Galaxy Zoo: Clump Scout: Surveying the Local Universe for Giant Star-forming Clumps

Galaxy Zoo: Clump Scout was a citizen science project that was active from 2019 September 19 to 2021 February 11 on the Zooniverse platform. ⁷ It presented volunteers with image cutouts of galaxies from the Sloan Digital Sky Survey (SDSS; York et al. 2000); for each galaxy image (referred to as a subject) the volunteer was asked to identify its central bulge, followed by all of its off-center clumps. The central bulge location was requested in order to discourage volunteers from marking the galaxy center as a clump, as well as to remove any identified "clumps" coinciding with galaxy center. To improve classification quality, new volunteers were presented with a classification tutorial; we also provided a field guide, as well as help pages for each task, which showcased many examples of quality clump annotations. In addition, the majority of volunteers ⁸ were shown a small sample of expert-classified "training" images when they began classifying (≲10 randomly interspersed throughout their first 20 classifications). After classifying a training image, the volunteer was given feedback on how the classification compared to that of the experts.

For the clump-marking task, volunteers were provided with a "normal clump marker" and an "unusual clump marker" (see Figure 1). The "unusual" marker was intended to identify foreground star contaminants, i.e., Milky Way stars that overlap with the angular area of the target galaxy. Like clumps, foreground stars appear as point sources in SDSS images, and their colors in the i, r, and g bands can be very similar to clumps; this makes them very difficult to distinguish from clumps by any simple rule. We therefore instructed volunteers to mark clumps as "unusual" if they were particularly bright, differently colored, or especially offset from their host galaxy. Examples of "unusual clumps" (which were generally foreground stars) were provided in the tutorial and field guide. A total of 11,089 distinct volunteers provided classifications while logged into the Zooniverse website, while volunteers who were not logged in undertook 10,200 distinct classification sessions. In total, we obtained 1,707,485 classifications on our galaxy sample.

Zoom In Zoom Out Reset image size

In this study, our goal was to identify as thorough a sample of clumpy galaxies in the local universe as possible, where we take "local" to refer to a region nearby enough that little to no cosmological evolution takes place (i.e., z ≲ 0.15). To select for potentially clumpy galaxies, we relied on data from the Galaxy Zoo 2 (GZ2) citizen science project, which provides morphological classifications for over 300,000 local galaxies from the SDSS legacy survey. GZ2 itself consists of roughly 25% of galaxies identified in the SDSS main galaxy sample and comprises "the nearest, brightest, and largest systems for which fine morphological features can be resolved and classified" (Willett et al. 2013). From 243,500 GZ2 galaxies with spectroscopic redshifts, we selected for galaxies with detectable features by requiring a weighted vote fraction ⁹ of >50% for the presence of "features or disk" (herein called f_featured). Major mergers were removed by requiring that the debiased vote fraction ¹⁰ for the presence of "merger" (herein called f_merger) was <50%. (For an overview of GZ2 vote fractions, see Willett et al. 2013.) Galaxies with z < 0.02 were removed to ensure that the vast majority of clumps could not be resolved and would appear as point sources; this was required so that realistic-looking simulated clumps could be added to these galaxies for comparison. Finally, we limited our sample to galaxies whose masses had been estimated by the SDSS DR7 MPA-JHU value-added catalog ¹¹ (Kauffmann et al. 2003; Brinchmann et al. 2004). We did not make any cuts on galaxy size, as GZ2 already selects its galaxies to be resolvable (petroR90_r > 3 arcsec, where petroR90_r is the radius containing 90% of galaxy flux in the Petrosian aperture in the r band). The resulting sample contained 53,613 galaxies.

In addition to this main sample, we included a sample of 4937 additional galaxies from GZ2 with 0.02 < z < 0.075 and for which the GZ2-weighted vote fraction for "features or disk" was ≤50%. The redshift limit of z < 0.075 was applied to include a larger proportion of low-mass galaxies in our sample, since SDSS is dominated by high-mass galaxies at higher redshifts. In total, 168,603 galaxies in the GZ2 spectroscopic sample met the "features or disk" vote fraction cut (f_featured ≤ 0.5), and 74,519 of these additionally met the z < 0.075 redshift cut. We selected only a subsample of these to study, as they were not classified as having features or a disk and therefore were unlikely candidates for hosting clumps. The 4937 galaxies chosen will be referred to as the "extra" sample, and we included the sample to permit us to extrapolate its clumpy statistics over the full population. With the "extra" sample included, a total of 58,550 galaxies were studied. Unless otherwise specified, photometry describing galaxies in our sample was obtained from the SDSS DR15 PhotoPrimary table (Aguado et al. 2019). Table 1 summarizes our galaxy selection criteria and number counts.

Given this sample, we created image cutouts for all galaxies from the SDSS DR15 Legacy survey that were presented to volunteers. We mapped the SDSS i-, r-, and g-band imaging to the red, green, and blue values of the image cutouts using asinh color scaling (Lupton et al. 2004) and scaled galaxies to be approximately the same size in each cutout. Cutout creation is described more fully in Appendix A.

