A Machine Learning Approach to Measuring the Quenched Fraction of Low-Mass Satellites Beyond the Local Group
MMNRAS , 1–11 (2020) Preprint 11 February 2021 Compiled using MNRAS L A TEX style file v3.0
A Machine Learning Approach to Measuring the QuenchedFraction of Low-Mass Satellites Beyond the Local Group
Devontae C. Baxter, (cid:63) † M. C. Cooper, Sean P. Fillingham Center for Cosmology, Department of Physics & Astronomy, University of California, Irvine, 4129 Reines Hall, Irvine, CA 92697, USA Department of Astronomy, University of Washington, Box 351580, Seattle, WA 98195, USA
11 February 2021
ABSTRACT
Observations suggest that satellite quenching plays a major role in the build-up of passive, low-mass galaxies at late cosmic times. Studies of low-mass satellites,however, are limited by the ability to robustly characterize the local environmentand star-formation activity of faint systems. In an effort to overcome the limitationsof existing data sets, we utilize deep photometry in Stripe 82 of the Sloan DigitalSky Survey, in conjunction with a neural network classification scheme, to study thesuppression of star formation in low-mass satellite galaxies in the local Universe. Us-ing a statistically-driven approach, we are able to push beyond the limits of existingspectroscopic data sets, measuring the satellite quenched fraction down to satellitestellar masses of ∼ M (cid:12) in group environments ( M halo = 10 − h − M (cid:12) ). At highsatellite stellar masses ( (cid:38) M (cid:12) ), our analysis successfully reproduces existing mea-surements of the quenched fraction based on spectroscopic samples. Pushing to lowermasses, we find that the fraction of passive satellites increases, potentially signaling achange in the dominant quenching mechanism at M (cid:63) ∼ M (cid:12) . Similar to the resultsof previous studies of the Local Group, this increase in the quenched fraction at lowsatellite masses may correspond to an increase in the efficacy of ram-pressure strippingas a quenching mechanism in groups. Key words: galaxies: evolution – galaxies: star formation – galaxies: dwarf – galaxies:formation
The recent generation of large-scale galaxy surveys have re-vealed that the population of non-star-forming (i.e. “qui-escent” or “quenched”) galaxies increased by more than afactor of two in the past 7 −
10 Gyr, such that quenchedsystems, as opposed to their star-forming counterparts, com-prise the majority of the stellar mass budget at z ∼ (cid:63) e-mail: [email protected] † LSSTC DSFP Fellow put forth to explain how galaxies transition from star form-ing to quiescent. In general, these processes are split intotwo distinct categories, namely, internal and environmentalquenching. The former, which acts independent of local envi-ronment (i.e. on both central and satellite systems), refers toany quenching process that suppresses star formation fromwithin a galaxy. Examples of internal quenching mechanismsinclude feedback from star formation (Oppenheimer & Dav´e2006; Ceverino & Klypin 2009) and active galactic nuclei(AGN, Di Matteo et al. 2005; Hopkins et al. 2005; Crotonet al. 2006). On the other hand, environmental quenching,which typically applies to low-mass satellites ( (cid:46) M (cid:12) ),refers to a range of quenching mechanisms that suppress starformation due to environmental factors – e.g. ram-pressurestripping (Gunn & Gott 1972; Abadi et al. 1999), tidalstripping (Merritt 1983; Moore et al. 1999; Gnedin 2003),strangulation or starvation (Larson et al. 1980; Kawata &Mulchaey 2008), and harassment (Moore et al. 1996, 1998).In general, environmental quenching mechanisms suppressstar formation by either preventing satellites from accret- © a r X i v : . [ a s t r o - ph . GA ] F e b Baxter et al. ing gas (e.g. strangulation) or by removing pre-existinggas reservoirs through galaxy-galaxy interactions (i.e. ha-rassment), gravitational tidal forces (e.g. tidal stripping),or interaction with the circumgalactic medium of the host(e.g. ram-pressure stripping).At z ∼
0, galaxy surveys find that satellites, not cen-trals, comprise the largest fraction of passive systems overa wide range of stellar masses ( (cid:46) . M (cid:12) , Wetzel et al.2013). Furthermore, observations of low-mass ( (cid:46) M (cid:12) )galaxies in the local Universe have demonstrated that nearlyall field galaxies are star forming, signaling that environ-mental quenching is primarily responsible for suppressingstar formation in the low-mass regime (Haines et al. 2008;Geha et al. 2012). Altogether, these observations demon-strate the importance and ubiquity of satellite quenching atlate times and especially low satellite masses. Yet, hydrody-namic and semi-analytic models, which successfully predictthe fraction of quiescent centrals, continue to significantlyoverpredict the relative number of passive satellites, espe-cially at low-masses (Kimm et al. 2009; Hirschmann et al.2014; Wang et al. 2014, but see also Henriques et al. 2017).This discrepancy between theoretical predictions and obser-vations is driven by a failure to properly model the physicalprocesses responsible for satellite quenching. This lack ofagreement between observations and theoretical models fur-ther emphasizes that understanding the details of satellitequenching is tantamount to advancing our understanding ofgalaxy formation.Our current understanding of satellite quenching at lowmasses is largely derived from studies of dwarf galaxies( M (cid:63) ∼ − M (cid:12) ) in the very local Universe, includingour own Local Group. First and foremost, a range of ob-servations demonstrate that the vast majority of low-masssatellites are gas-poor and passive, in contrast to their gas-rich, star-forming counterparts in the