Environment in the 3D-HST fields

# [

M. Fossati11affiliation: Universitäts-Sternwarte München, Scheinerstrasse 1, D-81679 München, Germany 22affiliation: Max-Planck-Institut für Extraterrestriche Physik, Giessenbachstrasse, D-85748 Garching, Germany , D.J. Wilman11affiliation: Universitäts-Sternwarte München, Scheinerstrasse 1, D-81679 München, Germany 22affiliation: Max-Planck-Institut für Extraterrestriche Physik, Giessenbachstrasse, D-85748 Garching, Germany , J.T. Mendel22affiliation: Max-Planck-Institut für Extraterrestriche Physik, Giessenbachstrasse, D-85748 Garching, Germany 11affiliation: Universitäts-Sternwarte München, Scheinerstrasse 1, D-81679 München, Germany , R.P. Saglia22affiliation: Max-Planck-Institut für Extraterrestriche Physik, Giessenbachstrasse, D-85748 Garching, Germany 11affiliation: Universitäts-Sternwarte München, Scheinerstrasse 1, D-81679 München, Germany , A. Galametz22affiliation: Max-Planck-Institut für Extraterrestriche Physik, Giessenbachstrasse, D-85748 Garching, Germany 11affiliation: Universitäts-Sternwarte München, Scheinerstrasse 1, D-81679 München, Germany , A. Beifiori11affiliation: Universitäts-Sternwarte München, Scheinerstrasse 1, D-81679 München, Germany 22affiliation: Max-Planck-Institut für Extraterrestriche Physik, Giessenbachstrasse, D-85748 Garching, Germany , R.Bender11affiliation: Universitäts-Sternwarte München, Scheinerstrasse 1, D-81679 München, Germany 22affiliation: Max-Planck-Institut für Extraterrestriche Physik, Giessenbachstrasse, D-85748 Garching, Germany , J.C.C. Chan11affiliation: Universitäts-Sternwarte München, Scheinerstrasse 1, D-81679 München, Germany 22affiliation: Max-Planck-Institut für Extraterrestriche Physik, Giessenbachstrasse, D-85748 Garching, Germany , M. Fabricius22affiliation: Max-Planck-Institut für Extraterrestriche Physik, Giessenbachstrasse, D-85748 Garching, Germany , K. Bandara22affiliation: Max-Planck-Institut für Extraterrestriche Physik, Giessenbachstrasse, D-85748 Garching, Germany , G.B. Brammer33affiliation: Space Telescope Science Institute, 3700 San Martin Drive, Baltimore, MD 21218, USA , R. Davies22affiliation: Max-Planck-Institut für Extraterrestriche Physik, Giessenbachstrasse, D-85748 Garching, Germany , N.M. Förster Schreiber22affiliation: Max-Planck-Institut für Extraterrestriche Physik, Giessenbachstrasse, D-85748 Garching, Germany , R. Genzel22affiliation: Max-Planck-Institut für Extraterrestriche Physik, Giessenbachstrasse, D-85748 Garching, Germany 44affiliation: Department of Physics, Le Conte Hall, University of California, Berkeley, CA 94720, USA 55affiliation: Department of Astronomy, Hearst Field Annex, University of California, Berkeley, CA 94720, USA , W. Hartley66affiliation: Department of Physics & Astronomy, University College London, Gower Street, London, WC1E 6BT, UK , S.K. Kulkarni22affiliation: Max-Planck-Institut für Extraterrestriche Physik, Giessenbachstrasse, D-85748 Garching, Germany , P. Lang22affiliation: Max-Planck-Institut für Extraterrestriche Physik, Giessenbachstrasse, D-85748 Garching, Germany , I.G. Momcheva66affiliation: Department of Physics & Astronomy, University College London, Gower Street, London, WC1E 6BT, UK , E.J. Nelson77affiliation: Astronomy Department, Yale University, New Haven, CT 06511, USA 22affiliation: Max-Planck-Institut für Extraterrestriche Physik, Giessenbachstrasse, D-85748 Garching, Germany , R. Skelton88affiliation: South African Astronomical Observatory, P.O. Box 9, Observatory, Cape Town, 7935, South Africa , L.J. Tacconi22affiliation: Max-Planck-Institut für Extraterrestriche Physik, Giessenbachstrasse, D-85748 Garching, Germany , K. Tadaki22affiliation: Max-Planck-Institut für Extraterrestriche Physik, Giessenbachstrasse, D-85748 Garching, Germany , H.Übler22affiliation: Max-Planck-Institut für Extraterrestriche Physik, Giessenbachstrasse, D-85748 Garching, Germany , P.G. van Dokkum77affiliation: Astronomy Department, Yale University, New Haven, CT 06511, USA , E. Wisnioski22affiliation: Max-Planck-Institut für Extraterrestriche Physik, Giessenbachstrasse, D-85748 Garching, Germany , K.E. Whitaker99affiliation: Department of Astronomy, University of Massachusetts, Amherst, MA 01003, USA $*$$*$affiliation: Hubble Fellow , E. Wuyts22affiliation: Max-Planck-Institut für Extraterrestriche Physik, Giessenbachstrasse, D-85748 Garching, Germany , S. Wuyts1010affiliation: Department of Physics, University of Bath, Claverton Down, Bath, BA2 7AY, UK
###### Abstract

We make publicly available a catalog of calibrated environmental measures for galaxies in the five 3D-HST/CANDELS deep fields. Leveraging the spectroscopic and grism redshifts from the 3D-HST survey, multi wavelength photometry from CANDELS, and wider field public data for edge corrections, we derive densities in fixed apertures to characterize the environment of galaxies brighter than mag in the redshift range . By linking observed galaxies to a mock sample, selected to reproduce the 3D-HST sample selection and redshift accuracy, each 3D-HST galaxy is assigned a probability density function of the host halo mass, and a probability that is a central or a satellite galaxy. The same procedure is applied to a sample selected from SDSS. We compute the fraction of passive central and satellite galaxies as a function of stellar and halo mass, and redshift, and then derive the fraction of galaxies that were quenched by environment specific processes. Using the mock sample, we estimate that the timescale for satellite quenching is Gyr; longer at lower stellar mass or lower redshift, but remarkably independent of halo mass. This indicates that, in the range of environments commonly found within the 3D-HST sample (), satellites are quenched by exhaustion of their gas reservoir in absence of cosmological accretion. We find that the quenching times can be separated into a delay phase during which satellite galaxies behave similarly to centrals at fixed stellar mass, and a phase where the star formation rate drops rapidly ( Gyr), as shown previously at . We conclude that this scenario requires satellite galaxies to retain a large reservoir of multi-phase gas upon accretion, even at high redshift, and that this gas sustains star formation for the long quenching times observed.

galaxies: evolution, galaxies: star formation, galaxies: statistics, methods: statistical

Environment in the 3D-HST fields]Galaxy environment in the 3D-HST fields.
Witnessing the onset of satellite quenching at .

## 1. Introduction

It has long been known that galaxies are shaped by the environment in which they reside. Works by e.g., Oemler (1974), Dressler (1980), and Balogh et al. (1997) showed that galaxies in high-density environments are preferentially red and early-type compared to those in lower density regions. The more recent advent of large scale photometric and spectroscopic surveys confirmed with large statistics those early findings (Balogh et al., 2004; Kauffmann et al., 2004; Baldry et al., 2006). Meanwhile, space and ground based missions have probed the geometry of our Universe. Those observations coupled to cosmological models have built the solid Lambda cold dark matter (CDM) framework (White & Rees, 1978; Perlmutter et al., 1999), in which lower mass haloes are the building blocks of more massive structures. One of the major tasks for modern studies of galaxy formation is therefore to understand how and when galaxy evolution is driven by internal processes or the evolving environment that each galaxy experiences during its lifetime. While internal mechanisms, including ejective feedback from supernovae or active galactic nuclei, are deemed responsible for suppressing star formation in all galaxies (Silk & Rees, 1998; Hopkins et al., 2008), a galaxy can also directly interact with its environment when falling into a massive, gas- and galaxy-rich structure such as a galaxy cluster.

At low redshift detailed studies of poster child objects (Yagi et al., 2010; Fossati et al., 2012, 2016; Merluzzi et al., 2013; Fumagalli et al., 2014; Boselli et al., 2016) coupled with state-of-the-art models and simulations (Mastropietro et al., 2005; Kapferer et al., 2009; Tonnesen & Bryan, 2010) have started to explore the rich physics governing those processes (e.g., Boselli & Gavazzi, 2006, 2014; Blanton & Moustakas, 2009, for reviews). Broadly speaking, they can be grouped into two classes. The first of them includes gravitational interactions between cluster or group members (Merritt, 1983) or with the potential well of the halo as a whole (Byrd & Valtonen, 1990), or their combined effect known as “galaxy harrassment” (Moore et al., 1998). The second class includes hydrodynamical interactions between galaxies and the hot and dense gas that permeates massive haloes. This class includes the rapid stripping of the cold gas via ram pressure as the galaxy passes through the hot gas medium (Gunn & Gott, 1972). Ram-pressure stripping is known to effectively and rapidly suppress star formation in cluster galaxies in the local Universe (Solanes et al., 2001; Vollmer et al., 2001; Gavazzi et al., 2010, 2013; Boselli et al., 2008, 2014b).

Less directly influencing the galaxy’s current star formation, the multi-phase medium (e.g. warm, hot gas) associated to the galaxy (known as the “reservoir”) should be easier to strip than the cold gas. Even easier, the filamentary accretion onto the galaxy from the surrounding cosmic web will be truncated as the galaxy is enveloped within the hot gas of a more massive halo (White & Frenk, 1991). Both of these processes will suppress ongoing accretion onto the cold gas disk of the galaxy and lead to a more gradual suppression of star formation, variously labelled “strangulation” or “starvation” (e.g. Larson et al., 1980; Balogh et al., 1997) These processes are complicated in nature and the exact details of their efficiency and dynamics are still poorly understood. The situation is even more complicated when several of those processes are found to act together (Gavazzi et al., 2001; Vollmer et al., 2005).

A different approach to disentangle the role of environment from the secular evolution is to study large samples of galaxies and correlate their properties (e.g. star formation activity) to internal properties (e.g. stellar mass) and environment. In the local Universe, the advent of the Sloan Digital Sky Survey (SDSS) has revolutionized the field of large statistical studies and allowed for the effects of the environment on the galaxy population as a whole to be studied (Kauffmann et al., 2004; Baldry et al., 2006; Peng et al., 2010, 2012; Wetzel et al., 2012, 2013; Hirschmann et al., 2014). One of the main results is that environmental quenching is a separable process that acts on top of the internal processes that regulate the star formation activity of galaxies. A crucial parameter to understand the collective effect of the several environmental processes is the timescale over which the star formation activity is quenched. Several authors took advantage of excellent statistics to estimate the average timescale for environmental quenching, accounting for internal quenching processes, and found that in the low redshift Universe this is generally long ( Gyr; McGee et al., 2009; De Lucia et al., 2012; Wetzel et al., 2013; Hirschmann et al., 2014), while possibly shorter in clusters of galaxies ( Gyr; Haines et al., 2015; Paccagnella et al., 2016) .