To estimate the completeness of our sample, we created additional cutouts of galaxies from the target sample with artificial clumps added. These will be called "simulated" subjects, whereas cutouts with no added clumps will be called "real." The simulated sample consists of 84,565 simulated clumps in 26,736 galaxies, approximately half the galaxy count in the real sample. During Clump Scout, each volunteer was shown a random sequence of subjects drawn uniformly from the pool of all subjects, i.e., both real and simulated. A subject was retired (no longer shown to volunteers) after receiving 20 independent classifications.

Galaxies were selected for the simulated sample such that their mass distribution matched the mass distribution of clumpy galaxies in the Guo et al. (2018) sample (1132 galaxies spanning 0.5 < z < 3). This lowered the characteristic mass of galaxies in the simulated sample: the galaxy sample from Guo et al. (2018) has a median mass of 10^9.7 M_⊙, compared to 10^10.6 M_⊙ for galaxies in the real sample. This was appropriate, as massive galaxies tend to be redder and smoother; visual inspection confirmed that a large fraction of star-forming clumps inserted into high-mass galaxies were easily distinguished as simulations. We allowed galaxies to appear in the simulated sample multiple times, applying a different image transformation (i.e., combination of rotations and reflections) to each cutout made of the galaxy to ensure that the final subject was unique.

To determine clump luminosity and color, we simulated clump spectra using spectral templates generated by the software Flexible Stellar Population Synthesis (Conroy et al. 2009; Conroy & Gunn 2010). We treated each clump as a single stellar population (with delta-function star formation history), assigning it an age and a V-band total extinction A_V . Clump ages spanned 10^−2.5 Gyr (i.e., ∼3 Myr) to 10¹ Gyr. Dust extinction was given by a Calzetti et al. (2000) attenuation curve, and the clump's A_V value varied narrowly about the SDSS-estimated dust content for the host galaxy (σ = 0.04 in $\mathrm{ln}({A}_{V})$). Metallicity was fixed to the solar value. The resulting spectrum was redshifted to match the host galaxy and integrated to determine the clump's broadband flux in each SDSS band.

Clump mass was selected uniformly from a distribution that depended on the clump age, shown in Figure 2. Qualitatively, we excluded low-mass, high-age clumps to avoid extremely faint ("known invisible") objects. Similarly, we excluded the brightest clumps (high mass, low age), as these were "known visible" objects. The resulting sample probes the region where we are least certain of volunteers' recovery capability. We discarded and regenerated a clump if its apparent magnitude was >22.8 in each of the g, r, i, and z bands, as well as >24.8 in the u band, ¹² since these clumps were considered "known invisible." The resulting distribution in the age and mass of simulated clumps is shown in Figure 2.

Zoom In Zoom Out Reset image size

Each galaxy in the simulated sample was assigned a number of clumps selected from a Poisson distribution with mean 3, where 0 results were rejected and resampled. (Since 0 results were rejected, the actual mean number of clumps per galaxy was 3.16.) This distribution was chosen to maximize the clump density per galaxy without appearing unrealistic to volunteers and is not meant to reflect the true distribution of clumps per galaxy. To assign locations to clumps, image segmentation was performed on the r-band imaging field containing the host galaxy using Source Extractor (Bertin & Arnouts 1996). For each field, a centered cutout was made, smoothed with a boxcar filter, and then segmented by Source Extractor to determine which pixels belonged to the host galaxy. A pixel was chosen uniformly at random from the host galaxy's segment to be the clump's location within the image. In order to probe the low surface brightness regions of a galaxy (without letting our sample be dominated by clumps in these regions), we randomly assigned 25% of clumps to a "wide" segment that encompassed a larger area than the standard galaxy segment. ¹³ Figure 3 provides an example of the simulation placement process. Each clump was then simulated as a point source with a γ = 2.5 Moffat profile; of the profiles we tried, it was found by visual inspection by the authors that a Moffat profile looked the most "real" to observers and was most difficult to distinguish from real clumps. For most clumps, the FWHM of this profile was equivalent to the FWHM of the r-band point-spread function (PSF) in the image. We also allowed a small number of clumps to be "extended" by assigning each clump an effective physical radius, selected from a uniform distribution over the range [10 pc, 500 pc] (based on size limits observed by Messa et al. 2019). If this physical radius exceeded that of the PSF, this radius was used as the effective radius of the clump's profile. Approximately 19% of simulated clumps (16,342 of 84,565) exceeded the seeing PSF size, by a median of 27%. The distribution of simulated clump sizes allows us to probe the effect of clump size on recovery statistics and is not intended to match the true distribution.

