Quenching or Bursting: Star Formation Acceleration--A New Methodology for Tracing Galaxy Evolution
D. Christopher Martin, Thiago Goncalves, Behnam Darvish, Mark Seibert, David Schiminovich
aa r X i v : . [ a s t r o - ph . GA ] M a y Accepted for publication in ApJ
Preprint typeset using L A TEX style emulateapj v. 12/16/11
QUENCHING OR BURSTING: STAR FORMATION ACCELERATION–A NEW METHODOLOGY FORTRACING GALAXY EVOLUTION
D. Christopher Martin , Thiago S. Gonc¸alves , Behnam Darvish , Mark Seibert , and David Schiminovich , Accepted for publication in ApJ
ABSTRACTWe introduce a new methodology for the direct extraction of galaxy physical parameters from multi-wavelength photometry and spectroscopy. We use semi-analytic models that describe galaxy evolutionin the context of large scale cosmological simulation to provide a catalog of galaxies, star formationhistories, and physical parameters. We then apply stellar population synthesis models and a simpleextinction model to calculate the observable broad-band fluxes and spectral indices for these galaxies.We use a linear regression analysis to relate physical parameters to observed colors and spectral indices.The result is a set of coefficients that can be used to translate observed colors and indices into stellarmass, star formation rate, and many other parameters, including the instantaneous time derivative ofthe star formation rate which we denote the
Star Formation Acceleration (SFA) , We apply the methodto a test sample of galaxies with GALEX photometry and SDSS spectroscopy, deriving relationshipsbetween stellar mass, specific star formation rate, and star formation acceleration. We find evidencefor a mass-dependent SFA in the green valley, with low mass galaxies showing greater quenching andhigher mass galaxies greater bursting. We also find evidence for an increase in average quenching ingalaxies hosting AGN. A simple scenario in which lower mass galaxies accrete and become satellitegalaxies, having their star forming gas tidally and/or ram-pressure stripped, while higher mass galaxiesreceive this gas and react with new star formation can qualitatively explain our results.
Subject headings: galaxies: evolution—ultraviolet: galaxies INTRODUCTION
There has been growing interest in the nature ofthe observed color bimodality in the distribution ofgalaxies (Balogh et al. 2004; Baldry et al. 2004), whichis echoed in other galaxy properties (Kauffmann et al.2003). The color bimodality is revealed in a variety ofcolor-magnitude plots, and is particularly dramatic inthe UV-optical color magnitude diagram (Wyder et al.2007). The red and blue galaxy concentrations are com-monly denoted the red sequence and the blue “cloud”,although we elect to call both concentrations sequences.Recently the blue cloud translated into the specific starformation rate (SSFR)-stellar mass plane is tight enoughto be denoted a blue sequence or a “main-sequence”for star forming galaxies. Deep galaxy surveys are nowprobing the evolution of the red and blue sequences.Work using the COMBO-17 (Bell et al. 2004), DEEP2(Willmer et al. 2006; Faber et al. 2007), and more re-cently the UltraVISTA (Ilbert et al. 2013) surveys pro-vide evidence that the red sequence has grown in massby a factor of three since z ∼
1. It is natural to askwhat processes have led to this growth, and in partic-ular whether the red sequence has grown via gas richmergers, gas-less (dry) mergers, or simple gas exhaus-tion. There is also considerable controversy regardingwhether AGN feedback has played a role in accelerat- California Institute of Technology, MC 405-47, 1200 EastCalifornia Boulevard, Pasadena, CA 91125 Observatorio do Valongo, Universidade Federal do Rio deJaneiro, Ladeira Pedro Antonio, 43, Saude, Rio de Janeiro-RJ20080-090, Brazil Department of Astronomy, Columbia University, New York,New York 10027 Observatories of the Carnegie Institution of Washington, 813Santa Barbara St., Pasadena, CA 91101 ing this evolution, with many authors supporting thishypothesis (e.g., Springel, DiMatteo & Hernquist 2005;Di Matteo et al. 2005; Maiolino et al. 2012; Olsen et al.2013; Dubois et al. 2013; Shimizu et al. 2015), and manyothers claiming that energy injection from other feedbackmechanisms would dominate the quenching process (e.g.,Coil et al. 2011; Aird et al. 2012).Likewise, it has long been assumed that environmentplays a significant role in quenching star formation ingalaxies. In his seminal work, Dressler (1980) has showna strong relation between galaxy morphology and the lo-cal density, a relation which translates to an environmen-tal dependency of color and star formation properties onenvironment (e.g., Zehavi et al. 2002; Balogh et al. 2004;Blanton 2005; Darvish et al. 2016). Peng et al. (2010)have shown that this dependence is stronger for low-massgalaxies – indicating that quenching of satellite galax-ies in clusters is particularly relevant. Peng et al. (2015)have later argued that the main quenching mechanism ingalaxies is “strangulation” within clusters. Nevertheless,this results relies on average metallicities and star for-mation properties of tens of thousands of galaxies, with-out any regards to processes happening within individualgalaxies.Therefore, we would like very much to identify galax-ies which may be in the process of evolving from theblue to the red sequence. Martin et al. (2007)[M07] havemade a first attempt using the D n (4000) and H δ A in-dices as defined in Kauffmann et al. (2003), and inferredthe total mass flux between both sequences at redshift z ∼ .
1. Gon¸calves et al. (2012) have extended the anal-ysis to intermediate redshifts ( z ∼ .
8) and noticed anincreased mass flux density at earlier times and and formore massive galaxies, meaning that the phenomenon of Martin et al.star-formation quenching has suffered a sizeable downsiz-ing in the last 6–7 Gyr. Nevertheless, these results relyon the (simplistic) assumption of a star formation historydominated by an exponential decrease in star formationrates in all green valley galaxies, which cannot be true.In this paper, we develop a new methodology in-spired by earlier work developing simple broad-bandand spectral index fitting formulae (Calzetti et al.2000; Kauffmann et al. 2003; Seibert et al. 2005;Johnson et al. 2007a,b) designed to extract physicalparameters without explicit SED fitting. Our methodstarts with model galaxies produced by a semi-analyticmodel set based on an N-body cosmological simulation(Millennium) ( § n (4000) spectralindex to model galaxy physical parameters and starformation histories ( § Star Formation Acceleration(SFA) which is the time-derivative of the NUV-i color( § § H =70 kms − Mpc − , Ω m =0.3 andΩ Λ =0.7. Magnitudes are expressed in the AB system(Oke & Gunn 1983) and stellar mass and star forma-tion rates are based on a Salpeter initial mass function(Salpeter 1955). METHOD: GALAXY MODELS
