Quantitative Galaxy Morphology (and Simulations)

Jennifer Lotz Space Telescope Science Institute

Sydney- Galaxy Zoo - Sept 2013 quantitative morphology

statistics that describe shape, size, irregularity of galaxy light profiles - quantitative numbers, error-bars easy to compute

- can be automated and fast

- can be more easily connected to predictions

Non-parametric Morphology -- often designed to trace irregular features Concentration - Asymmetry (Abraham 1994, Conselice 2000), Gini-M20 (Lotz et al. 2004, Abraham et al. 2003), ψ(multiplicity) (Law et al. 2007) M-I-D (Freeman et al. 2012)

Parametric Morphology/structure -- fits a model to light profile Sersic n, reff, b/a, B/D -- GALFIT, GIM2D (Peng et al. 2002, Simard 1998) Mergers -- IDENTIKIT (Barnes & Hibbard 2009) Model&for&the&Best&Fit&Kinematics + Morphology to probe Mergers

Y& Y&

X& V&

V& Z&

IDENTIKIT (Barnes & Hibbard 2009) fits tidal tail morphology + X& X& kinematics constrain orbital parameters → angular momentum in merger A. Mortazavi & J. Lotz, in prep remnants ( e.g. Bois et al. 2012) connecting physics to galaxy morphology

• what is the galaxy merger rate?

• what is the relative importance of mergers (v. gas accretion) in galaxy assembly and star-formation?

• how do galaxy disks settle into thin rotationally-supported spirals?

• how are bulges and spheroids created? how do these quench?

• how are bulge formation and SMBH growth connected? the Extended Groth Strip

aegis.ucolick.org the Extended Groth Strip

aegis.ucolick.org the Extended Groth Strip

aegis.ucolick.org 1996ApJS..107....1A Concentration-Asymmetry

No. 2, 2005 FIELD GALAXIES FROM z = 0.5 TO 3 575

Abraham et al. 1996

early HST studies find strong evolution in asymmetric galaxies Conselice et al. 2005

Fig. 10.—Luminosity density and luminosity fraction as a function of morphological type and redshift. The upper solid line and open circles show the total B-band luminosity density in the HDF-N and HDF-S. The solid line and filled circles show the luminosity density evolution for peculiar galaxies, while the triangles and dashed line and the boxes and dotted line are the luminosity densities for disks and ellipticals, respectively. The larger open symbols at z < 1 for the total and morphologically divided luminosity densities are taken from Brinchmann & Ellis (2000).

their integrated stellar mass density evolution are described in detail in Papovich et al. (2001), Dickinson et al. (2003), and Fontana et al. (2003). In Figure 12 mass functions are plotted as afunctionofmorphologicaltype,whileFigure13showsthe mass density evolution, and the fraction of mass in various mor- TABLE 3 phological types, as a function of redshift. These stellar mass Luminosity Densities ( )ofI < 27 Galaxies of Various Morphologies LB densities are tabulated in Table 4 as a function of redshift. Figures 11 and 13 demonstrate that the stellar mass density Redshift Elliptical Spiral Peculiar decreases as one goes to higher redshifts (Dickinson et al. 2003; HDF-N Fontana et al. 2003; Rudnick et al. 2003; Drory et al. 2004). Figures 11 and 12 show that the decrease in stellar masses is not 0.88...... 3.63 0.94 2.81 0.73 1.38 0.36 Æ Æ Æ due to any one type of galaxy, but is the result of galaxies of all 1.68...... 0.32 0.08 0.78 0.20 1.66 0.43 Æ Æ Æ morphologies growing in mass at lower redshifts. Some mas- 2.22...... 0.60 0.16 0.93 0.24 2.19 0.57 Æ Æ Æ 2.71...... 0.31 0.18 0.10 0.06 3.25 1.89 sive galaxies appear to have already formed at 0:5 < z < 1:4 Æ Æ Æ (Fig.12)in theHDF-N.Disks and ellipticalsin theHDF-Nwith HDF-S stellar masses M > 1011:5 have a comoving stellar mass density similar to the totalà density of these objects at z 0 (Cole et al. 0.79...... 1.47 0.38 4.57 0.94 0.72 0.21  Æ Æ Æ 2001). This has been observed at higher redshifts as well 1.62...... 0.98 0.46 0.62 0.06 1.30 0.17 Æ Æ Æ (Glazebrook et al. 2004; Franx et al. 2003), where some massive 2.12...... 1.41 0.11 1.47 0.10 6.50 0.42 Æ Æ Æ 2.67...... 4.57 0.10 1.23 0.10 10.4 1.17 galaxies appear to be already formed by z 1:5. While we do not Æ Æ Æ see massive galaxies in the HDF-S aroundz 1, as we do in the Note.—Luminosity densities are in units of 1026 ergs s 1 Hz 1 Mpc 3. HDF-N, we do find massive HDF-S systems at z 2 3. This À À À ¼ G-M20 in the local universe

G-M20 very effective at selecting multiply-nucleated galaxies Lotz, Primack & Madau 2004 G-M20 finds galaxy mergers out to z~1 188 LOTZ ET AL. Vol. 672

Fig. 10.—G vs. M20 for the luminosity evolution sample with the >70% completeness cut in EGS as a function of redshift. The solid lines are the same as right-hand of Fig. 7 and show the division betweenLotz E/S0/Sa, Sb/Sc/et Ir,al. and merger2008a, candidates (AEGISfirst panel ). Spectroscopically team confirmed chance superpositions are marked as cyan boxes. Visually ambiguous merger candidates are marked with orange diamonds. The error bars show the typical uncertainty for S/ N per pixel =2.5 galaxies. The majority of galaxies lie along a well-defined sequence in G-M , while 10% lie in the merger candidate region. h i HST ACS 20V(z<0.6) and I (0.6 < z < 1.2) misclassification rate with redshift, we adopt the same G-M20 object by SExtractor. These objects are also blended in ground- classification cuts for all redshiftweak bins. evolution in “mergerbased images, fraction”? and the red-blue pairs in particular may have un- reliable photometric redshifts. Sixteen of our merger candidates 3.2. G-M Distribution ersus Redshift 20 v are very close pairs with only photometric redshifts available. In Figure 10 we plot the G-M distribution of our >70% Nine of these show V I color differences >0.2 as measured in 20 À complete volume-limited LB > 0:4LBà sample as a function of 0.500 apertures around each nucleus in the ACS images. These redshift. The rest-frame B-band G-M20 distribution at 0:2 < z < blended sources have a negligible contribution to the derived 1:2 is remarkably similar to local galaxies, with the majority of merger fraction and evolution. We have chosen to include them galaxies lying along aclearsequenceinG-M20. The error bars in the final merger candidate sample, but excluding them would are for a S/N per pixel 2:5galaxyinACSimages(G not affect our results. h i ¼ ¼ 0:03, M20 0:1; see Lotz et al. 2006 for tests of G and M20 We plot the morphological fractions as a function of redshift inÆ deep HST ACS¼Æ images); the typical S/N for our sample is for the samples with and without the >70% completeness size- h i 4Y6withG 0:025, M20 0:03. magnitude cut (Fig. 11, solid lines and points). The fractions have We have visually¼Æ inspected all¼Æ of the merger candidates, and been corrected for incompleteness (Table 1), visually ambiguous find that 83% (332/402) show merger signatures such as offset merger candidates and chance superpositions. The fraction of or multiple nuclei, visual asymmetries, and close companions. objects that are too compact to classify are plotted as gray points; The remaining 17% are ambiguous and usually lie close to the their contribution is negligible for all redshift bins. The solid lines dividing line between mergers and ‘‘normal’ galaxies (Fig. 10, are for the entire sample, and the dashed lines are the spectro- orange diamonds). These are often spirals or irregulars with bright scopic redshift subsample. We find that the fractions derived for off-center star clusters. We use the DEEP2 spectroscopic survey to objects with spectroscopic redshifts and for the full samples are estimate the number of chance superpositions that result in false very similar, with a slightly lower/higher fraction of early types/ merger detections. Five percent of the galaxies in our sample with late types for the spectroscopic sample in our highest redshift bins. spectroscopic redshifts (83/1530) have multiple systems at differ- We also find similar evolution in morphologies for the sample ent redshifts in a single DEIMOS slit, due to either chance super- with the size-magnitude cut and the sample with no such cut, with positions or gravitational lenses (Fig. 10, cyan boxes). Roughly the lowest redshift bins showing slightly higher fractions of disk- a quarter (21/83) of the chance superpositions are classified as dominated late-type galaxies when no cut is applied. The merger merger candidates. Of our merger candidates, 223 have spectro- fractions are identical. Given the similarity between these two scopic redshifts, hence we expect 9% of all merger candidates samples, we will only refer to the sample with the >70% com- to be chance superpositions. Extrapolating to the photometric pleteness cut for the rest of the paper. redshift sample, we find the correction for chance superpositions To estimate the uncertainties in the fractions associated with the has a negligible effect on derived merger fractions ( 1%). measurement errors, we have also created 10,000 bootstrapped  Some of our merger candidates are very close pairs with over- realizations of the G-M20 distributions and compute the average lapping isophotes and are identified in the ACS images as a single morphological fractions and 1  standard deviations for each ‘merger fractions’ don’t agree...

2009: major disagreement in literature over merger fraction and it’s evolution

(see also Brinchman et al. 2000, Bundy et al. 2005, Jogee et al. 2008, Bridge et al. 2009, Robaina et al. 2010, Xu et al. 2011...) Calibrating Morphology with Simulations

T.J. Cox, P. Jonsson Timescale for Observing a “Merger”

timescales for finding mergers depends on method to find merger and type of merger (major/minor, gas-rich, gas-poor)

Lotz et al. 2008b, Lotz et al. 2010a, b

Figure 7: An N-body/hydrodynamical model from Lotz et al. (2008, 2010a,b) showing two equal size disk galaxies merging as a function of time. The numbers on the top of the realizations of this model show the various snap shots of time through the simulation while the bottom panel shows the changes in the asymmetry, Gini, concentration and M20 values for this particular simulation. This demonstrates the changing form of quantitative indices during a merger and how these systems are only identifiable within the different morphological systems as a merger at specific times. (courtesy Jennifer Lotz)

to simulations of galaxy structure the quantitative parameters measured are similar to those seen in nearby galaxies and correlate in the same way with other parameters (e.g., Lotz et al. 2008; Hambleton et al. 2011). In a fundamental study Lotz et al. (2008) include the first measurements of CAS and

Gini/M20 parameters on numerical simulations that includes old and young stars, star formation, gas and dust. Lotz et al. (2008) and later Lotz et al. (2010a,b) use GADGET/N- body/hydrodynamical simulations of galaxies when imaging the appearance of these galaxy mergers. Lotz et al. (2008) utilize disk galaxies of the same total mass, while Lotz et al. (2010a) investigate mergers with a variety of mass ratios, and Lotz et al (2010b) examine how the amount of cold gas mass in the progenitor galaxies influences morphology. These simulation results are passed through the SUNRISE Monte-Carlo radiative transfer code to produce, as realistically as possible, how galaxies wouldappearbasedonthesimulation output. Lotz et al. (2008b, 2010a,b) further investigate the location of different phases of different

18 Christopher J. Conselice Cosmologically-weighted timescales

Increasing gas fraction with redshifts ⇒ strongly increasing Asymmetry timescales with redshift Lotz et al. 2011, ApJ, 742, 103 10 Merger Rates per 10 M galaxy at z<1.5

normalize by consistent T(z) and use same parent sample selection:

α ℜpairs ~ (1+z) α = 1.7 ± 3.0 (stellar mass); 2.1± 0.2 (luminosity)

ℜG-M20 (major+minor) α = 0.5 ± 1.6 (stellar mass); 0.8 ± 1.4 (luminosity) Lotz et al. 2011 10 Merger Rates per 10 M galaxy at z<1.5

major+minor mergers

major mergers

normalize by consistent T(z) and use same parent sample selection:

α ℜpairs ~ (1+z) α = 1.7 ± 3.0 (stellar mass); 2.1± 0.2 (luminosity)

ℜG-M20 (major+minor) α = 0.5 ± 1.6 (stellar mass); 0.8 ± 1.4 (luminosity) Lotz et al. 2011 Did mergers form bulges, quench galaxies?

~ 3-4x more major mergers at 1 < z < 3 ? (Lotz et al. 2011)

peak of SF activity/bulge formation (e.g. Bouwens et al. 2009) HST WFC3 needed at z~2

need high-spatial resolution NIR imaging to probe rest-frame optical structures at z > 1.5

Cosmic Assembly Near-infrared Deep Extragalactic Legacy Survey (CANDELS) - PI S. Faber & H. Ferguson

HST WFC3 NIR imaging wide fields: UDS, EGS, COSMOS, 1-orbit depth J + H, ~0.2 sq. degrees

deep fields: GOODS-N + S, ~4-orbit depth Y, J, H, ~0.04 sq. degrees

z~2 : star-forming disks and quiescent bulges The Astrophysical Journal,742:96(20pp),2011December1 Wuyts et al.