Zoom In Zoom Out Reset image size

After subjects had been examined by Clump Scout volunteers, the locations of clumps needed to be determined from the collected annotations on each subject. To this end, we developed an aggregation algorithm with which all volunteer annotations on each subject were transformed into consensus clump locations. Broadly, our aggregation process consisted of two steps: first, clump candidates were identified via a clustering algorithm; second, clumps marked "unusual" by a sufficient fraction of volunteers (>0.35) were discarded, since these are likely to be foreground star contaminants.

The clustering algorithm we employed is adapted from Branson et al. (2017) and is specialized for citizen science applications. A complete description of the algorithm can be found in H. Dickinson et al. (2022, in preparation). Briefly, we assign each volunteer a "false-positive probability" (i.e., the chance that an annotation by this volunteer is not associated with any clump candidates), a "false-negative probability (i.e., the chance that the volunteer failed to mark a given clump candidate), and a "scatter" value that estimates the distance between an annotation and its intended target. These values inform a clustering algorithm that identifies clump candidates; in turn, the identified clump candidates update the volunteer statistics, and so on. To determine when each image has been fully classified, a "risk" value is computed for each one. Once the risk falls below a threshold value, clustering is no longer performed and its clump candidates are finalized. Each clump candidate is assigned a "false-positive probability" based on the number and properties of volunteers who marked it. To improve the purity of our sample, we discard clumps with false-positive probability >0.6. By comparison with a sample of classifications by the authors, we found that the majority of volunteer-identified clumps with false-positive probabilities larger than 0.6 did not correspond to any expert-identified clumps, while the majority of those below the threshold did. We additionally remove any clumps that coincide with the volunteer-identified central bulge of a galaxy. To locate a galaxy's central bulge, we take the median x and y coordinates of central bulge annotations from all volunteers; we then prune outlying annotations by removing any volunteer's central bulge annotation that falls more than 20 pixels from this location (in the 400 × 400 cutout image), and we recalculate the central bulge location without these. We then remove any clumps within 1 PSF-FWHM of the central bulge.

In total (excluding unusual clumps), we identify 10,738 clumps over 7050 galaxies in our sample. An additional 3858 unusual clumps were found; although these are most likely foreground contaminants, we include them in our public catalog for transparency.

Along with the electronic release of this paper, we release the catalog of all of the clumps identified by the Clump Scout aggregator and their estimated properties. The columns are fully described by Table 3 at the end of this paper. Clumps with a high fraction (≥35%) of "unusual" annotations are included but are marked by the flag unusual_flag=1.

To use this catalog for scientific purposes, we make a few "best practices" suggestions on how to filter this catalog:

• 1.  
  Selecting a clean sample: We strongly recommend that clumps with unusual_flag=1 should be rejected, as these are probable nonclump contaminants (i.e., foreground stars, background galaxies, or other point-like sources).
• 2.  
  Mass completeness: This galaxy catalog is not mass complete, and the lower-limit mass on galaxies evolves significantly with redshift. We estimate that the catalog is mass complete down to 10⁹ M_⊙ for z < 0.035. If a mass-complete catalog is needed, care must be taken to limit the sample's redshift.

A major difficulty in clumpy galaxy literature is that the definition of a "clump" is highly inconsistent. Past works have defined clumps as those objects identified by visual investigation (e.g., Elmegreen et al. 2007; Puech 2010; Overzier et al. 2009) or by applying detection algorithms that are robust to changes in resolution and depth, including the clumpfind algorithm from Williams et al. (1994) and others (e.g., Livermore et al. 2012; Guo et al. 2012; Tadaki et al. 2014; Zanella et al. 2019). However, comparisons between these different methods are not straightforward.

Guo et al. (2015) proposed an empirically motivated definition that the ratio of clump to galaxy UV luminosity (f_LUV) must exceed 8%. The 8% cutoff was chosen to select for star-forming regions at high redshift while excluding common star-forming regions locally; specifically, it includes many star-forming regions in HST-imaged galaxies spanning 0.5 < z < 3 but excludes >99% of star-forming regions identified in the galaxy M101 (blurred to match the resolution of the high-redshift sample). Local clumps exceeding the f_LUV > 8% threshold are therefore expected to be rare, exceptional objects. Several other recent works use this or a similar criterion (e.g., Shibuya et al. 2016; Mandelker et al. 2017; Fisher et al. 2017). However, it is not universally applicable: Dessauges-Zavadsky & Adamo (2018) rejected it to allow for study of the mass function of high-redshift clumps down to much lower masses, while Huertas-Company et al. (2020) used a clump mass cut of M_clump > 10⁷ M_⊙ instead to facilitate comparison with simulations.

In this paper, we calculate f_clumpy by specifying a relative flux cutoff in the SDSS u band, i.e., the ratio of clump to galaxy flux in the u band (f_Lu ) is greater than some specified fraction. In particular, we use the relative flux cuts f_Lu > 8% and f_Lu > 3%, and call the clumpy fractions under these criteria f_clumpy,8% and f_clumpy,3%, respectively. The 8% fraction was selected to be comparable to existing works with a similar criterion, while the 3% fraction allows for larger number statistics and is easier and more accurate to estimate for the low-redshift universe, where clumps are less common.