One of the principle activities in the field of galaxy evo-lution is the translation of multi-wavelength photometryand spectroscopy into galaxy physical parameters. Thevast majority of methods use a spectral energy distribu-tion (SED) fitting approach. Modelers translate physicalparameters and star formation histories into SEDs, andsearch for the SED (and corresponding parameters) orrange of SEDs which give the best statistical fit. Exam-ples of such an approach are given by Kauffmann et al.(2003) and Salim et al. (2005, 2007), who use a Bayesiananalysis of observations fit to a large library of modelSEDs that populate galaxy physical parameter space.The outputs include probability distributions for derivedphysical parameters.At the same time, a number of workers have shownthat in certain cases simple fitting formulae can pro-vide a direct translation of observables into physicalparameters. For example, the UV slope is related tothe infrared excess (IRX, the ratio of Far or Total In-frared luminosity to Far UV luminosity) for starburst(Calzetti et al. 2000) and normal (Seibert et al. 2005)galaxies. More complex fitting formulae can be de-rived using the D n (4000) spectral index (Johnson et al.2007a,b). Kauffmann et al. (2003) and these papersdemonstrated that D n (4000) does an excellent job of iso-lating stellar population age from other parameters suchas extinction.This paper introduces a generalization of the fittingformula approach to many physical parameters and mo-ments of the star formation history. A summary of the approach follows:1. We use a semi-analytic model (De Lucia et al.2006) linked to the Millennium cosmological N-body simulation (Springel et al. 2005) to providea large sample of galaxies, star formation histories,and associated physical parameters.2. We use a simple extinction model and stellar pop-ulation synthesis code to translate the star forma-tion histories into observable broad-band fluxes andspectral indices.3. We bin model SEDs by D n (4000) to remove theprinciple source of variation, stellar population age.4. Within each D n (4000) bin we perform a linear re-gression fit between model physical parameters andthe multiple observables (colors and spectral in-dices) for the complete galaxy sample. We findin general linear (in the log) relationships betweenthe two over a large dynamic range. Fit disper-sion varies with physical parameter and with thecollection of available observables.5. The matrix of regression coefficients can be usedto translate observables into physical parameters(after introducing some offsets), and to derive ob-servable influence functions, degeneracies and errorpropagation matrices. Cosmological Simulation and Semi-analytic Model
We use a set of 24,000 model galaxies produced by theDe Lucia et al. (2006) semi-analytic model (SAM) ap-plied to the Millennium cosmological simulation. Galax-ies are modeled in 63 time steps of ∼
300 Myr each overthe redshift range (0 < z < particles since red-shift z = 127 in a cosmological volume 500 h − Mpc ona side. Assuming a cold dark matter cosmology, it pro-vides a framework in which one can follow the formationof dark matter haloes and the large-scale structure oncosmologically significant scales. De Lucia et al. (2006)used this framework and applied a semi-analytic modelwhich, following dark matter haloes even after accretiononto larger systems, assumed a star formation law thatdepended on the cold gas mass and a minimum criticalvalue of gas surface density above which new stars wereallowed to form. With the addition of active galacticnuclei (AGN) feedback, the authors are able to repro-duce the observed trend of short formation time-scales ofthe most massive elliptical galaxies (e.g., Thomas et al.2005).We used 24,000 galaxies (at snapnum=63 or z=0) fromthe volume range (0 < x <
65 Mpc, 0 < y <
65 Mpc,0 < z <
65 Mpc), where x , y , and z are the galaxy coor-dinates in the Millennium catalog, and absolute magni-tude M r < −
17. Each z=0 galaxy is the base of a mergertree. Each tree and all galaxy predecessors was loaded,giving a total of 900,000 galaxy models over all 63 timesteps and over the redshift range (0 < z < all galaxies in all time-steps(subdivided only by D n (4000) and in 9 course redshiftbins), using rest-frame observables. Hence, all results uenching or Bursting: Star Formation Acceleration 3 given below can be applied to galaxies at any redshift, us-ing k-corrected observables.
Spectral Energy Distributions
Stellar Population Synthesis
We use the SAM model star formation rate for eachgalaxy and the merger tree to calculate a star formationhistory for each galaxy at each time step/redshift. Thestar formation rate (SFR) vs. time is calculated at eachtime step and is the sum of the star formation historiesof all predecessor galaxies in the merger tree. Updatedsingle-stellar population (SSP) stellar population synthe-sis models of Bruzual & Charlot (2003, CB07) are usedto predict broad-band luminosities and spectral indices.These models are available in seven metallicity bins. Ineach time step, a SSP is created associated with the SFRand time interval in that time step. The metallicity ofthe SSP in this time step is derived from the gas phasemetallicity from the SAM (using the closest available SSPmodel). We use a Salpeter initial mass function.
Dust Extinction
We have used a simple geometric model for dust extinc-tion. The SAM predicts gas phase metallicity ( Z gas ), gasmass ( M gas ), and galaxy size ( r gal ). We assume that gasand dust are distributed in a uniform absorbing slab withselective extinction E B − V given by E B − V = C µZ gas M gas r gal − (cos i ) − (1)where C is a constant (obtained by using the Milky Wayvalues) and i is the galaxy inclination. The constant µ allows for a larger absorption for young stars than forevolved stars (Calzetti et al. 1994). We use µ = 1 forstars younger than 10 Myr and µ = 0 . F UV or IR-excess (IRX) vs. UV slope withA
F UV and IRX increasing with β , the slope of the SEDin the FUV/NUV region. 2) The Milky Way extinc-tion law from Cardelli, Clayton & Mathis (1989) has anIRX- β relationship that is flattened and even reversedbecause of the 2200˚A bump. 3) A mixed extinctionmodel in which a fraction f M of the dust follows MilkyWay extinction, and a fraction 1 − f M follows the star-burst extinction, where f M is chosen randomly over arange 0 < f M < f M,max . For the results given below weuse this third method, which gives a fitting error of 0.3magnitude for f M,max = 0 . f M,max = 1. In order to incorporate the positive defi-nite quantity A
F UV as a derived parameter, we fit thequantity
IRX
F UV = log (10 . A FUV − Nebular Emission
We do not incorporate nebular emission in this versionof the model. In a future paper we will incorporate emis-sion lines and examine additional physical parametersthat these trace, including SFR and IMF.
Sample Star Formation Histories
In Figures 1-5, we show sample star formation historiesand evolution in the NUV-i vs. M i color-magnitude di-agram from five galaxies (a massive quiescent, a galaxy slow-quenching at z ∼
2, a disk galaxy with relativelyconstant SFR, a galaxy fast-quenching at z ∼ .
5, and alow mass recent starburst galaxy). METHOD: GALAXY PHYSICAL PARAMETERS
Mathematical Motivation
We would like to recover measures of recent star forma-tion history (SFH) that are non-parametric. Our tech-nique relies on linearization, effectively Taylor expansionto the linear term of a multi-dimensional non-linear func-tion around fixed points. There is a complex, non-linearrelationship between observed colors and spectral indicesand physical parameters. For a Single Stellar Population(SSP) the principal source of variation is age. A robustmeasure of SSP age is the spectral index D n (4000) , sinceextinction has almost no effect (metallicity has some ef-fect, and we defer discussion of this until § n (4000) is specified, there is a lin-ear relationship between observable colors and indicesand star formation metrics such as SFR, specific SFR,stellar mass, and recent changes in SFR. This relation-ship can be tested with a family of star formation histo-ries and a stellar population synthesis models, as long asthis family spans the space of real galaxy star formationhistories. We also assume that physical parameters suchas stellar and gas metallicity, gas mass, and extinctionalso have this linear relationship with observables. Test-ing this requires relating the star formation histories tothe physical parameters with for example a semi-analyticmodel connected to a realistic cosmological simulation. Regression Method and Star FormationAcceleration Parameter