field (e.g. Grcevich &Putman 2009; Spekkens et al. 2014; Weisz et al. 2014a,b).Furthermore, studies of the accretion history of these sys-tems using N -body simulations demonstrate that quench-ing is highly efficient, such that the typical timescale overwhich quenching occurs is ∼ M (cid:63) (cid:46) M (cid:12) (likelydriven by an increase in the efficacy of ram-pressure strip-ping, Fillingham et al. 2015, 2016, 2018; Wetzel et al. 2015;Weisz et al. 2015). On the other hand, studies of the moremassive satellites ( M (cid:63) (cid:38) M (cid:12) ) in the Local Group andnearby groups/clusters find that these systems have signif-icantly longer quenching timescales ( (cid:38) M (cid:63) ∼ M (cid:12) (atleast within Milky Way-like host halos, M halo ∼ M (cid:12) ,Fillingham et al. 2016; Rodriguez Wimberly et al. 2019).A major step towards increasing our understanding ofsatellite quenching involves determining if the aforemen-tioned results extend beyond the Local Group. Is a similarincrease in the quenched fraction observed at low massesoutside of the Local Group (and/or in more massive hosthalos), indicating a corresponding increase in the efficiencyof environmental (or satellite) quenching at this mass range?Unfortunately, the current generation of spectroscopic sur-veys lack the necessary combination of depth, area, and/orcompleteness to reliably probe this mass regime. For exam- ple, at the magnitude limit of the main spectroscopic survey,the Sloan Digital Sky Survey (SDSS, York et al. 2000) canonly probe galaxies with stellar masses less than 10 M (cid:12) at z < .
01. While more recent surveys push fainter, in-cluding the Galaxy and Mass Assembly (GAMA) (GAMA,Driver et al. 2009, 2011) survey, the corresponding area ofsky mapped is significantly smaller, again limiting the num-ber of nearby hosts around which we can study their satel-lites. In contrast to spectroscopic data sets, wide and deepimaging programs are able to probe both star-forming andpassive galaxies down to stellar masses of ∼ M (cid:12) at z (cid:46) .
1, covering significant areas on the sky.Herein, we present a method for measuring the satel-lite quenched fraction down to M (cid:63) ∼ M (cid:12) by apply-ing machine learning and statistical background subtractiontechniques to wide and deep photometric data sets, push-ing beyond the limits of current spectroscopic samples. In §
2, we describe the spectroscopic and photometric data setsutilized in our analysis. In §
3, we discuss the training, test-ing, and performance of our neural network classifier (NNC)as well as our use of the trained model to classify galaxiesin our photometric sample as star forming or quenched. In §
4, we describe our statistical background subtraction tech-nique and use it to measure the satellite quenched fractionaround nearby groups. Lastly, in §
5, we discuss and sum-marize our results. When necessary, we adopt a flat ΛCDMcosmology with H = 70 km s − Mpc − and Ω m = 0.3. Allmagnitudes are on the AB system (Oke & Gunn 1983). Our analysis utilizes the co-added images and photometryfrom the Sloan Digital Sky Survey, focusing on the deeperStripe 82 data set (S82, Annis et al. 2014; Bundy et al.2015). Stripe 82 is centered on the Celestial Equator andis comprised of an area of ∼
300 deg that spans between − ◦ < α < ◦ and − . ◦ < δ < +1 . ◦ . The co-addedimages in S82 reach a depth ∼ ugriz relative to the SDSS single-pass data. Overall, the wide areaand impressive depth ( r ∼ .
4, 95% complete for galaxies)of Stripe 82 make it well-suited for studying the propertiesof low-mass galaxies in the local Universe. For the purposeof our analysis, we limit the S82 sample to only includegalaxies (defined using the SDSS
TYPE parameter) with 13 5. This apparent r -band magnitude cut is appliedto ensure that galaxies in our sample are below the SDSSsaturation limit and above the 95% completeness limit forgalaxies in the gri passbands.We exclude the shallower and less complete u and z bands throughout our analysis. Furthermore, as discussedin Bundy et al. (2015), the TYPE -based galaxy classifica-tion is contaminated with a non-negligible fraction of stars( ∼ < r < 18 that are classified as stars in the correspondingsingle-pass SDSS images. At the very brightest magnitudes MNRAS , 1–11 (2020) tudying Satellite Quenching with Machine Learning ( r < ∼ 6% of sourcesat r < 18 from our sample, such that our final catalog in-cludes 1 , , 392 galaxies with non-extinction-corrected gri photometry in S82. Accounting for Galactic extinction doesnot change our qualitative results, in part due to the lowextinction in the S82 field (Schlegel et al. 1998). To train our classification scheme, which aims to identifygalaxies as star forming or quenched, we use spectroscopicdata products from the Max Planck Institute for Astro-physics and Johns Hopkins University DR7 catalog (MPA-JHU, Kauffmann et al. 2003; Brinchmann et al. 2004) alongwith photometry from SDSS Data Release 7 (Aihara et al.2011). The MPA-JHU catalog is a value-added data set de-rived from the spectroscopic SDSS DR7, containing stellarmass and star formation rate (SFR) estimates for nearly amillion galaxies up to z ∼ . 