones with no obvious systematic offset. A total of 23% of the galaxies at 0.1 < z < 1.5 and 17% of the galaxies at 1.5 < z < 1.5 are refit with fixed n. This changes the measured effective radius, with between 1.2 and 4.

In the third stage, each of the individual galaxies, their Sèrsic models, and the subtracted background images produced by GALFIT are visually inspected. Any “obviously” unreasonable fit is manually refit as above. We rejected 14 galaxies because they are almost invisible in the DASH image. A total of 918 galaxies passed this final quality control step and formed the sample for our size–mass analysis. In the remainder of the paper we are describing the results for these galaxies only. The fraction of rejected objects is similar to that in previous studies.

As explained above and in Section B.1, the stellar masses are corrected so that they are self-consistent with the best-fit Sèrsic model and consistent with the mass estimates from van der Wel et al. (2014) sample. The sizes are corrected for color gradients, following the procedure of van der Wel et al. (2014); details are given in Appendix B.2. The final sample is selected such that . We find a total of 918 galaxies at 0.1 < z < 3.b0, of which 749 are measured from the ACS-COSMOS image (z < 1.5) and 169 are measured from the COSMOS-DASH image (z > 1.5). Figure 8 shows the distribution of stellar mass and structural parameters of our sample galaxies.

We also include the galaxies with from the CANDELS field measured by van der Wel et al. (2014) that are not in our study. Hence, the total number of massive galaxies used in the size–mass analysis are 1090, where 813 are quiescent and 277 are star-forming. All our data products are available at our MAST website https://archive.stsci.edu/prepds/cosmos-dash MAST.

In order to estimate the uncertainty in the measured size of an individual galaxy, we place the best-fitting Sèrsic models in empty regions of our image mosaics and refit them with GALFIT using the exact same procedures as described above. For each galaxy we create 100 realizations, using randomly chosen regions in the image mosaics. The uncertainties in r_e are then taken as the 16th and 84th values in the ordered list of 100 effective radii. This procedure ensures that the exact noise properties of the mosaics are taken into account. Uncertainties range between 0.01 and 0.25 dex, and the typical uncertainty is 0.1 dex.

We first examine the distribution of stellar mass within our mass-limited sample. The median stellar mass of all galaxies with at z ∼ 0.25 is . At this epoch quiescent and star-forming galaxies have a similar median stellar mass. At z ∼ 2.75, the median stellar mass of all galaxies is log(M_⋆/M_⊙) = 11.45 ± 0.03. The star-forming galaxies have a similar median stellar mass to the full sample, as they make up the bulk of the population at this epoch.

Next, we use the biweight estimator for the location and scale of a distribution to calculate the median size and its scatter, as this estimator gives higher weights to the center of distribution and is insensitive to outliers.

Figure 10 shows the evolution of the median size of galaxies in 0.1 < z < 3.0. The median sizes of all galaxies and of the two subpopulations have increased from z ∼ 3 to z ∼ 0.1. The median size of all galaxies at 2.5 < z <3.0 was 4.4 ± 0.3 kpc, which has increased to 9.8 ± 0.1 kpc at 0.1 < z < 0.5. The median size of quiescent galaxies at 2.5 < z < 3.0 was 4.9 ± 0.9 kpc, which has increased to 9.3 ± 0.1 kpc at 0.1 < z < 0.5. The median size of star-forming galaxies at 2.5 < z < 3.0 was 4.3 ± 0.3 kpc, which has increased rapidly to 15.2 ± 2.1 kpc at 0.1 < z < 0.5. Note that the median size of all galaxies changes more slowly with redshift than that of either of the subpopulations; this reflects the fact that the fraction of quiescent galaxies increases from 13% at 2.5 < z < 3.0 to 90% at 0.1 < z < 0.5. This is discussed in more detail in Section 7.2. We determine the significance of the difference in the sizes of quiescent and star-forming galaxies with the two-sided Mann–Whitney test. The probability that the quiescent and star-forming galaxies are drawn from the same sample at 0.1 < z <0.5 is less than 5 × 10⁻⁵. This probability rises to more than 40% at 2.5 < z < 3.0, and we conclude that the sizes of the most massive star-forming and quiescent galaxies are not significantly different at 2.5 < z < 3.0. However, due to the small sample of Q galaxies at z > 2.5, we cannot rule out that a small size difference emerges when more data are available.