Regarding the relationship between f_Lu and f_LUV, it is worth noting that several past studies have used a relative flux threshold in the UV (∼2500 Å) to define clumps (e.g., Guo et al. 2015; Shibuya et al. 2016). Because UV data are not available in SDSS, we instead use the lowest available wavelength band, the u band at ∼3500 Å. Therefore, in order to compare our f_clumpy value with past studies, we must demonstrate that clumps selected under our f_Lu cut are comparable to those selected under the more commonly used f_LUV cut. To do so, we examined a highly complete sample of clumps from the Guo et al. (2018) sample, requiring f_LUV > 5% to select for bright clumps and a highly complete sample. This sample is herein called the Guo+2018 sample. Guo+2018 was chosen because it includes a large sample of bright clumps (523 clumps meet the f_LUV > 5% criterion) and because it spans a similar physical resolution to Clump Scout: a typical SDSS g-band PSF-FWHM at z ∼ 0.05 is ∼1.2 kpc, compared with ∼1.1–1.3 kpc for HST sources spanning 1 < z < 2.5 for similar wavelengths.

For each clump in the Guo+2018 sample, we examined its flux fraction in CANDELS filter bands that were analogous to near-UV and the SDSS u band in the rest frame. ¹⁴ We find that there is a strong correlation between f_Lu and f_LUV using these filters, with the median clump having f_Lu = 0.86f_LUV. A total of 1170 clumps from the Guo+2018 sample meet the f_LUV > 8% criterion, compared with 961, which meet f_Lu > 8%, a reduction of ∼18%.

We performed a similar experiment on clumps in Clump Scout. Though we could not calculate f_LUV directly since SDSS does not provide near-UV data (∼2500 Å), we obtained near-UV fluxes for local galaxies from the GALEX survey (Martin et al. 2005), using the cross-matched GALEX-SDSS catalog created by Bianchi & Shiao (2020). We then assumed that local clumps matched the SED distribution of clumps from the Guo+2018 sample and multiplied each clump's u-band flux by the UV-to-u ratio of a randomly selected Guo+2018 clump. The resulting values for f_Lu and f_LUV are plotted alongside the Guo+2018 values in Figure 7. For both groups, f_Lu is a reasonably strong predictor of f_LUV. Performing the same experiment using the g band rather than the u band revealed that f_Lg values are not as well correlated to f_LUV and are typically much smaller (the median clump had f_Lg = 0.73f_LUV).

Zoom In Zoom Out Reset image size

Based on these experiments, we conclude that f_Lu is the best available analog of f_LUV for SDSS data. We choose not to apply a conversion factor to convert f_Lu values to f_LUV, since no statistically large sample of UV-measured local clumps exists that could verify such a conversion factor. Further, our results in this section suggest that f_Lu - and f_LUV-defined values of f_clumpy are closely related and can be meaningfully compared, with the caveat that u-band-estimated values of f_clumpy are likely to be slightly smaller than UV-estimated values.

The calculation of f_clumpy from the Clump Scout catalog has several steps. We calculate f_clumpy in the full sample, as well as in three distinct bins of galaxy mass, and the selection cuts and galaxy counts for each mass bin are detailed in Table 2. Here, we detail the steps for calculating f_clumpy in the broadest mass bin (M > 10⁹ M_⊙), though the same process applies to every bin.

First, we isolate a star-forming, mass-complete sample of galaxies. SDSS is complete for galaxies down to 10⁹ M_⊙ at redshifts z < 0.035. Therefore, beginning with the Clump Scout parent sample defined in Section 2.2, we limit the sample to galaxies with sSFR > 10⁻¹, M > 10⁹ M_⊙, and z < 0.035. In addition, because clumps may be more difficult to detect in edge-on galaxies than face-on galaxies, we remove all galaxies for which the ratio of the galaxy's major to minor axis is less than 0.3, where this axis ratio is estimated by the SDSS exponential fit in the r band (expAB_r in the PhotoPrimary table). Our sample contains N_tot = 5843 galaxies passing these cuts.

We then combine the contributions from the "regular" Clump Scout sample of 53,613 galaxies and the "extra" sample of 4937 galaxies used to extrapolate over all galaxies in SDSS that Clump Scout did not directly examine. In total, N_reg = 2640 of 5843 galaxies passing all cuts for f_clumpy were examined in the regular sample.

Of the remaining 3203 galaxies, a sample of 230 were examined by volunteers as part of the "extra" sample. We use N_extra,samp to refer to the size of the sample of these galaxies that volunteers examined directly, i.e., N_extra,samp = 230, and N_extra,tot to refer to the size of the total population from which these galaxies were drawn, i.e., N_extra,tot = 3203.