At higher redshift, the situation is made more complex due to the more limited availability of spectroscopic redshifts which are paramount to depict an accurate picture of the environment. In the last decade, several ground based redshift surveys started to address this issue (Wilman et al., 2005; Cooper et al., 2006). By exploiting the multiplexing of spectroscopic instruments at 8-10 meter class telescopes (e.g. VIMOS and GMOS, Lilly et al., 2007; Kurk et al., 2013; Balogh et al., 2014), these works showed that the environment plays a role in quenching the star formation activity of galaxies accreted onto massive haloes (satellite galaxies) up to (Muzzin et al., 2012; Quadri et al., 2012; Knobel et al., 2013; Kovač et al., 2014; Balogh et al., 2016), although the samples are limited to massive galaxies or a small number of objects.

Low-resolution space-based slitless spectroscopy is revolutionising this field providing deep and highly complete spectroscopic samples. The largest of those efforts is the 3D-HST survey (Brammer et al., 2012) which, by combining a large area, deep grism observations and a wealth of ancillary photometric data, provides accurate redshifts to (Bezanson et al., 2016) for a large sample of objects down to low stellar masses (, and at and respectively). The public release of their spectroscopic observations (Momcheva et al., 2016), in synergy with deep photometric observations (Skelton et al., 2014) has opened the way to an accurate quantification and calibration of the environment over the redshift range .

Another source of uncertainty in the interpretation of correlations of galaxy properties with environment is the inhomogeneity of methods used for different surveys (e.g., Muldrew et al., 2012; Haas et al., 2012; Etherington & Thomas, 2015) and the lack of calibration of important parameters such as halo mass. In Fossati et al. (2015), we studied how to link a purely observational parameter space to physical quantities (e.g., halo mass, central/satellite status) by analysing a stellar mass limited sample extracted from semi-analytic models of galaxy formation. To do so, we computed a projected density field in the simulation box and we tested different definitions of density at different redshift accuracy. Our method is Bayesian in nature (galaxies have well-defined observational parameters, while the calibration into physical parameters is probabilistic). This approach is best suited to statistical studies where the application of selection functions and observational uncertainties can be fully taken into account.

In this paper, we extend this method to the 3D-HST survey by building up an environment catalogue which we make available to the community with this work. We then explore the efficiency and timescales for quenching of satellite galaxies over cosmic time () by combining the 3D-HST data at high redshift with SDSS data in the local Universe in a homogeneous way. We also address the long standing issue of impurity and contamination of the calibrated parameters (the fact that the observations do not perfectly constrain the halo mass of the parent halo for each galaxy or its central/satellite status) by recovering the “pure” trends using the mock sample as a benchmark.

The paper is structured as follows. In Section 2, we introduce the 3D-HST dataset. In Section 3, we derive the local density for 3D-HST galaxies including accurate edge corrrections. Section 4 presents the range of environments in the 3D-HST area and how they compare to known galaxy structures from the literature. In Section 5, we introduce the mock galaxy sample and how we calibrate it to match the 3D-HST sample. We then link models and observations in Section 6, and assign physical quantities to observed galaxies. In Section 7 we study the quenching of satellite galaxies at , and derive quenching efficiency and timescales. Lastly, we discuss the physical implications of our findings in Section 8 and summarize our work in Section 9.

All magnitudes are given in the AB system (Oke, 1974) and we assume a flat CDM Universe with , , and unless otherwise specified. Throughout the paper, we use the notation for the base 10 logarithm of .

## 2. The observational sample

In this work we aim at a quantification and calibration of the local environment for galaxies in the five CANDELS/3D-HST fields (Grogin et al., 2011; Koekemoer et al., 2011; Brammer et al., 2012) namely COSMOS, GOODS-S, GOODS-N, AEGIS and UDS. The synergy of these two surveys represents the largest effort to obtain deep space-based near-infrared photometry and spectroscopy in those fields. For a description of the observations and reduction techniques, we refer the reader to Skelton et al. (2014) and Momcheva et al. (2016) for the photometry and spectroscopy respectively. The CANDELS observations provide HST/WFC3 near infrared imaging in the F125W and F160W filters ( and  hereafter) for all the fields, while 3D-HST followed-up a large fraction of this area with the F140W filter ( hereafter) and the WFC3/G141 grism for slitless spectroscopy. The novelty of this approach is to obtain low resolution () spectroscopy for all the objects in the field. Taking advantage of the low background of the HST telescope, it is possible to reach a depth similar to traditional slit spectroscopy from 10m class telescopes on Earth. Hereafter, we use the term “3D-HST” sample to refer to the combination of CANDELS and all the other space- and ground-based imaging datasets presented in Skelton et al. (2014), plus the grism spectroscopy of the 3D-HST program.

The 3D-HST photometric catalog (Skelton et al., 2014) used  or  as detection bands and its depth varies from field to field and across the same field due to the observing strategy of CANDELS. However, even in the shallowest portions of each field, the 90 depth confidence level is mag. Beyond this magnitude limit, the star/galaxy classification (which is a key parameter for the environment quantification) becomes uncertain.

The 3D-HST spectroscopic release (Momcheva et al., 2016) provides reduced and extracted spectra down to222The 3D-HST spectroscopic catalog is based on magnitudes. We therefore quote limits in this band when referring to their catalog. However in this paper the sample selection is performed in  to ensure that the footprint of our sample is entirely covered by G141 grism observations and direct imaging in F140W. mag. The spectra are passed through the EAZY template fitting code (Brammer et al., 2008) along with the extensive ground- and space-based multiwavelength photometry. This results in “grism” redshifts, which are more accurate than photometric redshifts thanks to the wealth of stellar continuum and emission line features present in the spectra. However, only objects brighter than mag have been visually inspected, and have a use_grism flag that describes if the grism spectrum is used to compute the redshift. Incomplete masking of contaminating flux from nearby sources in the direction of the grism dispersion, residuals from spectra of bright stars, and corrupted photometric measurements can lead to this flag being set to 0 (“bad”).

We include in the present analysis all galaxies brighter than mag, therefore limiting our footprint to the regions covered by grism and  observations. We limit the redshift range to . The lower limit roughly corresponds to the redshift where the line enters the grism coverage and the upper limit is chosen such that the number density of objects above the magnitude cut allows a reliable estimate of the environment. It also allows follow-up studies targeting the rest-frame optical features from ground based facilities in the , , and bands (e.g. , Sharples et al. 2013 and MOSFIRE, McLean et al. 2012)

We exclude stars by requiring star_flag to be 0 or 2 (galaxies or uncertain classification). We do not use the use_phot flag because it is too conservative for our goals. Indeed this flag requires a minimum of 2 exposures in the F125W and F160W filters, and the object not being close to bright stars. The quantification of environment requires a catalog which is as complete as possible even at the expenses of more uncertain photometry (and photo-z) for the objects that do not meet those cuts. Nonetheless a mag cut allows a reliable star/galaxy separation for 99% of the objects and is at least 1 mag brighter than the minimum depth of the mosaics, thus alleviating the negative effects of nearby stars on faint sources. The final sample is made of 18745 galaxies.

As a result of the analysis in Momcheva et al. (2016), each galaxy is assigned a “best” redshift. This is:

1. a spectroscopic redshift from a ladder of sources as described below.

2. a grism redshift if there is no spectroscopic redshift and use_grism = 1

3. a pure photometric redshift if there is no spectroscopic redshift and use_grism = 0.

A zbest_type flag is assigned to each galaxy based on the conditions above. The best redshift is the quantity used to compute the environment for each galaxy in the 3D-HST fields.

Spectroscopic redshifts are taken from the compilation of Skelton et al. (2014) which we complement with newer data. For the COSMOS field we include the final data release of the zCOSMOS bright survey (Lilly et al., 2007). We find 253 new sources with reliable redshifts in the 3D-HST/COSMOS footprint mainly at . In COSMOS and GOODS-S ,we include 95 objects from the DR1 (Tasca et al., 2016) of the VIMOS Ultra Deep Survey (Le Fèvre et al., 2015, VUDS, [). This survey mainly targets galaxies at therefore complementing zCOSMOS. We include 105 redshifts from the MOSFIRE Deep Evolution Field Survey (MOSDEF, Kriek et al., 2015) which provides deep rest frame optical spectra of galaxies selected from 3D-HST. For the UDS field, we also include 164 redshifts from VIMOS spectroscopy in a narrow slice of redshift (, Galametz et al. in prep.) Lastly, we include 376 and 33 secure spectroscopic redshifts from (Wisnioski et al., 2015) and VIRIAL (Mendel et al., 2015) respectively. Those large surveys use the multiplexing capability of the integral field spectrometer KMOS on the ESO Very Large Telescope to follow-up 3D-HST selected objects. The former is a mass selected survey of emission line galaxies at , while the latter observed passive massive galaxies at .

In the selected sample, of the galaxies have a spectroscopic redshift, have a grism redshift, and only have a pure photometric redshift. In the next Section, we explore the accuracy of the grism and photometric redshifts as a function of the galaxy brightness and the of emission lines in the spectra.

Stellar masses and stellar population parameters are estimated using the FAST code (Kriek et al., 2009), coupled with Bruzual & Charlot (2003) stellar population synthesis models. Those models use a Chabrier (2003) initial mass function (IMF) and solar metallicity. The best redshift is used for each galaxy together with the available space- and ground-based photometry. The star formation history is parametrized by an exponentially declining function and the Calzetti et al. (2000) dust attenuation law is adopted.

### 2.1. Redshift accuracy

A careful quantification of the grism and photometric redshift accuracy is paramount for a good calibration of the environmental statistics into physically motivated halo masses. In Section 6, we will show how these masses are obtained from mock catalogues selected to match the number density and redshift uncertainty of 3D-HST galaxies.

The low-resolution spectra cover different spectral features as a function of galaxy properties and redshift. The most prominent features are emission lines, which are however limited to star forming objects. On the other hand, stellar continuum features (Balmer break, absorption lines) are present in the spectra of all galaxies with a that depends on the galaxy magnitude. Because all those features contribute to the redshift fitting procedure, we explore their impact on the redshift accuracy in bins of of the strongest emission line in the spectrum and  total magnitude. Given the limited spectral coverage of the G141 grism, it is common to find only one prominent emission line feature in the spectrum (Momcheva et al., 2016); this justifies our approach of using the of the strongest line. We define the redshift accuracy () as half the separation of the 16 and 84 confidence levels obtained from the probability density function (PDF) of grism redshifts as derived from the EAZY template fitting procedure. In the case of fits obtained without including the spectral information, it becomes a pure photometric redshift uncertainty. A comparison of grism redshifts to spectroscopic redshifts shows that should be added to the formal uncertainty on the grism redshifts to obtain a scatter in with a width of unity. This “intrinsic grism” uncertainty can arise from morphological effects, i.e. the light-weighted centroid of the gas emission can be offset from that of the stars (see Nelson et al., 2016; Momcheva et al., 2016). In this analysis, we added the intrinsic uncertainty of the grism data in quadrature to the formal uncertainty from the fitting process.

Figure 1 shows , for bins of emission line and  magnitude. The bottom right panel (f) shows the accuracy of photometric redshifts for the same sources highlighting the significant improvement on the redshift quality when the spectra are included. From the top panels of Figure 1, it is clear how an emission line detection narrows the redshift PDF to the intrinsic uncertainty, irrespective of the stellar continuum features. At where the emission line becomes less dominant, we start to witness a magnitude dependence of the redshift accuracy. Brighter galaxies have better continuum detections and therefore a more accurate redshift. Even when there is no line detection (Panel e), the typical redshift uncertainties are a factor 2-3 lower than pure photometric redshifts. The inclusion of the spectra helps the determination of the redshifts even when the spectra are apparently featureless. The grism redshift accuracy is comparable to the pure photometric redshift accuracy only for the faintest objects ( 23 mag) with no emission line detection (), a population which accounts for of our grism sample.