The Astrophysical Journal,752:134(14pp),2012June20 Wang et al.

0.8 0.8 0.8 non−X−ray quiescents dSFGs

0.6 Spheroid Disk Irr/Merger

0.4

0.6 0.6 0.2 −0.5 −1.0 −1.5 −2.0 −2.5 Gini Gini Figure 1. Surface brightness profile shape in the SFR–mass diagram. A “structural main sequence” is clearly present at all observed epochs, and well approximated by a constant slope of 1 and a zero point that increases with lookback time (white line). While SFGs on the MS are well characterized by exponential0.4 disks,quiescent 0.8 galaxies at all epochs are better describedWuyts by de et Vaucouleurs al. 2012 profiles. Those galaxies that occupy the tip and upper envelope of the MS also have cuspier light profiles, X−ray 0.4 intermediate between MS galaxies and red and dead systems. 0.6 (A color version of this figure is available in the online journal.)

Table 1 0.4 Color-morphologyOverview Deeprelationship Lookback Surveys in place as 0.2 a b c c −0.5 −1.0 −1.5 −2.0 −2.5 Fieldearly Area as Filter z>morph 2.5 Image(Kriek Depth et al.Sample 2010) Depth N0.510 M our sample counts 53,2131, 31,127, and 8895 formation is immediately apparent, and its presenceshow apersists rest-frame out UV excess, which is likely due to an is systematically smaller with an offset of 0.20 and a scatter of galaxies at z ! 0.1, z 1, and z 2, respectively. Above to the highest observed redshifts. This “structural MS” consists 0.17. This is consistent with previous studies− for z 2samples 11 ∼ ∼ ∼ additional young stellar population component (see also Yan ∼ M>10 M ,thenumbersdropto147,922,2767,and of galaxies with near-exponential profiles (net al.1)2004 and shows). However, a the UV excess does not affect the resulting (Muzzin et al. 2009;Marchesinietal.2009). We also compared 1059 galaxies! at z 0.1, z 1, and z 2, respectively. similar behavior as the conventional “number≈ MS” as identified photometric redshifts, which are mainly determined by the rest- our stellar mass estimates with that derived using the approach An overview of the sample∼ size∼ per field is provided∼ in Table 1. on the basis of number densities in the SFR–mass diagram frame optical-to-MIR SEDs. in Wuyts et al. (2007, 2008), which fitted three different SFHs: (e.g., Noeske et al. 2007;Elbazetal.2007;Daddietal.2007). an SSP without dust, a constant star formation history with dust 3. RESULTS ON GALAXY STRUCTURE Namely, an upward shift of the zero point isThe observed dSFGs with are much more diverse in that they span a wide (Av varying from 0 to 4), and an exponentially declining SFH increasing lookback time. At each epoch, therange MS in in theirFigure [31.6] [24] colors and show a large variety of 3.1. Profile Shape − with an e-folding timescale of 300 Myr and the same range of is well approximated by a slope of unitymorphological (white line). The characteristics. We fit these dusty galaxies using the “Easy and Accurate Zphot from Yale” (EAzY; Brammer Av.Thetwomethodsgivefairlyconsistentresultswithanoffset We start by analyzing the surface brightness profile shape as SFR at which the median n reaches a minimum in a mass of 0.02 and a scatter of 0.13. afunctionofpositionintheSFR–massdiagraminFigure1. slice around log(M) 10 roughly coincideset al. with2008 the). mode We allow for a linear combination of six templates − = which can recover the entire rest-frame color space occupied by The mass and redshift distributions are shown in Figure 12. The three panels show from left to right the z 0.1, z 1, of the log(SFR) distribution in that mass slice, but depending We also derive the mass completeness limit as a function of ∼ ∼ on the fitting method and sample definitionobserved used to weed galaxies. out An accuracy of σNMAD 0.07 was obtained and z 2bins,respectively.Insteadofindicatingtherelative = redshift for a 3.6 µm selected ([3.6] < 21.5) sample. This ∼ quiescent galaxies, a somewhat shallower slopefor than the 19 unity dSFGs may with spectroscopic redshifts, and their SEDs abundance of galaxies in different regions of the diagram, we completeness limit is calculated using the full and deeper use the color-coding to mark the median value of the Sersic´ be measured for the “number MS” at the massiveare shown end (see, in Figure e.g., 11. FIREWORKS catalog following the method in Marchesini et al. index n of all galaxies in each [SFR,M] bin. For displaying Rodighiero et al. 2010). (2009). While these IEROs span a wide range of 1 z 4, purposes, we restrict the range of the color bar to 1 =4, respectively.= The fraction massive quiescent galaxies≈ is present at all observed epochs. Our at zph 1.8. Their derived stellar masses are more striking, SEDs of both the quiescent and dSFGs using “Fitting and = 11 (fn<1 fn>4)ofgalaxieslyingoutsidetheseboundsamountsto first and foremost conclusion from Figure 1 is therefore that with a median value of 1 10 M . All this is in broad ; Assessment of Synthetic Templates” (Kriek et al. 2009b). We agreement with the prototype∼ IERO× sample$ of Yan et al. (2004). 5 fixed their redshifts at the derived redshift, and fit the SEDs These IEROs are clearly among the most massive galaxies. to a set of simple stellar population models. These models At M>1011 M (where our sample is nearly complete; see have exponentially declining star formation histories (SFH) with below), the fraction$ of quiescents increases significantly from 0.1 < τ < 10 Gyr and 0 A 4 assuming Calzetti law. ! V ! 22% at 2 ! z ! 2.5to 43% at 1.5 ! z ! 2(Table1), suggesting∼ that we are seeing∼ the quenching process in action in 16 Defined as 1.48 median( zspec zph /(1 + zspec)) (Brammer et al. 2008). the most massive systems (also see, e.g., Cameron et al. 2011). × | − | 8 bulge/central mass concentration = quenching The Astrophysical Journal,760:131(25pp),2012December1 Cheung et al. tail of outliers with blue colors exists (colored points, except the red in Figure 7). The existence of these outliers was seen at both low and high redshifts by Bell (2008)andBelletal.(2012), who expressed the role of n in quenching as “necessary but not The Astrophysical Journal,760:131(25pp),2012December1 sufficient,”Cheung i.e., all et quenched al. galaxies have high n,butnotall high-n galaxies are quenched. We see the same thing. Unlike Figure 5(c) (which plotted color versus M /re), there ∗ (a) (b) is no interval in n where the color scatter is markedly larger than elsewhere (Figure 7(a)), and thus no impetus to search for asecondparameterwithinanarrow region of n.Toinvestigate Figure 7. (a) The U B vs. n diagram is reproduced from Figure 5(e) with the scatter, we have replotted Figure 7,thistimehighlighting (a)median values of color− in each n bin plotted (b) as open black triangles. The red (c) galaxies within narrow bins of various second parameters. The horizontal line represents the division between red and blue galaxies, while results are shown in Figure 8,wheregalaxiesaredividedinto the black vertical solid line at log n 0.36 represents the point at which 2 bins of stellar mass (top row), M /re (middle row), and M /re the median is halfway between the red= andCheung blue values. et al. The 2012 medians show ∗ p ∗ a step-like behavior in U B vs. n,suggestiveofaphysicalthresholdinn. (bottom row), collectively termed M /re .Theoutlierregion − ∗ Exceptions to the step function are the blue9 “outlier” galaxies2 in the lower right. from Figure 7(a) is outlined in blue. In each row, the behavior Quenching happens when central Σ* (<1 kpc) > 10 M/kpc p These are highlighted in strips of color for further discussion in Section 4.3.2 is the same. Galaxies with low values of M /re are seen to be stronger correlation thanand Figurewith 9total: pink stellar points encompass mass orU SersicB<0 .70,n cyan points encompass ∗ − mainly blue. A few leak into the high-n “outlier” regime, but 0.70 ! U B<0.95, and green points encompass 0.95 ! U B<1.20. their blue colors always agree with other galaxies in the same Bluish red-sequence− galaxies are highlighted for comparison and− lie within 1.20 U B<1.30. Images of these outliers are shown in Figure 9. parameter bin, i.e., their star formation rates are not depressed ! − p (d)Roughly 40% of the log n>0.36 galaxies (e) are outliers. (b) U B color vs. (f) by having high n.AsM /re increases, the mean color of low-n − ∗ inner stellar mass surface density Σ1kpc∗ .Notethatsomegalaxiesdonothave galaxies becomes redder while the number of outliers remains Σ1kpc∗ measurements due to insufficient S/N. Most outliers now fall into line, relatively constant. Again, the colors of the outliers still agree suggesting that inner stellar mass surface density is a cleaner predictor of p with the average color of all galaxies in the same M /re bin. At quenching than n. p ∗ the highest values of M /re ,virtuallyallgalaxiesarequenched (A color version of this figure is available in the online journal.) and the fraction of outliers∗ is negligible. Two points are clear: are needed to rule out fading. An important new insight from dividing galaxies into bins has not destroyed the basic step-like our work is that evolution to the red sequence appears to be ac- nature of the behavior in that galaxies within each bin still trend companied by a significant rearrangement of inner stellar mass smoothly but sharply (apart from outliers) from their “native” (g) (h) (i) in which existing stars move to the centers of galaxies, and/or star-forming state to a quenched state. The second point is that all trends with color at low n remain flat within each bin of new stars are formed there. We discuss processes whereby that p M /re .ThisshowsthatthestrongtrendofcolorversusM or might happen in Section 5. ∗ ∗ M /re within the blue cloud (Figures 5(b) and (c)) is not caused ∗ 4.3. Sersic´ Index and Inner Surface Density by some hidden dependence on n. To summarize, we have reproduced findings by previous 4.3.1. A threshold in n? authors that indicate that high n typically predicts a quenched galaxy, and we have set the half-power point between blue and The previous section considered M /re as the main quenching ∗ red galaxies at ncrit 2.3. This value is very near the SDSS (j)parameter and looked at scatter (k) around it to discover secondary (l) = value, implying no large evolution in ncrit from z 0.65 down effects. In this section, we use a similar tack but focus on Sersic´ ∼ index n.Anenlargedversionofthecolor-n plot is shown in to z 0. The rise in color near the critical value is sharp, while above∼ and below this value there is no trend in color with n, Figure 7(a), which indicates median U B in bins of n.The p − even within narrow slices of M /re .Athighn,mostgalaxies Figure 6. Galaxies in the overlap region of M /re (containing 316medians galaxies) illustrate from Figure the5 striking(c) are isolated step-like to examine behavior possible previously second-parameter color correlations ∗ ∗ are quenched with red colors, but a non-negligible fraction of with both global and disk/bulge properties. U B rest-frame colormentioned. is plotted Defining against the(a) riserglobal of stellar the step mass to beM where,(b)bulgestellarmass the medians M ,bulge,(c)diskstellar − ∗ objects∗ is blue despite having high n.Weturntothenatureof mass M ,disk, (d) global semimajor axis effective radius re, (e) bulgeare semimajor halfway between axis effective their radius red andre,bulge blue, (f) values, disk semimajor we place axis this exponential scale length rd,disk, ∗ 2 these outliers next. (g) M ,bulge/re,bulge,(h)M ,bulge/re,bulge,(i)bulge-to-totalratioB/Tpointin at the logI band,n (j)0.36, concentration which is markedC,(k)globalS with theersic´ vertical index n black,and(l)B/T based on stellar mass ∗ ∗ = M .The1σ error bars are displayed in the upper right of each panel.line. This The red value horizontal corresponds line in to eachn panel2.3, which represents is similar the division to the between red and blue galaxies. 4.3.2. Outliers Global∗ properties hardly differ between red and blue galaxies (whitevalue panels), of n butoften bulge used properties, to distinguish disk= scale quenched length, and (orn early-type)show key differences (colored panels and panel (c)). Specifically, red sequence bulges are physically smaller,galaxies yet more from massive, star-forming than those ones of the locally blue cloud. (e.g., Moreover, Shen et al. red2003 sequence; disksAlthough are less massiven acts than like a threshold for the vast majority their blue cloud counterparts. These trends cannot be produced byBell simple et disk al. 2004a fading;Schiminovichetal. but require a concentration2007 of; inner Drory stellar & Fisher mass. of galaxies, there are obvious exceptions, namely, the blue, (A color version of this figure is available in the online journal.) 2007). high-n (log n ! 0.36) “outliers” highlighted in Figure 7(a) and The medians also emphasize how flat the color trends are elsewhere. Understanding these objects is clearly crucial for above and below the threshold n value. Evidently, in the unraveling the quenching mechanism—why are they blue when Panels (a), (d), (j), and (k) of Figure 6 plotextreme integrated high-n anddifferences low-n regimes, in disk starmass, formationbulge historymass, is and bulgetheireffective photometric radius structure resembles that of quenched objects? quantities, while the remaining panels introduceindependent structural of n.between This differs blue markedly and red from overlap the behavior galaxies of (panelsWe (b), have (c), highlighted and (e)). 151 outliers in Figure 7 using color to in- parameters (e.g., M and r )forbulgesanddisksseparately.M /re;Figure5(c)The shows disks a strong of red correlation sequence between galaxiesM /r aree lessdicate massive their U by aboutB ranges; they make up 40% of all n>2.3 e ∗ ∗ − ≈ Among the integrated∗ properties, virtually no trendand is seen color in for star-forming0.2 dex galaxies than thebelow bluethe cloud overlap galaxies region. (panel (c)),galaxies while (the the red bulges points immediately above the red horizontal either stellar mass (panel (a)) or r (panel (d)), but a mildThe “step lack of importanceof red sequence of n above galaxies and below are the more threshold massive bydashed about line 0.3 at dexU thanB 1.20 are not outliers; they are quiescent e is further emphasized by the large color scatter in both of these red sequence galaxies− = shown for comparison). function” is seen with Sersic´ index in that n is significantlyregimes. This scatterthe is, blue however, cloud of galaxies two types. (panel At low (b),n,thereis in light tan).Several At the same possibilities time, come to mind to explain these objects. higher for quenched galaxies (panel (k), gray). Concentration,aratheruniformspreadincolor,i.e.,SSFRcanassumeanyvaluedisk sizes remain constant but bulge sizesOne decrease possibility by is about that they are artifacts due to the presence of C,showssimilarbehavior,albeitlesscleanly(panel(j)).Awithin a large range,0.3 and dexn does as bluenot predict cloud what galaxies SSFR will transition be. tobright the point-like red sequence AGNs. Adding a blue AGN to a normal star- similar trend with n was seen for all galaxies (FigureAt high5(e)),n, n predicts(panel color much (e), better, in blue). i.e., the These color distributiondifferences betweenforming red galaxy sequence would make the global colors bluer and increase but it is important to see the same effect for overlapis strongly galaxies peaked towardbulges red and (quenched) blue cloud colors, bulges but a significant amount to a differencen (and concentration) of 0.6 dex (Pierce et al. 2010). To pursue this, we alone. This establishes beyond doubt that M /r alone does not in bulge M /r (panel (h), in green). A similar trend is e ,bulge e,bulge 13 fully encapsulate the processes needed to quench∗ star formation. seen in B/T∗ ratios, but it is weaker due to the large spread of A possible interpretation is that some galaxies are “ripe” for blue galaxies. quenching based on M /re and that a second process, which These trends collectively demonstrate a real structural differ- drives galaxies to high ∗n,ultimatelyquenchesstarformation. ence between the inner stellar mass distributions of quenched We return to this idea later in Section 5. versus star-forming galaxies, and furthermore that this differ- The remaining panels in Figure 6 focus on the properties ence exists even within a narrow range of M /re.Highercentral of bulge and disk components separately (the subcomponent stellar mass densities in quenched galaxies∗ have been inferred sample; see Section 2.3). These parameters are derived from in previous work from higher integrated Sersic´ values (Weiner GIM2D photometric fits and M /LB values from the V I et al. 2005; Bundy et al. 2010), but photometric data by them- colors of bulges and disks separately∗ (Section 2.7), for which− selves do not rule out a simple fading picture in which disks high-resolution two-color HST imaging is required. The striking decline in brightness, permitting an underlying high-n bulge to result from the subcomponent panels in Figure 6 is the marked emerge. Actual stellar masses for bulges and disks separately