We use standard multiple linear regression (MLR) torelate physical parameters to observed properties. Forthis initial work, we use the following observables. Allsamples are binned in D n (4000) with ∆D n (4000) =0.05.Other observables used in this initial study are the colors:FUV-NUV, NUV-u, u-g, g-r, r-i; the spectral index H δ A ,and the absolute magnitude M i . FUV and NUV areGALEX bands, and u,g,r,i,z are SDSS bands.We perform MLR between all of these observables andeach of the following physical parameters: stellar mass(log M ∗ ), star formation rate (log SF R ), FUV extinction( A F UV ), extinction correction to NUV-i (∆(
N U V − i ) =( N U V − i ) − ( N U V − i ) obs where ( N U V − i ) is theextinction-corrected N U V − i , mass-weighted stellar age(log t ∗ ), gas mass (log M gas ), gas metallicity ( Z gas ), andstellar metallicity ( Z ∗ ).We also fit two additional functions related to mo-ments of the star formation history. We call the “StarFormation Acceleration (SFA)” the time derivative ofthe extinction-corrected NUV-i color ( SF A ≡ d ( N U V − i ) /dt ) (note that the SFA defined using NUV-r vs. SFAdefined using NUV-i differ by only 1%). The SFA is cal-culated using the current and previous time steps, andis quantified as mag Gyr − . In the lowest redshift bin(0 < z < . d ( SF R ) /dt , d ( sSF R ) /dt , d log( sSF R ) /dt , and d ( N U V − i ) /dt ), we have chosento use the latter for the following reasons. 1) d ( SF R ) /dt Martin et al.is not mass normalized and will scale with galaxy mass,making direct comparisons between mass bins less infor-mative. 2) sSF R can vary over many orders of magni-tude making comparisons of galaxies in different sSF R bins less informative. 3) d log( sSF R ) /dt is more use-ful and can track changes across the CMD. But it cantake on large negative and even indefinite values whenquenching occurs rapidly that can only be bounded byusing arbitrary parameters to limit the change. We haveexperimented with using log(sSFR), finding that the fitsare slgnificantly worse than with our adopted definition(2 . σ ( SF A sSF R ) = 4 . σ ( SF A
NUV − i ) = 1 . N U V − i ) is well correlated with log sSFR (with ( N U V − i ) ≃ Const. − . sSF R for 1 < ( N U V − i ) < N U V − i ) > n (4000) , andin 9 redshift bins or 20 8 ×
11 matrices. The matrix ele-ments are denoted M p,o,d,z where p refers to the physicalparameter, o to the observable, d to the D n (4000) value,and z the course redshift bin. In Figure 6 we show somesample fits combined for all D n (4000) and redshift bins.We note that there is moderate error in the SFA fit aswell as some bias. Fitting error is included in assessingthe error in our mean SFA calculations. Biases are smalland discussed in Appendix § B.Physical parameters are derived from P p ( est ) = o =8 X o =1 M o,p,d,z O o (2)or for the observable set used here, P p ( est ) = M ,p,d,z ( F U V − N U V ) + M ,p,d,z ( N U V − u ) + M ,p,d,z ( u − g ) + M ,p,d,z ( g − r ) + M ,p,d,z ( r − i ) + M ,p,d,z D n (4000) + M ,p,d,z H δA + M ,p,d,z M i + constant (3) Influence Functions
In general not all observables used in the above fitsare available. Some, such as H δ A , may be difficult toobtain. It is useful therefore to quantify the impact eachobservable has on each derived physical parameter. We do this by calculating the relative decrease in variancewhen using the observable to that when not using theobservable. This is normalized to the total variance inthe physical parameter over the full sample in a givenD n (4000) bin: I [ p, o, d, z ] ≡ [ < σ [ p, ¯ o,d,z ]2 > − < σ [ p,o,d,z ]2 > ] σ [ p,d,z ]2 (4)where for physical parameter p , D n (4000) bin d , and ob-servable o either used o or not used ¯ o . The mean is takenover all possible non-trivial combinations of observables(with or without observable o ). A value of 1.0 wouldmean that the observable completely eliminates the pa-rameter variance when introduced, and a value 0.0 meansthe observable has no influence on the fit.For example, for D n (4000) =1.40, the influencefunction for A F UV is (0.24, 0.34, 0.30, 0.30, 0.49,0.07, 0.10) for (FUV-NUV, NUV-u, u-g, g-r, r-i,H δ A , M i ). Each photometric color makes a con-tribution to the fit variance reduction, with NUV-i reducing over 50% of the variance. Specific SFR(log sSF R , or the log SF R/M ∗ , has influence functions(0.54,0.29,0.06,0.08,0.20,0.17,0.20). The bulk of the in-formation comes from FUV-NUV and NUV-u, with vir-tually no impact from u-g or g-r. Finally, SFA has influ-ence functions (0.19,0.16,0.03,0.11,0.11,0.49,0.08). Mostof the information comes from H δ A .Table 2 gives the mean influence functions (averagedover all D n (4000) ). Figure 8 shows a color-coded displayof the same information. Degeneracies/Observational Basis
This method allows us to quantify parameter degen-eracies in a simple fashion. Consider the 7-dimensionalspace of observations, and a single physical parameter P i . A vector exists in this space in the direction thatproduces the maximum change in derived physical pa-rameter. This is just the gradient in P i which is given bythe matrix coefficients: ∇ ~P i = X o M i,o ˆ j o . (5)where ˆ j o is a unit vector in the direction of the observable o in this multi-dimensional space. The degeneracy of twophysical parameters P i and P j can be determined fromthe dot-product of these two gradients: D i,j ≡ ∇ ~P i • ∇ ~P j |∇ ~P i ||∇ ~P j | (6)A degeneracy of D i,j = 1 would mean that the twoderived physical parameters come from the same linearcombination of observables and are completely degener-ate. Degeneracy can be negative, if two observables givethe same information but with opposite dependencies.The degeneracies averaged over D n (4000) and redshiftbins are shown in Figure 9.We note for example that the mass-weighted age havea degeneracy of -0.72, since both depend strongly onH δ A (and D n (4000) ). This means that their influencevectors are ∼ n (4000) bin. Agalaxy with a smooth SFR will have a particular H δ A as-sociated with that D n (4000) . If there was more SFRin the past (quenching), H δ A will be higher than thissmooth baseline since it peaks at hundreds of Myr. Themass-weighted age will also be younger. If there wasless SFR in the past (e.g., more in the present, burst-ing) then H δ A will be lower than the baseline and themass-weighted age will be older.In some sense all colors and spectral indices are “light-weighted ages” with different averaging kernals. For ex-ample, extinction-corrected NUV-i is highly correlatedwith sSFR, since NUV tracks SFR (short-term light-weighted age) and i-band has a very long averaging kernaland therefor is a stellar mass tracer. Thus SFA is derivedfrom color/index differences (see plots in § A) that can belinearized within individual D n (4000) bins. Error Propagation/Observable Figure of Merit
Since the derived parameters are linear functions of theobservables, it is a simple matter to propagate observa-tional errors to determine the total observational errorcomponent of the derived parameters. This can then becombined with the fitting error derived from the MLRstep. If the observational error is large, and its influenceis small, including the observation will actually increasethe uncertainty of the derived parameter. Clearly thecriterion for including an observable o with an observa-tional error σ o is: σ [ p,o,d,z ]2 + M o,p,d,z σ o < σ [ p, ¯ o,d,z ]2 (7) APPLICATIONS: GALEX/SDSS GALAXIES
Once we determine the matrix of linear coefficients,we can proceed to apply the method to real galaxies. Wepresent this simply as an illustration of the potential ofthe methodology presented in this work, and expect thatthe full scientific yield will be realized over a range ofstudies and applications in the future.
Observed Sample
We use the same GALEX/SDSS-spectroscopic sampleas in Martin et al. (2007). Our sample is NUV selected inthe GALEX Medium Imaging Survey (MIS; Martin et al.2005). The MIS/SDSS DR4 co-sample occupies 524 sq.deg. of the north galactic polar cap and the southernequatorial strip. Our sample is cut as follows: 1) NUVdetection, nuv weight > z conf > .
67 and specclass=2; 3) 14 . < r < . < N U V < .
0; 4) nuv artifact <
2; 5) field radiusless than 0.55 degrees; 6) 0 . < z < .