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We also present the measurement of the observed scatter in the sizes for all massive galaxies and the subsamples of quiescent and star-forming galaxies. We find no strong evolution in the observed scatter for the full sample or either of the subpopulations. The scatters range between 0.2 and 0.3 dex, in good agreement with the values found by previous studies (see van der Wel et al. 2014). Table 1 provides the median size and scatter of galaxies in 0.1 < z < 3 for all, quiescent and star-forming most massive galaxies.

We parameterize the evolution of the median size of the galaxies as

The gray, red, and blue lines in Figure 10 represent the evolution of the median sizes of all galaxies, the quiescent galaxies, and the star-forming galaxies, respectively. We find β = 0.95 ± 0.05 for the full sample. For the star-forming galaxies β_z = 1.40 ± 0.07, and for quiescent galaxies we find β = 1.09 ± 0.15. The difference in size evolution of the star-forming and the quiescent galaxies is only marginally significant. This is consistent with the results of Faisst et al. (2017), who found a similar evolution for ultramassive star-forming and quiescent galaxies at 0.5 < z < 2.5 (although they found a slightly faster evolution of 1.21 ± 0.20 for the quiescent population). This behavior is qualitatively different from the evolution of lower-mass galaxies, where quiescent galaxies show a more rapid size evolution than star-forming galaxies. Specifically, van der Wel et al. (2014) find that galaxies with have β_z = 1.24 ± 0.08 and 0.72 ± 0.09 for quiescent and star-forming galaxies, respectively.

We fit the size–mass relation of the combined sample of the most massive galaxies of this study and the van der Wel et al. (2014) sample. Following Shen et al. (2003), we assume a lognormal distribution N(log(r_eff), ), where log(r_eff) is the mean and is the dispersion. Similar to van der Wel et al. (2014), r_eff is taken to be a function of galaxy mass such that

where . The basic characteristics of the galaxy size distribution are given by the slope α, intercept A, and intrinsic scatter of size as a function of mass. Following van der Wel et al. (2014), we fit all star-forming galaxies with M_⋆ > 3 × 10⁹ M_⊙, and for the quiescent sample we fit galaxies with M_⋆ > 2 × 10¹⁰ M_⊙, in the redshift range 0.1 < z < 3.0. This stellar mass limit is derived from the integrated magnitude limit, as GALFIT is able to reasonably estimate effective radius for galaxies with m < 24.0 and Sèrsic index for galaxies with m < 23.

The analytic fits to the size–mass distributions are shown in Figure 11. The lines in Figure 11 indicate the best-fit relations, while the evolutions of the individual parameters (intercept A and slope α) are shown in Figure 12. The best-fit parameters are also given in Table 2. These new analytic fits have been performed on the same data for stellar mass log(M_⋆/M_⊙) < 11.3 as of van der Wel et al. (2014) but on a three times larger data set for log(M_⋆/M_⊙)  > 11.3 at z > 1.5 and on a five times larger data set at z < 1.5. Our size–mass relation of star-forming galaxies agrees well with that found by van der Wel et al. (2014); in other words, the sizes of the most massive star-forming galaxies are similar to those expected from their relations. The slope of the size–mass relation of star-forming galaxies is ≈0.25, with the slope slightly decreasing with redshift. However, we find a shallower size–mass relation of quiescent galaxies than van der Wel et al. (2014); we find an approximate constant slope at all redshifts of 0.5–0.6, whereas van der Wel et al. (2014) found a slope of ≈0.75 (at all redshifts). We note that we have not taken the contamination between the star-forming and quiescent galaxies into account, as had been done by van der Wel et al. (2014), and this may be a contributor to the difference in slope.

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Finally, we fit the redshift evolution of the parameters of the best-fitting relations, to arrive at a complete description of the sizes of galaxies as a function of mass and redshift. For the full sample of galaxies the parameters evolve as log A = − 0.26 log(1 + z) + 0.60 and α = − 0.17 log(1 + z) + 0.16. For the star-forming galaxies we find log A = − 0.29 log(1 + z) + 0.91 and α = − 0.15 log(1 + z) + 0.31. For the quiescent galaxies we derive log A = − 0.54 log(1 + z) + 0.72 and α = 0.31 log(1 + z) + 0.44.