3. When available, the SFRsare derived using the extinction-corrected H α emission lineluminosities. For galaxies that lack emission lines, the SFRsare estimated using a relationship between SFR and the4000˚A-break index ( D , Bruzual A. 1983; Hamilton 1985;Brinchmann et al. 2004). Likewise, the stellar masses arecomputed using model fits to the broad-band ugriz pho-tometry (Kauffmann et al. 2003).We match galaxies in the MPA-JHU and SDSS DR7catalogs using their unique MJD, plate ID, and fiber ID toconstruct a cross-matched catalog that includes both photo-metric and spectroscopic galaxy properties. These propertiesinclude gri model magnitudes, specific star-formation rates(sSFR; SFR divided by stellar mass), redshifts, and stellarmasses. Furthermore, we limit our cross-matched catalog toonly include galaxies in which CLEAN = 1, RELIABLE (cid:54) =0. The former is a photometric flag that removes sourcessuffering from saturation, deblending, and/or interpolationissues. The latter is a spectroscopic flag that omits galaxieswith unreliable line profiles and physical parameters. Over-all, these cuts remove roughly 3% of galaxies from the orig-inal MPA-JHU catalog. Finally, we limit our sample to onlyinclude galaxies at z < . M (cid:63) > . M (cid:12) , with mea-sured specific star formation rates. Overall, our final sampleincludes ∼ , 000 galaxies, with a median redshift of 0 . . × M (cid:12) , and median r -bandmagnitude of 17. Our spectroscopically-confirmed host sample is selectedfrom the group catalog of Yang et al. (2007). We selectgroups within the Stripe 82 footprint at z < . < M halo h − M (cid:12) < , excluding groups that arelocated within 0 . . 077 and a median halo mass of 1 . × M (cid:12) . Thecentral galaxies in these groups have a median stellar massof 1 . × M (cid:12) . g r i g − r g − i r − i sSFR g r i g − r g − i r − i s S F R − . − . − . − . . . . . . P e a r s o n s C o rr e l a t i o n C o e ffi c i e n t Figure 1. A heatmap displaying the correlation between ob-served colors, apparent magnitudes, and specific star-formationrates for galaxies in our spectroscopic training set. In general, su-pervised neural network classifiers rely heavily on an existing cor-relation between input features and target variables (i.e. quenchedor star-forming label). For our sample, we detect a relativelystrong correlation between observed color and sSFR. The first step in constructing our training set for supervisedmachine learning involves selecting the appropriate featuresthat will enable our machine learning model to accuratelyclassify galaxies as either star forming or quenched. More-over, we can only include photometric features since we ul-timately seek to apply our neural network classifier (NNC)to galaxies without spectra. To that end, we construct aheatmap to visualize the degree of correlation, as measuredby the Pearson correlation coefficient, between the specificstar formation rate of the MPA-JHU galaxies and their pho-tometric properties. As shown in Figure 1, we find a rela-tively strong negative correlation between the optical colorsof the galaxies and their specific star formation rates, whichimplies that optically blue (red) galaxies tend to have higher(lower) specific star formation rates. With this correlationin mind, we construct our training set using only the g − r , r − i , and g − i observed colors as features. The inclusion ofmagnitude information (i.e. apparent gri magnitudes) has anegligible effect on the resulting classifications, and as suchwas not utilized in the final configuration.The second important step in constructing our train-ing set for supervised machine learning involves systemat-ically labeling galaxies as either star forming or quenched.We achieve this by taking advantage of the strong bimodal-ity in sSFR- M (cid:63) space, which for our MPA-JHU sample isillustrated if Figure 2. In particular, we adopt a cut ofsSFR = 10 − yr − as our quenching threshold, such thatgalaxies above (below) this threshold are labeled as starforming (quenched). This results in a balanced training set MNRAS000 The first step in constructing our training set for supervisedmachine learning involves selecting the appropriate featuresthat will enable our machine learning model to accuratelyclassify galaxies as either star forming or quenched. More-over, we can only include photometric features since we ul-timately seek to apply our neural network classifier (NNC)to galaxies without spectra. To that end, we construct aheatmap to visualize the degree of correlation, as measuredby the Pearson correlation coefficient, between the specificstar formation rate of the MPA-JHU galaxies and their pho-tometric properties. As shown in Figure 1, we find a rela-tively strong negative correlation between the optical colorsof the galaxies and their specific star formation rates, whichimplies that optically blue (red) galaxies tend to have higher(lower) specific star formation rates. With this correlationin mind, we construct our training set using only the g − r , r − i , and g − i observed colors as features. The inclusion ofmagnitude information (i.e. apparent gri magnitudes) has anegligible effect on the resulting classifications, and as suchwas not utilized in the final configuration.The second important step in constructing our train-ing set for supervised machine learning involves systemat-ically labeling galaxies as either star forming or quenched.We achieve this by taking advantage of the strong bimodal-ity in sSFR- M (cid:63) space, which for our MPA-JHU sample isillustrated if Figure 2. In particular, we adopt a cut ofsSFR = 10 − yr − as our quenching threshold, such thatgalaxies above (below) this threshold are labeled as starforming (quenched). This results in a balanced training set MNRAS000 , 1–11 (2020) Baxter et al. log ( M ? / M (cid:12) ) − − − − − l og ( s S F R y r − ) Figure 2. Specific star formation rate versus stellar mass forgalaxies in our spectroscopic training set. The contours highlightthe star-forming and quenched galaxy population within our sam-ple. We divide the galaxy sample at sSFR = 10 − yr − , suchthat galaxies above this threshold are labeled as star forming andgalaxies below this threshold are labeled as quenched. where 49% (51%) of galaxies are classified as quenched (starforming). This is important because imbalanced trainingsets can result in uninformative models that naively over-predict the majority class and underpredict the minorityclass. Furthermore, we standardize the features of our train-ing set to have a mean of zero and standard deviation of oneaccording to X st = ( X − µ ) /σ , where X , µ , and σ are theinput feature, mean, and standard deviation of the sample,respectively. This pre-processing procedure is implementedto optimize the performance and stability of the neural net-work classifier, which assumes that the inputs are standard-ized.Lastly, to construct our validation set, we remove 6600out of the ∼ , 000 galaxies in our training set. The val-idation set is composed of a subset of those galaxies cross-matched between the MPA-JHU and the S82 photometriccatalogs using a search radius of 1 (cid:48)(cid:48) . We omit these galaxiesfrom the training and testing process, so that they can ulti-mately be used to evaluate the performance of the resultantNNC. The supervised neural network classifier is a machine learn-ing model that is trained using labeled observations in orderto learn a mapping function between input features and out-put targets. The utility of these models is that once they aretrained they can be readily used to classify unlabeled obser-vations. Moreover, neural network classifiers are constructedusing a variety of hyperparameters that influence the over-all performance of the machine learning model. The optimal hyperparameters for our NNC are obtained using a K-foldcross-validation grid search. The names and values of thesehyperparameters are as follows: (i) the number of hiddenlayers is two; (ii) the number of nodes in the first and sec-ond hidden layer are 8 and 4, respectively; (iii) the batchsize is 64; (iv) the number of epochs is 10; (v) the dropoutis 20%. As is standard for binary classification, we use therectified linear unit (ReLU) activation function for the in-put and hidden layers, while the sigmoid activation functionis used for the output layer. Our model is compiled usinga binary cross-entropy loss function and stochastic gradientdescent with a learning rate of 0.01. Lastly, we use a strati-fied K-fold cross validation procedure with k=5 to determinethe average accuracy and logarithmic loss of our model. The K-fold cross validation yields an average classificationaccuracy of 0.94 and logarithmic loss of 0.17. Here, the ac-curacy measures the fraction of galaxies that are correctlyclassified during the training/testing process, while the log-arithmic loss measures the uncertainty of the predictionsmade by the NNC. Therefore, the high average classificationaccuracy and low logarithmic loss suggest that our NNC re-turns both accurate and precise classifications. Another di-agnostic for determining the reliability of the NNC involvesapplying the trained model to labeled data that was notutilized during the training or testing process. In our case,we use our validation set that is composed of a subset ofthe galaxies cross-matched between our spectroscopic train-ing set and the S82 photometric sample. Upon applying theNNC to our validation set, we find that 93% of galaxies inthe validation set are correctly classified as quenched, and95% of star forming galaxies in the validation set are cor-rectly classified as star forming. Moreover, we find that thetrue quenched fraction for the validation set is reproducedby the NNC with an average percent error of ∼ > . − CPwhen CP < . 5. The mean and median classification confi-dence are 0 . 927 and 0 . 98, respectively. Overall, these resultsprovide further confidence in the reliability and accuracy ofthe predictions made by the neural network classifier.Using the validation set, we also explore how the clas-sification accuracy varies with galaxy properties. As shownin Figure 3, we find that the classification accuracy remainsrelatively constant across our specified redshift range, suchthat host halos at slightly lower redshift are not biased rel-ative to their higher- z counterparts within the sample. Wedo find, however, a modest correlation between classifica-tion accuracy and stellar mass, such that the NNC achieveshigher levels of accuracy when classifying lower-mass galax-ies ( M (cid:63) (cid:46) M (cid:12) ). While the spectroscopic training set isdominated by more massive galaxies ( ∼ 90% of the spec-troscopic training set has M (cid:63) > . M (cid:12) ), the classifi-cation accuracy – and our primary results regarding the MNRAS , 1–11 (2020) tudying Satellite Quenching with Machine Learning . . . . . . . . . log ( M ? /M (cid:12) ) . . . . . . . . . . . C l a ss i fi c a t i o n a cc u r a c y log ( M ? /M (cid:12) )Redshift − . . . . . . . . . g − r g − rg − i . 03 0 . 04 0 . 05 0 . 06 0 . 07 0 . 08 0 . Redshift − . . . . . . g − i Figure 3. Classification accuracy in the validation set as a function of redshift and stellar mass ( left ) along with observed g − r and g − i color ( right ). The accuracy of the NNC is largely independent of host halo redshift and weakly dependent on stellar mass, withhigh-mass galaxies more likely to be incorrectly classified. Despite the training set being largely composed of high-mass galaxies ( ∼ M (cid:63) > . M (cid:12) ), we find that the overall classification accuracy as well as our primary satellite quenched resultsremain qualitatively unchanged when high-mass systems are omitted from the training set. As expected, the NNC is less reliable atclassifying galaxies at intermediate colors (i.e. in the “green valley” of the color bimodality) precisely due to the binary nature of theclassification scheme. satellite quenched fraction – are qualitatively unchangedwhen limiting the