22. We useD n (4000) and H δ A as calculated and employed for theSDSS spectroscopic sample by Kauffmann et al. (2003)and available as the MPIA/JHU DR4 Value-Added Cat-alog. H δ A is corrected for nebular emission. The sampleproperties, galactic extinction and k-correction, and cutsare discussed further in M07.There are slight differences in the mean colors of theobserved sample with respect to the model colors. Theseare typically ∼ . ∼ . n (4000) .Also, model H δ A are higher than observed H δ A by about 0.5 over a range of D n (4000) . Model color dispersionsare comparable to the observed dispersions when obser-vation errors are included. The model mean colors ineach D n (4000) bin have been adjusted to match the ob-served mean colors prior to model fitting in order to en-sure that the range of derived parameters is not outsidethe bounds of the fitted parameters. Please see AppendixA for further details.We compare the stellar mass derived by our new ap-proach to that derived by Kauffmann et al. (2003) inFigure 7a. The derived masses compare well, with anrms deviation of ∼ Application 1: Quenching and Starbursts in theGreen Valley
One of our main goals with this technique is to un-derstand the transition of galaxies between the star-forming, blue sequence (or “main sequence”) and thepassively evolving red sequence. In previous papers(Martin et al. 2007; Gon¸calves et al. 2012) we have eval-uated the timescales required for a galaxy to quenchstar formation and complete the transition from blueto red, both at low ( z ∼ .
1; Martin et al. 2007) andintermediate ( z ∼ .
8; Gon¸calves et al. 2012) redshifts,using a combination of the
N U V − r color and thespectroscopic indices D n (4000) and H δ A . Neverthe-less, those papers assume a simplistic model of star for-mation histories in which galaxies move single-handedlyfrom blue to red sequence with exponentially declin-ing star formation rates. We do know, however, thatsome intermediate-color galaxies are actually bursting ,getting temporarily bluer perhaps due to a sudden in-flow of gas and subsequent star formation episode (e.g.,Rampazzo et al. 2007; Thomas et al. 2010; Thilker et al.2010; Salim et al. 2012; Fang et al. 2012).Recognizing this two-way flow, the Star Formation Ac-celeration (SFA) is an appropriate measure of the rate ofcolor evolution across the Green Valley. Again, SFA ispositive for quenching galaxies, and negative for galaxiesundergoing starbursts. Figure 6 shows the result for SFAfor model galaxies and Figure 8 shows the observable in-fluence function.We applied this to the identical set of galaxies usedin Martin et al. (2007), and Figure 10 shows the result-ing SFA vs. extinction-corrected NUV-i color in twomass bins. Several phenomena can be seen in this fig-ure. Ignoring mass-dependence for the moment, blue-sequence galaxies show colors correlated with their SFA –the bluest galaxies have negative, “bursting” SFAs, whileredder blue-sequence galaxies are “quenching”. The red Martin et al.sequence has a similar “tilt” in the diagram: the bluestgalaxies have negative, “bursting” SFAs, while redderred-sequence galaxies are “quenching”. The origin ofsome of the spread in both sequences can be ascribedto recent changes in the SFR.We can plot the color derivatives on the sSFR vs. stel-lar mass diagram. We show this in Figure 12. This dia-gram represents a first attempt to capture the “flow” ofgalaxies on the color-magnitude diagram (or equivalentsSFR-mass diagram). In this diagram red arrows rep-resent average quenching and blue average bursting forgalaxies in each sSFR-mass bin. The total length of thetwo arrows is proportional to the rms spread of the SFA,while the relative proportion of red and blue depends onthe mean SFA (see caption). The head of each arrowcorresponds to the current mass-sSFR, while the tail isthe previous location on the diagram scaled to roughly100 Myr in the past. We can also calculate the meanSFA in each sSFR-mass bin. This is shown in Figure 11.In M07 we reported a measurement of the mass fluxof galaxies across the green valley as an upper limit, be-cause we used a simple monotonic quenching model toderive the color-derivative (dy/dt, now relabeled SFA).Using the same sample but revising the color derivativein each mass bin, we can calculate the true mass fluxfrom blue to red taking into account net bursting andquenching. The revised flux vs. mass is given in Table4. Our new mass flux (calling this method 4 to maintaincontinuity with the three methods presented in M07) is˙ ρ BR = (2 . ± . × − M ⊙ yr − M pc − . It is entirelyconsistent with the value derived by M07, and also withthe estimates based on the mass evolution of the bluesequence (Blanton 2006; Martin et al. 2007) and red se-quence (Faber et al. 2007). We plot this result in Figure13.Now consider the dependence on stellar mass. Lowermass galaxies in the green valley are mostly quenching,while higher mass galaxies are both quenching and burst-ing. This is demonstrated in the sSFR-mass diagramsFigure 12 and Figure 14. In Figure 14 we have calcu-lated average SFA and display them vs. specific SFR(sSFR) for two mass cuts. The mean SFA is 1-3 higherfor galaxies with M ∗ < . M ⊙ compared to galaxieswith M ∗ > . M ⊙ . A plausible scenario for this isgiven in Figure 15: lower mass galaxies are accreting andbecoming satellite galaxies, having their star forming gastidally and/or ram-pressure stripped, while higher massgalaxies are receiving this gas and reacting with newstar formation. These mass differences are extremelyimportant for galaxy models, and obtaining significantnumbers of low mass green-valley galaxies and compar-ing them to high mass galaxies requires an analysis of alarger SDSS/GALEX dataset.It is interesting to compare these observed results tothe predictions of the semi-analytic models used to gen-erate the star formation histories and parameter coeffi-cients. As we discuss in the appendix ( § B), the modelspredict trends that are qualitatively similar but quanti-tively much weaker than those we observe. The observedresults are quite distinct from the model predictions.
Application 2: The AGN/SFA connection
AGNs are potentially powerful source of feedback thatcould accelerate quenching and maintain galaxies onthe red sequence (Croton et al. 2006; Martin et al. 2007;Nandra et al. 2007; Schawinski et al. 2009). Further-more, there is growing evidence that quenching (espe-cially at high stellar masses) might be related to thegrowth of stellar density in the central of the galaxy,probably due to AGN activity and concomitant bulgegrowth (e.g., Cheung et al. 2012; Mancini et al. 2015).As Figure 16 shows, AGNs preferentially occupy thegreen valley. We would like to attempt to answer asimple physical question: All else being equal, doesthe presence of an AGN accelerate quenching in tran-sition galaxies? There is preliminary evidence for this,which we show in Figure 17. At intermediate sSFR,the presence of an AGN appears to accelerate quench-ing by roughly a factor of 2-3. This would appearto support a scenario in which the presence of anAGN might also be connected with a starburst event(e.g., King et al. 2005; Gaibler et al. 2012; Rovilos et al.2012), and only unequivocally quenches star formationat later stages, when feedback drives the gas away(Springel, DiMatteo & Hernquist 2005; Di Matteo et al.2005).However, a large, statistically robust sample is requiredto confirm this tentative conclusion. AGN fraction cor-relates with many other properties, and it must be es-tablished that these correlations do not artificially cre-ate this dependence. The larger GALEX Legacy Sur-vey/SDSS sample will allow us to test this dependencewhile other correlates are held fixed, and even investigatewhether there is a relation between quenching timescalesand AGN luminosities. One of the future goals of thisstudy is to firmly establish whether AGNs acceleratequenching, and under what circumstances.Our preliminary results can also be used to placesome constraints on the formation of the most massive( M ∗ > . M ⊙ ) quiescent galaxies. Let’s use a cutof log SSFR(Gyr − ) = − M ∗ > . M ⊙ ) quiescent galaxies arethe result of dry mergers between already quiescent lessmassive systems, then in principle, there should not bea change in their SFA. However, we clearly see in Figure11 that even the most massive quiescent systems showsome degree of bursting. Wet mergers can qualitativelyexplain the bursting phase for them. The most burstingis happening in the most massive star-forming systemsas seen in Figures 11 and 14. These star-forming systemsare likely going through wet major mergers that result ingas in the outskirts of them falling toward the center andgetting compressed, causing the burst of star-formation.Very massive star-forming systems ( M ∗ > . M ⊙ andlog(SSFR) > -0.5) are rare (see, e.g.; Figure 11) becausethey have already been quenched and moved to the mas-sive quiescent population likely through wet major merg-ers of less massive star-forming systems. Therefore, partof the evolution of the most massive quiescent galaxies( M ∗ > . M ⊙ ) is due to wet major mergers of lessmassive star-forming systems. We note that wet minormergers can have a similar effect too, without changingthe mass of the massive quiescent galaxies much. Staruenching or Bursting: Star Formation Acceleration 7Formation Jerk (SFJ) and a larger sample can potentiallyhelp distinguish between these scenarios.Interestingly, wet major mergers might also explainwhat we see in Figure 17 for AGNs. Wet major merg-ers tend to rejuvenate the nuclear activity but with sometime delay after the star-bursting phase (due to star for-mation). According to Figure 17, for high SSFR values(star-forming phase), both AGN and non-AGN hosts arebursting (in the star-formation phase of merger) but af-ter a while, they enter the quenching phase with AGNhosts showing higher quenching possibly due to the re-vived nucleus (as mergers cause the gas to funnel to-ward the nucleus), which is subsequently followed by out-flows/feedback to help quench galaxies more effectively.SFJ contains information about the timescale of quench-ing/bursting events and can potentially be used to con-strain this picture. In a following paper, we will studythis in more details. DISCUSSION AND SUMMARY
Issues and Caveats
Aperture and Volume Effects SDSS spectroscopy is ob-tained with 3 arcsecond fibers which often do not sub-sume the full galaxy. M07 discussed this effect and dis-missed it as not significant, mainly on the strength of nodetected average redshift dependence. There are smallvariations in < SF A > vs. redshift that may be cor-related with large scale structure. There is no trendwith increasing redshift. The mass trend of SFA doesnot diminish when the redshift range is restricted to0 . < z < .