12 iue13. Figure Milky Way/ Andromeda progenitors14 ∗

aea gr 2 o rgntr fa Wlk aayfrom galaxy MW-like an of progenitors for 12, figure as Same EVOLUTION OF M GALAXIES 19

star-forming galaxies to quiescent galaxies. It is also during this period that the morphologies of the progen- itors become more spheroid-like, with Sérsic indexes exceeding n =3. Thisisthephasewherethegalxies “transition to quiescent/spheroid galaxies”. Again, the Andromeda-like progenitors enter and move through this phase earlier (at higher redshift) than the MW-like

AOIHE AL. ET PAPOVICH progenitors. z =3tothe There are strong correlations between the different indepen- dent observables. In Phase III, where the rest-frame colors z =0 resemble the colors of more quiescent stellar populations, is . 5. accompanied by the decline in the total IR luminosities. These are mutually reinforcing observations. The abrupt change in the Sérsic index from n =1forthe star-forming Phases I and II to the monotonic increase in Sér- sic index during Phase II correlates with the decline in the gas-mass fraction implied from the IR luminosities and op- tical sizes. Both the Andromeda-like and MW-like progen- itors switch from having n =1disks,constantwithredshfit, to a slowly rising Sérsic index with n > 1oncetheimplied gas-mass fraction drops below 0.5. The increase in Sérsic in- Papovich et al, in prep Figure 18. Evolution of the implied gas fraction of M∗ galaxies. The top panel shows the evolution of the gas fraction, where the gas fraction is de- dex anticorrelates linearly with the drop in gas-mass fraction, fined as fgas = Mgas/(Mgas + M∗). The solid lines show the median and 68%- where n = 2 for f (gas) = 0.4andn = 3 for f (gas) = 0.2 − 0.25. Most Milky Way/Andromeda-sized galaxies are quenchedtile range for the today Andromeda-like progenitors and the dashed lines show the The final evolution to quiescence, with specific SFRs < median and 68%-tile range for the MW-like progenitors. The evolution of −1 the gas fraction mirrors that of the Sérsic index, which is shown in the bot- 0.3 Gyr occurs once the implied gas-mass fraction drops to tom panel (solid line for the Andromeda-like progenitors and dashed line for f (gas < 0.2. Transition to bulge-dominated system at z~1- 1.5 the MW-like progenietors). This implies the decline in the gas fraction may Taken together this implies very homogeneous evolution for correlated with decline in star-formation/inferredbe relatedgas-fraction to the formation of galaxy spheroids. Andromed-like and MW-like progenitors. The only differ- halos of such galaxies are rare (and not the normal mode of ence is Andromeda advances through each evolution stage at (also Patelgrowth) 2012, or that such van mergers Dokkum conspire to2012) keep the number den- earlier redshifts. As the primary difference between the two sity of galaxies constant at all redshifts. galaxies is the final stellar mass of each galaxy, we conclude Both the Andromeda-like and MW-like galaxies go through that the mass of the galaxy drives when it passes through these the similar stages of evolution, but the Andromeda-like pro- evolutionary stages. genitors advance to the next stages at earlier epochs. This is 9. CONCLUSIONS based on three independent datasets: the rest-frame U − V, V − J color evolution, the evolution of sizes and Sérsic in- We have studied the evolution of the progenitors to dexes, and evolution in the far-IR luminosities. The stages Andromeda-like and MW-like galaxies from z =0.5toz 3 ∼ are the following. using data from zFourGE. The data span three widely sepa- rated 10 10 arcmin2 fields in the the COSMOS, CDF-S, and Phase I: At the earliest epochs the progenitors of both UDS fields,× and overlap with deep CANDELS HST imaging. • galaxies are blue, relatively unattenuated galaxies at Throughout we denote Andromeda-like progenitors to be early times. This is the “Lyman-break galaxy” phase those galaxies with a present-day (z =0)stellarmassof 10 of their evolution. During this phase, the morpholo- 10 10 M", and MW-like progenitors to be those galax- gies are consistent with disks (Sérsic index n = 1, that × 10 ies with a present-day stellar mass of 5 10 M".Theex- −1 grow as H(z) ,asexpectedforthesmoothgrowthof pected stellar masses for these progenitors× are taken from the the dark-matter halos. For Andromeda-like progenitors Moster et al. (2013) abundance-matching model, and corre- this phase occurs at z =3.1, and for MW-like progeni- spond to the expected evoluition of the stellar mass within a tors this phase occurs at z =2.1 − 2.5. 13 present-day dark-matter halo of mass Mh =1 10 M" for × 12 an Andromeda-like progenitor, and M =2.2 10 M" for a Phase II: In the next phase the progenitors of h × • both galaxies become dusty, IR-luminous star-forming MW-like progenitor. The zFourGE near-IR data are complete galaxies. This is seen as increase in the dust attenuation in stellar mass to z =2forMW-likeprogenitorsandtoz =3 of rest-frame U − V and V − J optical colors, and the for Andromeda-like progenitors. evolution of the IR luminosity from Spitzer and Her- The build-up of stellar mass in both the Andromeda-like schel.ForAndromeda-likeprogenitorsthisphasebe- and MW-like galaxies is on average smooth and monotonic, gins around z =2.5andcontinuestoz =1.0. For MW- and matches the growth that would be derived by selecing pro- like progenitors this phase begins later, at z 2, and genitors of these galaxies at fixed number density from mass also lasts to z =1.0. This is the “Luminous IR∼ galaxy” functions. This implies that either major mergers between phase of their evolution. halos of such galaxies are rare (and not the normal mode of growth) or that such mergers conspire to keep the number den- Phase III: At the lateset times both the Andromeda-like sity of galaxies constant at all redshifts. • and MW-like progenitors, the IR luminosity begins a Both the Andromeda-like and MW-like galaxies go through steady decline. This corresponds to evolution in the the similar stages of evolution, but the Andromeda-like pro- rest-frame U −V and V − J colors from dust-embedded genitors advance to the next stages at earlier epochs. This is 3

COMPACT −2.5 0.5

− −1.5 −1 −0.5 COMPACT 0 SF 0.5 Twolog sSFR [Gyr pathways to create quiescent galaxies? 1 L = 1042−43 X 1.5 L > 1043 5 extendedX compact DELS in GOODS-S and UDS, we analyze stellar masses, 10 SFRs and sizes of a sample of massive (M! > 10 M") −2.5 1.8