For each group, the observed clumpy fraction f_clumpy,obs is calculated and the completeness correction from Section 4.3 is applied. The corrected fraction ${f}_{\mathrm{clumpy},\mathrm{extra}}^{\mathrm{corr}}$ over the "extra" sample is then extrapolated over all SDSS galaxies not examined by Clump Scout. This yields the total clumpy fraction:

$$\begin{eqnarray}&&{f}_{\mathrm{clumpy}}=\displaystyle \frac{{N}_{\mathrm{reg}}}{{N}_{\mathrm{tot}}}{f}_{\mathrm{clumpy},\mathrm{reg}}+\displaystyle \frac{{N}_{\mathrm{extra},\mathrm{tot}}}{{N}_{\mathrm{tot}}}{f}_{\mathrm{clumpy},\mathrm{extra}}.\end{eqnarray} \tag{ 2 }$$

Here f_clumpy,reg and f_clumpy,extra are the fraction of galaxies out of N_reg and N_extra,samp, respectively, that were estimated to be clumpy.

The sampling error is estimated separately on the "regular" and "extra" samples using the standard error formula on a proportion, taking the sample size N to be the number of examined galaxies in the "regular" or "extra" group:

$$\begin{eqnarray}\begin{array}{rcl}{\sigma }_{\mathrm{clumpy},\mathrm{reg}} & = & \sqrt{\tfrac{{f}_{\mathrm{clumpy},\mathrm{reg}}(1-{f}_{\mathrm{clumpy},\mathrm{reg}})}{{N}_{\mathrm{reg}}}}\\ {\sigma }_{\mathrm{clumpy},\mathrm{extra}} & = & \sqrt{\tfrac{{f}_{\mathrm{clumpy},\mathrm{extra}}(1-{f}_{\mathrm{clumpy},\mathrm{extra}})}{{N}_{\mathrm{extra},\mathrm{samp}}}}.\end{array}\end{eqnarray} \tag{ 3 }$$

We then scale these by their contribution to the total value of f_clumpy and add them in quadrature to obtain

$$\begin{eqnarray*}\begin{array}{rcl}{\sigma }_{\mathrm{clumpy}}^{2} & = & {\left(\displaystyle \frac{{N}_{\mathrm{reg}}}{{N}_{\mathrm{tot}}}\right)}^{2}{\sigma }_{\mathrm{clumpy},\mathrm{reg}}^{2}\\ & & +\ {\left(\displaystyle \frac{{N}_{\mathrm{extra},\mathrm{tot}}}{{N}_{\mathrm{tot}}}\right)}^{2}{\sigma }_{\mathrm{clumpy},\mathrm{extra}}^{2}.\end{array}\end{eqnarray*}$$

To estimate the total error on f_clumpy, we use a Monte Carlo method to include contributions from the uncertainty on clump fluxes and clump incompleteness, as well as from sampling error. Over 100 trials, clump fluxes are allowed to randomly vary within a normal distribution defined by their estimated error values (see Section 3), while the clump completeness map is recalculated on each trial by the method described in Appendix B. On each Monte Carlo trial, we include sampling error by calculating an initial value of f_clumpy and then reassigning it to a random value selected from N(f_clumpy, σ_clumpy). Of these sources of error, sampling error is by far the most significant: in a trial run where error contributions from clump flux error and the completeness correction were ignored, the error bars were typically within 10% of their original values.

Our estimate of f_clumpy must also take into account the incompleteness of our clump catalog. We therefore use the following method for completeness-correcting the clumpy fraction of galaxies.

The end goal of the f_clumpy completeness correction is to calculate P_FN, the probability that a galaxy is a "false negative" for clumps—in other words, the probability that the galaxy contains one or more clumps, but that none of its clumps were detected. To calculate P_FN, we work in steps from the completeness estimates on individual clumps in the sample. We define P_rec,i to be the recovery fraction of clump i. (Refer to Appendix B for a full overview of how P_rec,i is determined for each clump.)

We begin by calculating the recovery probability of a randomly selected clump within the sample, P_rec:

$$\begin{eqnarray}&&{P}_{\mathrm{rec}}=\displaystyle \frac{{n}_{\mathrm{obs}}}{{n}_{{true}}}\approx \displaystyle \frac{{n}_{\mathrm{obs}}}{\sum _{i=1}^{{n}_{\mathrm{obs}}}1/{P}_{\mathrm{rec},i}},\end{eqnarray} \tag{ 4 }$$

where for each clump i, 1/P_rec,i approximates the true number of clumps with similar properties.

Next, we estimate the true distribution of clumps per clumpy galaxy, P_count(n_c ). To do so, we begin with a proposed distribution P_count(n_c ) and then simulate 10,000 clumpy galaxies with this distribution. We then remove a fraction P_rec of clumps at random to simulate the observed distribution, discarding galaxies with no observed clumps. The proposed distribution is adjusted until the mean number of clumps per galaxy in the simulated distribution closely matches the observed mean. For mathematical expediency, we used an exponential distribution to model P_count(n_c ) with coefficient λ, i.e., P_count(n_c ) ∼ ${e}^{-\lambda {n}_{c}}$. (It should be noted, though, that the observed distributions are also well fit by Poisson distributions, and the exponential model does not necessarily have physical significance.) In Figure 8, we plot the observed distributions of f_Lu > 3% clumps per galaxy for each galaxy mass bin we examine, along with the best-fit exponential model.