So far we have considered the relation between size and mass at fixed redshifts. In Figure 13 we show the complementary information, that is, the relation between size and redshift for particular masses. The median sizes are calculated from the combined sample of this study and van der Wel et al. (2014). The trends in this figure show the same behavior as discussed earlier in the paper. The slope of the evolution of the full sample does not change significantly with stellar mass. The evolution of quiescent galaxies is not strongly mass dependent and is more rapid than that of star-forming galaxies. The rate of evolution of star-forming galaxies increases with stellar mass, such that the redshift evolution of the most massive star-forming galaxies is very similar to that of the most massive quiescent galaxies. Table 3 provides the median sizes of all, quiescent and star-forming galaxies in 0.1 < z < 3.

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We present the first comprehensive measurements of the sizes of the most massive galaxies with M_⋆ > 2 × 10¹¹ M_⊙ within 0.1 < z < 3.0 measured at HST resolution. As shown in Figure 13, we confirm that the galaxies in this study are larger in size than the less massive galaxies (Shen et al. 2003; Carollo et al. 2013; van der Wel et al. 2014) at the same epoch. The bottom left panel of Figure 13 shows the ratio of median sizes of star-forming galaxies to that of quiescent galaxies. For intermediate-mass to massive galaxies, with stellar masses between 10⁹ and 10¹¹ M_⊙, quiescent galaxies are, on average, smaller than star-forming galaxies (Carollo et al. 2013; van der Wel et al. 2014). At z ∼ 2.25, for stellar mass of M_⊙ the median size of star-forming galaxies is 3.39 ± 0.08 kpc and the median size of quiescent galaxies is 1.20 ± 0.03 kpc, which is almost one-third of the size of the star-forming galaxies. However, for galaxies with stellar masses the two classes of galaxies are found to have similar sizes of kpc and kpc.

Our results are consistent with the measurements of van der Wel et al. (2014) in the same mass range, although their sample is smaller by a factor of 3–4. More precisely, they confirm the extrapolated size–mass relations of van der Wel et al. (2014), which were dominated by less massive galaxies. Our results are also in agreement with the ground-based measurements of Faisst et al. (2017) and Hill et al. (2017). Faisst et al. (2017) studied galaxies with , slightly more massive than galaxies in our sample. Within the uncertainties, the sizes of these galaxies are fully consistent with our median sizes.

Studies of the central galaxy density out to z = 3 (Cheung et al. 2012; Saracco et al. 2012; Barro et al. 2013, 2017) find that the innermost structure of galaxies correlates with the star formation rate. Quenching of galaxies (whether by AGN feedback or other mechanisms) is thought to become very efficient when the central density reaches a certain threshold (van Dokkum et al. 2015; Whitaker et al. 2015). As stellar density and velocity dispersion are closely related, observations therefore indicate that galaxies are statistically more likely to be quiescent once they have surpassed a threshold in either density or velocity dispersion. This has been studied in detail by Whitaker et al. (2015), who found an abrupt cessation of star formation when galaxies reach a threshold central stellar density.

We can use the information of the two-dimensional light profiles of the galaxies and their total stellar mass to infer the central stellar density of the galaxy, assuming spherical symmetry. We follow the prescription from Bezanson et al. (2009) and Whitaker et al. (2015) to calculate the central stellar density and central velocity dispersions of the galaxies. We perform an Abel transform to deproject the circularized, three-dimensional light profile using

with ρ the 3D luminosity density in a particular filter, , r_eff the circularized effective radius, n the Sèrsic index, and b_n the n-dependent normalization parameter of the Sèrsic profile. We note that this methodology may lead to errors for galaxies that are far from spherical symmetry, in particular for flat disks. The mass within r = 1 kpc is calculated by integrating the 3D luminosity profiles. Assuming that mass follows light and neglecting color gradients, we convert the central luminosity to central stellar mass using the corrected total stellar masses from the UVISTA catalog. The central density is calculated by numerically integrating the following equation:

The central velocity dispersion is calculated assuming (see, e.g., Franx et al. 2008; van Dokkum et al. 2015), where and G is the gravitational constant equal to kpc (km s⁻¹)². Figure 15 shows the central stellar densities of star-forming and quiescent galaxies in our sample. As can be seen, the central stellar densities of both populations of galaxies are lower at z = 0 than at z ∼ 3, but the central density of quiescent galaxies is always higher than that of star-forming galaxies: the equivalent velocity dispersion of star-forming galaxies decreased from 181 to 67 km s⁻¹, whereas that of quiescent galaxies decreased from 285 to 180 km s⁻¹ between z ∼ 2.63 and z ∼ 0.13. For comparison, we have plotted the threshold central velocity dispersion of 234 km s⁻¹ from van Dokkum et al. (2015) based on an analysis of compact star-forming galaxies at 1.5 < z < 3.0 with a median size of .