] The cSFG population is already in place at z 3, but 1

− −1.5 it completely disappears by z<1.4. A corresponding increase in the number of cQGs during the same time −1 period suggests an evolutionary link between them. A simple duty-cycle argument, involving quenching of −0.5 the star formation activity on time scales of ∆t =0.3 − 0 1 Gyr, is able to broadly reproduce the evolution of the density of new QGs formed since z = 3 in terms of fading 0.5 cSFGs. Under this assumption, we also need to invoke log sSFR [Gyr a replenishment mechanism to form new cSFG via gas- 1 rich dissipational processes (major mergers or dynamical instabilities), that then become quickly inefficient at z ! 1.5 1.5, as the amount of available gas in the halo decreases with time (e.g., Croton 2009). 8.5 9 9.5 10 10.5 11 11.5 8.5 9 9.5 10 10.5 11 11.5 8.5 9 9.5 10 10.5During11 the11.5 transformation processes, the compact log [M kpc−1.5] log [M kpc−1.5] log [M phase kpc is−1.5 probably] associated with: enhanced (probably Σ1.5 solar Σ1.5 solar Σ1.5 solarnuclear and dusty) star formation, the presence of an Fig. 4.— Schematic view of a two path (fast/slow track) for- AGN, and sometimes a short-lived quasar, followed by a 1.5 Barro et al. 201210 Fig. 2.— Evolution of the sSFR vs. Σ1.5≡M/re correlationmation at scenario 0.5 fraction10 M of !.Theredshiftbinsaredecline of the star formation in ∼1 Gyr (Hopkins et al. the massive SFGs at z =2− 3evolve(e.g.,throughgas-richdis- chosen to probe similar comoving volumes. The solid linessipational andcoloreddotsdepicttheselectionthresholdsforSFGs(blu processes) to a compact star-bursting remnant. Then, 2006).e) and All QGs these (red) phenomena fit with the observed prop- and compact (white region) and non-compact (shaded region)the star,asdefinedinFigure1.Theopenmarkersdepictsourcesdetec formation is quenched in ∼800 Myr ( perhaps by AGN erties of cSFGsted in presented the in this letter. cSFGs present 42 43 43 44 X-rayscompact at different star-forming luminosities: squares galaxies have 10 2, and stars galaxies have L fadeX > into10 cQGs.(10 Once;i.e,QSO)erg/s.Blueandno visible traces of mergers, but they do show lower red arrows indicate the median Σ1.5 of cSFGs and cQGs, respectively.in the red sequence, Green cQGs arrows grow envelopes, approximate over longer the local time sc mass-sizeales, relationsSFRs than (Shen the et bulk al. of massive SFGs, presumably be- de-populating the compact region by z∼1. Simultaneously, at . . 2003).30x The more black contourlikely showsto host the sSFR- luminousΣ1 5 distribution X-rayz ! for2, AGN other 90% (slower) of the mechanisms galaxies at have 0.5 already 1043erg s 1)X-raydetectedAGNsatz>2, sug- gesting that these might be playing a role in the quench- with α =1.5. The slope is roughly consistent withmechanisms those tocQGs reduce disappears the size of massive by z ∼ (larger)1. Simultaneously, SFGs ing of star we formation. identify given by Newman et al. (2012) for QGs at similarare red- gas-rich dissipationala population processes, of compact such as mergersSFGs (cSFGs) or Our whose observations number connect two recent results at z ∼ 2: −1 dynamical instabilities.density decreases These can steadily produce with compact, time sincea populationz =3.0, being of compact (n " 2) galaxies with en- shifts (α =0.59-0.69). The zero-point is chosenstar-bursting to in- remnants that would likely quench in a clude the majority of QGs with minimum contamination almost completely absent at z<1.4.hanced The starnumber formation of activity (Wuyts et al. 2011b) and α short period of time (Hopkins et al. 2006; Dekel et al. an increasing fraction of small, post-starburst galaxies from SFGs. For α =1.5, M/re (hereafter, Σ1.5) lies2009). be- WithoutcSFGs relying makes on mergers up less being than the 20% main of or all massiverecently SFGs, arrived but on the red sequence (Whitaker et al. tween the surface density, Σ =M/re2,andM/re,bothofsole driver of thisthey transformation, present similar we can number make a densities quan- as2012). cQGs The down emerging to picture suggests that the formation which follow strong correlations with color and SFRtitative up estimatez ∼ of2, the suggesting number of cSFGs an evolutionary assembled by linkof between QGs follows the two two evolutionary tracks, each one dom- this mechanismpopulations. by using typical numbers for major merg- inating at different epochs (as illustrated in Figure 4). to high redshifts (e.g., Franx et al. 2008). ers at these redshifts. Considering pair fractions of At z " 2 the formation of QGs proceeds on a fast track . roughly 10% (Williams et al. 2011), merger time scales of Figure 2 shows the evolution of sSFRs vs. Σ1 5 for mas- 3. CO-EVOLUTION OF COMPACT SFGS(right-region): AND QGS from z =3.0 − 2.0, the number of cQGs sive galaxies from z =3.0downtoz =0.5. In this1 Gyr dia- (Lotz et al. 2011) and a density of massive galax- builds up rapidly upon quenching of cSFGs at roughly −3 −3 ∼ gram, our size-mass-SFR selection is completely orthogo-ies of ! 10 MpcAn evolutionary(P´erez-Gonz´alez sequence et al. 2008), where we cSFGsconstant areΣ the1.5. Merely pro- 2 Gyrs later (z 1), cQGs almost obtain an assemblygenitors rate of for cQGs new cSFGs at lower via mergers redshifts of is supportedcompletely disappear by the due to: 1) size growth as a result nal. Although our analysis focuses on z>1.4, two panels∼ −4 −1 ∆ncSFG 10 factGyr that, which cSFGs is roughly first consistentappear before with cQGsof minor at high mergers red- satellite accretion (Naab & Ostriker at lower redshifts are shown to illustrate the extrapo-the observed densities for the predicted ∆tburst. 2009; Newman et al. 2012) or the re-growth of a remnant lated evolutionary trends. We find that the number of shift (z =2.6 − 3.0) and then disappear before them at In this model, the significant decrement− on the num- disk (Hopkins et al. 2009) which causes them to leave QGs (above the line) increases rapidly since z =3,start-ber cSFGs bylowz<1 redshift.4 implies (z that=1 the.0 formation1.4), implying mech- the that compact evolution region; is 2) a decrement in the efficiency of ing from very small number densities, n ∼ 10−5 Mpcanism(s)−3, becomefrom quickly blue through inefficient red at lower rather redshifts, than vice versa.the formation Therefore, mechanisms for new cSFGs, and therefore ∼ thereby truncatingif we the assume formation that of new cSFGs cSFGs would and thus see theirnew star cQGs. formation By z ! 2, other (probably slower) mech- at z 2.8. Among these, the number of compactcQGs. QGs This gradual decline of the efficiency of the dissi- quenched and fade at roughly constant anismsΣ . , these start to could populate the red sequence with larger, (cQG; Σ1.5>10.3) builds up first, and only at z

10.1

N=5211 fob=0.72 N=13991 fob=0.56 N=13640 fob=0.20 best-fitting model 2 triaxial component oblate component P(q) 1

0 −4 −3 Figure 4. Evolution in the structural properties of galaxies selectedataconstantcumulativenumberdensityof3 1

since z ∼ 3, with most of this change occurring at z<2. The apparent constant sizeP(q) at 1.5 1. The most striking feature is the large fraction of oblate, that is, disk-like galaxies in the high-mass effect (Naab et al. 1999; Bournaud et al. 2007). Overall, F¨orster Schreiber, N. M., Shapley, A. E., Erb, D. K., Genzel,R., bin. a consistent narrative is emerging in which merging and Steidel, C. C., Bouch, N., Cresci, G., Davies, R. 2010, ApJ, accretion explain the growth in size and change in struc- submitted, arXiv:1011.1507 TABLE 3 Franx, M., van Dokkum, P. G., F¨orster Schreiber, N. M., Wuyts, Double-component fitting results for z =0 ture of massive, passive galaxies over time. a b c d e S., Labb´e, I., & Toft, S. 2008, ApJ, 688, 770 Mass redshift(z) fob b σb T σT E σE PKS PMW Further support for the direct link between the disk- Genzel, R. et al. 2010, ApJ, submitted, arXiv:1011.5360 10.8-11.5 0.04-0.08 (SDSS) 0.20 ± 0.02 f 0.29 ± 0.02 0.07 ± 0.01 0.64 ± 0.06 0.08 ± 0.05 0.41 ± 0.02 0.19 ± 0.02 0.26 0.46 like galaxies at z ∼ 2andthepressure-supported, Hartley, W. G. et al. 2010, MNRAS, 407, 1212 10.5-10.8 0.04-0.08 (SDSS) 0.56 ± 0.06 0.28 ± 0.01 0.08 ± 0.01 0.68 ± 0.12Patel 0.08 ± 0.06 0 .45et± 0. 02al. 0.16 ±20130.03 0.29 0.19 massive elliptical galaxies in the present-day universe Hopkins, P. F. et al. 2010, ApJ, 715, 202 10.1-10.5 0.04-0.06 (SDSS) 0.72 ± 0.06 0.28 ± 0.−014 0.09 ± −0.013 0.48 ± 0.08 0.08 ± 0.06 0.49 ± 0.02 0.12 ± 0.02 0.84 0.28 Figure 5. Example postage stamps for galaxies selected at a constant cumulativea number density of nc =1.4 × 10 Mpc at different Hopkins, P. F., Hernquist, L., Cox, T. J., Keres, D., & Wuyts, S. fob is the fraction of the oblate component. is provided by the comparable stellar densities of b redshifts. At a given2009, redshift, ApJ, 691, objects 1424 were selected to havepropertiesthatfollowthegeneraltrendsseeninFigure4.b the intrinsic axis ratio of the oblate component and σb itsEach standard postage deviation. stamp ∼ c the z 2 galaxies and the cores of present-day Koekemoer, A. M., Fruchter, A. S., Hook, R. N., & Hack, W. T is the mean triaxiality parameter, with standard deviation σT;thesearesetto0or1fortheoblateandprolatemodels. is 30 kpc on a side and is rotated such that the major axis is aligned horizontally.d The PSF FWHM is indicated by the circle in the bottom ellipticals (Bezanson et al. 2009; Hopkins et al. 2009;z~2 massive2002, The 2002 HST early-type Calibration Workshop galaxies : Hubble after the appearE and σlessE are the ellipticityround/more (1 minus the intrinsic short-long disky axis ratio) and its standard deviation. right of each panel and the effective radius (in kpc), S´ersic index, and axis ratioeThefinal (q)aregiveninthebottomleft.Thehalf-lightellipse two columns list the KS and KW probabilities that the observed and best-fitting model projected axis ratio distributions are van Dokkum et al. 2010). Dynamical modeling(shown of very in white) growsInstallation larger of toward the ACS lower and the redshift NICMOS indicat Coolinging System, that337 more light isindistinguishable, added to the for a outer randomly parts, drawn realization leading of to the themodellarger distribution sizes, with S´ersic the same number of objects as the observed samples. Khochfar, S., & Silk, J. 2006, ApJ, 648, L21 These serve as a crude goodness-of-fit test. massive nearby ellipticals has revealed thatindices, whereas( and the→ the massive buildup of stellar fast mass. rotators Toward higher at reds hifts,high the z? median could axisf ratio declines, be mergers:Robertson suggestive of randomly oriented disks. & Bullock 2008) global rotation rate is small, the majority of the stars, Krist, J. 1995, ASPC, 77, 349 Uncertainties are obtained from bootstrapping. Kroupa, P. 2001, MNRAS, 322, 231 can use our superior knowledge of the low-redshift pop- component vary arbitrarily. That is, the parameters b, even in the inner parts, are on disk-likewith orbits the (see exponentLabb´e, I. being et al. 2003,, consistent ApJ, 591, L95 with the value of 0.25 1, from fob ∼ 0.2atz<1tofob =0.60 ± 0.24. constant medianPapovich,r arises C., Dickinson, because M., Giavalisco, SFGs are M., larger Conselice, than C. J., & van Dokkum et al. (2010). The S´ersic index evolution in- Kambiz Fathi for sharing his disk scale length measure- Ferguson,e H. C. 2005, ApJ, 631, 101 dicates that while most of the stars in 2M ! galaxies in ments and comments on the manuscript. QGs and theirPeng, relative C. Y., Ho,abundance L. C., Impey, changes C. D., & Rix, as H.-W. a function 2002, AJ, ∼ of redshift. Above124, 266z>3, the size evolution is likely de- the nearby universe are distributed in a bulge, the stars Quadri, R. et al. 2007, ApJ, 654, 138 in their progenitor galaxies at z>2 were distributed in REFERENCES termined almostRobaina, solely A. R., by Bell, SFGs E. 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Lotz et al. 2011 The Astrophysical Journal,753:114(25pp),2012July10 Wuyts et al.

The Astrophysical Journal,753:114(25pp),2012July10 Wuyts et al.

Clumps v. Mergers

Wuyts et al. 2013

Figure 2. (Continued)

2011a). In the resolvedbright-o case, theff SFR-weighted center age“clumps” of a galaxy canWhile look for galaxies that from integrated photometry are inferred is computed equivalently: to be the oldest, the age estimate does not depend sensitively on like interactions; the adopted approach, the recovered age of the younger systems (or at least those inferred to be the youngest from their integrated Npix tobs photometry) can increase by up to an order of magnitude in i 1 0 SFRi(t)(tobs t) dt agew, resolved = − . (3) the most extreme cases when taking into account the resolved = Npix tobs much! more"i 1 0 SFRcommoni(t) dt at z>1photometric constraints. Outshining of the underlying older = (Förster-Schreiber! " et al. 2006)7

can migrate to center to form a bulge Figure 2. (Continued)

Fig. 2.—Face-on snapshots of the disk mass density (gas and stars) for run 0N, which has a cuspy dark matter profile. Time is in Myr. Clumps form quickly in the disk and move to the center, where they coalesce into a bulge within 1 Gyr. Extra starElmegreen formation in the bulge region is triggered et at theal. time of2009 merging as well. Afewclumps 2011a). In the resolved case, the SFR-weighted age of a galaxy While for galaxies that fromremain inintegrated the disk when the photometry simulation ends. are inferred is computed equivalently: to be the oldest, the age estimate does not depend sensitively on the adopted approach, the recovered age of the younger systems (or at least those inferred to be the youngest from their integrated Npix tobs photometry) can increase by up to an order of magnitude in i 1 0 SFRi(t)(tobs t) dt agew, resolved = − . (3) the most extreme cases when taking into account the resolved = Npix tobs ! "i 1 0 SFRi(t) dt photometric constraints. Outshining of the underlying older = ! " 7

Fig. 3.—Same as Fig. 2, but for run 0B, where a primordial bulge of 10% of the disk mass is initially present in the model. The initial bulge stars are not shown here; only the gas and stars from the initial disk are shown. Resolved spectroscopy of lensed galaxies 1251

Clumpy galaxies at high spatial resolution 1250 T. A. Jones et al. 1250 T. A. Jones et al. 1260 T. A. Jones et al. Downloaded from http://mnras.oxfordjournals.org/