Zoom In Zoom Out Reset image size

Given P_rec and P_count(n_c ), P_FN is given by

$$\begin{eqnarray}&&{P}_{\mathrm{FN}}=\sum _{{n}_{c}=1}^{\infty }{P}_{\mathrm{count}}({n}_{c})\,{\left(1-{P}_{\mathrm{rec}}\right)}^{{n}_{c}}.\end{eqnarray} \tag{ 5 }$$

The P_FN sum is dominated by the first few terms. For f_Lu > 8% clumps in our broadest galaxy mass bin (M > 10⁹ M_⊙ with z < 0.035), we estimate P_rec ≈ 49.3% and λ ≈ 0.85; given these values, the first three terms of the P_FN sum account for approximately 78%, 92%, and 99% of missed clumpy galaxies, respectively.

Given the galaxy false-negative probability P_FN, the completeness of f_clumpy is given by (1 – P_FN). It is then straightforward to correct the clumpy fraction:

$$\begin{eqnarray}&&{f}_{\mathrm{clumpy}}^{\mathrm{corr}}={(1-{P}_{\mathrm{FN}})}^{-1}{f}_{\mathrm{clumpy}}^{\mathrm{obs}}.\end{eqnarray} \tag{ 6 }$$

Parameter f_clumpy ^corr should be taken as our estimate of the "true" value, as it accounts for galaxies whose clumps were not detected; however, we present both the observed and corrected values in our results.

Here we present our results for f_clumpy,8% and f_clumpy,3% (the clumpy fraction using the thresholds f_Lu > 8% and f_Lu > 3%, respectively), both overall and within several different galaxy mass bins. All of these numbers are collected in Table 4.

Within the regular Clump Scout sample (N_reg = 2640), we detected 104 galaxies with clumps passing f_Lu > 8%; corrected for incompleteness, we estimate the true number to be ∼156. Within the extra sample (N_extra = 230), we observed just two galaxies with clumps passing f_Lu > 8%, and we estimate the true number to be ∼3 correcting for incompleteness. In total, we estimate that 188 of N_tot = 5843 galaxies have clumps (corrected for incompleteness), leading to an estimate f_clumpy,8% ^corr = ${3.22}_{-0.34}^{+0.38} \%$.

We apply the same procedure to galaxies using the f_Lu > 3% cut and observe 410 clumpy galaxies in the regular sample (∼641 corrected for incompleteness) and 5 clumpy galaxies in the extra sample (∼9 corrected for incompleteness). This yields a total estimate ${f}_{\mathrm{clumpy},3 \% }^{\mathrm{corr}}={12.68}_{-0.88}^{+1.38} \%$.

To characterize the local distribution of clumps, we also examine f_clumpy in three different bins of galaxy mass: $9\lt {\mathrm{log}}_{10}(M/{M}_{\odot })\lt 9.8$, $9.8\lt {\mathrm{log}}_{10}(M/{M}_{\odot })\lt 10.6$, and $10.6\lt {\mathrm{log}}_{10}(M/{M}_{\odot })\lt 11.4;$ we refer to the galaxies in these bins as low-mass, medium-mass, and high-mass galaxies, respectively. These match the mass bins over which Guo et al. (2015) estimated the clumpy fraction. To obtain a complete galaxy sample, different redshift limits were applied to each bin: z < 0.035 for low-mass galaxies, z < 0.05 for medium-mass galaxies, and z < 0.09 for high-mass galaxies (see Figure 9).

Zoom In Zoom Out Reset image size

Following the same procedure as for the overall clumpy fraction, we estimate that ${f}_{\mathrm{clumpy},8 \% }^{\mathrm{corr}}$ is ${3.12}_{-0.26}^{+0.26} \%$ for low-mass galaxies, ${2.48}_{-0.83}^{+0.50} \%$ for medium-mass galaxies, and ${2.57}_{-0.47}^{+0.56} \%$ for high-mass galaxies. A more complete list of statistics can be found in Table 4; they are also plotted in Figure 10. Example images of galaxies in each of the mass bins are shown in Figure 11.

Zoom In Zoom Out Reset image size

Zoom In Zoom Out Reset image size

To place our estimates of f_clumpy,8% at z < 0.1 in context, we compare them with high-redshift (z > 0.5) results from other works, in particular Shibuya et al. (2016) for galaxies of all masses M > 10⁹ M_⊙ and Guo et al. (2015) for galaxies in bins of low, medium, and high mass (matching the mass bins used in this paper). We plot these values in Figure 12.