This difference in central density between star-forming and quiescent galaxies may seem surprising, given the fact that they have very similar sizes at fixed mass. However, the Sèrsic indices also enter the calculation of the central densities, and they are significantly different between the two samples: we find for quiescent galaxies at z ∼ 2.75 and for star-forming galaxies, as shown in Figure 14. The difference in central density between the two samples is driven by this difference in the profile shape.

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In Figure 15, the predicted redshift evolution of the quenching threshold for central galaxies from Voit et al. (2015) is shown as the black dotted line. They present a self-regulated feedback model linking a galaxy’s star formation history directly with the circular velocity of its potential well. They hypothesize that feedback leads to quenching when the halo mass reaches a critical value that allows supernovae and/or AGNs to push away the rest of the circumgalactic gas. The critical circular velocity is set to 300 km s⁻¹ at z = 2 here, resulting in a quenching threshold that tracks the upper envelope of the central density observed for the quiescent population.

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We show quenching threshold velocity dispersions from previous studies in Figure 15. As can be seen, the median central density of quenched galaxies is always above the threshold density, while that of star-forming galaxies is above the threshold density only at the highest redshifts. This analysis thus provides evidence that it is indeed the central density, rather than the average surface density within the effective radius (e.g., Franx et al. 2008; Maier et al. 2009), that determines whether a galaxy is star-forming or quenched.

We note here that quenching may not be a single event in the life of a galaxy; specifically, many of the massive star-forming galaxies at low redshift may be rejuvenated by fresh gas infall. These transitions change the fraction of quiescent and star-forming galaxies, with young quiescent galaxies being added to the sample (Figure 15, top panel; see also, e.g., van Dokkum & Franx 2001; Carollo et al. 2013).

Owing to the shifts during the exposures, the reduction of DASH data is more complex than that of guided exposures. Here we provide a summary of the reduction procedures; we also refer to Momcheva et al. (2017), where the reduction of a subset of the COSMOS-DASH data was first described.

Each DASH orbit consists of one guided and seven unguided exposures with offsets of roughly 2′ between each. Momcheva et al. (2017) describe the overall mosaic strategy and detailed commanding instructions for the DASH visits. For uniformity of the data reduction, we process both guided and unguided exposures using the same analysis pipeline as outlined below.

The raw WFC3/IR images were downloaded from the Mikulski Archive for Space Telescopes (MAST¹⁹ ) and processed into calibrated exposure ramps (“IMA” products) with the calwf3 pipeline after disabling the pipeline cosmic-ray identification step (CRCORR = False). The IMA files provide a measure of the total charge on the detector sampled every 25 s over the duration of the exposure (253 or 278 s for exposures with NSAMP = 12 and 13, respectively). To reduce the degradation of the image quality of a given exposure due to the telescope drifts, we take image differences up the ramp and generate NSAMP − 2 essentially independent calibrated exposures with drifts now integrated over 25 s rather than the full exposure duration.²⁰ The properties of these difference images are essentially identical to normal calibrated WFC3/IR “FLT” products, though with slightly different noise characteristics. Taking image differences increases the effective read noise by a factor of , and the the read noise of two adjacent image differences will be anticorrelated, as the measured (noisy) flux of a given read appears as negative in the first difference image and positive in the second. In the case of guided exposures with no drifts, the image differences are equivalent to taking the pixel values of the last read minus the first, with read noise from just those two reads. The differences do not cancel out for sequences with drifts, where the pixel indices of the difference images are effectively shifted when they are combined into the output mosaic.