1252 T. A. Jones et al. Downloaded from Downloaded from by guest on July 21, 2013 http://mnras.oxfordjournals.org/ http://mnras.oxfordjournals.org/ T. Jones et al. 2010 ; Keck AO Figure 8. Hα-inferred SFR as a function of H II region size. Red circles Figure 7. Size versus dynamical mass of individual star-forming regions represent individual H II regions from our lensed sample. Cl 0949 5152 was within our high-redshift sample, compared to local star clusters and H II + lensed z~2 have massive, large star clusters observed in [O III]withtheHα flux taken to be 1.2 times the [O III]λ5007 II regions. The high-redshift H regions have size and mass consistent with flux as determined from long-slit NIRSPEC observations. The value for Downloaded from Figure 2. Source plane properties of the lensed galaxy(consistentthe sample. largest From left- star-forming to with right-hand unstable panels complexes in each row: ACSdisk in broad-band the localpicture?) emission, universe. line intensity, Local velocity data are and velocity dispersion derived from the OSIRIS nebular emission line data. Axes are in kpc with 1–2 pixels per OSIRIS resolution element. Each galaxy MACS J2135 0102 was determined from the Hβ flux assuming case B Figure 1. True colour ACS images of the sample derived from the multiband data referred totaken Table 1. fromThe xy scale Harris is in arcseconds. (1996) Critical and Pryor lines for & the Meylanarc (1993) for Galactic globular − shows morphological and kinematic structure on scales down to 100–200 parsec. The nebular line flux distribution is similar by guest on July 21, 2013 to the rest-UV morphology recombination. The SFRs are all derived from Hα luminosities using the redshifts, derived from lens modelling (Section 2.3), are shown in red. The critical line for Cl 0024 1709∼ falls outside the image. Figure 1. True colour ACS images of the sample derived from the multiband data referredwith to multiple Table 1. The resolvedxy scale clumps, is in arcseconds. shown as red Critical crosses lines on thefor+ theACS arc images. Red contours on the line intensity maps denote clumps which are spatially extended clusters; Has¸egan by guest on July 21, 2013 et al. (2005), Hilker et al. (2007) and Evstigneeva et al. Kennicutt (1998) prescription. Red squares are from the lensed z 4.92 redshifts, derived from lens modelling (Section 2.3), are shown in red. The critical line forand Cl 0024unconfused1709 fallsat the outside3σ flux the image. isophote in narrow-band→expect emission line images,more as described from in SectionHST 4. Best-fitting Frontier disc model Fields contours are shown on the " = done in a standard ABBA positionvelocity sequencesub-kpc maps+ for to those achieve galaxies good resln whose sky dynamicsearlier are relevant consistent(2007) articles with for rotation (Kneib ultra-compact (Section et al. 1993, 3.1). 1996; Dashed dwarf Smith boxes etgalaxies; in al. the 2005; ACS images McCrady of MACS & J0451 Graham and MACS (2007) J0712 for galaxy presented by Swinbank et al. (2009), black points are H II regions in subtraction. In the case of Cl0024indicate1709 the we smaller chopped regions 8 arcsec for which to OSIRISJullo data et are al.M82 displayed. 2007) clusters;within Caustics which are Fuentes-Masip further shown details as dashed can blue be et found. lines al. (2000)in the ACS for images giant of multiply H II regions; imaged arcs. and Bastian done in a standard ABBA position sequence to achieve good sky earlier relevant+ articles (Kneib et al. 1993, 1996; Smith et al. 2005; 1 sky, whilst in the remaining cases we chopped the galaxy within Our basic approach is to use the code LENSTOOL (Kneib et al. local spiral galaxies from Gonzalez Delgado & Perez (1997), and blue open subtraction. In the case of Cl0024 1709 we chopped 8 arcsec to Jullo et al. 2007) within which further details can be found.et al. (2006) for star-forming complexes in the Antennae. The dashed line + the IFU. Individual exposures were 600–900 s and each observ- 1993;1 Jullo et al. 2007) to constrain a parametrized model of the circles are star cluster complexes in the interacting galaxies NGC 4038/4039 http://mnras.oxfordjournals.org/ sky, whilst in the remaining cases we chopped the galaxy within Our basic approach is to use the code LENSTOOL (Kneib et al. Downloaded from ing block was 2.4–3.6 ks whichderive wasbest-fitting typically repeated parameters three on to the massdark matter distribution. distribution.LENSTOOL For each cluster,We can the verify model this comprises value by two computing the total magnification from the IFU. Individual exposures were 600–900 s and each observ- 1993; Jullo et al. 2007) to constrain a parametrized modelrepresents of the a model for regions which are optically thick to far-infrared ra- from Bastian et al. (2006). The vectors A and B are explained in the text. six times. The total integrationuses time a for Markov each Chainobject isMonte given Carlo in (MCMC)components: sampler 1 or to 2 derivecluster-scale a darkthe matter ratio of haloes, the sizes parametrized (or equivalently, the total fluxes) between the ing block was 2.4–3.6 ks which was typically repeated three to dark matter distribution. For each cluster, the model comprisesdiation two and have undergone adiabatic expansion (Murray 2009). Dynamical Table 1. family of mass models suitably fitting thewith strong a dual lensing pseudo-isothermal constraints, ellipticalimage mass and its distribution source plane (dPIE; reconstruction. As the magnification fac- The dashed line shows a fit to the data from local spiral galaxies, and the six times. The total integration time for each object is given in components: 1 or 2 cluster-scale dark matter haloes, parametrized 2 Our data reduction methods closelyand we followed use these those to derive described the uncertainty in El´ıasd on eachottir´ mass etparameter al. 2007), for of the and the high-redshift50 galaxy-scaletor is not isotropic, data dPIE dark is the calculated matter angular size as of eachMdyn image isC more(Rσ highly/G)with Table 1. with a dual pseudo-isothermal elliptical mass distribution (dPIE; ∼ dotted line is the same but increased by a factor of 100 times in SFR density. detail by Stark et al. (2008). Wemass used distribution. the OSIRIS data reduction haloes, centred on massive cluster membersstretched occupying along a specific the strong orientation (Fig. 1) thus= affecting our Our data reduction methods closely followed those described in El´ıasdottir´ et al. 2007), and 50 galaxy-scale dPIE darkassumed matter C 5 appropriate for a uniform-density sphere. The mass error The high-redshift star-forming regions have significantly higher density of pipeline (Larkin et al. 2006) to performFor each sky of subtraction, the sources∼ spectral presented inlensing this paper, region the in best order model to account= forsource the presence plane resolution. of substructure. The linear factors µ1 and µ2 of the magni- http://mnras.oxfordjournals.org/ detail by Stark et al. (2008). We used the OSIRIS data reduction haloes, centred on massive cluster members occupyingbars the strong account for statistical uncertainty in R and σ . extraction, wavelength calibration,was and then form used the to data derive cube. the To geometrical ac- These transformation galaxy-scale necessary haloes are assumedfication to have (with massµ propertiesµ1 µ that2) together with their associated errors are massive stars than H II regions in nearby spirals, but are comparable to the pipeline (Larkin et al. 2006) to perform sky subtraction,curately combine spectral the individuallensing data region cubes, in order we created to account images for theof presencefollow of a substructure. scaling relation based on the luminosity of the= underlying× extraction, wavelength calibration, and form the data cube. To ac- Thesefor galaxy-scale mapping the haloes image are plane assumed coordinates to have mass into propertiesthe source that plane. This listed in Table 1. A detailed illustration of the uncertainties of the brightest star cluster complexes found in the local universe. the integrated emission line andtransformation used the peak intensity enables to us centroid to reconstructgalaxy, the HST assumingmorphology a constant and mass-to-lightmass ratio modelling (e.g. Natarajan method et for al. MACS J2135 0102 is given in Stark curately combine the individual data cubes, wethe created object. images We then of spatiallyfollow aligned a scaling andrelation co-added based the individual on the luminosity1998; of the Smith underlying et al. 2005). − the integrated emission line and used the peak intensity to centroid galaxy,H assumingα emission a constant line images mass-to-light in the source ratio plane (e.g. assuming Natarajanclusters conservation et al. in the localet al. universe. (2008). Statistical uncertainty in the dynamical data cubes to create the finalof mosaic. surface Flux brightness. calibration The was spot per- magnificationDetailsµ onand the its construction associated of eachA gravitational key parameter lens model in our are analysis is the physical resolution we the object. We then spatially aligned and co-addedformed the by individual equating the flux1998; density Smith of et the al. 2005).tip-tilt stars measured given inxy Dye et al. (2007) for MACS J2135 0102, in Limousin H II regions to merge together giving the appearance of a larger error are computed with LENSTOOL at different positionsmass across is 20–60 the perachieve cent, in the so source the plane additional for each target. factor To measure of this,2systematic we use data cubes to create the final mosaic. Flux calibrationfrom Two was Micron per- All SkyDetails Survey photometryon the construction with the of observed each gravitationalet al. lens (in preparation) model are for Cl0024 1709 and− MACS J0744 3927 ∼ formed by equating the flux density of the tip-tilt stars measured givenobject, in Dye using et al. the (2007) family for of MACS mass modelsJ2135 0102, from the inuncertainty Limousin MCMC sampler. in +Cobservationscontributes of the tip-tilt significantly+ reference stars. to These the serve dynamical this purpose mass region with similar surface brightness. Since the surface brightness OSIRIS spectra. We estimate that the uncertainty in flux calibration −and in Richard et al. (in preparation) for the remaining three sources from Two Micron All Sky Survey photometry withis typically the observed 10 per cent. et al. (in preparation) for Cl0024 1709 and MACSin Table J0744 1. Strong3927 lensing constraints originate from the identifica- of the high-redshift H II regions is 100 higher than in local spi- by guest on July 21, 2013 + estimate.+ The mass–radius relation of the high-redshift clumps by guest on July 21, 2013 is OSIRIS spectra. We estimate that the uncertainty in flux calibration and inC Richard2010 The et al. Authors. (in preparation) Journal compilation for the remainingCtion2010 of RAS, three2–5 multiplyMNRAS sources404, imaged1247–1262 systems per cluster within the various ∼ × % % rals, we conclude that the offset cannot be explained by different is typically 10 per cent. 2.3 Gravitational lens modellingin Table 1. Strong lensing constraints originateACS from images. theshown identifica- We use in the Fig. astrometric 7 along positions with and spectroscopic/ a sample of local star clusters and giant tion of 2–5 multiply imaged systems per clusterphotometric within the redshifts various of these sources2 as individual constraints to H II regions for comparison. This shows that the H II regions studied resolution and sensitivity of the various data sets. Metallicity also 2.3 Gravitational lens modelling In order to investigate theACS source images. plane We properties, use the astrometric we must first positions and spectroscopic/ correct for the distortion andphotometric magnification redshifts by the of clusterthese sources lens. We2 as individual constraintshere are to comparable in size and mass to the largest local star-forming fails to explain the offset, as demonstrated by MACS J2135 0102 In order to investigate the source plane properties,summarize we must here first the ingredients necessary to construct the relevant 1 http://www.oamp.fr/cosmology/lenstool − IV correct for the distortion and magnification by thecluster cluster mass lens. models. We We will follow the methodology defined by 2 Spectroscopiccomplexes redshifts are available and for consistent a majority of the with systems. the mass–radius relation observed which has an R23 index and C P Cygni profile suggesting summarize here the ingredients necessary to construct the relevant 1 http://www.oamp.fr/cosmology/lenstool 0.4–1 Z metallicity (Stark et al. 2008; Quider et al. 2010). This 2 locally.Figure 2 – continued cluster mass models. We will follow the methodology defined by Spectroscopic redshifts are available for a majorityC of the systems. C # 2010 The Authors. Journal compilation # 2010 RAS, MNRAS 404, 1247–1262 $ In Fig. 8, we compare the size–luminosity relation of these star- implies that the luminosities in the high-redshift H II regions are C 2010 The Authors.well as Journal they arecompilation point sourcesC 2010 observedRAS, MNRAS with404, conditions1247–1262 and an elements along the direction of highest magnification (Table 1). We # # forming regions with equivalent data observed locally (from Gon- truly much larger than in local spirals. Furthermore, the observed instrumental configuration identical to those of our distant targets. fit Gaussian profiles to the strongest emission line (Hα or [O III]) at We ‘reconstruct’ these stars in the source plane aszalez if they Delgado were each & spatial Perez pixel 1997 using a for weighted normalχ 2 minimization spirals, procedure and Bastian and et al. diameters are consistent with the Jeans length for support by ve- located at the arc position using the same transformation as for determine the two-dimensional intensity, velocity and velocity dis- locity dispersion, suggesting that they collapsed as a result of disc the lensed galaxies, and fit a bivariate Gaussian to the2006 point for spread intensepersion starbursts maps. To compute such the as emission the Antennae) line fits we first and subtracted with a lensed function in order to determine the source plane resolution.arc at z The 4.92the median (Swinbank value at each et spatial al. pixel 2009). to remove The any sizes source con- observed in instabilities. We expect this to occur since the Toomre Q parameter typical FWHM of each arc in the direction of highest magnification= tinuum and residual sky background. A blank region of sky within is less than unity for all galaxies in our sample. It therefore seems is listed in Table 1 and, with the exception of Cl0024the1709 high-redshift which each galaxies data cube was are used comparable to determine the sky to variance the largest spectrum local star- + 1 is not highly magnified, varies from 60 to 350 pc withforming a mean of (H II)V regions(λ). The spectra but to with be fit are100 weighted byhigherw(λ) SFRsV − appropri- than in local likely that intense star-formation in high-redshift galaxies is driven 200 pc. ate for Gaussian noise, so that∼ regions× of higher noise= (e.g. strong spiral galaxies.sky However, emission lines) thedo not implied cause spurious SFR fits. We densities compute the areχ 2 roughly by the fragmentation of gravitationally unstable systems. statistic for the best-fitting Gaussian as well as a for a featureless consistent withspectrum that observed [f (λ) 0] and in require the a most minimum vigorous improvement local over the starbursts. 3ANALYSIS This result is notfit with significantly no line of=$χ 2 16–25 affected for the various by the arcs (i.e.resolution 4–5σ emis- of differ- = 5CONCLUSIONS First, we reconstruct the reduced, flux-calibrated dataent cubes observations, to the sion line although detection). varying If this criterion the was selection not met, we isophote averaged the alters the source plane using transformations from the gravitational lens mod- surrounding 3 3 spatial pixels to achieve higher signal to noise. No × els described in Section 2.3. The resulting data cubes were binned fit was made if the 3 3 averaging still failed to produce the mini- radius–luminosity relation.× We note that the flux isophotes used to We have utilized strong gravitational lensing together with laser- such that each spatial pixel corresponded to 0.5–1 FWHM resolution mum $χ 2 improvement. We calculated the formal 1σ error bounds define H II regions in local spirals are much lower, so to quantify assisted guide star adaptive optics at the Keck observatory to study