As a final note of caution, we highlight that whenever the information in the spectra is limited, the final grism redshift accuracy depends largely on the photometric data, whose availability depends on the field. Indeed, COSMOS and GOODS-S have been extensively observed with narrow or medium band filters (Taniguchi et al., 2007; Cardamone et al., 2010; Whitaker et al., 2011) resulting in better photometric redshifts compared to the other fields. However, as shown in Section 6 these field-to-field variations have negligible effects on our calibration of halo mass.

## 3. Quantification of the environment

There are many ways to describe the environment in which a galaxy lives (e.g., Haas et al., 2012; Muldrew et al., 2012; Etherington & Thomas, 2015). In this work, we apply to observational data the method we explored and calibrated in Fossati et al. (2015) and based on the work of Wilman et al. (2010). We use the number density of neighbouring galaxies within fixed cylindrical apertures because it is more sensitive to high overdensities, less biased by the viewing angle, more robust across cosmic times, and easier to physically interpret and calibrate than the N nearest neighbour methods (Shattow et al., 2013).

### 3.1. Density

We consider all 3D-HST galaxies selected in Section 2 to be part both of the primary (galaxies for which the density is computed) and neighbour samples. We calculate the projected density in a combination of circular apertures centered on the primary galaxies with radii . The apertures range from 0.25 to 1.00 Mpc in order to cover from intra-halo to super-halo scales.

For a given annulus defined by , the projected density is given by

 Σrap=wrapπ×r2ap (1)

where is the sum of the weights of galaxies in the neighbour sample falling at a projected distance on the sky from the primary galaxy and within a relative rest-frame velocity . For the 3D-HST galaxies with a grism or spectroscopic redshift, the weights are set to unity (non weighted sum), while for galaxies with pure photometric redshifts, we apply a statistical correction for the less accurate redshifts as described in Section 3.2. The primary galaxy is not included in the sum therefore isolated galaxies have .

We set the velocity cut at . This value is deemed appropriate for surveys with complete spectroscopic redshift coverage (Muldrew et al., 2012) and for 3D-HST given the quality of grism redshifts shown in Figure 1. A small value of avoids the peaks in the environmental density to be smoothed by interlopers in projection along the redshift axis. On the other hand, if only less accurate redshifts are available, a larger cut must be used to collect all the signal from overdense regions which is artificially dispersed along the redshift axis (see Figure 4 in Fossati et al., 2015; Etherington & Thomas, 2015).

Because the mean number density changes continuously with redshift, it is not possible to compare the local density () across time. Instead we define a relative overdensity , which is given by:

 δrap=Σrap−Σmean(z)Σmean(z) (2)

where is the average surface density of galaxies at a given redshift. This is obtained by computing the volume density of galaxies (per Mpc) in the whole survey and parametrising the redshift dependence with a third degree polynomial. This value is multiplied by the depth of the cylindrical aperture at redshift to obtain the surface density . Throughout the paper, we will mainly use the overdensity in terms of the logarithmic density contrast defined as .

### 3.2. Edge corrections

The calculation of the environment of primary galaxies at the edges of the 3D-HST footprint (see Figure 2, red areas) suffers from incomplete coverage of neighbours that results into an underestimated density in the considered aperture. In large scale surveys (e.g. SDSS, Wilman et al., 2010), it is common practice to remove galaxies too close to the edges of the observed field. In the case of deep fields, however, the observed area is relatively small and the removal of such galaxies would reduce total number of objects significantly. One possible solution is to normalize the densities by the area of the circular aperture which is within the survey footprint in equation 1. Although this is a simple choice, it assumes a constant density field and neglects possible overdense structures just beyond the observed field. A more accurate solution consists of building up galaxy catalogues for a more extended area than 3D-HST and then use galaxies within these areas as “pure neighbours” for the environment of the primary 3D-HST galaxies. Given the amount of publicly available data, this is possible in GOODS-S, COSMOS and UDS (see Figure 2, blue areas). In appendix A we describe the data, depth and redshift quality of the catalogues we built in those fields. Here we present the edge correction method we developed and how it was tuned to perform the edge corrections in the other two fields GOODS-N and AEGIS.

#### 3.2.1 Edge correction method for GOODS-S, COSMOS, and UDS

The availability of spectroscopic redshifts in the extended area catalogs is limited (from in COSMOS and UDS to in GOODS-S). We thus need to deal with the limited accuracy of photometric redshifts for the galaxies in those fields. The photo-z accuracy, which varies from field to field and depends on the redshift, brightness and color of the objects (Bezanson et al., 2016), is such that most of the sources which are part of the same halo in real space would not be counted as neighbours of a primary galaxy, simply due to the redshift uncertainty. Fossati et al. (2015) show that increasing the depth of the velocity window would recover most of the real neighbours but at the expense of a larger fraction of interlopers (galaxies which are not physically associated to the primary). Here, we thus exploit a different method. We assume that galaxies which are at small angular separation and whose redshifts are consistent within the uncertainties are, with a high probability, physically associated (e.g., Kovač et al., 2010; Cucciati et al., 2014). If one of them has a secure spectroscopic redshift, we assign this to the others.

Our method works as follows:

• For each galaxy with a photometric redshift, we select all neighbours with a redshift within . This value is chosen to recover most of the real neighbours given the average photo-z uncertainties.

• Among those neighbours, we select the closest (in spatial coordinates) which has a secure spectroscopic (or grism) redshift. Here we assume grism redshifts to have a negligible uncertainty compared to photo-z.

• We replace the photo-z of the galaxy of interest with this spec-z (or grism-z). Since the statistical validity of the assumption of physical association depends on the distance of the neighbour, for increasing distances we underestimate the true clustering. We correct for the bias by assigning a weight to each galaxy.

The weight is evaluated on a training sample made of galaxies in 3D-HST with mag. For each galaxy in the three fields, we compute the “real” density ( in a 0.75Mpc radius and ) using spec-z or grism-z from 3D-HST. We then take for each galaxy its photometric redshift, and follow the procedure described above, but, instead of choosing the closest neighbour with a secure redshift, we select a random neighbour in different bins of projected sky distance (from 0 to 3 Mpc in bins of 0.5 Mpc width). Then we compute densities with each of those distance replacements separately and the fractional bias () as:

 bd=Σd−ΣrealΣreal (3)

where the subscript denotes the replacement with a spec-z of a galaxy found at distance . By using the 3D-HST data, we make sure that there are always a large number of neighbours with a secure redshift, and we repeat this procedure 1000 times in order to uniformly sample the neighbours. Figure 3 left panel shows as a function of the real density in four bins of . Clearly, the larger is, the more underestimated the real density will be, due to a decreasing fraction of correct redshift assignments.

We then derive the median weight where the median is computed among all galaxies that have (see the vertical dashed line in Figure 3 left panel). The density dependence of is negligible at these densities, therefore by avoiding underdense regions (where the uncertainty on is large) we obtain a robust determination of . Figure 3 middle panel shows versus , which we fit with a quadratic relation obtaining:

 wph,d=9.66×10−2×d2+0.155×d+0.946 (4)

with the additional constraint that which corresponds to for Mpc. We tested that this relation, although obtained combining all fields, holds within the uncertainties when each field is considered separately. Lastly we show in Figure 3 right panel how the systematic bias is removed when the weight is applied to all neighbours when computing the density. This is consistent with no bias within the uncertainties for all the distance bins.

#### 3.2.2 Edge correction method for GOODS-N and AEGIS

The GOODS-N and AEGIS fields do not have deep and extended near-infrared public catalogues that can be used to derive the edge corrections as presented above. As shown in Figure 2 (light blue shaded areas) the 3D-HST/CANDELS footprint slightly extends beyond the area covered by G141 grism observations (the main requirement for our primary sample). Therefore the 3D-HST/CANDELS catalogue itself can be used to perform edge corrections. We derive  magnitudes from the  magnitudes using a linear function derived from the five 3D-HST fields (). We then use 3D-HST photometric redshifts (or spec-z where available) and apply the method described in Section 3.2.1.

However, the 3D-HST/CANDELS photometric catalogues do not extend enough beyond the primary sample area to ensure the apertures used to compute the density are entirely covered by the photometric catalog footprint. For this reason, we compute the densities using the area of the circular aperture within the photometric catalogue. We test this method by comparing the density () in a 0.75Mpc aperture measured using the extended catalogues for COSMOS, GOODS-S, UDS and the density () measured correcting for the fraction of the aperture () in the 3D-HST/CANDELS footprint. The result is shown in Figure 4. We note that although the median (red solid line) is consistent with no bias, the area correction introduces a scatter (dotted and dashed lines) which increases by decreasing the fraction of the aperture in the footprint.

In conclusion, the environment catalogue released with this work includes all the primary galaxies in the five 3D-HST fields. The structure of the catalogue is described in Appendix E. However, in the rest of this work we only include galaxies for which for the GOODS-N and AEGIS fields. The total number of objects in the primary 3D-HST sample with a robust determination of the environmental density is therefore reduced to 17397 ( of the original sample).

## 4. Overdensities in the 3D-HST deep fields

In order to explore correlations of galaxy evolution with environment, we need to make sure the 3D-HST fields span a wide range of galaxy (over-)densities, and use known structures as a sanity check of our density estimates. Figures 5, 6, 7, 8, and 9 present the primary sample of 3D-HST galaxies in the five fields color coded by their overdensity in the 0.75 Mpc aperture in different redshift slices. This aperture corresponds to the typical virial radius of massive haloes () in the redshift range under study. The range of density probed is wide and spans from isolated galaxies to objects for which the local number of neighbours is up to ten times larger than the mean at that redshift, reaching the regime of clusters or massive groups.

In each Figure, we overplot the position and extent of X-Ray extended emission from the hot intragroup (and intracluster) medium that fills massive haloes. The exquisite depth of X-Ray data in the deep fields (Finoguenov et al., 2007, 2010, 2015; Erfanianfar et al., 2013) allows the detection of the hot gas from haloes down to . We find a very satisfactory agreement between our overdensities and the X-Ray emission position. Indeed, most of the X-Ray groups are coincident with large overdensities in our maps. On the other hand, not all the overdense structures identified in our work are detected in X-Ray. We speculate this is mainly due to the presence of more than one massive structure along the line of sight or that low mass groups may not yet be virialized. Lastly, we note that the redshift of the X-Ray emission is assigned based on the photometric or spectroscopic information available at the epoch of the publication of the catalogue; these data might not have been as accurate as the density field reconstruction performed in this work. Our analysis has therefore the potential to spectroscopically confirm more X-Ray groups and improve the quality of previous redshift assignments.

Several other works have also analysed, with different techniques, the presence of overdense structures in the deep fields. We overplot on Figure 5 the position of overdensities found in the GOODS-S field by Salimbeni et al. (2009). These have been derived from the GOODS-MUSIC catalogue using a smoothed 3D density searching algorithm. These data have 15% spectroscopic redshifts and photometric redshifts for the remaining fraction. Because the smoothing technique is less able to constrain the size of the structure, we plot circles with an arbitrary radius. The structures within the 3D-HST footprint (except those at ) are confirmed with our data to be at least a factor of denser than the mean. The differences in samples and techniques hamper a more quantitative comparison. Our data confirm with a high degree of significance the detection of two well known super-structures, one at redshift (Gilli et al., 2003; Adami et al., 2005; Trevese et al., 2007) and one at redshift first detected by Kurk et al. (2009). The latter is made of 5 peaks in the photo-z map (which correspond to putative positions for the X-Ray emission, see Table 1 in Finoguenov et al. 2015). The main structure is robustly recovered by our analysis while the other sub-structures are only mild () overdensities.