DASH visits consisting of NSAMP − 2 difference image “exposures” of a single pointing are then processed in an identical way with guided archival visits consisting of N guided, dithered exposures. We first compute an internal alignment of the visit exposures using sources detected in the images (both stars and galaxies), which corrects the DASH drifts between samples and small pointing errors typical of the guided sequences. We generate a small mosaic of the visit exposures to detect fainter sources, and we align these mosaics to galaxies in the I_814W catalogs provided by the COSMOS collaboration (Koekemoer et al. 2007). Point sources are excluded from the catalog alignment, as stars can have significant proper motions between the COSMOS-ACS and DASH epochs. Since we do not identify cosmic rays in the DASH exposures at the pipeline level as with normal WFC3/IR exposures, we detect and mask the cosmic rays using the standard tools of the AstroDrizzle (Gonzaga 2012) package when creating the combined visit/pointing image (turning on cosmic-ray identification is useful even for the guided exposures to mask unflagged hot pixels and weaker cosmic rays missed by calwf3). We note that many sequences of eight pointings were broken up owing to South Atlantic Anomaly (SAA) passages. There was typically a large offset of 10″−15″ between the “before” and “after” exposures, due to the spacecraft drift during the SAA passage; nevertheless, no observable degredation of the PSF was found in these sequences. We conclude that in future DASH programs it will not be necessary to require avoidance of SAA passages.

Final mosaics consisting of all of the aligned DASH difference images and archival exposures in a given filter were produced with astrodrizzle. We weight the exposures in the final mosaic by their exposure time and drizzle to a pixel scale of 01 using a square kernel and pixfrac = 0.8. The final WFC3/IR mosaic (Figure 1) spans 9100 × 10,200 pixels, centered at R.A. = 10:00:25.4, decl. = +2:34:51.2. A list of the archival H_160W images that were included in the mosaic is provided in Table 4.

An example PSF is shown in Figure 16 at four contrast levels, to demonstrate the different levels of structure: the core of the PSF, the first Airy ring (∼0.5%), and the diffraction spikes (∼0.5%). The curves of growth, which show the fraction of light enclosed as a function of aperture size, for the DASH H₁₆₀ PSFs, normalized at 2″, are shown in the left panel of Figure 16. The PSFs are in agreement with each other and with the encircled energy as a function of aperture provided in the WFC3 handbook, also normalized to maximum radius of 2″. This demonstrates that the DASH technique does not induce a significant smoothing or other PSF degradation.

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The depth of the data is determined by the background noise, which is expected to scale with the size of the aperture that is used for photometry. To determine how the background noise scales with aperture size, we measure the distribution of counts in empty regions of increasing size within the noise-equalized H₁₆₀ image. For each aperture size we measure the flux in >2000 apertures placed at random positions across the DASH mosaic. We exclude apertures that overlap with sources in the detection segmentation map. Figure 17 shows the distribution of flux counts in empty apertures of 05, 07, 10, 12, 15, and 2″ diameter in the DASH H₁₆₀ image. Each histogram can be well described by a Gaussian, with the width increasing as aperture size increases. The increase in standard deviation with linear aperture size , where A is the area within the aperture, can be described as a power law. A power-law index of 1 would indicate that the noise is uncorrelated, while if the pixels within the aperture were perfectly correlated, the background noise would scale as N². The right-hand panel of Figure 17 shows the measured standard deviation as a function of aperture size in the DASH noise-equalized H₁₆₀ image. We fit a power law of the form

where σ₁ is the standard deviation of the background pixels fixed to a value of 1.5 here, α is the normalization, and 1 < β < 2 (Whitaker et al. 2012). The fitted parameters are shown in Figure 17. The power-law fit is shown by the solid line in the figure.

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The DASH technique should not affect the photometric calibration. Nevertheless, we performed an empirical check, making use of the fact that there is a (deliberate) overlap region between the COSMOS-DASH imaging and the CANDELS imaging in the COSMOS field (see Momcheva et al. 2017 and Figure 1). We measured the fluxes of stars between H₁₆₀ = 18 and H₁₆₀ = 24 in both data sets, adopting the default zero-point of 25.95 and using identical photometric apertures (of 07). The results are shown in Figure 18; we find that the zero-point is consistent to within 0.03 mag.

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With the PSF, noise, and zero-point in hand, we can calculate the photometric depth of the mosaic. In the right panel of Figure 18 we show the 5σ depth as a function of aperture size. In each aperture, we calculate the noise within the aperture, apply a multiplicative aperture correction based on the flux that falls outside that aperture for a point source, and multiply the resulting number by 5. For very small apertures the S/N is suppressed because of the large aperture corrections that need to be applied, and for very large apertures the S/N is suppressed because of the high noise within the aperture. The optimal aperture is 025, and the 5σ depth within that aperture is 25.1. This can be compared to the expected depth for guided exposures of the same exposure time, as determined by the Exposure Time Calculator. The expected depth is ≈25.3, which means that the DASH technique likely imposes a penalty of ≈20% in the flux. This may be because of correlated noise on small scales, due to the shifting of the exposures.