10. This indicates that neither aperture,color selection, mass selection, or volume effects explainthe mass trend.
Extinction
We considered a number of variants of theextinction law behavior to determine whether our ap-proach impacted the star formation history extraction.In all cases the derived extinction has sensible depen-dence on SFR, SSFR, metallicity and gas mass. As wenoted above, even when the extinction law is permittedto vary randomly between Milky Way and Calzetti, therms error in the A
F UV rises only to ∼ . Model Biases
It is important to ascertain whether theparticular SAMs we have chosen to generate star for-mation histories are biasing the results for the observedSDSS sample. As we mentioned earlier, we believe thatthe SAMs provide a space of possible star formation his-tories, and if those histories span a similar space as actualgalaxies (not necessarily with the same demographics),then the SFA we derive will not be sensitive to the mod-els. We show in Appendix § B that the SAMs give aquantitatively different SFA vs. mass and sSFR thanthe observed galaxies.We experimented with changing the star formation his-tories in the SAMs by adding a large random component(by replacing SFR with 2*SFR*r where 0 < r < α (extinc-tion corrected) in model independent way, so does SFA(effectively the derivative of log sSFR) traces the colorderivative in an essentially model-independent way. Thecaveat to this discussion is metallicity, which we turn tonext. Metallicity
Spectral indices and photometric colors aredependent on the metallicity of the stars producing themas well as on the star formation histories. As we discussedin § δ A -D n (4000) relation can produce the mass trends that weobserve. Consider a SSFR range of − < logSSF R < −
2, in three mass bins (9 < logM ∗ <
10, 10 < logM ∗ <
11, and 11 < logM ∗ < n (4000) of1.54, 1.70, and 1.76. Using the mass-metallicity relationof Tremonti et al. (2004) and the H δ A -metallicity varia-tion for fixed D n (4000) from Bruzual & Charlot (2003),we can calculate d H δ A /d ( logM ∗ ), and using the fit-ting coefficients dSF A/d H δ A we find a spurious slopeof dSF A/d ( logM ∗ ) = − . < logM ∗ < < logM ∗ <
11, and dSF A/d ( logM ∗ ) = +0 . < logM ∗ <
11 and 11 < logM ∗ <
12. This should be compared with the observed dSF A/d ( logM ∗ ) = − . Summary
We propose a novel methodology to investigate galaxyproperties through use of a combination of photometricand spectroscopic measurements. By using stellar pop-ulation synthesis models, we are able to recover a largearray of physical properties of model galaxies using suchcombination. In particular, we define a new quantity,star formation acceleration (SFA), which traces the in-stantaneous time derivative of the specific star formationrate of an individual galaxy by measuring the NUV-icolor time derivative, and which is also recovered by useof the aforementioned measurements.The approach offers the following benefits:1. Physical parameters are derived not by fitting butby a single matrix of linear coefficients;2. The method makes no assumptions about star for-mation histories;3. Moments of star formation history (the star for-mation rate and higher derivatives) can be derivednon-parametrically; Martin et al.4. The method works over all stellar masses with asingle set of matrices;5. Degeneracies between the derived physical param-eters and covariance are explicitly derived;6. Error propagation is simple;7. The influence of each observable on each derivedphysical parameter can be calculated and the re-sulting sensitivities provide useful context for erroranalysis and observation planning;8. The method is easily generalized to incorpo-rate new observables (e.g., morphological indices,other line indices, emission line fluxes, sersicindices, environmental parameters) and model-generated physical parameters (e.g., bulge-to-diskratio, galaxy density); 9. The method is linear and therefore stacked spec-tra (within constant D n (4000) bins) can be used toderive average physical parameters. For example,galaxies can be stacked in bins, (e.g., extinction-corrected color-magnitude bins), obtaining an av-erage physical parameter for the bin.GALEX (Galaxy Evolution Explorer) is a NASA SmallExplorer, launched in April 2003. We gratefully acknowl-edge NASA’s support for construction, operation, andscience analysis for the GALEX mission, developed incooperation with the Centre National d’Etudes Spatialesof France and the Korean Ministry of Science and Tech-nology. Behnam Darvish acknowledges financial sup-port from NASA through the Astrophysics Data Analy-sis Program (ADAP), grant number NNX12AE20G. Wethank the anonymous referee for valuable comments thatstrengthed the paper. Facilities:
GALEX, SDSS
APPENDIX
COLOR AND SPECTRAL INDEX CORRECTION AND IMPACT ON SFA
We have adjusted model colors and spectral indices so that they are similar to those of the observed sample. We dothis so that the range of observational parameters used to extract the physical parameters are comparable to the modelrange. In order to make this comparison as representative as possible, we use a filtered sample of the model galaxiesselected to be detected in SDSS and GALEX NUV as a function of their redshift. In other words the color-correctionmodel sample is magnitude-limited in the same way as the observed sample. We note that the entire model samplewas used to derive the regression coefficients, not the filtered sample.For each D n (4000) bin, we compare the distribution of model and observed colors and indices, notably H δ A . Wehave tried using two methods: simple means and maximizing the cross-correlation. These give results typically within ∼ β (the FUV-NUV slope parameter), NUV-u (and correspondingly NUV-i), and H δ A . Wealso show in Figure 19b the impact on SFA. Over a most of the range of D n (4000) there is an increase in SFA in therange of 0.7-2.0 mag/Gyr, with a mean change of ∆ SF A = 1 . δ A for the D n (4000) =1.25 bin. In Figure 20a, we show the uncorrected observed values vs.the model distribution. The plot also shows SFA contours using mean values for the other (observed) parameters,to show how variations in NUV-u and H δ A affect SFA. In Figure 20b we show the corrected observed values, modeldistribution, and SFA contours using the corrected mean observed values. See caption for further details. In Figure21 we show the same information for NUV-i. We show the distributions of SFA in the D n (4000) 4=1.25 bin in Figure22. We repeat these figures for D n (4000) =1.45 (Figures 23, 24, 25); and for D n (4000) =1.75 (Figures 26, 27, 28). Thefigures showing the SFA distributions illustrate that the observable adjustments bring the derived SFA into agreementwith the model SFAs in their mean values. Without the corrections the two SFA distributions would be significantlydiscrepent. In general the spread in the derived SFA is similar to or higher than that in the model SFAs (Figures22,25, 28).Finally in Figure 29 we show a version of Figure 12 with arrows added indicating how the observable correctionsand associated SFA changes impact the flux diagram. There is a modest impact, typically moving the quench/burstpoint about 0.1 dex down in the quench direction in log SSFR.We note as further evidence of the validity of this approach that the quenching rate derived in Table 4 and Figure13 is consistent with the results of Martin et al. (2007), which was obtained using an independent method. Both ofthese results are quanititatively consistent with the observed evolution in the galaxy main sequence and red sequences.Without reconciling the model and observation distributions, there would be a very significant discrepency betweenthe derived quenching mass flux and the main and red sequence evolution. COMPARISON TO SEMI-ANALYTIC MODEL TRENDS
We have repeated the analysis of § < z < . ρ BR = (3 . × − M ⊙ yr − M pc − , a factor of ∼
100 lower thanour observed mass flux and that inferred from the evolution of the blue and red galaxy luminosity functions.
