arXiv subjects

Yicheng Guo

Publications and source records attributed to Yicheng Guo.

125 records · Page 7Linked to original sources

arXiv2011

CANDELS: The Cosmic Assembly Near-infrared Deep Extragalactic Legacy Survey - The Hubble Space Telescope Observations, Imaging Data Products and Mosaics

This paper describes the Hubble Space Telescope imaging data products and data reduction procedures for the Cosmic Assembly Near-IR Deep Extragalactic Legacy Survey (CANDELS). This survey is designed to document the evolution of galaxies and black holes at $z\sim1.5-8$, and to study Type Ia SNe beyond $z>1.5$. Five premier multi-wavelength sky regions are selected, each with extensive multiwavelength observations. The primary CANDELS data consist of imaging obtained in the Wide Field Camera 3 / infrared channel (WFC3/IR) and UVIS channel, along with the Advanced Camera for Surveys (ACS). The CANDELS/Deep survey covers \sim125 square arcminutes within GOODS-N and GOODS-S, while the remainder consists of the CANDELS/Wide survey, achieving a total of \sim800 square arcminutes across GOODS and three additional fields (EGS, COSMOS, and UDS). We summarize the observational aspects of the survey as motivated by the scientific goals and present a detailed description of the data reduction procedures and products from the survey. Our data reduction methods utilize the most up to date calibration files and image combination procedures. We have paid special attention to correcting a range of instrumental effects, including CTE degradation for ACS, removal of electronic bias-striping present in ACS data after SM4, and persistence effects and other artifacts in WFC3/IR. For each field, we release mosaics for individual epochs and eventual mosaics containing data from all epochs combined, to facilitate photometric variability studies and the deepest possible photometry. A more detailed overview of the science goals and observational design of the survey are presented in a companion paper.

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arXiv2011

CANDELS: The Cosmic Assembly Near-infrared Deep Extragalactic Legacy Survey

The Cosmic Assembly Near-infrared Deep Extragalactic Legacy Survey (CANDELS) is designed to document the first third of galactic evolution, over the approximate redshift (z) range 8--1.5. It will image >250,000 distant galaxies using three separate cameras on the Hubble Space Telescope, from the mid-ultraviolet to the near-infrared, and will find and measure Type Ia supernovae at z>1.5 to test their accuracy as standardizable candles for cosmology. Five premier multi-wavelength sky regions are selected, each with extensive ancillary data. The use of five widely separated fields mitigates cosmic variance and yields statistically robust and complete samples of galaxies down to a stellar mass of 10^9 M_\odot to z \approx 2, reaching the knee of the ultraviolet luminosity function (UVLF) of galaxies to z \approx 8. The survey covers approximately 800 arcmin^2 and is divided into two parts. The CANDELS/Deep survey (5σ point-source limit H=27.7 mag) covers \sim 125 arcmin^2 within GOODS-N and GOODS-S. The CANDELS/Wide survey includes GOODS and three additional fields (EGS, COSMOS, and UDS) and covers the full area to a 5σ point-source limit of H \gtrsim 27.0 mag. Together with the Hubble Ultra Deep Fields, the strategy creates a three-tiered "wedding cake" approach that has proven efficient for extragalactic surveys. Data from the survey are nonproprietary and are useful for a wide variety of science investigations. In this paper, we describe the basic motivations for the survey, the CANDELS team science goals and the resulting observational requirements, the field selection and geometry, and the observing design. The Hubble data processing and products are described in a companion paper.

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arXiv2011

Galaxy Structure and Mode of Star Formation in the SFR-Mass Plane from z ~ 2.5 to z ~ 0.1