We apply two corrections to the stellar masses from the Muzzin et al. (2013) UltraVISTA catalog. The first correction is a constant offset to bring the masses onto the same system as van der Wel et al. (2014). The Muzzin et al. (2013) catalog is based on ground-based data, whereas the 3D-HST catalog used by van der Wel et al. (2014) is selected from HST WFC3 imaging; furthermore, the treatment of the sky background and other steps in the transformation from fluxes to masses can lead to systematic differences. We first ask whether the DR1-based masses of Muzzin et al. (2013) are consistent with the more recent COSMOS2015 catalog from Laigle et al. (2016). In the left panel of Figure 19 we show the difference in masses between matched massive galaxies. There is a significant offset; the median offset for galaxies with M_*(COSMOS2015) > 2 × 10¹¹ M_⊙ is 0.14 dex, such that our masses are smaller than those of COSMOS2015. In the right panel we show the difference between our masses and those of van der Wel et al. (2014). Van der Wel et al. (2014) use masses from the 3D-HST catalogs (Skelton et al. 2014) corrected to an infinite aperture using the GALFIT fits (see below). The objects shown in Figure 19 are objects in the CANDELS/3D-HST COSMOS field, which is inside the UltraVISTA area. There is evidence for a similar offset of ∼0.1 dex at low masses, but at higher masses the COSMOS2015 and van der Wel et al. (2014) masses appear to be consistent. Unfortunately, the number of overlapping objects is too small for a definitive result.

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We can derive the mass offset between the Muzzin et al. (2013) UltraVISTA catalog and the van der Wel et al. (2014) masses in a different way, making use of all five CANDELS fields. The mass function is very steep in this regime, which means that small differences in mass lead to large differences in the number density of galaxies above a particular mass limit. This means we can derive the mass offset by requiring that the number densities of galaxies with M_* > 2 × 10¹¹ M_⊙ in the two surveys are consistent with each other. The correction to the UltraVISTA masses that we derive this way is ∼0.1 dex, in good agreement with the directly measured offset between COSMOS2015 and our UltraVISTA masses. Hence, we applied a +0.1 dex to all stellar masses of galaxies with M_⋆ ≥ 10¹¹M_⊙ in the Muzzin et al. (2013) catalog. We stress that this correction is uncertain and that it does not necessarily imply that the 3D-HST/van der Wel et al. (2014) masses are “more correct” than the Muzzin et al. (2013) masses. We apply the correction to ensure that our data are on the same system as van der Wel et al. (2014), so we can meaningfully combine the samples for a joint analysis.

The second correction is from the effective aperture in the catalog to . This correction is based on the GALFIT fits to the galaxies and ensures that the sizes and masses are self-consistent. This correction is not important at high redshift but significant at low redshift, as these massive galaxies with large Sèrsic indices typically have a large fraction of their flux outside standard photometric apertures. We show this effect in Figure 20, for the I₈₁₄ photometry at 0.1 < z < 1.5 (left panel) and for the H₁₆₀ photometry at 1.5 < z < 3.0 (right panel). The difference between the catalog magnitudes in the corresponding band and the GALFIT total magnitudes is a strong function of the effective radius (in arcseconds), as expected. Red circles are the SExtractor “AUTO” magnitudes, and blue circles are “total” magnitudes that have been corrected for flux outside of the AUTO aperture. This flux correction is based on point sources and is insufficient to bring the measurements into agreement with the GALFIT magnitudes.

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We correct the masses for this effect in the following way. For each galaxy we convolve the best-fitting GALFIT model with the ground-based K-band PSF (which was used to determine the overall scaling of the SED in the UltraVISTA catalog) and measure the GALFIT model flux inside the AUTO aperture. We then apply the point-source-based aperture correction that is listed in the UltraVISTA catalog for the object and define the mass correction as the ratio between the total GALFIT flux and this aperture-corrected Kron aperture flux. This correction removes the trends seen in Figure 20.