In the COSMOS field (see Figure 6), Scoville et al. (2007) applied an adaptive smoothing technique (similar to Salimbeni et al., 2009) to find large scale structures at . While their results do not constrain the size of the structure and are less sensitive to very compact overdensities, we do find that their detections in the 3D-HST footprint correspond to high overdensities in our work.

Similarly in the UDS field, we do detect a very massive cluster surrounded by filaments and less massive groups (upper left panel of Figure 7) at (Galametz et al. in prep.). Another well known structure in this field is located at (Papovich et al., 2010; Tanaka et al., 2010). Despite being only partially covered by the 3D-HST grism observations (isolated pointing on the left of the contiguous field), we do find it corresponds to a large overdensity of galaxies thanks to our accurate edge corrections using UKIDSS-UDS photometric data.

In summary, our reconstruction of the density field in the 3D-HST deep fields recovers the previously known massive structures across the full redshift range analysed in this work.

## 5. The model galaxy sample

The goal of this work is to understand the environment of galaxies in the context of a hierarchical Universe. To reach this goal, we need to calibrate physically motivated quantities using observed metrics of environment by means of semi-analytic models (SAM) of galaxy formation. We make use of light cones from the latest release of the Munich model presented by Henriques et al. (2015). This model is based on the Millennium N-body simulation (Springel et al., 2005) which has a size of Mpc. The simulation outputs are scaled to cosmological initial conditions from the Planck mission (Planck Collaboration XVI, 2014): . Although those values are slightly different from those used in our observational sample, the differences in cosmological parameters have a much smaller effect on mock galaxy properties than the uncertainties in galaxy formation physics (Wang et al., 2008; Fontanot et al., 2012; Guo et al., 2013a).

This model includes prescriptions for gas cooling, size evolution, star formation, stellar and active galactic nuclei feedback and metal enrichment as described by e.g. Croton et al. (2006); De Lucia & Blaizot (2007); Guo et al. (2011). The most significant updates concern the reincorporation timescales of galactic wind ejecta that, together with other tweaks in the free parameters, reproduce observational data on the abundance and color distributions of galaxies from to (Henriques et al., 2015). Our choice of this model is therefore driven by those new features which are critical for an accurate quantification of the environment.

We make use of the model in the form of 24 light cones, which are constructed by replicating the simulation box evaluated at multiple redshift snapshots. Before deriving the density for the light cones, as described in Section 3.1, we first match the magnitude selection and redshift accuracy of the 3D-HST survey.

### 5.1. Sample selection

SAMs are based on N-body dark matter only simulations. Therefore (and opposite to observations), the galaxy stellar masses are accurate quantities, while observed magnitudes are uncertain and rely on radiative transfer and dust absorption recipes implemented in the models. On the other hand, magnitudes are direct observables in a survey (like 3D-HST) are therefore known with a high degree of accuracy.

To overcome these limitations and the fact that  magnitudes are not given in Henriques et al. (2015) cones, we employ a method that generates observed magnitudes for SAM galaxies by using observational constraints from 3D-HST. Each model galaxy is defined by its stellar mass (), rest frame color () and redshift (). Similarly, 3D-HST galaxies are defined by stellar mass (), rest frame color (), redshift (), and magnitude (). The method works as follows:

• For each bin of stellar mass (0.25 dex wide) and redshift (0.1 wide) we select all the model and 3D-HST galaxies.

• For each model galaxy in this bin we rank the and we find the that corresponds to the same ranking.

• We assign to the model galaxy a randomly selected stellar mass-to-light ratio at drawn from the distribution of 3D-HST galaxies in the stellar mass and redshift bin of the mock galaxy of interest.

• From , , and , we compute for the model galaxy.

This method generates  magnitudes for all the model galaxies down to . This is much deeper than the 3D-HST magnitude limit even at the lower end of our redshift range. We then select model galaxies down to a magnitude that matches the total number density of the primary targets ( mag) in the five 3D-HST fields to that in the 24 lightcones. This protects us from stellar mass function mismatches between the models and the observations (although those differences are very small in Henriques et al. 2015). We employ a mag, which is very close to 24 mag further supporting the quality of the stellar mass functions in the models.

### 5.2. Matching the redshift accuracy

After the model sample is selected, the next goal is to assign to each galaxy a redshift accuracy that matches as closely as possible to the one in 3D-HST. To do so, we should not only assign the correct fraction of spec-z, grism-z and photo-z as a function of observed magnitude but also assign an accuracy for the grism-z and photo-z as a function of physical properties such that the final distributions resemble those in Figure 1. We showed in Section 2.1 that the grism redshift accuracy depends on the signal-to-noise of the strongest emission line and the galaxy magnitude. For the latter, we use  as derived above, while the former quantity needs to be parametrized in terms of other quantities available in the models.

Figure 10 left panel shows how the emission line depends both on the line flux and the  magnitude for galaxies with a measured line flux. For each galaxy, we take the flux (in units of erg cm s) of the strongest line and we define the line magnitude as . At fixed line flux, brighter galaxies have more continuum, thus decreasing the line . This relation is well reproduced by the following parametrization:

 log(S/N)=−0.33×(2×mline−JH140)+19.85 (5)

Figure 10 right panel shows the line obtained with this equation. The small differences between the two panels can be due to additional variables not taken into account (e.g. dust extinction or grism throughput). We tested (by perturbing the assigned to each model galaxy) that a more accurate parametrization of this relation is not required for the purpose of this paper.

In order to obtain a synthetic line for the model galaxies, we first convert the star formation rate (SFR) of the model galaxies into an flux (or flux where is redshifted outside the grism wavelength range) by inverting the relation given in Kennicutt (1998a). We then obtain from , and using equation 5. The rank in (and not the absolute value) is then matched to that in for the 3D-HST galaxies.

Lastly, we assign to each mock galaxy a random grism redshift accuracy such that the observed distributions shown in Figure 1 are reproduced for the mock sample. A photometric redshift accuracy is also generated using the same distributions (as a sole function of ).

Each model galaxy is then defined by three redshifts: a spectroscopic redshift which is derived from the geometric redshift () of the cones plus the peculiar velocity of the halo, a grism like redshift which is derived from the spec-z plus a random value drawn from a gaussian distribution with sigma equal to the grism redshift accuracy derived above, and a photometric redshift derived as the previous but using the photometric redshift accuracy.

The last step in this procedure requires that for each galaxy only one of these three redshifts is selected to generate a “best” redshift. To do so, we work in bins of  magnitude. For each bin of magnitude, the fraction of 3D-HST galaxies with spec-z, grism-z and photo-z is computed. Then in order of descending , the spec-z is taken for a number of galaxies matching the fraction of galaxies with spec-z in the observational catalog, a grism-z is taken for an appropriate number of galaxies and lastly a photo-z is taken for the galaxies with the lowest which mimic line non-detections in the grism data. We stress that since the grism redshift accuracy is a function of , the quality of grism redshifts for objects with marginal line detections is preserved by this method.

Once a catalog of model galaxies is selected and their redshift accuracy matches the 3D-HST catalog, we compute the environment parameters as described in Section 3.1. The only minor difference is that, as the number of model galaxies is very large, we can remove objects closer than 1.0 Mpc from the edges of the cone, to avoid edge biases.

## 6. Calibration of physical parameters

The local density of galaxies is not the only parameter that describes the environment in which a galaxy lives. Another important parameter is whether a galaxy is the dominant one within its dark matter halo (Central), or if it orbits within a deeper potential well (Satellite). The definition of centrals and satellites in the mock sample is obtained from the hierarchy of subhaloes (the main units hosting a single galaxy). First, haloes are detected using a friends-of-friends (FOF) algorithm with a linking length (Springel et al., 2005). Then each halo is decomposed into subhaloes running the algorithm SUBFIND (Springel et al., 2001), which determines the self-bound structures within the halo. As time goes by, the model follows subhaloes after they are accreted on to larger structures. When two haloes merge, the galaxy hosted in the more massive halo is considered the central, and the other becomes a satellite.

In this Section, we describe how we use the mock catalog to assign a halo mass probability density function (PDF) and a probability of being central or satellite to 3D-HST galaxies. The method builds on the idea of finding all the galaxies in the mock lightcones that match each 3D-HST galaxy in redshift, density, mass-rank (described below), and stellar mass (within the observational uncertainties). The main advantage of using multiple parameters is to break degeneracies which are otherwise dominant if only one parameter is used (e.g. to account for the role of stellar mass at low density, where halo mass depends more significantly on stellar mass than density; Fossati et al., 2015).

### 6.1. The stellar mass rank in fixed apertures

Fossati et al. (2015) explored how the rank in stellar mass of a galaxy in an appropriate aperture can be a good discriminator of the central/satellite status for a galaxy. This method, which complements the one usually used in local large scale surveys of galaxies based on halo finder algorithms, is more effective with the sparser sampling of high redshift surveys.

We refer the reader to Fossati et al. (2015) for the details of how this method is calibrated. Here, we recall that we define a galaxy to be central if it is the most massive (mass-rank = 1) within an adaptive aperture that only depends on the stellar mass. Otherwise, if it is not the most massive (mass-rank ), it is classified as a satellite.

The adaptive aperture is motivated by the fact that ideally, the aperture in which the mass-rank is computed should be as similar as possible to the halo virial radius to maximize the completeness of the central/satellite separation and reduce the fraction of spurious classifications. Fossati et al. (2015), defined this aperture as a cylinder with radius:

 r0=3×10(αlogM∗+β) [Mpc] (6)

where is the stellar mass, , and are the parameters which describe the dependence of the virial radius with stellar mass. These values are calibrated using the models (see Fossati et al., 2015). We also limit the aperture between 0.35 and 1.00 Mpc. The lower limit is set to avoid small apertures which would result in low mass galaxies being assigned mass-rank = 1 even if they are satellites of a large halo. The upper limit is approximately the radius of the largest haloes in the redshift range under study. The adaptive aperture radius (in Mpc) is therefore defined as:

 r=⎧⎨⎩0.35if r0<0.35r0if 0.35≤r0≤1.001.00if r0>1.00 (7)

In this work, we have to consider the variable redshift accuracy of 3D-HST galaxies. Therefore fixing the depth of the cylinder to does not optimize the central versus satellite discrimination. We set the depth of the adaptive aperture cylinder (in ) to:

 dv=⎧⎪⎨⎪⎩1500if σv,acc<1500σv,accif 1500≤σv,acc≤75007500if σv,acc>7500 (8)

where is the redshift accuracy of the primary galaxy. By using the mock sample, we tested that this combination of upper and lower limits gives a pure yet sufficiently complete sample of central galaxies.

The simple classification of centrals and satellites based on mass-rank only is subject to a variety of contaminating factors. For instance in galaxy pairs or small groups (where the mass of the real central and satellites are very close), it is difficult to use the stellar mass to robustly define which galaxy is the central. On the other hand, in the infalling regions beyond the virial radius of massive clusters, many central galaxies would be classified as satellites as analysed in detail in Fossati et al. (2015). In this work, we go beyond the simple dichotomic definition that each galaxy is either central or satellite using the mass-rank only. We combine multiple observables to derive a probability that each 3D-HST galaxy is central or satellite by matching observed galaxies to mock galaxies. This probabilistic approach naturally takes into account all sources of impurity and is of fundamental importance to separate the effects of mass and environment on the quenching of galaxies.