C CII this effect# we2010 extract The Authors. individual Journal compilation H# 2010regions RAS, MNRAS from404, narrow-band1247–1262 Hα the internal characteristics of six z 1.7–3 star-forming galax- images of local galaxies from the Spitzer Infrared Nearby Galaxies ies with a spatial resolution down to =100–200 parsec. Extending Survey (SINGS; Kennicutt et al. 2003) and 11 Mpc Hα and Ul- beyond the diffraction limited capability∼ of current 8–10 m class traviolet Galaxy Survey (11HUGS; Lee et al. 2007) using various telescopes, our study provides an interesting preview of the science isophotes. The effect on the size–luminosity relation as the isophote that will routinely be possible with future 30 m class optical/infrared is increased is shown in Fig. 8 as the vector A, which demonstrates telescopes with adaptive optics systems. We demonstrate that en- that the extracted regions become smaller with higher average sur- hanced resolution allows us to resolve morphological and kine- face brightness. The vector B shows the effect of degrading the matic structure which has not been (and cannot be) discerned in resolution while the isophote is kept fixed, which causes distinct AO-based surveys of similar non-lensed sources. In particular, we

C C % 2010 The Authors. Journal compilation % 2010 RAS, MNRAS 404, 1247–1262 10 P. E . Fre e m a n e t a l .

5.2 The relationship between the number of annotators New (better) way to find z~2 Mergers and classification efficiency Detection of disturbed galaxy6 morphologiesP. E . Fre e m3 a n e t a l . 4 P. E . Fre e m a n e t a l . 6 P. E . Fre e m a n e t a l . An astronomer’s time is a valuable commodity. Given a set of N Table 2. Classifier performance 104 – H-band/non-regular. Table 2. Classifier performance× 104 – H-band/non-regular. that the results of applying each were similar: in the vast majority Table 1. Confusion matrix: definitions. This table displays sample mean plus/minus× 1σ standard error, astronomers with nominally similar annotation ability, is it best to of cases, galaxies were either classified correctly or incorrectly by each multipledThis table by displays 104. sample mean plus/minus 1σ standard error, 4 have all of them train a machine-learning algorithm by visually all four algorithms. Thus, in this work we describe only the con- Predicted Predicted each multipled by 10 . Detection of disturbed galaxy morphologies 3 ceptually simplest of the four algorithms, random forest (Breiman regular/ non-regular/ ID A-ID A-MID Full inspecting hundreds if not thousands of galaxy images? Or can ID A-ID A-MID Full 2001). For an example of an analysis code that uses random forest, non-merger merger Figure 1. Example of pixel grouping for computing the multimode (M) Figure 2. Example of pixel grouping for computing the intensity (I)statis- Sens 7562 14 7907 11 7873 11 7874 13 using a subset of size n N yield similar detection efficiency? statistic.see Appendix To the left we display A. the H-band pixel intensities for an example Actual TN FP Sens± 7562 14± 7907 11± 7873 11± 7874 13 tic. To the left we display pixel intensities for an example of a merger galaxy Spec 8071 13± 8187 78136± 78181± 10 ± " of a merger galaxy (see Fig. 3), while to the right we show only those pixels (see Fig. 3). These data are smoothed using a symmetric Gaussianregular/ kernel (True negatives) (False positives) Spec± 8071 13± 8187 78136± 78181± 10 To attempt to answer these questions, we utilize an analysis car- associated with the largest 5.8 per cent of the sorted intensity values. The of width σ 1pixel,asufficientlysmallscaletoremovelocalintensity Risk 4366 83906± 83991± 83945± 8 ± two pixel regions have areas A(1) 21 and A(2) 14, so that R0.942 = non-merger Risk± 4366 83906± 83991± 83945± 8 = = = maxima caused by noise without removing local maxima intrinsic to the Toterr 2056 7188341930418975 (143.1/21) Random14 9.33. The forestM statistic regression is the largest of the R values computed ± ± ± ± ried out by the CANDELS collaboration (Kartaltepe et al., in prepa- × = galaxy itself. (See the text for details on how we select the appropriate Toterr± 2056 71883± 41930± 41897± 5 for a sufficiently large number of threshold percentiles. PPV 5712 13 5943 958659597711

smoothing scale σ .) To the right we display pixel regions associatedActual with Downloaded from FN TP ± ± ± ± Figure 1. Example of pixel grouping for computing the multimode (M) Figure 2. Example of pixel groupingeach for computing local intensity the intensity maximum (I)statis- remaining after smoothing. Pixel intensities PPV± 5712 13± 5943 95865± 95977± 11 statistic. To the left we displayThe the H-band first pixel step intensities in for applying an example random forest is a regression step: we non-regular/ (False negatives) (True positives) NPV 9089 49215± 49199± 49194± 4 ± ration) in which 200 objects observed in the J-andH-bands by the nuclei are present, and towards 0 if not. Becausetic. To the this left ratio we display is sensi- pixel intensitiesare for summed an example within of a mergereach region, galaxy with the intensity statistic then being the NPV± 9089 49215± 49199± 49194± 4 of a merger galaxy (see Fig. 3),tiverandomly while to noise,to the right we we sample multiply show only it those50 by A per pixels, cent which(see of tends Fig. the 3). towards galaxies These data 0 if are the (i.e. smoothed populate using a symmetric a training Gaussian kernel associated with the largest 5.8 per centFreeman of the sorted intensity values. etl,(2) The al. 2013 ratio of the second-largest to largest sum. In this example, themerger statistic is ± ± ± ± 4 of width σ 1pixel,asufficientlysmallscaletoremovelocalintensity HST WFC3 in the DEEP-JH region of the GOODS-S field were two pixel regions have areassecond-largestA(1) 21 and A group(2) 14, is so a manifestation that R0.942 of noise. The=M statistic is I 0.935. set)= and regress= the fraction= maxima of annotators, caused by noise withoutYi removing[0,= local1], maxima who intrinsic view to the (14/21) 14 9.33. The Mthestatistic maximum is the largestRl ofvalue, the R values i.e. computed 4 × = galaxy itself. (See the text for details∈ on how we select the appropriate Table 3. Classifier performance 10 – H-band/merger. This for a sufficiently large number ofgalaxy threshold percentiles.i as a non-regular/merger upon that galaxy’ssymmetry, set both of theimage intensity centroid and the maximum associated 4 http://mnras.oxfordjournals.org/ smoothing scale σ .) To the right we display pixel regions associated with Downloaded from Table 3. Classifier performance× 10 – H-band/merger. This each annotated by 42 voters. The details of voting are similar to M max Rl . each local intensity maximum(2) remainingwith afterI(1) smoothing.should lie Pixel at intensities the galaxy’s core.where Pˆ [h(X, c ) 0 Y 1] and Pˆ [h(X, c ) 1 Y 0] are the table displays sample mean plus/minus 1×σ standard error, each statistics.= l In random forest, bootstrap samples of the training set are j j table displays sample mean plus/minus 1σ standard error, each nuclei are present, and towards 0 if not. Because this ratio is sensi- are summed within each region, with theWe intensity define statistic the intensity then being centroid the of a galaxy as = | = = | = 4 multipled by 10 . Downloaded from tive to noise, we multiply it by Al,(2), which tends towards 0 if the estimated probabilities of misclassifying a non-regular/merger and 4

ratio of the second-largest to largest sum. In this example, the statistic is thoseDownloaded from described above in Section 4, except that in this analysis each used to grow t trees (e.g. t 500), each of which has n nodes (e.g. Downloaded from multipled by 10 . second-largest group is a2.2 manifestation Intensity of (I noise.)statistic The M statistic is I 0.935. = = 1 aregular/non-merger,respectively.Weseektheminimumvaluefor1 the maximum Rl value, i.e. nnew8). At statistics each node in each M-I-D tree, a random examine subset(xcen of ,y sizecen) m of the ifi,j , jfi,j . The M statistic is a function of the footprintsymmetry, areas of non-contiguous both the intensity centroid and the maximum=  nseg associated nseg  ˆ annotator’s vote is recorded, so there is no ambiguity about the frac- = i j thishttp://mnras.oxfordjournals.org/ estimatei j of risk. We smooth the discrete function Rj f (cj ) MI A-MI A-MID Full M max Rl . statistics is chosen (e.g.(2) C, Mwith20I andshouldI may lie at the be galaxy’s chosen core. from the full# # # # MI A-MI A-MID Full = l groups of image pixels, but does not take into account(1) pixel inten- =

  Downloaded from sities.setthe To of complement statistics). ratios it, we The defineof best a similar splitWe statistic, of define the the data intensityintensity along centroid eachwith of a galaxy the of summation the as m axes being overall nwithseg pixels a Gaussian with the segmentation profile of width 0.05 and choose as our final value tion of annotators identifying particular galaxies as either mergers map. The distance from (x , y ) to the maximum associated with 5 Sens 6917 22 7520 22 7790 17 7816 17 2.2 Intensity (I)statisticor I statistic. A readily apparent, simple definition of this statistic is cen cen of cˆ that value for which the smoothed function Rˆ (c) is minimized. Sens 6917 22 7520 22 7790 17 7816 17 is determined, with the one overall best1 split retained.I 1 will This be affected process by the absolute size of the galaxy; it generally ± ± ± ± the ratioarea of the sums(M), of intensities intensity in the two(xcen pixel,y cen(I)) groups and used to theifi,j , (1) distancejfi,j . (D) Spec 8683 14± 8546 15± 8564 98591± 8 ± =  n n 

at Space Telescope Science Institute on August 2, 2013 or non-regulars. The M statistic is a function of the footprint areas of non-contiguous seg i j willseg bei largerj for, e.g. galaxies at lower redshifts. Thus, we normalize Spec± 8683 14± 8546 15± 8564 98591± 8 computeis repeatedM. However, for this each is not node optimal, and as in anyeach given tree; image# subsequently it is# # the# training groups of image pixels, but does not take into account pixel inten- Risk 4400 13± 3934 13± 3646 13± 3594 13 ± http://mnras.oxfordjournals.org/

the distance using an approximate galaxy ‘radius,’ n /π.The http://mnras.oxfordjournals.org/   seg Risk 4400 13 3934 13 3646 13 3594 13 http://mnras.oxfordjournals.org/ possible, e.g. that a high-intensity pixel groupwith with the summation small footprint being overall nseg pixels with the segmentation ± ± ± ± sities. To complement it, wedata definebetween are a similar pushed statistic, down the1stintensity each and tree 2nd to determine brightestt classdeviation predictions clumpsstatistic is then for Toterr 1477 12± 1547 12± 1506 71480± 6 ± After removing 15 objects from the sample that were subse- or I statistic. A readily apparent,may not simple enter definition into the of computation this statistic is of M inmap. the first The distanceplace. from (xcen, ycen) to the maximum associated with 3.3 Measures& of classifier performance Toterr± 1477 12± 1547 12± 1506 71480± 6 eachThere are galaxy myriad ways (i.e. in to which generate one can defineI(1) awill set pixel be of affected groupst numbers by over the absolute for size each of theπ galaxy, galaxy; it generally all PPV 3562 20± 3525 20± 3541 13± 3603 13 ± the ratio of the sums of intensities in the two pixel groups used to D (x x )2 (y y )2 . (4) PPV 3562 20 3525 20 3541 13 3603 13