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F UV -0.055 -0.606 0.496 0.530 0.806 -0.456 0.029 -0.034 -0.482(NUV-r) -0.113 -0.281 0.274 0.334 0.559 -0.340 0.018 -0.037 0.037SFA 0.430 1.977 0.168 -2.063 -0.758 1.673 1.102 -0.015 -5.552SFJ 0.114 0.314 -0.152 -0.406 -0.085 0.597 0.132 0.013 -1.673log(SFR) -0.259 -0.846 0.388 0.568 0.502 -0.454 -0.025 -0.442 18.630log(sSFR) -0.244 -0.616 0.255 0.332 0.279 -0.436 0.016 -0.027 0.903log(M ∗ ) -0.015 -0.230 0.133 0.236 0.223 -0.018 -0.041 -0.415 17.727log(Age) -0.007 -0.075 0.013 0.084 0.027 0.032 -0.030 -0.010 1.247log(M gas ) -0.042 -0.061 0.045 0.041 0.065 -0.113 -0.055 -0.255 11.201Z gas -0.039 -0.143 0.114 0.115 0.137 -0.040 -0.035 -0.336 12.459Z ∗ -0.053 -0.428 0.250 0.369 0.331 0.021 -0.041 -0.504 19.218Ext 0.869 3.710 0.407 -3.735 -1.508 2.669 1.882 -0.007 -9.502 TABLE 2Influence Function
Parameter β NUV-u u-g g-r NUV-i D n (4000) H δ a M i log(M ∗ ) 0.13 0.14 0.12 0.10 0.13 0.00 0.08 0.88A F UV gas ) 0.09 0.05 0.00 0.00 0.01 0.00 0.05 0.55Z gas ∗ TABLE 3Degeneracy Function
Parameter A
F UV ∆(NUV-i) SFA SFJ log(SFR) log(sSFR) log(M ∗ ) log(Age) log(M gas ) Z gas Z ∗ A F UV ∗ ) -1.00 -1.00 -1.00 -1.00 -1.00 -1.00 1.00 0.42 0.56 0.79 0.98log(Age) -1.00 -1.00 -1.00 -1.00 -1.00 -1.00 -1.00 1.00 0.01 0.19 0.47log(M gas ) -1.00 -1.00 -1.00 -1.00 -1.00 -1.00 -1.00 -1.00 1.00 0.88 0.49Z gas -1.00 -1.00 -1.00 -1.00 -1.00 -1.00 -1.00 -1.00 -1.00 1.00 0.77Z ∗ -1.00 -1.00 -1.00 -1.00 -1.00 -1.00 -1.00 -1.00 -1.00 -1.00 1.00 uenching or Bursting: Star Formation Acceleration 11 TABLE 4Mass Flux Table Method 4 M r log M ∗ φ dy/dt [M07] dy/dt ˙ ρ BR σ [ ˙ ρ BR ]-23.75 11.63 1.84e-07 5 0.82 0.82 1.3e-04 1.8e-05-23.25 11.49 1.08e-06 22 0.70 0.69 4.6e-04 6.2e-05-22.75 11.32 6.53e-06 100 0.85 0.54 1.5e-03 1.9e-04-22.25 11.12 2.20e-05 217 0.87 0.53 3.1e-03 3.2e-04-21.75 10.93 4.02e-05 252 0.94 0.61 4.2e-03 3.2e-04-21.25 10.73 5.63e-05 211 0.87 0.69 4.2e-03 2.5e-04-20.75 10.50 7.42e-05 154 1.05 0.81 3.8e-03 2.8e-04-20.25 10.25 6.80e-05 77 1.37 0.93 2.3e-03 2.0e-04-19.75 10.00 6.94e-05 40 1.69 1.17 1.6e-03 2.5e-04-19.25 9.85 6.06e-05 21 1.50 1.32 1.1e-03 2.0e-04-18.75 9.52 7.22e-05 9 2.90 1.22 5.8e-04 1.4e-04Sum 2.3e-02 7.4e-04 TABLE 5Color/Index Corrections D n (4000) β NUV-u u-g g-r NUV-i H δ a Fig. 1.—
Simulated star formation history for a galaxy most like a massive quiescent at the present day. a. Color-magnitude diagram(extinction corrected NUV-i vs. M i ) showing evolutionary tracks of all the galaxies that eventually merge into the single quiescent galaxy.The final merger occurs at z=0.2. Circle size is keyed to log ( M ∗ ), and color is keyed to specific star formation rate. b. Specific SFR (sSFR)vs. redshift for all constituent and final galaxy. c. SFR vs. redshift plotted as in panel b. d. NUV-i vs. redshift. e. Star FormationAcceration (cf. § Fig. 2.—
Simulated star formation history for a galaxy starting a slow quench at z ∼
2. a. Color-magnitude diagram (extinction correctedNUV-i vs. M i ). Circle size is keyed to log ( M ∗ ), and color is keyed to specific star formation rate. b. Specific SFR (sSFR) vs. redshift forall constituent and final galaxy. c. SFR vs. redshift plotted as in panel b. d. NUV-i vs. redshift. e. Star Formation Acceration (cf. § Fig. 3.—
Simulated star formation history for a galaxy like a star-forming with a late minor merger at z ∼ .
8. a. Color-magnitudediagram (extinction corrected NUV-i vs. M i ) showing evolutionary tracks of all the galaxies that eventually merge into the single galaxy.Circle size is keyed to log ( M ∗ ), and color is keyed to specific star formation rate. b. Specific SFR (sSFR) vs. redshift for all constituentand final galaxy. c. SFR vs. redshift plotted as in panel b. d. NUV-i vs. redshift. e. Star Formation Acceration (cf. § uenching or Bursting: Star Formation Acceleration 13 Fig. 4.—
Simulated star formation history for a galaxy starting fast quench at z ∼ .
5. a. Color-magnitude diagram (extinction correctedNUV-i vs. M i ) showing evolutionary tracks the galaxy. Circle size is keyed to log ( M ∗ ), and color is keyed to specific star formation rate.b. Specific SFR (sSFR) vs. redshift for all constituent and final galaxy. c. SFR vs. redshift plotted as in panel b. d. NUV-i vs. redshift.e. Star Formation Acceration (cf. § Fig. 5.—
Simuated star formation history for a dwarf galaxy quenching at early times and then bursting at z ∼ .