spectroscopic training set to systems with10 . M (cid:12) < M (cid:63) < . M (cid:12) .As suggested in Figure 1, g − r and g − i color are themost informative features with respect to predicting whethera galaxy is star forming or quenched. In Figure 3, we ex-plore the relationship between the classification accuracyand these two features. As expected, the classification accu-racy is highest for very blue and red galaxies, with a modestdecrease for galaxies residing in the green valley. This is inpart due to the binary nature of our classification scheme(i.e. the lack of a transitory phase between star formingand quenched) along with the overlap between dusty star-forming galaxies and quiescent systems in rest-frame opticalcolor (e.g. Yan et al. 2006; Maller et al. 2009; Williams et al.2009). Using the hyperparameters discussed in § § g − r , g − i , and r − i colors of the galaxies in our S82 photometric sample to havea mean of zero and standard deviation of one using the sameprocedure outlined in § z galaxies.Many of these high- z sources have red apparent colors, and are more likely to be classified as quenched. Ultimately, thesuccess of our approach relies on correctly classifying thelow- z sources (i.e. the satellites of our targeted group sam-ple). With that objective, the next step in our analysis in-volves combining the classification results with a statisticalbackground subtraction technique to ultimately determinethe satellite quenched fraction of our low- z host sample. While deep imaging allows the satellite population aroundnearby hosts to be detected and our NNC is able to ro-bustly classify sources as star forming or quenched, iden-tifying the true satellites amongst the sea of backgroundsources remains a challenge. This is primarily due to thelack of highly-complete line-of-sight velocity information forour photometric sample, which is required to cleanly de-termine if a particular source is truly a satellite of a givenhost. However, instead of identifying properties of individ-ual satellites, we employ a statistically-driven backgroundsubtraction technique that enables us to robustly measurethe average properties of the satellite population. Figure 4illustrates our methodology, by which we compare the ra-dial distribution of galaxies around nearby hosts to thatmeasured in random positions on the sky. By subtractingthe random background, we are able to measure the averageproperties (e.g. radial profile, rest-frame color distribution,quenched fraction) of the underlying satellite population.This statistical approach has proven effective in pre- MNRAS000 MNRAS000 , 1–11 (2020) Baxter et al. Host Random 200 300 400 500 600 700 800 900 1000 d proj (kpc) . . . . . . . . < N ga l / k p c > × − Background+SatellitesBackground Figure 4. An illustration of our background subtraction technique, in which we measure the radial number density of galaxies around ourhost galaxies ( left ) and in randomly-selected background fields ( middle ). Using the photometric sample, we compute the mean numberdensity profile as a function of projected radial distance, averaged over our sample of hosts and 6 × background fields ( right ). Theerror bars for both radial profiles correspond to 1- σ Poisson errors in the measured surface density of galaxies. vious studies of satellites at intermediate redshift (Talet al. 2013; Kawinwanichakij et al. 2014; Nierenberg et al.2011, 2012). In general, the background subtraction proce-dure utilized in these studies involves measuring the radialdistribution of galaxies around spectroscopically-confirmedhosts and subtracting the contribution from the back-ground/foreground galaxies. For our analysis, we utilizethe 110 centrals from the Yang et al. (2007) group cata-log that overlap with the S82 footprint as our sample ofspectroscopically-confirmed host galaxies. As stated in § z < . and 10 h − M (cid:12) .Our technique for estimating the contribution frombackground galaxies involves measuring the radial distribu-tion of galaxies at random positions within the S82 foot-print. In particular, we generate 10 random positions withinStripe 82, assigning each a corresponding redshift between0 . < z < . . d proj > − . < z < . 1. For agiven redshift bin, we count the number of quenched andstar-forming galaxies in annuli centered on the hosts in binsof r -band magnitude. This procedure is repeated at the lo-cation of the background pointings, for which we count thenumber of quenched and star-forming galaxies in bins of r -band magnitude within annuli centered on 100 random po-sitions. Specifically, the photometric sample is partitionedinto seven r -band magnitude bins between 13 < r < . r -band magnitude and redshift combi-nation, we calculate the average number of quenched andstar-forming galaxies per annuli for both the background and the spectroscopically-confirmed centrals. Moreover, foreach individual host/random position, we calculate the 1- σ Poisson error associated with our measurement and propa-gate this error in the calculation of the average number ofgalaxies per annuli. Increasing the number of random point-ings used to determine the background (i.e. > r -band magnitude andstellar mass at fixed redshift. To determine this mappingfrom r and z to stellar mass, we fit the following relation togalaxies in the MPA-JHU catalog M (cid:63) ( r, z ) = γ ∗ r + b ( z ) , (1)where γ and b ( z ) correspond to the slope and y -intercept ofthe fit in a given redshift bin. In particular, we fit this rela-tion in redshift bins (with typical width of ∆ z = 0 . r -band magnitude (following background subtraction) canbe mapped to stellar mass based on the redshift of the hostsystem. In Figure 5, we compare the stellar masses esti-mated using our best-fit parameters for Equation 1 to thecorresponding stellar masses from the MPA-JHU catalog,which are based on fitting the multi-band photometry tomodel spectral energy distributions. Our stellar mass esti-mates, inferred solely from the observed r -band magnitude,are relatively accurate with a median difference of − . σ scatter of 0 . 