cen I cen at Space Telescope Science Institute on August 2, 2013 I compute M. However, thiswhich is not optimal, to sum as intensities. in any given In image this it work, is wewill utilize be larger a two-pronged for, e.g. galaxies at lower= redshifts.n Thus, we− normalize(1) + − (1) ± ± ± ± quently identified as stars (J. Lotz, private communication), we of which are either 0 or 1). Let si [0, t] equal the sum ofseg the class WeFigure use 4.a numberRelative of importance measures of of statistics classifier in performance. differentiating between regu- NPV 9662 29723± 29752± 29753± 2 ± possible, e.g. that a high-intensityapproach. pixel First, group we with smooth small footprintthe data in eachthe distance image with using a an sym- approximate galaxy' ‘radius,’( nseg/π.The Figure 4. Relative importance of statistics in differentiating between regu- NPV± 9662 29723± 29752± 29753± 2 deviation∈statistic is then We have designed the D statisticlar to capture and non-regular evidence of galaxy galaxies (x-axis) and non-merger and merging galaxies ± ± ± ± may not enter into the computationmetricpredictionsbeats bivariate of M in theGaussian for firstG-M place. galaxy kernel,20 selectingi,; thenCAS the the optimal randomat width findingσ forestby prediction CANDELS for& the visuallylar andclassified non-regular galaxies mergers (x-axis) and non-merger and merging galaxies analyse the H-band images of the remaining 185 galaxies in a man- There are myriad ways in which one can define pixel groups over π asymmetry. It is thus complimentary to(i) the ASensitivity.statistic definedThe in C03, proportion of non-regular/merger galaxies that maximizing the relative importance ofˆ the I statistic in correctly 2 2 (y-axis) in CANDELS-team-processed H-band data, as output by the ran- galaxy’s classification is Y D s /t. (xcen xI(1) ) (ycen yI(1) ) . (4) which to sum intensities. In this work, we utilize a two-pronged i =i n − + which− is computed by rotating an image by 180◦(,y taking-axis) the in absolute CANDELS-team-processed H-band data, as output by the ran- identifyingfor morphologiesWFC3/H (i.e. how well< we24= can differentiate'galaxiesseg classes are correctly classified: TP/(TP FN). (This is also dubbed com- the distributions of these statistics for mergers (green points), non- approach. First, we smooth theWhile data in each fitting image the with a training sym- data, random( forest keepsdifference track between of rotated all and unrotateddom forestimages,dom classification normalizing forest classification by algorithm. algorithm. The values The of values all data of allpoints data have points been have been the distributions of these statistics for mergers (green points), non- ner similar to that described in Section 4. The principal difference using the I statistic alone, relative to how wellWe we have can designed differentiate the D statistic to capture evidence of galaxy + http://mnras.oxfordjournals.org/ metric bivariate Gaussian kernel, selecting the optimal width σ by the value of the unrotated image, andpleteness.) summing the resulting values classes by using other statistics by themselves;asymmetry. see ItSection is thus complimentary 3.3). to the A statistic defined in C03, normalized by the value of the I statistic for the regular/non-regular analysis. regularsregulars that are that not are mergers not mergers (blue points) (blue points) and regulars and regulars (red contour (red contour maximizing the relative importancet trees of it the creates,I statistic in i.e. correctly all of the data splits it performs.pixel-by-pixel. Thus, In Section any 4, we compute both Anormalizedand D for a sample by the value of the I statistic for the regular/non-regular analysis. which is computed by rotating an image by 180◦, taking the absolute between analyses is that for computational efficiency, we use only identifying morphologiesThen, (i.e. how we well define we can groups differentiate using classes maximum gradient paths. For each See(ii) SectionSpecificity. 3.3 forThe the definitionproportion of of statistic regular/non-merger importance, and galaxies Section 4.1 lines). The reader should intuitively picture classification via ran- new datum (from the remainingdifference 50 between per cent rotated of and the unrotatedof data,high-redshift images, or the normalizing galaxies test and by show that while thereSee is a Section large positive 3.3 for the definition ofFigure statistic importance, 11. Distribution and Section 4.1 of effectivelines). The radius reader should (rˆ in intuitively the text) picture versus classification median via ran- using the I statistic alone,pixel relative in to the how smoothed well we can image, differentiate we examine the surrounding eight the value of the unrotated image, andsample summing correlation the resulting coefficient values betweenthatfor the arepractical two correctly statistics, interpretation there classified: are ofTN the/( results.TN FP The). error bars indicate sample dom forest as placing vertical and horizontal lines on these plots so classes by using other statisticspixels and by themselves; move to the see one Section for which3.3). the increase in intensity is for practical interpretation of the results. The error bars indicateSˆ sample dom forest as placing vertical and horizontal lines on these plots so the MID statistics; it is not imperative to use all available statistics set) may be ‘pushed’ downpixel-by-pixel. these trees, In Section resulting 4, we computemany again bothinstancesA inandt whereDclassfor aD samplecaptures stronger evidence of asymmetry + Then, we define groups usingmaximized, maximum repeating gradient the paths. process For each until we reach a local maximum. standard(iii) Estimated deviation risk. givenThe 1000 sum separate of 1 – runs sensitivitypixel of random wiseand forest, 1 – S specificity./ andN( thus( are)inthetext)forour1639-galaxysample.Dashedlinesas to maximize the proportion of, e.g. non-regulars on one side and