Color gradients and color evolution affect the size measurements of galaxies, as has been found by previous studies (Szomoru et al. 2011; van der Wel et al. 2014). The mass-weighted sizes of galaxies are smaller than the luminosity-weighted sizes, and the sizes in blue bands are generally larger than the sizes in red bands. We follow van der Wel et al. (2014) and correct the size measurements to a common rest-frame wavelength of 5000 Å. This is achieved by measuring the sizes of galaxies in the I₈₁₄ band at 0.1 < z < 1.5 and in the H₁₆₀ band at 1.5 < z < 3.0 and then applying redshift-dependent corrections. The form of the correction is

where F denotes either I₈₁₄ (for galaxies at z ≤ 1.5) or H₁₆₀ (for galaxies at z > 1.5), and z_p is the “pivot redshift” for these respective filters (z_p = 0.6 for I₈₁₄ and z_p = 2.2 for H₁₆₀).

Again following van der Wel et al. (2014), the color gradient adopted for star-forming galaxies is

and for quiescent galaxies it is simply Δ log . These corrections are small, as shown in Figure 21.

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In order to test the effect of uncertainty in stellar mass on the fit to the size–mass distribution, we have generated a mock catalog of galaxies at z ∼ 0.4 with the size–mass relation from Table 2, but with varying degrees of scatter in stellar mass between 0 and 0.1 dex. Figure 22 shows the results of the simulation. The points represent the median sizes in bins of stellar mass, while the lines show the best fits of Equation (4) to quiescent (left), star-forming (middle), and all (right) galaxies. The scatter in stellar mass does have an effect on the size–mass relation of quiescent galaxies, particularly because of the small size of the sample. However, it has very little effect on the fits of star-forming and all galaxies, and the differences in slopes are within the error margin.

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We have measured more information for the sample of massive galaxies than just sizes and fluxes. Although these other parameters are not the main topic of the paper, we provide an overview in Figure 23 of the correlations between total magnitude, Sèrsic index, effective radius, axis ratio, and PA. The PA is largely a “control,” as no correlations are expected. We see several expected trends, e.g., quiescent galaxies are, on average, rounder than star-forming galaxies. It is interesting that the median apparent magnitude of quiescent galaxies is brighter than that of star-forming galaxies, contrary to what one might expect based on their mass-to-light ratios. However, this is simply a reflection of the fact that star-forming massive galaxies are only present in large numbers at high redshifts.

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It is difficult to deal with fits that do not converge as a result of reaching the maximum Sèrsic index that we used in GALFIT (n = 8 for the DASH imaging at z > 1.5 and n = 6 for the ACS imaging at z < 1.5). As discussed in the main text, we decided to fix the Sèrsic index of objects at z > 1.5 to that measured by SExtractor. In Figure 24 we show the correlation between the GALFIT-derived n and the SExtractor n, for objects at z > 1.5 fitted in the COSMOS-DASH image. There is an excellent correlation, and visual inspection confirmed that the fits obtained by fixing Sèrsic n to that of SExtractor give a better fit (smaller residual) than fixing it to 8. For low-redshift objects observed with ACS the correlation has a very large scatter, and we simply use a fixed n = 6 for objects that did not converge.

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In order to test whether the depth of the COSMOS-DASH image is sufficient for proper structural parameter measurement of faint galaxies, we measure structural parameters of objects in the overlap region from our mosaic and compare them to measurements of the same objects in the CANDELS field by van der Wel et al. (2014). A similar test was carried out in Momcheva et al. (2017, hereafter M17), and we refer to Section 4.4 and Figure 12 of that paper for detailed analysis. In M17 the test was reported for galaxies with H₁₆₀ mag brighter than 22 and shows remarkable agreement between the structural parameters.

Here we repeat the diagnostic test, measuring sizes of galaxies with H₁₆₀ mag brighter than 23.5 (similar to our sample). Figure 25 shows the results of the diagnostic test. As can be seen, there is good agreement between the axis ratio, total magnitude, Sèrsic index, and effective radius of the objects. There is a slight systematic offset between the sizes of the galaxies which correlates with the slight systematic offset between the Sèrsic indices, which is negligible for galaxies with low Sèrsic n and/or small sizes. The median size difference for all objects is 0.03 dex or <10%, with objects in COSMOS-DASH smaller than in CANDELS, and the scatter is 0.1 dex. Since the effect is small, we have made no attempt to correct for the sizes.

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