### 6.2. Matching mock to real galaxies

In this Section, we describe how we match individual 3D-HST galaxies to the mock sample to access physical quantities unaccessible from observations only. Our method heavily relies on the fact that the distributions of stellar mass and density (and their bivariate distribution) are well matched between the mocks and the observations across the full redshift range.

In the upper and right panels of Figure 11, we show the distributions of density and stellar mass respectively, while the main panel shows the 2D histogram of both quantities. The overall agreement is very satisfactory and relates to the agreement of the observed stellar mass functions to that from Henriques et al. (2015), and to our careful selection of objects. The match of the density distributions also confirms that the redshift assignment for mock galaxies is accurate enough to reproduce the observed density distributions. A good match between models and observations is found for other apertures as well. In the future, it should be possible to improve our method by combining density information on several scales by means of machine learning algorithms.

To match observed galaxies to mock galaxies, we also require an estimate of the uncertainty on both the density and the stellar mass. For the stellar mass, we use dex (Conroy et al., 2009; Gallazzi & Bell, 2009; Mendel et al., 2014). For the density, the error budget is dominated by the redshift uncertainty of each galaxy and the fact that for a sample of galaxies with given  and emission line , the redshift accuracy has a distribution with non zero width. This means that the redshift uncertainty of mock galaxies can only match the observational sample in a statistical sense. To test how the densities of individual galaxies are affected by the redshift uncertainty, we repeat 50 times the process of assigning a redshift to mock galaxies described in Section 5.2. We then compute the density for each of those samples independently and analyse the distribution of densities for each galaxy. We find that the distribution roughly follows a Poissonian distribution:

Based on this evidence, we match each 3D-HST galaxy to the mock galaxies within in redshift space and within and for the stellar mass and density on the 0.75 Mpc scale respectively.

The local density is a quantity that depends on the redshift accuracy both of the primary galaxy and of the neighbours, which in turn depends on the emission line strength in the grism data and the galaxy brightness (see Section 2.1). As a result the density peaks are subject to different degrees of smoothing if the neighbouring galaxies have a systematically poorer redshift accuracy in a given environment. Our mock catalogue is a good representation of the observational sample only if the SFR (from which the syntetic line is derived) and the stellar mass distributions as a function of environment are well reproduced by the SAM. Henriques et al. (2016) have shown that the H15 model is qualitatively able to recover the observed trends of passive fraction as a function of environment. By matching model galaxies with a redshift accuracy within to that of the observed galaxy we introduce no bias in the halo mass distributions: for galaxies with less accurate redshifts, we simply obtain broader PDFs of halo mass.

Lastly, we restrict the match for the most massive galaxies (mass-rank ) to the most massive mock galaxies. The rest of the population (mass-rank ) was matched to the same population in the mocks.

#### 6.2.1 A probabilistic determination of central versus satellite status

The central and satellite fractions of those matched mock galaxies are used to define a probability that the 3D-HST galaxy under consideration is central () or satellite ():

 Pcen=Nmatched cenNmatched,  Psat=Nmatched satNmatched=1−Pcen (9)

Figure 12 shows the average values of those quantities in bins of logarithmic density contrast (see Section 3.1) in the 0.75 Mpc aperture and stellar mass for all the 3D-HST galaxies included in our sample. The average value of decreases with increasing density and decreasing stellar mass, and the opposite trend occurs for . High mass haloes (high density regions) are indeed dominated by the satellite population, but objects with high stellar masses are more likely to be centrals. Galaxies in low density environments () are almost entirely centrals. However, in the analysis performed in the next sections we use the values of and computed for each galaxy instead of the average values (Kovač et al. 2014 performs instead an average correction as a function of galaxy density). This takes into full account possible second order dependencies on mass-rank, redshift, or redshift accuracy.

We also examine how varies as a function of the distance from the center of over-dense structures, such as massive groups or clusters of galaxies. To do so, we take the haloes more massive than in the mock lightcones. We then select all galaxies in a redshift slice centered on the redshift of the central galaxy and within and compute their projected sky positions with respect to the central galaxy. We normalize their positions to the virial radius of the halo and remove the central galaxy.

Figure 13, top panel, shows the average value of as a function of normalized R.A. and Dec. offset from the center of the haloes. The black solid circles mark and . Figure 13, bottom panel, shows the average value of (black solid line) as a function of radial distance from the center of the haloes. The red solid line shows the fraction of satellites in the same radial bins but using the mock definition of satellites. Lastly, the red dashed line shows the value of including only SAM satellites living in the same halo of the central galaxy.

Our Bayesian definition tracks well the SAM definition of satellites as a function of halo mass. However the real trend is smoothed due to both the transformation from real to redshift space, and the intrinsic uncertainty of our method to extract based on observational parameters. Moreover, only drops to at . This is caused by satellites from nearby haloes, while the contribution from satellites belonging to the same halo becomes negligible at . Indeed, massive structures are embedded in filaments and surrounded by groups which will eventually merge with the cluster. Therefore, even at large distances from the center, the density is higher than the mean density (at the density is times higher than the average density). As a reference we show in Figure 13, bottom panel, the value of for a stellar mass and redshift matched sample of galaxies living in average density environments (, horizontal dashed line).

#### 6.2.2 The halo mass calibration

Similarly, we use the halo masses of matched central and satellite model galaxies to generate the halo mass PDFs given their type ( and respectively). Figure 14 shows three examples of such PDFs for one object with high , one with high , and one object with an almost equal probability of being a central or a satellite. The vertical dashed lines mark the median halo mass for a given type. Although the total halo mass PDF can be double peaked (middle panel), the degeneracy between the two peaks is broken once the galaxy types are separated, making the median values well determined for each type independently.

### 6.3. Testing calibrations

We test the halo mass calibration by comparing the halo mass distributions of the mock sample to the 3D-HST sample. In both panels of Figure 15, we plot the halo mass histograms for centrals and satellites of the entire mock sample. The number counts are scaled by the ratio of the volume between the 24 lightcones and the five 3D-HST fields.

In the left panel of Figure 15 the dashed lines are the halo mass distributions of 3D-HST galaxies obtained by summing the full halo mass PDFs for centrals (, red dashed) and satellites (, blue dashed) weighted by and for each galaxy. The agreement with the mock sample distributions is remarkable. Although this is in principle expected because the halo mass PDFs for observed galaxies are generated from the mock sample, it should be noted that we perform the match in bins of redshift, redshift accuracy, stellar mass, density and mass-rank. The good agreement for the whole sample between the derived PDFs and the mock distributions (for centrals and satellites separately) should therefore be taken as an evidence that our method has not introduced any bias in the final PDFs.

We take the median value of the halo mass PDFs given that each galaxy is a central () or a satellite () as an estimate of the “best” halo mass, weighted by and . These values are shown in Figure 15, right panel. The agreement with the mock distributions is good. For central galaxies, the shape and extent of the distribution is well preserved. For satellite galaxies, the halo mass range is less extended than the one in the mocks; values above and below indeed only contribute through the tails of the PDFs, and therefore do not appear when the median of the PDFs are used.

In the next Section, we make use of the full PDFs to derive constraints on the environmental quenching of satellite galaxies. However, the satisfactory agreement of single value estimates of halo mass with the mock distributions makes them a valuable and reliable estimate in science applications when the use of the full PDFs is not possible or feasible.

## 7. Constraining environmental quenching processes at z=0.5−2

In this Section, we explore the role of environment in quenching the star formation activity of galaxies over using 3D-HST data. It was first proposed by Baldry et al. (2006) that the fraction of passive galaxies depends both on stellar mass and environment in a separable manner. Peng et al. (2010), using the SDSS and zCOSMOS surveys, extended the independence of those processes to . More recently, Peng et al. (2012) interpreted these trends in the local Universe by suggesting that central galaxies are only subject to “mass quenching” while satellites suffer from the former plus an “environmental quenching”. Kovač et al. (2014) similarly found that satellite galaxies are the main drivers of environmental quenching up to using zCOSMOS data.

Here, we extend these analysis to higher redshift by exploring the dependence of the fraction of passive galaxies on stellar mass, halo mass and central/satellite status in order to derive the efficiency and timescale of environmental quenching. In Appendix B, we show that we obtain consistent results using the observed galaxy density as opposed to calibrated halo mass.

### 7.1. Passive fractions

The populations of passive and star-forming galaxies are typically separated either by a specific star formation rate cut (e.g. Franx et al., 2008; Hirschmann et al., 2014; Fossati et al., 2015) or by a single color or color-color selection (e.g. Bell et al., 2004; Weiner et al., 2005; Whitaker et al., 2011; Muzzin et al., 2013; Mok et al., 2013). In this work, we use the latter method and select passive and star forming galaxies based on their position in the rest-frame UVJ color-color diagram (Williams et al., 2009). Following Whitaker et al. (2011), passive galaxies are selected to have:

 (U−V)>0.88×(V−J)+0.59 (10)
 (U−V)>1.3,(V−J)<1.6 [0.5
 (U−V)>1.3,(V−J)<1.5 [1.5

where the colors are rest-frame and are taken from Momcheva et al. (2016). Figure 16 shows the distribution of 3D-HST galaxies in the rest frame UVJ color-color plane. The red solid line shows the adopted division between passive and star forming galaxies.

The fractions of passive centrals and satellites in bins of and are computed as the fraction of passive objects in a given stellar mass bin where each galaxy is weighted by its probability of being central or satellite and the probability of being in a given halo mass bin for its type. Algebraically:

 fpass|ty=∑i(δpass,i×δM∗,i×Pty,i×∫MhPMh,i|tydMh)∑i(δM∗,i×Pty,i×∫MhPMh,i|tydMh) (13)

where ty refers to a given type (centrals or satellites), is 1 if a galaxy is UVJ passive and 0 otherwise, is 1 if a galaxy is in the stellar mass bin and 0 otherwise, is the probability that a galaxy is of a given type (see Section 6.2.1) and is the halo mass PDF given the type integrated over the halo mass bin limits (see Section 6.2.2).

The data points in Figure 17 show the passive fractions in two bins of halo mass (above and below ) and in three independent redshift bins. The median (log) halo masses for satellites are 12.36, 13.53 at for the lower and higher halo mass bin respectively; 12.41, 13.44 at ; and 12.43, 13.34 at .

The uncertainties on the data points cannot be easily evaluated assuming Binomial statistics because the number of galaxies contributing to each point is not a priori known. Indeed, and act as weights and all galaxies with a stellar mass within the mass bin do contribute to the passive fraction. To assess the uncertainties we use the mock lightcones (where each mock galaxy has been assigned a and and halo mass PDFs as if they were observed galaxies). In a given stellar mass bin we assign each model galaxy to be either passive or active such that the fraction of passive galaxies matches the observed one. Then we randomly select a number of model galaxies equal to the number of observed galaxies in that bin and we compute the passive fraction of this subsample using equation 13. We repeat this procedure 50000 times to derive the errorbars shown in Figure 17. This method accounts for uncertainties in the estimate of and as well as cosmic variance.