standard deviation given 1000 separate runs of random forest, and thus are at Space Telescope Science Institute on August 2, 2013 predictions and thus a predictedof high-redshift response galaxies (or and show dependent)than that whileA, and there vice-versa, variable is a large positive demonstrating that D and A are not simply N as to maximize the proportion of, e.g. non-regulars on one side and at Space Telescope Science Institute on August 2, 2013 pixel in the smoothed image, we examine the surrounding eight at Space Telescope Science Institute on August 2, 2013 A single group consists of all pixels linkedsample to a correlation particular coefficient local between the two statistics, there are not(iv) measuresTotal error. of theThe standard proportion error of of the misclassified mean; the 1σ galaxies.uncertainties in the pixels and move to the oneˆ for which the increase in intensity is redundant. not measures of the standard error of the mean; the 1σ uncertainties in thethe proportion of regularsSˆ on the other. Given this intuitive picture, because our aim in this analysis is to observe how the estimated risk maximum.Yi si (See/t. Fig. 2.) Once we define allmany pixel instances groups, where we sumD captures stronger evidence of asymmetry the proportion of regulars on the other. Given this intuitive picture, maximized, repeating the process until we reach a local maximum. means(v) Positive are given predictive by shrinking vlue the (PPV). error barsTheindicate by proportion a factor of the of√ actual1000 values non-31.62.rˆ 0.6 arcsec and ( ) 15. The 563 galaxies each the intensities= within each and sort the summedthan A, intensities and vice-versa, in de- demonstrating that D and A are not simply means are given by shrinking the error bars by a factor of √1000 31.62. the relative efficacy of,N e.g. the I statistic with respect to the other A single group consists of all pixels linked to a particular local = = = the relative efficacy= of, e.g. the I statistic with respect to the other varies as a function of the number of annotators, n, without regard scending order: I(1), I(2),.... The intensity statisticredundant. is then 3STATISTICALANALYSIS:RANDOMFORESTregular/merger galaxies among those predicted to be non-regulars maximum. (See Fig. 2.) Once we define all pixel groups, we sum within the lower-left andstatistics upper-rightstatistics is clearly is regions clearly evident. evident. Also (as definedevident Also evident from relative Fig. from 5 Fig. is to our 5 where is relative our relative the intensities within each andI sort(2) the summed intensities in de- We use the MID (and other) statisticsor tomergers: populate a TPp-dimensional/(TP FP). (This is also dubbed purity.) I 3.2 Random. forest classification (3) inability to separate mergers and irregular galaxies using MID and to its actual value. scending order: I(1), I(2),.... The intensity statistic is then 3STATISTICALANALYSIS:RANDOMFORESTspace, where each axis represents the values of the ith statistic and+ inability to separate mergers and irregular galaxies using MID and = I(1) (vi) Negative predictive value (NPV).theThe dashed proportion lines of actual cross) comprise the ‘low’ and ‘high’ data sets, respectively. I(2) We use the MID (and other) statisticseach to data populate point a representsp-dimensional one galaxy. Ideally, in this space, the set A alone. Furthermore, work is needed to develop image statistics I . (3) A alone. Furthermore, work is needed to develop image statistics = I Once we predict response variablesspace, where each for axis the represents testof the set points values galaxies, representing, of the ith statistic we e.g. and visuallyregular/non-merger identified mergers is offset from galaxies among those predicted to be regulars We assume that a new expert voter will randomly identify a (1) 2.3 Deviation (D)statistic that will optimize merger irregular class separation. perform the second step ofeach random data point forest, represents the one galaxy. classificationthose Ideally, representing in this space, step. non-mergers. the set Toor determine non-mergers: an optimal boundaryTN/(TN FN). that will optimize merger irregular class separation. of points representing, e.g. visually identified mergers is offset from given galaxy i as a non-regular/merger with probability p ,wherep 2.3 Deviation (D)statisticGalaxiesFirst, that the are continuous clearly irregular fractions or peculiarY willassociated exhibit marked with thebetween test set these galaxies point sets directly in the n-dimensional space, we + The resultsThe results in Fig. in 4 were Fig. 4 generated were generated by analysing by analysing the entire the entire eight- eight- i i deviations from elliptical symmetry. A simplethose measurei representing quantifying non-mergers. Toapply determine machine-learning-based an optimal boundary methods of regression and classifi- Galaxies that are clearly irregular or peculiar will exhibit marked between these point sets directly in the n-dimensional space, we We define the symbols used above in Table 1. dimensional space of image statistics with random forest. Given thisare deviation mapped is the to distanceYclass, fromi a galaxy’s0 if Y intensityi < 0.5 centroid and Yclass,cation.i To ensure1 if robustYi > results, it is good practice to apply a number high S/N + large sizedimensional space oflow image S/N statistics + withsmall random size forest. Given is the recorded vote fraction for the set of 42 annotators. Thus, to deviations from elliptical symmetry. A simple measure quantifying= apply machine-learning-based methods of= regression and classifi- this deviation is the distanceto0.5. the from local (Ties a galaxy’s maximum are intensity broken associated centroid by with randomlyI(1)cation., the Topixel ensure assigning group robust with results, galaxies it isof good methods practice to to classes.) to see apply if a any number one or moreRandom provide significantly forest assessesbetter the efficacy of each statistic for disam- that thethat number the number of possibly of possibly useful useful statistics statistics will only will increase only increase in in maximum summed intensity. We expect this quantity to cluster near results. In our analysis of HST data in Section 4, we tested four al- to the local maximum associated with I(1), the pixel group with of methods to see if any one or more provideˆ significantly better biguating classes by computing Gini importance scores for each the future, it is important to determine we can disregard any of simulate the number of votes for non-regularity/merging for each maximum summed intensity.zeroThen We for expect spheroidal the this predicted quantity and disc to cluster galaxies. responses near For thoseresults. for disc In the our galaxies analysis test with set of HST galaxies,datagorithms: in SectionY randomi 4,, weare tested forest, also four lasso al- regression, support vector machines the future, it is important to determine we can disregard any of zero for spheroidal and discwell-definedmapped galaxies. For bars to those discrete and/or disc galaxies spiral classes. arms, with we Intuitively, wouldgorithms: still random expect one forest, near- might lasso regression, expectand principal support the splitting components vector machines regression(see, (for details e.g. chapter on these, see, 9 ofe.g. HTF09; note that the Gini importance score our currentour current statistics statistics with little, with iflittle, any, if loss any, in loss classifier in classifier perfor- perfor- at Space Telescope Science Institute on August 2, 2013 well-defined bars and/orzero spiral values, arms, we as wouldbetween still the expect bulge near- and generallyand principal expected components structure regressionHastie, (for details Tibshirani on these, & Friedman see, e.g. 2009, hereafter HTF09). We found galaxy, given n annotators, we sample from a binomial distribution zero values, as between thepoint bulge and between generally expected predicted structure classes,Hastie, Tibshiranic, to & be Friedman 0.5. 2009, However, hereafter HTF09). because We found differs from the Gini statistic G). At any given node of any tree, mance.mance. (This is (This not is a trivial not a trivial issue, issue, as we as discuss we discuss in Section in Section 5.3: 5.3: the proportions of regular and non-regular galaxies in the training the n samples to be split belong to two classes (e.g. merger/non- the numberthe number of statistics of statistics we incorporate we incorporate may limit may future limit future analy- analy- with parameters n and pi. The result is an integer number of votes set are unequal, as are the proportions of non-merger and merger merger), with proportions p1 n1/n and p2 n2/n. A metric of ses.) Toses.) that To end, that we end, define we define and analyse and analyse three reducedthree reduced statistic statistic = 2 =2 Z [0, n], with the simulated vote fraction being F Z /n.Given class impurity at this node is i 1 p p .Thesamplesare sets for both the regular/non-regular case (ID,A-ID,A-MID)andthe i i i galaxies, regression will be biased towards fitting the galaxies of the = − 1 − 2 sets for both the regular/non-regular case (ID,A-ID,A-MID)andthe ∈ = more numerous type well. For instance, regular galaxies outnumber then split along the axis associated with one chosen image statistic, non-merger/mergernon-merger/merger case (MI case,A- (MIMI,,AA--MIDMI,A),-MID based), based on rankings on rankings of of F and the MID statistics for all 185 galaxies, we run random forest with proportions p n /n and p n /n being assigned to two non-regular galaxies by approximately three-to-one, so a priori we l = l r = r relativerelative statistic statistic importance. importance. and output the estimated risk. We repeat the process of simulation expectthebestvaluefor c to be around 1/(3 1) 0.25. To determine daughter nodes. New values of the impurity metric are computed See TablesSee Tables 2 and 3. 2 andThe 3. interpretation The interpretation of these of tables these tables depends depends on on + = at each daughter node; call these values i and i . The reduction in c,weselectasequenceofvalues c1, c2,...,cn [0, 1], and for l r the performancethe performance metric metric one prefers: one prefers: e.g. sensitivity e.g. sensitivity (or catalogue (or catalogue and risk estimation 100 times for each value of n so as to build { } ∈ impurity achieved by splitting the data is !i i p i p i .Each each cj we map the predicted responses to two classes, e.g. we call l l r r completeness),completeness), estimated estimated risk or risk PPV or (or PPV catalogue (or catalogue purity), purity), etc. If etc. If value of !i is associated with one image statistic;= − the average− of the up an empirical distribution of estimated risk values. Note that as all galaxies with predicted responses Yˆi >cj non-regulars/mergers. we assumewe assume that one that would one would wish to wish strike to strike a balanceDetection a balance between between all of all disturbed galaxy morphologies 11 !i’s for each image statistic over all nodes and all trees is the Gini Call this classifying function h(X, cj), where X is the set of observed three ofthree these of measures, these measures, we find we that find the that reduced the reduced statistic statistic set A-ID set A-ID we increase n,weonlyrandomlysamplenew votes. For instance, importance score. statistics. Our estimate of risk as a function of cj is the overall is sufficientis sufficient for disambiguating for disambiguating regulars regulars from non-regulars, from non-regulars, while while Note that in this work, we are not as concerned with the absolute to go from n 5 to n 7, we add two new simulated votes to proportion of misclassified galaxies: Figure 12. Boxplots showingone requiresone the requires distribution the additional the additional information of M informationstatistic carried carried5.3 by for the identified Towards by full the set full of set of the future: eliminating visual annotation importance score of each statistic (which is not readily interpretable) Mergers = = ˆ ˆ ˆ Irregulars statisticsstatistics to disambiguate to disambiguate mergers mergers from non-mergers. from non-mergers. the five we already have. We feel that this is more realistic than Rj P [h(X, cj ) 0 Y 1] P [h(X, cj ) 1 Y 0], as we are with relative scores derived by,non-mergers e.g. dividing importance (f < 0.5), galaxies for which the vote was split (f 0.5) and = = | = + = | = Figure 5.FigureScatter 5. plotsScatter of plots the MID of theandMIDA statisticsand A statistics as computed as computed for for scores by the maximum observed importance score value. Relative = CANDELS-team-processedCANDELS-team-processedH-band images.H-bandmergers images. Green circles Green (f represent> circles0.5). represent galax- The galax- left- and right-hand panels show distributionsAs hinted for the at throughoutrandomly this sampling work, there a completely are many new issues set of with votes, an- as an increased n ies visuallyies visually identified identified as mergers as mergers and blue and crosses blue crosses represent represent non-regulars non-regulars4.2 Effect4.2 Effect of changing of changing the observation the observation wavelength: wavelength:J-bandJ-band 4 The size of the training set is arbitrary. Larger training sets generally yield ‘low’ and ‘high’ data sets, respectively. The distributions are similar,notating except galaxiesin and practice using generally the resulting will be morphologies implemented by to adding make to a core group that are notthat also are mergers. not also mergers. The red linesThe red are lines contours are contours indicating indicating the density the densityof ofdata data better final results. In this work, our principal goal is to demonstrate the 5 We note that this algorithm produces similar results to the Bayes classifier regular galaxies.regular galaxies. The non-zero The non-zero slopes of slopes thefor black of the line, black lack the line, best-fitting of the best-fittingidentified lin- lin- mergers with small M values in thequantitative ‘low’ data statementsof annotators about structure rather than formation. replacing Some that ofcore the group more in its entirety. efficacy of the MID statistics relative to other, commonly used ones, and so (see, e.g. chapter 2 of HTF09), which sets c l0/(l0 l1), where l0 and l1 RecallRecall that CANDELS-team that CANDELS-team labels labels are based are based primarily primarily on how on how ear regressionear regression functions, functions, indicate indicate the expected the= expected positive+ positive correlations correlations between between we do not explicitly address the issue of optimizing the training set size. are the number of objects in each identified class,set: respectively.M clearly correlates with thegalaxies ability appear of in annotators the H band. However, to identify in order small-size to, e.g. differenti- each of theseeach of statistics. these statistics. Note that Note for thatincreased for increased clarity, only clarity, 100 only randomly 100 randomlygalaxies appear in the H band. However, in ordernoteworthy to, e.g. differenti- issues areIn the Fig. following: 13, we display the median of our risk distributions for selectedselected non-regulars/mergers non-regulars/mergers are displayed. are displayed.and low-S/Nmergers.Thebehaviouroftheate trueate mergers true mergers from galaxies fromI statistic galaxies exhibiting exhibiting between disc instabilities, disc data instabilities, sets we will is we will the non-regular (blue points and lines) and merger (green points similar and is not shown. (i) Ambiguity. Expertand lines) annotators detection often cases. do The not agree thin and on thick whether lines a drawn through given galaxy is, e.g.each undergoing point indicate a merger the (as range opposed for the to, central e.g. under- 95 and 68 values in going star formationeach due distribution, to in situ respectively.disc instabilites). (Note This that the inability values of the risk are Both the ‘low’ and ‘high’ data sets contain 563 galaxies.to See agree, Fig. 11. which ledgenerally to the large much spread higher of heremerger than fraction in Tables estimates 2 and 3 because the training sets here are one-ninth the size of those in the analysis Figure 13. Median-estimatedIn Fig. risk 12, in we the display detection the distributions of non-regulars of the (theM statisticscompiled for both by Lotz et al. (2011), is a not-easily quantified source of of Section 4.) We observe that for both cases, the estimated risk lower sequence of pointsdata in each sets, panel, for merger denoted vote with fractions blue circles)f < 0.5, andf 0.5systematic and f > 0.5. error: e.g. how does one incorporate the experience and We immediately observe a lack of identified mergers= (finnate> 0.5) biases with of eachdecreases annotator somewhat into a sharply statistical when analysis?n 10; above Givenn 10, the risk mergers (the upper sequence of points in each panel, denoted with green ! ≈ triangles) in the analysissmall of 185M galaxiesvalues in described the ‘low’ in data Section set. (We 5.2, note as a that athe similar subject issue of thisfor paper, the non-regularambiguity is case perhaps still decreases, an obvious albeit issue more to slowly, while function of number of annotators.arises in The the right-hand analysis of panel regular shows galaxies, the same as data well as whenpoint we out, use but its deleteriousthe risk for effects the merger on structure case remains formation constant. analysis Imprecise estimation Downloaded from as the left, for the reducedthe rangeI statisticn 3–15. in place The of thinM and.) It thick is clear lines from drawn Fig. 12 thatcannot numerous be overstated.of the true vote fractions for small n and vote fraction discretization = through each point representssmall-S the/ centralN/size 95 mergers and 68 per are cent being of the mislabelled, empirical a systematic(ii) Loss error of Statisticallead to Information. the increase inAbove risk as andn beyond0, as the it becomes issue less and less likely that, e.g. a ‘true’ merger will→ be identified as a merger by both distribution of risk values,that respectively. throws into The doubt lines the are idea slightly that offset one from can accuratelyof ambiguity estimate is the fact that in the classification exercise, we are annotators and the machine classifier. each other for clarity. Seemerger Section fractions 5.2 for further at high discussion. redshifts via visual labelling. (Noteattempting that we to take a continuous distribution (e.g. all possible galaxy base this conclusion on the analysis of an 50 ks image; typical For the merger case, it is clear from Fig. 13 that little improvement morphologies) and discretize it (reduce it to, e.g. two bins: mergers CANDELS exposures will be one-tenth as long,≈ exacerbating this in risk estimation occurs when adding annotators beyond n 10. and non-mergers). Discretization can only have an adverse effect http://mnras.oxfordjournals.org/ ≈ error.) This result helps motivate the alternative analysis paradigm For the non-regular case, there is a slight improvement on average, that we discuss in Section 5.3. on statistical inferences,but there making is no guarantee them certainly that one would less precise see that improvement and in any perhaps less accurate. (iii) Waste of Resources. Annotation is, by definition, a time- consuming exercise that diverts astronomers from other activities. Our vision of (near) future analyses of galaxy morphology and hierarchical structure formation rests on the belief that simulation engines will be developed that can replicate the wide variety of observed morphologies at a resolution at least on par with current observations. If this occurs, then we can fit structure formation at Space Telescope Science Institute on August 2, 2013 models in the following manner: (i) Populate space of image statistics by analysing a set of ob- served galaxies. (ii) Pick a set of model parameters describing structure forma- tion. (iii) Run a simulator and project the simulated galaxies down on to a (set of) two-dimensional plane(s). (iv) Populate a space of image statistics by analysing the set of simulated galaxy images. (v) Directly compare the estimated distributions of the simulated and observed statistics. Figure 14. Histogram of the changes in estimated risk that occur when (vi) Return to step (ii), changing the model parameter values and we increase the number of annotators from 11 to 43 in each of the 100 iterate until convergence is achieved. simulations we run in our analysis of 185 galaxies (Section 5.2). Positive values of !R indicate a reduction in estimated risk. In 19 of 100 simulations, The comparison step, step (v), involves estimating the density func- the estimated risk increases: adding annotators led to worse results. tions from which the simulated and observed statistics were sam- pled, and then determining a ‘distance’ between those functions. single analysis. In Fig. 14 we show the histogram of the change in There exist numerous, mature methodologies for performing den- risk, !R, that occurs as we go from n 11 to n 43 annotators; each sity estimation and estimating distances between density functions. value is derived from one of our 100 simulations.= = In 19 of 100 cases, (A summary of possible distance measures is provided in, e.g. Cha there is an increase in estimated risk; adding 32 annotators made 2007.) The key to a computationally efficient comparison is to avoid our results worse. This lack of significant improvement in estimated the ‘curse of dimensionality’: density estimation is difficult in more risk, coupled with the time resources that would be expended by than even a few dimensions. Thus, even if annotators are no longer the additional annotators, argues strongly that an annotator pool of needed, there will always be a need to define new statistics that can size n 10 is sufficient for detecting non-regulars. better disambiguate the morphologies of galaxies. We≈ conclude that no more than 10 annotators are needed to effectively train a galaxy morphology≈ classifier using a given set 6SUMMARY of galaxy images when the goal is to detect non-regular galaxies or mergers. If more annotators are available, they should examine This work is motivated by the problem of detecting irregular and additional sets of galaxy images to increase the overall training set peculiar galaxies in an automatic fashion in low-resolution and low- size, and thereby reduce the misclassification risk. S/N images. This information, combined with estimates of galaxy Clumps v. Mergers: how can you tell?

0.7 0.7 irregular 0.6 0.6 bulge G

0.5G 0.5 z~3 0.4 WFC3/F160W z~3 WFC3/F160W 00.4 −1 −2 M20 0 −1 −2 M20 Cosmological hydro-dynamical simulations now have resolution and baryonic physics to predict morphology → tie morphologies to underlying physics

(Greg Snyder, P. Torrey, L. Hernquist, et al. - AREPO Ceverino, Primack, Dekel, et al. -- hydroART; + SUNRISE ) Summary

• Quantitative morphology is efficient tool for tracking galaxy evolution and connecting to physical models

• Mock images of galaxies from hydrodynamical simulations needed to understand morphological disturbances and TIMESCALES.

10 2 • Fraction of 10 M galaxies undergoing a major-merger increases as ~(1+z) the minor merger rate is several times higher (with weaker evolution)

• Quenching at z~2 is strongly linked to presence of bulge/central mass concentration (more so than total mass)

• Clumpy unstable disks and mergers very hard to distinguish at z~2; need more simulation work (but both can form bulges?)