Zoom In Zoom Out Reset image size

Shibuya et al. (2016) found that the clumpy fraction peaks between redshifts 1 and 2 at a value of >50%, before declining over z < 1. To model this trend, they use a fit function with the same form as is commonly used to model the trend in the cosmic SFR density with redshift (Madau et al. 1996; Lilly et al. 1996). To compare with their results, we take their best-fit model for z versus f_clumpy and extend it beyond their data to z ∼ 0; this is plotted in Figure 12. Their model predicts a value of f_clumpy,8% ∼ 4% at z ∼ 0, which is in line with our result of f_clumpy,8% ≈ 3.22%.

Guo et al. (2015) observed a nearly constant f_clumpy,8% ∼ 50% for low-mass galaxies over 0.5 < z < 3, while our results indicate a value of ∼3% at z ∼ 0 for galaxies of the same mass As explained in Section 4.1, these results can be meaningfully compared because the f_Lu > 8% cut used in this work is similar to the f_LUV > 8% cut used by Guo et al. (2015). We note that the differences between our z < 0.1 results for f_clumpy and the z > 0.5 results from Guo et al. (2015) are an order of magnitude or more, which is much larger than the difference we expect between f_clumpy computed with a UV versus u-band clump definition (as discussed in Section 4.1). These two works also probe a similar physical resolution: the physical resolution of CANDELS images is ∼1 kpc at all redshifts, compared to ∼0.5–1.7 kpc over the range 0.02 < z < 0.09 for SDSS. We therefore expect that this drop in the clumpy fraction between 0 < z < 0.5 is real and cannot be the result of different identification methods.

There are few other studies that estimate f_clumpy in the local universe. Murata et al. (2014) studied clumpy galaxies selected from HST/ACS F814W imaging from the COSMOS field spanning redshifts 0.2 < z < 1. The F814W filter approximately corresponds to the SDSS r and g bands over this redshift range, and the nearest galaxies in this sample (z ∼ 0.2) are likely similar to Clump Scout galaxies (z < 0.1). The fraction of optically bright galaxies with multiple star-forming clumps was found to decrease from 0.35 at z ∼ 1 to 0.05 at z ∼ 0.2. While this decrease is qualitatively in line with our results, the definition of f_clumpy used by Murata et al. (2014) is significantly different from that used here: rather than apply a relative flux criterion, clumpy galaxies were selected to have multiple star-forming clumps of comparable brightness. The low completeness of our sample prevents us from applying the Murata et al. (2014) condition, as it requires the detection of at least three clumps per clumpy galaxy. Overzier et al. (2009) also studied clumpy galaxies at z < 0.3 but only studied a sample of 30 "Lyman break analog" galaxies with extremely high UV fluxes; the clumpy fraction obtained from this sample is not comparable to that of our broader sample.

Given this paper's focus on the fraction of clumpy galaxies, it is worth discussing exactly how this quantity is defined and how it should be used. Parameter f_clumpy is a particularly good probe of trends in clumpiness across cosmic time: By controlling for galaxy mass and SFR, we ensure that f_clumpy is computed between groups of similar galaxies even at different redshifts. However, using a relative flux criterion (f_LUV > 8%) to define clumps may select for very different sets of physical objects depending on galaxy mass. Naively, assuming a linear relation between mass and u-band luminosity in our galaxy sample, our lowest galaxy mass bin (10⁹–10^9.8 M_⊙) includes clumps that are ∼2 dex less massive than our highest-mass bin (10^10.6–10^11.4 M_⊙). It is therefore not straightforward to compare f_clumpy between bins of different galaxy mass. The validity of this comparison depends on the clump luminosity function: for example, if the clump luminosity function experiences an exponential cutoff (e.g., as proposed by Livermore et al. 2012), the relation between f_clumpy and galaxy mass would depend on the location of this exponential cutoff with galaxy mass. Therefore, while f_clumpy can be compared for galaxies of similar mass across different redshifts, it is not straightforward to compare f_clumpy between galaxies of different mass. The remainder of this discussion focuses on trends in f_clumpy with redshift for this reason.

A major motivation for determining f_clumpy over large redshift ranges is to distinguish between different proposed modes of clump formation. There are two primary modes by which clumps are thought to form. In the in situ mode, clumps form owing to gas collapse within the host galaxy due to turbulent disk dynamics (i.e., VDI). VDI is expected in galaxies that are actively accreting gas via "cold-mode" accretion, in which gas flows into the galaxy via smooth, cold streams. This accretion process adds kinetic energy to the disk and can drive the Toomre parameter below unity, making gas unstable to collapse (Dekel et al. 2009). Alternately, in the ex situ mode of formation, clumps originate as minor mergers: the clump forms as a satellite galaxy with its own dark matter component, only later merging with its host. It should be noted that clumps are short-lived structures on a cosmological scale: simulations find that massive clumps in disk galaxies have a maximum lifetime of ≲500 Myr, by which time they are slowed owing to dynamical friction and have merged with their host's central bulge (Bournaud et al. 2014; Mandelker et al. 2014). Therefore, the presence of clumps indicates that the clump formation process is ongoing or recent, and f_clumpy can effectively act as a tracer of galaxy behavior. It remains unclear which is the dominant formation process, as different processes may dominate different galaxy populations.