The vertical dashed lines, in Figure 17, mark the stellar mass completeness limit derived following Marchesini et al. (2009). In brief, we use the 3D-HST photometric catalog (down to  = 25 mag) and we scale the stellar masses of the galaxies as if they were at the spectroscopic sample limit of = 24 mag (which defines the sample used in this work). The scatter of the points is indicative of the variations in the population at a given redshift. We then take the upper percentile of the distributions as a function of redshift as the stellar mass limit, which is approximately and for old and red galaxies at and respectively. Below this mass we limit the upper edge of the redshift slice such that all galaxies in the stellar mass bin are included in a mass complete sample. A stellar mass bin is included only if the covered volume is greater than of the total volume of the redshift slice. This typically results in only one stellar mass bin below the completeness limit being included in the analysis.

In the highest halo mass bin of Figure 17 at , the satellite passive fraction (integrated over all galaxies) is higher than the central passive fraction, with a marginal significance. The same trend can be observed in the other halo mass and redshift bins, although the separation of the observed satellite and central passive fractions becomes more marginal.

In each redshift bin we also identify a sample of “pure” central galaxies (, irrespective of overdensity or halo mass), which provides a reference for the passive fraction of galaxies subject only to mass-quenching. The passive fraction of this sample of centrals (which has an average ) is shown as the thick red line in both halo mass bins.

The separation of the observed satellite passive fraction from that of the pure sample of centrals is more significant (especially at ). Indeed, the passive fractions derived using equation 13 can be strongly affected by impurities in the central/satellite classification and by cross-talk between the two halo mass bins, given that each galaxy can contribute to both bins and types (see equation 13). Any contribution of central galaxies to the satellite passive fraction, and vice versa, will reduce the observed difference between the two populations with respect to the “pure”, intrinsic difference.

### 7.2. Recovering the “pure” passive fractions for satellite galaxies

In order to recover the “pure” passive fraction for satellite galaxies as a function of halo mass, we perform a parametric model fitting to our dataset.

We start by parametrizing the probability of a satellite galaxy being passive independently in each stellar mass bin as a function of log halo mass, using a broken function characterized by a constant value () below the lower break () and another constant value () above the upper break (). In between the breaks, the passive fraction increases linearly. Algebraically, this 4-parameter function is defined as:

 Ppass|sat(Mh)=⎧⎪ ⎪⎨⎪ ⎪⎩Ppass,loif Mh≤Mbr,lom×(logMhMbr,lo)+Ppass,loif Mbr,loMbr,hi (14)

where .

This function is chosen to allow for a great degree of flexibility. We make the assumption that satellite galaxies are not subject to environmental quenching below , and therefore treat as a nuisance parameter of the model with a Gaussian prior centered on the observed passive fraction of pure centrals and a sigma equal to its uncertainty. For , instead we assume a semi-Gaussian prior with the same center and sigma as above, but only extending below the observed passive fraction of central galaxies (this implies that satellites are affected by the same mass-quenching as centrals). Above this value we assume a uniform prior. For the break masses we assume uniform priors. Table 1 summarizes the model parameters, their allowed range, and the number of bins in which the range is divided to compute the posterior.

The probability that each 3D-HST galaxy, is passive is:

 Ppass,i=Pcen,i×Ppass|cen+Psat,i×∫MhPMhi|sat×Ppass|satdMh (15)

where is from equation 14 and .

The likelihood space that the star forming or passive activity of 3D-HST galaxies in a stellar mass bin is reproduced by the model is computed as follows:

 L=∏i{Ppass,iif i is UVJ passive1−Ppass,iif i is not UVJ passive (16)

We compute the posterior on a regular grid covering the parameter space. We then sample the posterior distribution and we apply the model described in equation 14 to obtain the median value of and its uncertainty as a function of halo mass. Lastly, we assign the probability of being passive to mock satellites in each stellar mass bin according to their model halo mass, and we compute the average passive fraction in the two halo mass bins (above and below ). This results in the thick blue () lines with confidence intervals plotted as shaded regions in Figure 17. We illustrate in Appendix C an example of this procedure applied to a single redshift bin.

We verify that the separation seen in the pure passive fractions in Figure 17 is real. To do so we randomly shuffle the position in the UVJ diagram for galaxies in each stellar mass bin (irrespective of environmental properties) to break any correlation between passive fraction and environment. Then we compute the observed passive fractions of centrals and satellites, and for the pure sample of centrals and we perform again the model fitting procedure.

At we find that the pure satellite passive fraction is inconsistent with the null hypothesis (no satellite quenching) at a level in each stellar bin at high halo mass and 7 out of 8 stellar mass bins at low halo mass. The combined probability of the null hypothesis is in either halo mass bin. The difference is smaller, but still very significant () at . At the hypothesis of no satellite quenching is acceptable () in the low halo mass bin, while it can be ruled out () at higher halo mass.

Van der Burg et al. (2013), Kovač et al. (2014), and Balogh et al. (2016) have found that the environment plays an important role in determining the star formation activity of satellites, at least up to . However these works have only probed relatively massive haloes (). The depth of the 3D-HST sample allows us, for the first time, to extend these results to higher redshift, to lower mass galaxies and to lower mass haloes.

### 7.3. Satellite quenching efficiency

In order to further understand the increased passive fractions for satellite galaxies we compute the “conversion fractions” as first introduced by van den Bosch et al. (2008). This parameter, sometimes called the satellite quenching efficiency, quantifies the fraction of galaxies that had their star formation activity quenched by environment specific processes since they accreted as satellites into a more massive halo (see also Kovač et al., 2014; Hirschmann et al., 2014; Balogh et al., 2016). It is defined as:

 fconv(M∗,Mh)=fpass|sat,pure(M∗,Mh)−fpass|cen,pure(M∗)1−fpass|cen,pure(M∗) (17)

where and are the corrected fractions of quenched centrals and satellites in a given bin of and obtained as described above.

In equation 17 we compare the sample of centrals at the same redshift as the satellites. This builds on the assumption that the passive fraction of central galaxies only depends on stellar mass and that the effects of mass and environment are independent and separable. The conversion fraction then represents the fraction of satellites which are quenched due to environmental processes above what would happen if those galaxies would have evolved as centrals of their haloes. A different approach would be to compare the passive fraction of satellites to that of centrals at the time of infall in order to measure the total fraction of satellites quenched since they were satellites (e.g., Wetzel et al., 2013; Hirschmann et al., 2014). However this measurement includes the contribution of mass-quenched satellite galaxies, which we instead remove under the assumption that the physical processes driving mass quenching do not vary in efficiency when a galaxy becomes a satellite.

We also caution the reader that equation 17 has to be taken as a simplification of reality as it does not take into account differential mass growth of centrals and satellites which can be caused by tidal phenomena in dense environments or different star formation histories.

Figure 18 shows the conversion fractions in the same bins of , and redshift as presented in Figure 17. Previous results from galaxy groups and clusters from Knobel et al. (2013), and Balogh et al. (2016) are plotted in our higher halo mass bin (colored points with errorbars). We also add the conversion fractions from Kovač et al. (2014) obtained from zCOSMOS data as a function of local galaxy overdensity. We plot their overdensity bins above the mean overdensity in our higher halo mass bin and the others in our lower halo mass bin following the overdensity to halo mass conversion given in Kovač et al. (2014). The agreement of our measurements with other works is remarkable considering that different techniques to define the environment (density and central/satellite status) and passiveness are used in different works.

The satellite quenching efficiency tends to increase with increasing stellar mass and to decrease with increasing redshift at fixed stellar mass. In the lower halo mass bin, we note the presence of similar trends as at higher halo masses although the uncertainties are larger due to the smaller number of satellites. In our probabilistic approach this is due to the lower in low density environments as shown in Figure 12. Moreover, is poorly constrained at due to small number statistics of high mass satellites in the 3D-HST fields.

### 7.4. Quenching timescales

A positive satellite conversion fraction can be interpreted in terms of a prematurely truncated star formation activity in satellite galaxies compared to field centrals of similar stellar mass.

We define the quenching timescale () as the average time elapsed from the first accretion of a galaxy as satellite to the epoch at which the galaxy becomes passive, and we estimate it by assuming that galaxies which have been satellites for longer times are more likely to be quenched (Balogh et al., 2000; McGee et al., 2009; Mok et al., 2014). Indeed, the quenching can be interpreted to happen a certain amount of time after satellite galaxies cease to accrete material (including gas) from the cosmic web (see Section 8).

In practice, we obtain quenching timescales from the distribution of for satellite galaxies, which we define as the time the galaxy has spent as a satellite of haloes of any mass since its first infall (e.g., Hirschmann et al., 2014). For each bin of , , and redshift we select all satellite galaxies in our mock lightcones which define the distribution of . Then we select as the quenching timescale the percentile of this distribution which corresponds to . This method builds on the assumption that the infall history of observed satellites is well reproduced by the SAM. Systematic uncertainties can arise in the analytic prescriptions used for the dynamical friction timescale of satellites whose parent halo has been tidally stripped in the N-body simulation below the minimum mass for its detection (the so-called “orphan galaxies”). When this time is too short, too many satellites merge with the central galaxy and are removed from the sample, and vice-versa when the time is too long. De Lucia et al. (2010) explored the dynamical friction timescale in multiple SAMs, finding a wide range of timescales. However a dramatically wrong dynamical friction recipe impacts the fraction of satellites, the stellar mass functions, and the density-mass bivariate distribution, which we found to be well matched between the mocks and the observations.

In principle low stellar mass galaxies () are more affected by the resolution limit of the simulation and their derived quenching timescales might be subject to a larger uncertainty compared to galaxies of higher stellar mass. We verified that this is not the case by comparing the distribution of in two redshift snapshots ( and ) of Henriques et al. (2015) built on the Millennium-I and the Millennium-II simulations. The latter is an N-body simulation started from the same initial conditions of the original Millennium run but with a higher mass resolution at the expense of a smaller volume. The higher resolution means that the sub-haloes hosting low mass satellites galaxies, which can be tidally stripped, are explicitly tracked to lower mass and later times: while these are detected the recipe for dynamical friction is not invoked. We obtain consistent quenching timescales for Millennium-I and Millennium-II based mock catalogues, and therefore we conclude that the analytical treatment of orphan galaxies does not bias our results.

Figure 19 shows our derived quenching timescales (black points) in the same bins of and and redshift as presented in Figures 17 and 18. The observed trend of with stellar mass that is found in both redshift bins turns into a trend of . Quenching timescales increase to lower stellar mass in all redshift and halo mass bins, mainly a consequence of the decreasing conversion fraction. This parameter ranges from Gyr for low mass galaxies to Gyr for the most massive ones, and is in agreement with that found by Balogh et al. (2016).

Remarkably, the dependence of quenching timescale on halo mass is very weak. We overplot in each panel, as gray symbols, the quenching timescales obtained from our sample with the same procedure described above but without separating the data in two halo mass bins. In most of the stellar mass bins we find a good agreement, within the uncertainties, between the black and the gray points.

The lack of a strong halo mass dependence is a consequence of the typically shorter time since infall for satellite galaxies in lower mass haloes which largely cancels the lower conversion fraction in low mass haloes, and suggests that the physical process responsible for the premature suppression of star formation in satellite galaxies (when the Universe was half of its present age) is largely independent of halo mass.

A mild redshift evolution is also seen when comparing the redshift bins: passive satellites at higher redshift are quenched on a shorter timescale. In the next section we will further explore the redshift evolution of the quenching timescales from by combining the 3D-HST sample with a local galaxy sample from SDSS.

### 7.5. Redshift evolution of the quenching timescales

Figures 20 and 21 show the evolution of the conversion fraction and the quenching timescale from redshift 0 to 2. We now concentrate on three bins of stellar mass, each of 0.5 dex in width, and ranging from to .