22 dex. There is a slight bias to-wards our method under- and over-predicting the masses ofhigh-mass and low-mass galaxies, respectively. Not surpris-ingly, the fits to Equation 1 are best at intermediate stellarmasses, where the spectroscopic training set is more abun-dant. Tuning our fits to better reproduce the stellar massesof low-mass systems does not yield a significant change inour results, with our measurements of the satellite quenchedfraction computed in bins of stellar mass that exceed thetypical measurement uncertainty. MNRAS , 1–11 (2020) tudying Satellite Quenching with Machine Learning log ( M ?, MPA /M (cid:12) ) l og ( M ? , e s t / M (cid:12) ) Figure 5. Comparison between our estimated stellar masses andthose provided by the MPA-JHU catalog. Our stellar mass esti-mator, which we infer by fitting galaxies in the MPA-JHU catalogusing Equation 1, provides robust mass measurements in the ab-sence of multi-band photometry. In comparison to the MPA-JHUmeasurements, the median stellar mass difference is − . 030 dexwith a standard deviation of 0 . 22 dex. Altogether, the statistical background procedure pro-vides us with a measure of the average number ofquenched and star-forming galaxies as a function of pro-jected distance and stellar mass at the location of both thespectroscopically-confirmed host galaxies and the randombackground positions. With these galaxy counts and classi-fications, we compute the average number of quenched andstar-forming satellites as a function of stellar mass and pro-jected distance according to¯ N sats ( d proj , M (cid:63) ) = (cid:88) ( ¯ N back+sats − ¯ N back ) , (2)where ¯ N back+sats and ¯ N back are the average number of galax-ies measured in annuli centered on the spectroscopically-confirmed centrals and random positions, respectively.In Figure 6, we show the resulting average number ofsatellites as a function of stellar mass and projected host-centric distance. We adopt 400 kpc as the outer extent ofour groups (roughly R ) based upon a comparison to sim-ilar halos in the IllustrisTNG project (Nelson et al. 2018,2019; Naiman et al. 2018; Marinacci et al. 2018; Springelet al. 2018; Pillepich et al. 2018). For host halos at z = 0and 10 h − M (cid:12) < M < h − M (cid:12) within theTNG300 simulation, a sample of > M ∼ . × h − M (cid:12) , the median R is 430 h − kpc with a 1 σ scatter of 97 h − kpc. Given thatour measurements are made in projection, we limit our se-lection of the satellite population to projected distances of < 400 kpc. While this excludes a subset of satellites at host-centric distances of 400 kpc < R < R , it also reducescontamination from objects in the surrounding infall regions( R ∼ R ). As discussed in § . . . . . . . . . log ( M ? / M (cid:12) ) . ¯ N s a t s ¯ N s a t s a nd ¯ N s a t s d proj < 200 kpc d proj < 400 kpc d proj < 600 kpc d proj < 800 kpc d proj < Figure 6. The average number of satellites as a function of stellarmass in projected distance bins. The vertical error bars gives thestandard deviation in the distribution of the number of satellitesafter repeating the background subtraction procedure 100 times,whereas the horizontal error bars represent the standard deviationwithin the stellar mass bin. For our analysis, we limit our satellitepopulation to systems at d proj < 400 kpc. tively unchanged when including satellites out to projecteddistances of 600 kpc or 800 kpc.Selecting satellites within 400 kpc, we find excellentagreement between our inferred satellite stellar mass func-tion and that measured for the IllustrisTNG hosts. As shownin Figure 7, our integrated satellite counts are very tightlybracketed by the corresponding predicted counts in theTNG100 and TNG300 simulations, where we select satel-lites at projected distances of < 400 kpc for hosts with M = 10 − h − M (cid:12) . In addition, we compare to the ob-served satellite mass function from Yang et al. (2008, 2009),based on a sample of spectroscopically-confirmed satellitesin ∼ , 000 low- z groups (see also V´azquez-Mata et al.2020). Overall, our measured satellite mass function is in re-markably good agreement, especially at low masses (or faintmagnitudes). While our background-subtraction techniqueis unable to identify individual satellite galaxies, it is quiterobust at indirectly identifying the satellite population, suchthat its properties may be characterized. As a benchmark for comparison, we measure the quenchedfraction as a function of satellite stellar mass for thespectroscopically-confirmed satellites in the Yang et al.(2007) group catalog. We limit our sample of host halos tothose with 10 h − M (cid:12) < M halo < h − M (cid:12) , iden-tifying satellites as quenched according to the sSFR cut of10 − yr − described in § MNRAS000 000 low- z groups (see also V´azquez-Mata et al.2020). Overall, our measured satellite mass function is in re-markably good agreement, especially at low masses (or faintmagnitudes). While our background-subtraction techniqueis unable to identify individual satellite galaxies, it is quiterobust at indirectly identifying the satellite population, suchthat its properties may be characterized. As a benchmark for comparison, we measure the quenchedfraction as a function of satellite stellar mass for thespectroscopically-confirmed satellites in the Yang et al.