07 a. Color-magnitudediagram (NUV-i vs. M i including extinction) showing evolutionary tracks of galaxy. Circle size is keyed to log ( M ∗ ), and color is keyedto specific star formation rate. b. Specific SFR (sSFR) vs. redshift for all constituent and final galaxy. c. SFR vs. redshift plotted as inpanel b. d. NUV-i vs. redshift. e. Star Formation Acceration (cf. § a b c de f g h Fig. 6.—
Results of using linear regression parameter recovery compared to actual model parameter. For each parameter the modelparameter is plotted on the abscissa and recovered parameter using observables (fit) plotted on the ordinate. We include all valued ofD n (4000), all galaxies, and all redshifts. The rms deviation of the fit parameter from the input parameter is given above each panel. a.Stellar mass. b. FUV extinction A F UV . c. Unextincted NUV-i. d. Star formation rate (SFR). e. Specific star formation rate (sSFR). f.Star formation acceleration (SFA) or d(NUV-i)/dt in magnitudes per Gyr. g. Gas mass ( M gas ). h. Stellar ( Z ∗ ). uenching or Bursting: Star Formation Acceleration 15 (a) * [K03]89101112 M * [ M ] (b) −4 −3 −2 −1 0 1 2log SFR −4−3−2−1012 l og S F R [ S ] (c) l og S F R (d) −1 0 1 2 3 Σ gas −5−4−3−2−10 Σ S F R Fig. 7.—
Observational parameters derived from the SDSS sample. a. Comparison of stellar mass derived from this work [M17] vs. thatderived from (Kauffmann et al. 2003) [K03] (modified to a Salpeter IMF for consistency). For an assumed unity slope the rms deviationis 0.16 magnitudes. A linear fit shows a slightly lower slope (0.91) for M17 with respect to K03. The rms deviation from this line is 0.07magnitudes. The origin of this slight difference of slope is beyond the scope of this paper and has no impact on the preliminary results wepresent. b. Comparison of SFR derived from this work to that derived by Salim et al. (2007) from GALEX UV. Agreement is good withrms deviation 0.2 dex. c. SFR vs M(gas) from observed sample. SFR shows a steep dependence on M(gas) for log M(gas) > SF R in M ⊙ yr − kpc − vs gas surface density Σ gas in M ⊙ pc − . Red lines show approximaterange of observations from Bigiel et al. (2008) and Wyder et al. (2009). FUV−NUV NUV−u u−g g−r NUV−i D n (4000) H dA M i FUV−NUV NUV−u u−g g−r NUV−i D n (4000) H dA M i l og ( M * ) A F U V D ( NU V − i ) l og ( S F R ) l og ( s S F R ) S F A S F J l og ( A ge ) l og ( G a s ) Z ga s Z s t a r Fig. 8.—
Influence functions for each parameter. This gives a graphic representative of the sensitivity of a given observable on recoveringa given physical parameter (see text). The influence functions are normalized for each observable so that the observable with the maximuminfluence is 1.0. For example, M i has a strong influence on log ( M ∗ ), log SFR, log M gas , Z gas , and Z ∗ . Extinction and extinction correctedNUV-i [D(NUV-i) = (NUV-i) -(NUV-i)] are strongly influenced by NUV-i, g-r, u-g, NUV-u, and FUV-NUV. uenching or Bursting: Star Formation Acceleration 17 A NUV
D(NUV−i)SFASFJlog(SFR)log(sSFR)log(M * )log(Age)log(M gas )ZgasZstar A NUV
D(NUV−i)SFASFJlog(SFR)log(sSFR)log(M * )log(Age)log(M gas )ZgasZstar A NU V D ( NU V − i ) S F A S F J l og ( S F R ) l og ( s S F R ) l og ( M * ) l og ( A ge ) l og ( M ga s ) Z ga s Z s t a r −1.0 −0.5 0.0 0.5 1.0Degeneracy Fig. 9.—
Degeneracy between derived physical parameters. A negative degeneracy implies the parameters are inversely correlated. Thisgives a graphic representative of the degeneracy D i,j between parameter i and j (see text). A degeneracy of D i,j = 1 or D i,j = − M ∗ ) and Z ∗ are highly degenerate, as is the change extinctioncorrection to NUV-i [D(NUV-i) = (NUV-i) -(NUV-i)] and A F UV . −4−2024 S F A BurstQuench M * <10 M * >10 Fig. 10.—
Star Formation Acceleration (SFA) vs. (NUV-i) for SDSS galaxies in two mass bins cut at transition mass M < M ⊙ and M > M ⊙ . Contours show distribution of galaxies in the two mass bins. Dots and error bars show mean SFA and error in colorbins. The following trends are apparent. Bluer galaxies of both blue and red sequences have bursting SFAs, while redder galaxies of bothsequences tend toward quenching SFA. Also, at all (NUV-i) colors, on average, lower mass galaxies have higher SFA (more quenching)than higher mass galaxies. uenching or Bursting: Star Formation Acceleration 19 * −5−4−3−2−101 l og SS F R [ G y r − ] −0.0 −0.2 −0.5 −0.8 −0.3 −1.3 −0.5 −0.0 −0.5 −1.0 −0.2 −0.8 −1.1 −1.9 −3.4 −3.9 −1.8 −2.8 −2.9 −3.7 −4.9 −5.4 −2 −1 0 1 20
Mean Star Formation Acceleration (SFA) indicated by color on the log sSFR vs. log M ∗ diagram for SDSS galaxies. Largenumber in box is mean SFA, small number is the standard error of the mean. * −5−4−3−2−101 l og SS F R [ G y r − ] * −5−4−3−2−101 l og SS F R [ G y r − ] Fig. 12.— a. Star Formation Acceleration (SFA) plotted as a flux vector on the sSFR vs. M ∗ diagram for SDSS galaxies. There is alarge spread in each bin, with galaxies that are bursting and those that are quenching in each bin. The purpose of this diagram is to try torepresent this diversity using red (quenching) and blue (bursting) arrows whose length is roughly proportional to the typical quench andburst rate. These arrows then show the evolution of the average galaxy on the CMD, including effects of star formation (mass growth) andsSFR evolution (tracked by SFA). The length of the arrows is 1.5 σ SF A , 1.5 times the standard deviation of the SFA in that bin. Red andblue arrows give the relative amplitude of quenching and bursting respectively, with the length of red (blue) arrow equal to 1 . σ SF A + SF A (1 . σ SF A − SF A ), multiplied by a factor that converts the SFA into ∆ sSF R assuming a 100 Myr time interval. The head of each arrow isthe current mass and sSFR, while the tail gives the typical point on the CMD where galaxies making up the current mass-sSFR were located100 Myrs in the past. The sum of the two vectors is proportional to the average SFA in each bin displayed in Figure 11. The followingtrends are apparent. Blue galaxies have bursting SFAs, while red galaxies tend toward quenching SFA. Dots give individual galaxies coloredby SFA (red: SFA=5, purple: SFA=-5). b. Same as a. with volume-corrected density plotted in greyscale contours. Volume correction asin M07. Levels are logarithmic with equal spacing between 5 × − < φ [ Mpc − ] < − , where volume density is per unit 0.5 dex bin inlog M ∗ and log SSFR. uenching or Bursting: Star Formation Acceleration 21 l og ρ B R [ M O • y r - M p c - ] . Fig. 13.—
Total mass flux across the Green Valley (green dot with error bars) estimated using SFA and the galaxy sample of M07.Green dashed shows result of M07 method 1 (no extinction correction, color derivative calculated for the mean of all galaxies in the color-magnitude bin based on monotonically quenching star formation histores), green solid shows result of M07 method 3 (extinction correction,color derivative calculated for each galaxy based on monotonically quenching star formation histories). Both were interpreted in M07 asupper limits because of the possible presence of bursting galaxies. Red points show mass flux estimated from red sequence evolution ofFaber et al. (2007). Higher point is based on evolution over 0 < z <
1, while lower point on 0 < z < .