Given that (and consequently ) are poorly constrained at due to the low number statistics of massive satellites, we exclude more massive galaxies from these plots. Similarly, galaxies at are only included in the mass limited sample at the lowest end of the redshift range under study, therefore the redshift evolution of , and cannot be derived for those low mass galaxies. A stellar mass bin appears in Figures 20 and 21 only if the stellar mass range above the mass limit is more than half of the entire stellar mass extent of the bin.

The values (solid lines) and their associated uncertainties (dashed lines) are obtained by performing the procedure described in the previous sections in overlapping redshift bins defined such that where is the width of the redshift bin and its center. This means we span larger volumes at higher redshift, modulating the decrease in sample density (Malmquist bias) and retaining sufficient sample statistics. It is also close to a constant bin in cosmic time. The x-axis of both figures is scaled such that the width of the redshift bins is constant and is shown as the horizontal error bar. We include only galaxies in a stellar mass complete sample for each redshift bin. In addition to the 3D-HST based constraints, we add constraints at , obtained using the same method to ensure homogeneity. The observational sample is drawn from SDSS and the mock sample from the redshift zero snapshot of the Henriques et al. (2015) model. We describe the details of how those datasets are processed in Appendix D. For this sample we restrict to stellar masses above to avoid including low mass galaxies with large corrections.

The evolution of as seen in Figure 18 is now clearly visible over the large redshift range probed by 3D-HST. The fraction of environmentally quenched satellite galaxies is a function of , and redshift. At fixed redshift is higher for higher mass galaxies and at fixed stellar mass it is higher in more massive haloes. More notably, the redshift evolution follows a decreasing trend with increasing redshift such that at the excess of quenching of satellite galaxies becomes more marginal (at least for massive galaxies) as first predicted by McGee et al. (2009) using halo accretion models. Several observational works reached a similar conclusion. Kodama et al. (2004), De Lucia et al. (2007), and Rudnick et al. (2009) found a significant build-up of the faint end of the red sequence (of passive galaxies) in cluster environments from toward lower redshift. This implies an increase in the fraction of quenched satellites with decreasing redshift for low mass galaxies. Recently, Darvish et al. (2016) found that the environmental quenching efficiency tends to zero at , although their analysis is only based on local overdensity and does not separate centrals and satellites. With the 3D-HST dataset we cannot rule out that satellite quenching is still efficient for lower mass satellites at ; deeper samples are required to robustly assess the satellite quenching efficiency at .

Moving to the present day Universe (SDSS data) does not significantly affect the fraction of environmentally quenched satellites despite the age of the Universe nearly doubling compared to the lowest redshift probed by the 3D-HST sample.

The redshift dependence of the quenching timescale originates from the combination of the evolution of and the distributions of infall times for satellite galaxies. The redshift evolution of in the high halo mass bin is well matched by the halo assembly history (at lower redshift they have been satellites on average for more time) and therefore is mostly independent of redshift. However, for lower mass galaxies a mild redshift evolution of might be present. However the slope is much shallower than the ageing of the Universe. For this reason, going to higher redshift, approaches the Hubble time and the satellite quenching efficiency decreases.

Despite the large uncertainty on the quenching times at low halo mass, their redshift evolution appears to be largely independent of halo mass. This means that the halo mass dependence of the conversion fractions may be mostly driven by an increase in the time spent as satellites in more massive haloes. At a more significant difference is found between the quenching times in the two halo mass bins. In the next section we discuss which mechanism can produce these observational signatures.

## 8. Discussion

There is a growing consensus that the evolution of central galaxies is regulated by the balance between cosmological accretion, star formation and gas ejection processes in a so-called “equilibrium growth model” (e.g. Lilly et al., 2013). The reservoir of cold gas in each galaxy is replenished by accretion, and will fuel star formation. As the rate of cosmological accretion is correlated with the mass of the halo, this regulates mass growth via star formation. As a result the eventual stellar mass is also tightly correlated with halo mass, driving a tight relation between star formation rate and stellar mass for normal star forming galaxies (the main sequence - MS - of star forming galaxies, e.g. Noeske et al., 2007).

When galaxies fall into a more massive halo the accretion of new gas from the cosmic web is expected to cease: such gas will instead be accreted (and shock heated) when it reaches the parent halo (White & Frenk, 1991). More recently Dekel & Birnboim (2006) estimate that this process occurs at a minimum halo mass , which is largely independent of redshift. This roughly corresponds to the minimum halo mass at which satellites are detected in the 3D-HST survey (see Figure 15).

### 8.1. Identification of the main mechanism

There are several additional ways in which a satellite galaxy’s gas and stellar content can be modified through interaction with its environment, including stripping of the hot or cold gas, and tidal interactions among galaxies or with the halo potential itself. An important combined effect is to remove (partially or completely) the gas reservoir leading to the quenching of star formation. However, as pointed out by McGee et al. (2014), and Balogh et al. (2016), it might not be necessary to invoke these mechanisms of environmental quenching to be effective. The high SFR typical of galaxies at high redshift, combined with outflows, can lead to exhaustion of the gas reservoir in the absence of cosmological accretion.

Our approach to link the conversion fractions to the distributions of time spent as satellite is based on the assumption that a galaxy starts to experience satellite specific processes at the time of its first infall into a larger halo and, in particular, that the cosmological accretion is shut off at that time.

We now examine whether a pure exhaustion of the gas reservoir can explain the quenching times we observe, or whether additional gas-removal mechanisms are required. First we appeal to the similarity of quenching times in the two halo mass bins shown in Figure 21 to support the pure gas exhaustion scenario. Other than at , the derived quenching times are indeed consistent within the uncertainties, therefore the main quenching mechanism has to be largely independent of halo mass.

Ram pressure stripping is often invoked as the main quenching mechanism for satellite galaxies in low redshift clusters (e.g., Poggianti et al., 2004; Gavazzi et al., 2013; Boselli et al., 2014b). Its efficiency is a function of the intracluster medium (ICM) density and the velocity of galaxies in the halo. More massive haloes have a denser ICM and satellites move faster through it which exerts a stronger dynamical pressure on the gas leading to faster stripping (and shorter quenching times) in more massive haloes (Vollmer et al., 2001; Roediger & Hensler, 2005). Our 3D-HST dataset does not extend to the extreme high mass end of the halo mass function in which ram pressure effects have been clearly observed (e.g., Sun et al., 2007; Yagi et al., 2010; Merluzzi et al., 2013; Kenney et al., 2015; Fossati et al., 2016), and so the lack of significantly shorter quenching times in the higher halo mass bin is consistent with the lack of stripping, and indeed of any strong halo-mass dependent gas-stripping process. However Balogh et al. (2016) find a small halo mass dependence of the quenching times comparing their GEEC2 group sample () to the GCLASS cluster sample (). These evidences might indicate that dynamical stripping can play a minor role in more massive haloes even at .

At instead, thanks to the large area covered by the SDSS dataset, a number of very massive haloes are included in the higher halo mass bin. This, combined with the presence of hot and dense ICM in massive haloes in the local Universe might be sufficient to explain the shorter quenching times in the high halo mass bin. Haines et al. (2015), and Paccagnella et al. (2016) found quenching timescales which are possibly shorter in massive clusters of galaxies ( Gyr). However, a quantitative comparison is hampered by the different definitions of the quenching timescale.

### 8.2. Delayed then Rapid or Continuous Slow quenching?

Having ruled out gaseous stripping as the main driver of satellite quenching in the range of halo mass commonly probed by our samples (), we now concentrate on how the gas exhaustion scenario can explain the observed values of .

To explain the quenching times at , Wetzel et al. (2013) presented a model dubbed the “delayed then rapid” quenching scenario, shown in the top panel of Figure 22. This model assumes that can be divided into two phases. During the first phase, usually called the “delay time” (), the star formation activity of satellites on average follows the MS of central galaxies. After this phase the star formation rate drops rapidly and satellite galaxies become passive on a short timescale called the “fading time”. Wetzel et al. (2013) estimated an exponential fading with a characteristic timescale Gyr which depends on stellar mass at . At , Mok et al. (2014); Muzzin et al. (2014); and Balogh et al. (2016) estimated the fading time to be Gyr, by identifying a “transition” population of galaxies likely to be transitioning from a star forming to a passive phase. These values suggest little redshift evolution of the fading timescale with cosmic time.

McGee et al. (2014) developed a physical interpretation of this model. These authors assumed that the long delay times are only possible if the satellite galaxy has maintained a multi-phase reservoir which can cool onto the galaxy and replenish the star forming gas (typically molecular) at roughly the same rate as the gas is lost to star formation (and potentially outflows). A constant molecular gas reservoir produces a nearly constant SFR according to the Kennicutt-Schmidt relation (Schmidt, 1959; Kennicutt, 1998b). Then the eventual depletion of this cold gas results in the rapid fading phase.

An alternative scenario would be that satellite galaxies retain only their molecular gas reservoirs after infall. In this case, if we assume a constant efficiency for star formation we should expect a star formation history which immediately departs from the MS, declining exponentially as the molecular gas is exhausted (“slow quenching” model shown in the bottom panel of Figure 22). By using our data we directly test those two toy models.

We use the star formation rates () for 3D-HST galaxies presented in the Momcheva et al. (2016) catalogue. By limiting to galaxies in the redshift range , stellar mass range and a maximum offset below the main sequence of 0.5 dex, we make sure that the SFR estimates are reliable and, for 91% of the objects, are obtained from Spitzer 24m observations combined with a UV monochromatic luminosity to take into account both dust obscured and unobscured star formation. For the remaining 9% SFR estimates are from an SED fitting procedure (see Whitaker et al., 2014; Momcheva et al., 2016).

There is growing evidence of curvature in the MS, which becomes shallower at higher stellar mass. Whitaker et al. (2014), Gavazzi et al. (2015), and Erfanianfar et al. (2016) interpreted this as a decline in star formation efficiency caused by the growth of bulges or bars in massive galaxies. To study the effects of environment above the internal processes driving the star formation efficiency at fixed stellar mass, we convert the SFR into an offset from this curved MS: using the Wisnioski et al. (2015) parametrization of the MS from Whitaker et al. (2014).

In order to test the two models we again resort to the mock sample. For each central galaxy in the mocks we assign a random offset from the main sequence obtained from a pure sample () of observed centrals: . For satellite galaxies, instead, their is a function of their time spent as satellites () as follows:

 ΔMS=⎧⎪⎨⎪⎩<−1if Tsat>TquenchΔMS,cenif Tsat≤TdΔMS,cen+log(e−(Tsat−Td)/τf)if Tsat>Td (18)

where and are the total quenching time and the delay time respectively, and is the characteristic timescale of the exponential fading phase. The latter is computed for each galaxy independently such that the SFR drops 1 dex below the MS333This is the value that defines the typical division between UVJ star forming and passive objects. in () Gyr. As we already computed , the only free parameter remaining in this family of models is . We define the “slow quenching” model for , and “delayed then rapid” those where .

Figure 23 shows the distributions of for 3D-HST satellites in two stellar mass bins, obtained as usual by weighting all galaxies by , and for the two models obtained from the mock sample in the same way. The histograms are normalized to the total number of 3D-HST satellites in the same stellar mass bin (including UVJ passive galaxies). We stress that this comparison is meaningful because our models include the cross-talk between centrals and satellites.