(2007) group catalog. We limit our sample of host halos tothose with 10 h − M (cid:12) < M halo < h − M (cid:12) , iden-tifying satellites as quenched according to the sSFR cut of10 − yr − described in § MNRAS000 , 1–11 (2020) Baxter et al. log ( M ? / M (cid:12) ) N s a t s ( > M ? ) Baxter et al. ( d proj < 400 kpc)Baxter et al. ( d proj < 600 kpc) Yang et al. (2009)TNG100-1 ( d proj < 400 kpc)TNG300-1 ( d proj < 400 kpc) Figure 7. The cumulative satellite stellar mass function based onour statistical background subtraction technique in comparison tothat from spectroscopic observations and simulations. The darkand light crimson bands show our satellite counts (per group) at R < 400 kpc and R < 600 kpc, respectively. The purple bandcorresponds to the satellite stellar mass function for groups with M halo = 10 . − . h − M (cid:12) from Yang et al. (2009), while theblack dashed and dotted lines denote the satellite counts for hosthalos with M = 10 − h − M (cid:12) and satellites at projecteddistances of < 400 kpc within the TNG100 and TNG300 sim-ulations, respectively. We find excellent agreement between ourinferred satellite counts and those based on simulations and shal-lower spectroscopic samples. Stripe 82 footprint. From this parent population, we thenselect two subsamples at z < . 06 and at z < . 1. Thelower- z ( z < . 06) sample includes ∼ ∼ , 000 satellite galaxies, complete down to a stellar massof ∼ M (cid:12) . The higher- z sample includes more host sys-tems ( ∼ ∼ , 000 satellites), but onlyprobes down to ∼ . M (cid:12) . In agreement with many previ-ous studies of satellite properties at z ∼ > M (cid:12) with aquenched fraction of < 50% at ∼ M (cid:12) .In an effort to push measurements of the satellitequenched fraction to lower masses (i.e. < M (cid:12) ), we usethe background subtraction technique described in § f satsq ( d proj , M (cid:63) ) = ¯ N sats , q ¯ N sats , q + ¯ N sats , sf , (3)where ¯ N sats , sf and ¯ N sats , q are the average number of star-forming and quenched satellites detected at d proj < 400 kpc,respectively. As discussed in § M (cid:63) > M (cid:12) ), we find excellent agreement betweenthe independent measurements. This serves as a strong val-idation of the background-subtraction technique and ourclassification model.Using the deeper photometry in Stripe 82, we are ableto push our measurements of the satellite quenched fractiondown to ∼ M (cid:12) , probing satellite quenching in groupenvironments across four orders of magnitude in satellitestellar mass. In contrast to measurements in the high-massregime ( > M (cid:12) ), we find that the satellite quenchedfraction in M halo ∼ − h − M (cid:12) groups increases belowsatellite stellar masses of ∼ M (cid:12) . This transition in thequenched fraction suggests a change in the quenching effi-ciency (and possibly dominant quenching mechanism), suchthat the suppression of star formation in low-mass satellitesis increasingly efficient at M (cid:63) (cid:46) M (cid:12) . We have utilized a combination of supervised machine learn-ing and statistical background subtraction to measure thesatellite quenched fraction in group environments across fourorders of magnitude in satellite stellar mass ranging from M (cid:63) ∼ − M (cid:12) . Our analysis utilizes a neural networkclassifier trained on a spectroscopic training set to labelgalaxies in the co-added Stripe 82 photometric catalog aseither star forming or quenched based solely on their g − r , g − i , and r − i colors. The results from this procedure weresubsequently used to statistically identify the quenched andstar-forming satellite populations around spectroscopically-confirmed hosts within Stripe 82 with halo masses between10 − h − M (cid:12) . The main results from this analysis are asfollows:(i) Using our photometric approach, we successfully re-produce the measured satellite quenched fraction at M (cid:63) (cid:38) M (cid:12) , as derived from spectroscopic studies inthe local Universe. We find that the satellite quenchedfraction increases with increasing satellite mass at M (cid:63) (cid:38) M (cid:12) .(ii) We measure the satellite quenched fraction down to M (cid:63) ∼ M (cid:12) , pushing measurements of satellite quench-ing in ∼ − h − M (cid:12) halos to a new regime that isnot readily probed outside of the Local Group.(iii) We find that the satellite quenched fraction increasestowards lower satellite masses below ∼ M (cid:12) .(iv) The increase in satellite quenching at low masses poten-tially indicates a change in the dominant quenching mech-anism at ∼ M (cid:12) , where ram-pressure stripping beginsto become increasingly effective (see discussion that fol-lows).Given that low-mass field galaxies are almost entirelystar forming as a population, the increase in the satellitequenched fraction at < M (cid:12) can be interpreted as a corre-sponding increase in the satellite quenching efficiency within10 − h − M (cid:12) halos. This increase is similar to that ob-served in the Local Group, where there is an apparent tran- MNRAS , 1–11 (2020) tudying Satellite Quenching with Machine Learning . . . . . . . . . . log ( M ? / M (cid:12) ) . . . . . f s a t q M halo = 10 − h − M (cid:12) SDSS satellites ( z < z < Figure 8. The satellite quenched fraction as a function of stellar mass for group environments with M halo = 10 − h − M (cid:12) . The solidred points represent the median quenched fraction for our statistically-derived satellite population. The vertical error bars correspond tothe 1 σ Poisson error in the quenched fraction, while the horizontal error bars denote the standard deviation of the binned stellar masses.The shaded grey (light-grey) band represents the quenched fraction for the spectroscopic members of the Yang et al. (2007) groups at z < . z < . > M (cid:12) ), and pushes