8. Blue point shows estimate − ˙ ρ B based on blue sequence evolution (derived in M07). −5 −4 −3 −2 −1 0 1log SSFR [Gyr −1 ]−4−2024 S F A BurstQuenchM * <10 M * >10 Fig. 14.—
Average Star Formation Acceleration (SFA) in several sSFR bins for SDSS galaxies in two mass bins cut at transition mass M c = 10 M ⊙ . As in Figure 10, the following trends are apparent. High sSFR galaxies have bursting SFAs, while low sSFR galaxies tendtoward quenching SFA. For log(sSFR) < − . − lower mass galaxies have higher SFA (more quenching) than higher mass galaxies,which average zero quenching (equal numbers of quenching and bursting galaxies). Dashed lines show the full range of the distribution,while solid vertical error bars show the resulting standard error of the mean SFA. uenching or Bursting: Star Formation Acceleration 23 Fig. 15.—
Cartoon model for results displayed in Figures 10-14. Low mass galaxies are stripped as they enter higher-mass halos and aretidally or ram pressure stripped of gas and quench. High mass galaxies are preferentially central galaxies and occasional suffer bursts fromaccretion events (merging satellites or infalling circum-galactic gas).
Fig. 16.—
Color-magnitude diagram (contours in NUV-r vs. M r , extinction corrected) from Martin et al., (2007a). AGN fraction in eachcolor-magnitude bin shows that AGNs mostly occupy the green valley. uenching or Bursting: Star Formation Acceleration 25 −5 −4 −3 −2 −1 0 1log SSFR−1012 S F A No AGNAGN
BurstQuench
Fig. 17.—
Average Star Formation Acceleration (SFA) in several sSFR bins for SDSS galaxies for AGNs and non-AGNs. As in Figure14, SFA increases at lower sSFR. Since low mass galaxies dominate the number density, the average is net quenching at low sSFR. Galaxieswith AGN show detectably higher SFA (quenching) than galaxies without AGN. Vertical error bars show the standard error of the meanSFA.
Fig. 18.—
Recovered SFA vs model SFA in test sample for which a largr random SFR component as been added to decouple the starformation history from other physical parameters that affect observables such as extinction (compare to Figure 6f). Ratio of fitting error( σ = 2 .
28) relative to spread of SFA is approximately the same as in the reference models. uenching or Bursting: Star Formation Acceleration 27 (a) n (4000)−1012 ∆ X ∆β NUV−uu−gg−rr−iH δ a (b) n (4000)−4−2024 ∆ S F A Fig. 19.— a. Changes to colors and H δ A vs. D n (4000) required to match observational to model distributions. b. Resulting change tomean SFA produced by color/index changes vs. D n (4000) . −5 0 5 10H δ −6−4−20246 NU V − u − . − . − . − . − . − . − . − . . . . . . . −5 0 5 10−6−4−20246−5 0 5 10−6−4−20246 −5 0 5 10H δ −6−4−20246 NU V − u − . − . − . − . − . − . − . − . . . . . . . −5 0 5 10−6−4−20246−5 0 5 10−6−4−20246 Fig. 20.— a. Distribution of observables (H δ A and NUV-u) in black contours, and model values in red contours, with means shown withcrosses. For D n (4000) =1.25 bin. Contours show SFA vs. H δ A and NUV-u calculated using the mean values of the other observables inthis D n (4000) bin. Solid lines shows SFA calculated using FUV-NUV (or β ), while dotted lines show SFA calculated not using FUV-NUV.b. Same as a. with corrected observables and SFA contours calculated using corrected mean observables. −5 0 5 10H δ NU V − i − . − . − . − . − . − . − . − . . . . . −5 0 5 100246810−5 0 5 100246810 −5 0 5 10H δ NU V − i − . − . − . − . − . − . − . − . . . . . −5 0 5 100246810−5 0 5 100246810 Fig. 21.— a. Same as Figure 20 for NUV-i vs. H δ A . −10 −5 0 5 10SFA0.00.51.01.5 N o r m a li z ed Fig. 22.— —bf Histogram of derived SFA (with corrected observables, black) vs. model SFA. Dotted lines show mean values (black:observable SFA, red: model SFA). Dashed line shows mean derived SFA for uncorrected observables. All in D n (4000) =1.25 bin. −5 0 5 10H δ −6−4−20246 NU V − u − . − . − . − . − . − . − . . . . . . . . −5 0 5 10−6−4−20246−5 0 5 10−6−4−20246 −5 0 5 10H δ −6−4−20246 NU V − u − . − . − . − . − . − . − . − . . . . . . . . −5 0 5 10−6−4−20246−5 0 5 10−6−4−20246 Fig. 23.— a. Distribution of observables (H δ A and NUV-u) in black contours, and model values in red contours, with means shown withcrosses. For D n (4000) =1.45 bin. Contours show SFA vs. H δ A and NUV-u calculated using the mean values of the other observables inthis D n (4000) bin. Solid lines shows SFA calculated using FUV-NUV (or β ), while dotted lines show SFA calculated not using FUV-NUV.b. Same as a. with corrected observables and SFA contours calculated using corrected mean observables. uenching or Bursting: Star Formation Acceleration 29 −5 0 5 10H δ NU V − i − . − . − . − . − . − . − . . . . . . . −5 0 5 100246810−5 0 5 100246810 −5 0 5 10H δ NU V − i − . − . − . − . − . − . − . . . . . . . . . −5 0 5 100246810−5 0 5 100246810 Fig. 24.— a. Same as Figure 23 for NUV-i vs. H δ A . −10 −5 0 5 10SFA0.00.51.01.52.0 N o r m a li z ed Fig. 25.—
Histogram of derived SFA (with corrected observables, black) vs. model SFA. Dotted lines show mean values (black: observableSFA, red: model SFA). Dashed line shows mean derived SFA for uncorrected observables. All in D n (4000) =1.45 bin. −5 0 5 10H δ −6−4−20246 NU V − u − . − . − . − . − . − . . . . . −5 0 5 10−6−4−20246−5 0 5 10−6−4−20246 −5 0 5 10H δ −6−4−20246 NU V − u − . − . − . − . − . − . . . . . −5 0 5 10−6−4−20246−5 0 5 10−6−4−20246 Fig. 26.— a. Distribution of observables (H δ A and NUV-u) in black contours, and model values in red contours, with means shown withcrosses. For D n (4000) =1.75 bin. Contours show SFA vs. H δ A and NUV-u calculated using the mean values of the other observables in thisD n (4000) 4 bin. Solid lines shows SFA calculated using FUV-NUV (or β ), while dotted lines show SFA calculated not using FUV-NUV.b. Same as a. with corrected observables and SFA contours calculated using corrected mean observables. −5 0 5 10H δ NU V − i − . − . − . . . . −5 0 5 100246810−5 0 5 100246810 −5 0 5 10H δ NU V − i − . . . . . . −5 0 5 100246810−5 0 5 100246810 Fig. 27.— a. Same as Figure 26 for NUV-i vs. H δ A . −10 −5 0 5 10SFA0.00.51.01.52.0 N o r m a li z ed Fig. 28.—
Histogram of derived SFA (with corrected observables, black) vs. model SFA. Dotted lines show mean values (black: observableSFA, red: model SFA). Dashed line shows mean derived SFA for uncorrected observables. All in D n (4000) =1.75 bin. uenching or Bursting: Star Formation Acceleration 31 * −5−4−3−2−101 l og SS F R [ G y r − ] Fig. 29.—
Star Formation Acceleration (SFA) plotted as a flux vector on the sSFR vs. M ∗ diagram for SDSS galaxies. Same as Figure12. Added black arrows show change in quench/burst mean point produced by SFA change from observable distribution correction. * −5−4−3−2−101 l og SS F R [ G y r − ] −0.3 −0.1 −0.5 −0.1 −0.9 −0.2 −2.0 −1.4 −0.1 −1.1 −0.5 −0.2 −0.2 −0.0 −0.2 −0.5 −1.2 −1.3 −1.5 −1.1 −1.7 −4.8 −4.1 −4.5 −4.3 −4.6 −5.1 −2 −1 0 1 20
Star Formation Acceleration (SFA) plotted as a flux vector on the sSFR vs. M ∗∗