In the “delayed then rapid” scenario, the value of the delay time that best reproduces the observed data is Gyr for the () stellar mass bins respectively. This means the average satellite fades with an -folding timescale of Gyr. Our values are consistent with those from Wetzel et al. (2013) at and other independent estimates at high-z. Tal et al. (2014) performed a statistical identification of central and satellite galaxies in the UltraVISTA and 3D-HST fields and found that the onset of satellite quenching occurs 1.5-2 Gyr later than that of central galaxies at fixed number density. These values are in good agreement with the delay times estimated in our work.

Conversely the “slow quenching” model predicts too many galaxies below the main sequence but which are not UVJ passive (“transition” galaxies). The fraction of 3D-HST satellites for which is 65% (46%), which compares to 67% (47%) for the “delayed then rapid” model; instead it drops to 52% (39%) for the “slow quenching” model.

We tested that the distributions of and the estimated fading times are not biased by inaccurate UV+IR SFR for AGN candidates in the sample. Because the CANDELS fields have uniform coverage of deep Spitzer/IRAC observations, we remove the sources selected by the IRAC color-color criteria presented in Donley et al. (2012). We find that neither the distributions, nor the fading time estimates change appreciably.

In conclusion the fading of the star formation activity must be a relatively rapid phenomenon which follows a long phase where satellite galaxies have a SFR which is indistinguishable from that of centrals. This is further supported by the evidence that the passive and star forming populations are well separated in color and SFR and that the “green valley” in between them is sparsely populated across different environments (Gavazzi et al., 2010; Boselli et al., 2014b; Schawinski et al., 2014; Mok et al., 2014).

### 8.3. The gas content of satellite galaxies

Finally, we discuss the implications of the quenching times on the gas content of satellites at the time of infall. Because satellite galaxies are not thought to accrete gas after infall, their continued star formation occurs at the expense of gas previously bound to the galaxy.

As previously discussed, McGee et al. (2014) explain the fading phase by the depletion of molecular gas. The depletion time of molecular gas () has been derived by several authors (Saintonge et al., 2011; Tacconi et al., 2013; Boselli et al., 2014a; Genzel et al., 2015). There is general consensus that this timescale (which is an -folding time) is Gyr at and is Gyr at . Moreover it is independent of stellar mass. In this framework we might expect fading times shorter than (or similar to) , where shorter fading times are possible where a fraction of the gas is lost to outflows. Our fading times are indeed somewhat shorter than the molecular gas depletion times, consistent with this picture, but with a mass dependence which suggests a mass-dependent outflow rate.

In Figure 24 we show the ratio of the delay time to the fading time as a function of redshift in bins of stellar mass. Assuming that the fading phase is driven by depletion of molecular gas (in absence of further replenishment), this ratio informs us about the relative time spent refuelling the galaxy to keep it on the MS (from a gas reservoir initially in a warmer phase) to the time spent depleting the molecular gas. We note that the delay time is estimated via the quenching time (which is a function of stellar mass and redshift) while the fading time is computed only for 2 stellar mass bins at , with fading timescales taken from Wetzel et al. (2013). Errors in Figure 24 propagate only the errors on the total quenching time.

For all stellar mass bins this ratio is above unity, which we interpret to mean that gas in a non-molecular phase is required to supply fuel for star formation, and this gas is likely to exceed the molecular gas in mass. The longer delay times at suggest that a smaller fraction of the gas mass is in molecular form. This model also implies that a significant fraction of the final stellar mass of satellite galaxies is built-up during the satellite phase.

A multi-phase gas reservoir is observed in the local Universe in the form of ionized, atomic, and molecular hydrogen. Atomic hydrogen cools, replenishing the molecular gas reservoir which is depleted by star formation. In the local Universe, using the scaling relations derived from the Herschel Reference Sample (Boselli et al., 2014a), the observed mass of atomic hydrogen is found to be 2-3 times larger than the amount of molecular hydrogen for our most massive stellar mass bin. This ratio increases to for the lower mass objects, although with a large uncertainty. These numbers are consistent with the picture that much, if not all, of the reservoir required to maintain the satellite on the MS during the delay phase at can be (initially) in an atomic phase. It is also plausible that much of the gas reservoir bound to higher redshift galaxies is contained in a non-molecular form, and that this can be retained and used for star formation when the galaxies become satellites.

Assuming that outflows are not only active during the fading phase but rather during the entire quenching time, the mass in the multi-phase gas reservoir needs to be even larger, although it is not straightforward to constrain by how much.

In conclusion our work supports a “delayed then rapid” quenching scenario for satellite galaxies regulated by star formation, depletion and cooling of a multi-phase gas reservoir.

## 9. Conclusions

In this work, we have characterized the environment of galaxies in the 3D-HST survey at . We used the projected density within fixed apertures coupled with a newly developed method for edge corrections to obtain a definitive measurement of the environment in five well studied deep-fields: GOODS-S, COSMOS, UDS, AEGIS, GOODS-N. Using a recent semi-analytic model of galaxy formation, we have assigned physical quantities describing the properties of dark matter haloes to observed galaxies. Our results can be summarized as follows:

1. The 3D-HST deep fields host galaxies in a wide range of environments, from underdense regions to relatively massive clusters. This large variety is accurately quantified thanks to a homogeneous coverage of high quality redshifts provided by the 3D-HST grism observations.

2. As described in Fossati et al. (2015), a calibration of density into physically motivated quantities (e.g. halo mass, central/satellite status) requires a mock catalogue tailored to match the properties of the 3D-HST survey. We developed such a catalogue and performed a careful match to the observational sample. As a result, each 3D-HST galaxy is assigned a probability that it is a central or satellite galaxy with an associated probability distribution function of halo mass for each type. This Bayesian approach naturally takes into account sources of contamination in the matching process. We publicly release our calibrated environment catalogue to the community.

3. The 3D-HST sample provides us with a unique dataset to study the processes governing environmental quenching from to the present day over a wide range of halo mass. As no galaxy has a perfectly defined environment, a Bayesian analysis including forward modelling of the mock catalogue allows us to recover “pure” passive fractions of central and satellite populations. We also estimated robust and realistic uncertainties through a Monte Carlo error propagation scheme that takes into account the use of probabilistic quantities.

4. By computing conversion fractions (i.e. the excess of quenched satellite galaxies compared to central galaxies at the same epoch and stellar mass) (van den Bosch et al., 2008), we find that satellite galaxies are efficiently environmentally quenched in haloes of any mass up to . Above these redshifts the fraction of passive satellites is roughly consistent with that of central galaxies.

5. Under the assumption that the earliest satellites to be accreted become passive first, we derive environmental quenching timescales. These are long ( Gyr at ; 5-7 Gyr at ) and longer at lower stellar mass. As they become comparable to the Hubble time by , effective environmental quenching of satellites is not possible at earlier times. More remarkably, their halo mass dependence is negligible. By assuming that cosmological accretion stops when a galaxy becomes a satellite, we were able to interpret these evidences in a “gas exhaustion” scenario (i.e. the “overconsumption” model of McGee et al., 2014) where quenching happens because satellite galaxies eventually run out of their fuel which sustains further star formation.

6. We tested two toy models of satellite quenching: the “delayed then rapid” quenching scenario proposed by Wetzel et al. (2013) and a continuous “slow quenching” from the time of first infall. By comparing the observed SFR distribution for 3D-HST satellites to the predictions of these toy models we found that the scenario that best reproduces the data at is “delayed then rapid”. Consistently with the results of Wetzel et al. (2013) at , we find that the fading of the star formation activity is a relatively rapid phenomenon ( Gyr, lower at higher mass) which follows a long phase where satellite galaxies have a SFR which is indistinguishable from that of centrals.

7. By linking the fading to the depletion of molecular gas we conclude that the “delayed then rapid” scenario is best explained, even at high redshift, by the presence of a significant multi-phase reservoir which can cool onto the galaxy and replenish the star forming gas at roughly the same rate as the gas is turned into stars.

This analysis of satellite quenching is only one of many possible analyses that can be performed with the environmental catalogue built in this work. In the future, the advent of the James Webb Space Telescope, WFIRST and Euclid space missions, as well as highly multiplexed spectroscopic instruments from the ground (e.g., MOONS at VLT; PFS at Subaru), will provide excellent redshift estimates for fainter objects over a much larger area, to which similar techniques to calibrate environment can be applied. This, in combination with deeper scaling relations for the atomic and molecular gas components from the Square Kilometer Array and ALMA will revolutionize measurements to constrain how galaxies evolve and quench as a function of their environment.

It is a pleasure to thank Nikhil Arora for his help in a preliminary examination of the local SDSS data, to Alessandro Boselli, Gabriella de Lucia, Sean McGee, Greg Rudnick, and Andrew Wetzel for useful discussion, to Michael Balogh and Alexis Finoguenov for providing catalogs in useful format, and to Stefano Zibetti and Tamás Budavári for the work in helping deriving densities for the SDSS sample as presented in Wilman et al. (2010), and Phleps et al. (2014). We thank the anonymous referee for his/her comments that improved the quality of the manuscript. MFossati and DJW acknowledge the support of the Deutsche Forschungsgemeinschaft via Projects WI 3871/1-1, and WI 3871/1-2. JCCC acknowledges the support of the Deutsche Zentrum für Luft- und Raumfahrt (DLR) via Project ID 50OR1513. KEW gratefully acknowledge support by NASA through Hubble Fellowship grant #HF2-51368 awarded by the Space Telescope Science Institute, which is operated by the Association of Universities for Research in Astronomy, Inc., for NASA. This work is based on observations taken by the 3D-HST Treasury Program (GO 12177 and 12328) with the NASA/ESA HST, which is operated by the Association of Universities for Research in Astronomy, Inc., under NASA contract NAS5-26555. Based on observations made with ESO Telescopes at the La Silla or Paranal Observatories under programme ID(s) 175.A-0839(B), 175.A-0839(D), 175.A-0839(I), 175.A-0839(J), 175.A-0839(H), 175.A-0839(F), 092.A-0091, 093.A-0079, 093.A-0187, 094.A-0217, 094.A-0287, 095.A-0047, 095.A-0109, 096.A-0093, and 096.A-0025. The MOSDEF data were obtained at the W.M. Keck Observatory, which is operated as a scientific partnership among the California Institute of Technology, the University of California and the National Aeronautics and Space Administration. The Observatory was made possible by the generous financial support of the W.M. Keck Foundation. We recognize and acknowledge the very significant cultural role and reverence that the summit of Mauna Kea has always had within the indigenous Hawaiian community. We are most fortunate to have the opportunity to conduct observations from this mountain. We acknowledge all the teams and observatories that provided datasets included in the photometric and spectroscopic catalogues used in this work. Funding for SDSS-III has been provided by the Alfred P. Sloan Foundation, the Participating Institutions, the National Science Foundation, and the U.S. Department of Energy Office of Science. The SDSS-III web site is http://www.sdss3.org/. SDSS-III is managed by the Astrophysical Research Consortium for the Participating Institutions of the SDSS-III Collaboration including the University of Arizona, the Brazilian Participation Group, Brookhaven National Laboratory, Carnegie Mellon University, University of Florida, the French Participation Group, the German Participation Group, Harvard University, the Instituto de Astrofisica de Canarias, the Michigan State/Notre Dame/JINA Participation Group, Johns Hopkins University, Lawrence Berkeley National Laboratory, Max Planck Institute for Astrophysics, Max Planck Institute for Extraterrestrial Physics, New Mexico State University, New York University, Ohio State University, Pennsylvania State University, University of Portsmouth, Princeton University, the Spanish Participation Group, University of Tokyo, University of Utah, Vanderbilt University, University of Virginia, University of Washington, and Yale University.

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