beyond previous studies to probe satellite quenching down to 10 M (cid:12) . We find an increase inthe quenched fraction at low masses ( (cid:46) M (cid:12) ), potentially indicating an increase in the efficiency of quenching in the low-mass regime. sition in the dominant quenching mechanism at ∼ M (cid:12) with lower-mass satellites quenched more efficiently follow-ing infall. Both hydrodynamic simulations and analyticalmodeling of the satellite population find that ram-pressurestripping is much more efficient below 10 M (cid:12) within MilkyWay-like galaxies (Mayer et al. 2007; Fillingham et al. 2016;Simpson et al. 2018; Akins et al. 2020), while more mas-sive satellites are primarily quenched via starvation (Fill-ingham et al. 2015). Given that our host sample is moremassive ( M halo = 10 − M (cid:12) ) relative to Milky Way-likehalos, it is expected that an increase in infall velocities andthe density of the circumgalactic medium would cause thistransition mass to increase, such that starvation is the pri-mary driver of satellite quenching above ∼ . M (cid:12) andram-pressure stripping becoming increasingly important inthe low-mass regime. A more detailed study of the potentialquenching mechanisms at play requires further analysis ofthe timescales on which the observed satellites are quenchedfollowing infall to the host halos. In future work (Baxter etal. in prep), we aim to bridge this gap by combining themeasured satellite quenched fractions from this work withthe accretion and orbital histories determined using high-resolution cosmological simulations, to estimate the typicalquenching timescale as a function of satellite mass.The satellite quenched fractions that we obtain at low- masses ( M (cid:63) < M (cid:12) ) are generally lower than what havebeen reported in studies of dwarf galaxies in more mas-sive nearby clusters. For example, Weinmann et al. (2011)studied the satellite galaxy population in the nearby Virgo( M halo ∼ . × M (cid:12) ), Coma ( M halo ∼ . × M (cid:12) ),and Perseus ( M halo ∼ . × M (cid:12) ) clusters, finding redfractions between 70 − 80% at stellar masses of ∼ − M (cid:12) (see also Boselli et al. 2016). At slightly higher redshift( z ∼ . M halo ∼ M (cid:12) ) by Annunziatella et al. (2016) also findsan elevated quenched fraction relative to our results in lessmassive halos. Interestingly, while the study of Annunzi-atella et al. (2016) only probes down to ∼ . M (cid:12) in satel-lite stellar mass, the results show a quenched fraction thatdecreases from near unity ( ∼ M (cid:63) ∼ . M (cid:12) to ∼ 75% at M (cid:63) ∼ M (cid:12) (see also Sarrouh et al. in prep).Naively, if there is a transition in the dominant quenchingmechanism (or efficiency) in these massive clusters similarto that found in the Local Group and our group sample, wewould expect the transition scale to occur at higher satel-lite masses (e.g. (cid:38) . M (cid:12) ) as ram-pressure stripping (andother cluster-specific processes) should be increasingly effec-tive in hosts with M halo ∼ M (cid:12) . Extrapolations of themass functions from Annunziatella et al. (2016), however,do not support this picture. MNRAS000 75% at M (cid:63) ∼ M (cid:12) (see also Sarrouh et al. in prep).Naively, if there is a transition in the dominant quenchingmechanism (or efficiency) in these massive clusters similarto that found in the Local Group and our group sample, wewould expect the transition scale to occur at higher satel-lite masses (e.g. (cid:38) . M (cid:12) ) as ram-pressure stripping (andother cluster-specific processes) should be increasingly effec-tive in hosts with M halo ∼ M (cid:12) . Extrapolations of themass functions from Annunziatella et al. (2016), however,do not support this picture. MNRAS000 , 1–11 (2020) Baxter et al. Finally, we report satellite quenched fractions in thelow-mass regime ( < M (cid:12) ) that are potentially lowerthan expected when compared to studies of satellite quench-ing in the Local Group, where ∼ 90% of satellites with M (cid:63) < M (cid:12) are passive. As discussed above, environmen-tal quenching mechanisms are expected to be more efficientin our more-massive host halos relative to the Local Group.Of course, our results are based on a study of ∼ 100 groups,whereas studies of the Local Group satellites sample onlytwo host halos. While observations of the nearby M81 groupyield a satellite quenched fraction comparable to that mea-sured for the Local Group (Kaisin & Karachentsev 2013;Karachentsev et al. 2013), various studies also indicate thatthe Local Group satellites may be outliers relative to the cos-mic mean (e.g. Boylan-Kolchin et al. 2010; Busha et al. 2011;Tollerud et al. 2011; Ibata et al. 2013; Pawlowski & Kroupa2020). Moreover, recent results from the Satellites AroundGalactic Analogs (SAGA) Survey (Geha et al. 2017; Maoet al. 2020) find lower satellite quenched fractions ( ∼ M halo ∼ M (cid:12) . ACKNOWLEDGEMENTS DCB thanks the LSSTC Data Science Fellowship Pro-gram, which is funded by LSSTC, NSF Cybertraining Grant Astropy , a community-developed core Python pack-age for Astronomy (Astropy Collaboration et al. 2013, 2018).Additionally, the Python packages NumPy (Van Der Waltet al. 2011), iPython (P´erez & Granger 2007), SciPy (Vir-tanen et al. 2020), Scikit-learn (Pedregosa et al. 2011), Keras (Chollet et al. 2015), and matplotlib (Hunter 2007)were utilized for our data analysis and presentation. DATA AVAILABILITY Data sharing is not applicable to this article as no new datawere created or analyzed in this study. REFERENCES Abadi M. G., Moore B., Bower R. G., 1999, MNRAS, 308, 947Aihara H., et al., 2011, ApJS, 193, 29 Akins H. B., Christensen C. R., Brooks A. 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