To determine the primary formation process of clumps (i.e., via in situ or ex situ formation), we can examine trends in the rate of VDI and the minor merger rate over cosmic time and compare these with trends in f_clumpy. In Figure 12, we have plotted our estimate of f_clumpy,8%, along with comparable estimates at higher redshift (Guo et al. 2015; Shibuya et al. 2016) and estimates of the fraction of galaxies experiencing VDI and with observable signatures of minor mergers.

We use the minor merger rate estimate from Lotz et al. (2011), which was obtained by subtracting the number of galaxies with close pairs (major mergers) from the number with disturbed, uneven morphologies (major and minor mergers). The best-fit model to the minor merger fraction takes the form f_merg,minor ∝ T_obs(1 + z)^α , with best-fit exponent α = −0.2 ±0.2. The "observability timescale" refers to the time during which the host galaxy's morphology is measurably disturbed, which is dependent on the detection method (and distinct from the lifetime of an ex situ clump formed during a merger). To represent the uncertainties in these parameters, we plot the best-fit model for T_obs values of 0.5, 1.25, and 2 Gyr over the fit range (0 < z < 1.5). In all cases, the minor merger rate rises or remains constant over the full redshift range owing to the fit parameter α = −0.1 ± 0.1.

To determine the fraction of galaxies experiencing turbulence, we use measurements of galaxy kinematics from Kassin et al. (2012). These measurements reveal that galaxies of a wide range of masses (10⁸–10^10.7 M_⊙) tend to "settle" and become rotationally dominated over the period 0 < z < 1.2. Moreover, they find that the highest-mass galaxies have the lowest fraction of turbulence at any epoch. The "turbulent fraction," defined as the fraction of galaxies for which V_circ/σ_gas < 3 (i.e., the fraction of galaxies experiencing VDI), is plotted in Figure 12 for three of the mass bins examined by Kassin et al. (2012), spanning 10⁹–10^10.7 M_⊙. All turbulent fractions decline over 0 < z < 1.2, with higher-mass galaxies declining more quickly.

We then turn to trends in f_clumpy,8% and compare them to the trends in the two clump formation mechanisms (VDI and minor mergers) described above. Ignoring our low-redshift data for a moment, the data from Guo et al. (2015) suggested that two different clump formation mechanisms may be dominant in high-mass galaxies and low-mass galaxies. The clumpy fraction for high-mass galaxies declines significantly with time over the span 0.5 < z < 3 from ∼55% to ∼15%, while for low-mass galaxies it remains constant at f_clumpy ∼ 60% over the same time span. To explain this difference, it was suggested that the primary formation mechanism for clumps in high-mass galaxies may be VDI (in situ) and trace the turbulent fraction over this time span, while those in low-mass galaxies form owing to minor mergers (ex situ) that are roughly stable over the same time span.

However, our low-redshift estimates of f_clumpy challenge this two-mechanism formation model. For galaxies of all masses, we now observe a significant decline in f_clumpy,8% to <5% at z ∼ 0. Even assuming that our z ∼ 0 estimates of f_clumpy,8% are too small by a factor of several, the observed fraction would still be far lower at z ∼ 0 than at z > 0.5 in every mass bin. This result matches the conventional wisdom about clumps, i.e., that giant star-forming clumps are common at high redshift and rare locally. However, the roughly constant minor merger rate over the period 0 < z < 0.5 is inconsistent with the significant low-redshift decline that we observe.

Instead, we suggest that in situ, VDI-driven formation is the primary mode of clump formation in galaxies of all masses, at least over the redshift range 0 < z < 1.5. The trends in galaxy turbulence over this time span match closely with the trends in f_clumpy: all galaxies show evidence of a decline in turbulence, with low-mass galaxies remaining turbulent the longest. The VDI-driven formation model provides a natural mechanism for the decline in f_clumpy, which is the decline in the cosmological rate of gas accretion by galaxies: as the availability of intergalactic gas decreases, so too do the rates of star formation, turbulent dynamics, and clump formation (Dekel et al. 2009).

Adding to this picture, smaller case studies have already provided limited evidence to link VDI to clumpiness directly. Studies of the kinematics of high-redshift clumpy galaxies find that they have turbulent morphologies (Elmegreen et al. 2009; Genzel et al. 2011), with Genzel et al. (2011) in particular noting that clumps appear in regions of the galaxy where the Toomre instability parameter is subunity. However, these studies examined spirals with stellar masses ≳10^10.6 M_⊙, corresponding to the highest-mass bin in our work; similar kinematic examination of galaxies with lower masses remains to be done. In total, the current body of evidence points to a picture of clump formation that is dominated by in situ formation due to turbulent disk dynamics, though more concrete evidence is needed to confirm this.