We analyze the dependence of galaxy structure (size and Sersic index) and mode of star formation (Σ_SFR and SFR_IR/SFR_UV) on the position of galaxies in the SFR versus Mass diagram. Our sample comprises roughly 640000 galaxies at z~0.1, 130000 galaxies at z~1, and 36000 galaxies at z~2. Structural measurements for all but the z~0.1 galaxies were based on HST imaging, and SFRs are derived using a Herschel-calibrated ladder of SFR indicators. We find that a correlation between the structure and stellar population of galaxies (i.e., a 'Hubble sequence') is already in place since at least z~2.5. At all epochs, typical star-forming galaxies on the main sequence are well approximated by exponential disks, while the profiles of quiescent galaxies are better described by de Vaucouleurs profiles. In the upper envelope of the main sequence, the relation between the SFR and Sersic index reverses, suggesting a rapid build-up of the central mass concentration in these starbursting outliers. We observe quiescent, moderately and highly star-forming systems to co-exist over an order of magnitude or more in stellar mass. At each mass and redshift, galaxies on the main sequence have the largest size. The rate of size growth correlates with specific SFR, and so does Σ_SFR at each redshift. A simple model using an empirically determined SF law and metallicity scaling, in combination with an assumed geometry for dust and stars is able to relate the observed Σ_SFR and SFR_IR/SFR_UV, provided a more patchy dust geometry is assumed for high-redshift galaxies.

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arXiv2011

Deep 1.1 mm-wavelength imaging of the GOODS-South field by AzTEC/ASTE -- II. Redshift distribution and nature of the submillimetre galaxy population

We report the results of the counterpart identification and a detailed analysis of the physical properties of the 48 sources discovered in our deep 1.1mm wavelength imaging survey of the GOODS-South field using the AzTEC instrument on the Atacama Submillimeter Telescope Experiment (ASTE). One or more robust or tentative counterpart candidate is found for 27 and 14 AzTEC sources, respectively, by employing deep radio continuum, Spitzer MIPS & IRAC, and LABOCA 870 micron data. Five of the sources (10%) have two robust counterparts each, supporting the idea that these galaxies are strongly clustered and/or heavily confused. Photometric redshifts and star formation rates (SFRs) are derived by analyzing UV-to-optical and IR-to-radio SEDs. The median redshift of z~2.6 is similar to other earlier estimates, but we show that 80% of the AzTEC-GOODS sources are at z>2, with a significant high redshift tail (20% at z>3.3). Rest-frame UV and optical properties of AzTEC sources are extremely diverse, spanning 10 magnitude in the i- and K-band photometry with median values of i=25.3 and K=22.6 and a broad range of red colour (i-K=0-6). These AzTEC sources are some of the most luminous galaxies in the rest-frame optical bands at z>2, with inferred stellar masses of (1-30) x 10^{10} solar masses and UV-derived star formation rates of SFR(UV) > 10-1000 solar masses per year. The IR-derived SFR, 200-2000 solar masses per year, is independent of redshift or stellar mass. The resulting specific star formation rates, SSFR = 1-100 per Gyr, are 10-100 times higher than similar mass galaxies at z=0, and they extend the previously observed rapid rise in the SSFR with redshift to z=2-5. These galaxies have a SFR high enough to have built up their entire stellar mass within their Hubble time. We find only marginal evidence for an AGN contribution to the near-IR and mid-IR SEDs. (abridged)

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arXiv2011

Extreme Emission Line Galaxies in CANDELS: Broad-Band Selected, Star-Bursting Dwarf Galaxies at z>1

We identify an abundant population of extreme emission line galaxies (EELGs) at redshift z~1.7 in the Cosmic Assembly Near-IR Deep Extragalactic Legacy Survey (CANDELS) imaging from Hubble Space Telescope/Wide Field Camera 3 (HST/WFC3). 69 EELG candidates are selected by the large contribution of exceptionally bright emission lines to their near-infrared broad-band magnitudes. Supported by spectroscopic confirmation of strong [OIII] emission lines -- with rest-frame equivalent widths ~1000Å-- in the four candidates that have HST/WFC3 grism observations, we conclude that these objects are galaxies with 10^8 Msol in stellar mass, undergoing an enormous starburst phase with M_*/(dM_*/dt) of only ~15 Myr. These bursts may cause outflows that are strong enough to produce cored dark matter profiles in low-mass galaxies. The individual star formation rates and the co-moving number density (3.7x10^-4 Mpc^-3) can produce in ~4 Gyr much of the stellar mass density that is presently contained in 10^8-10^9 Msol dwarf galaxies. Therefore, our observations provide a strong indication that many or even most of the stars in present-day dwarf galaxies formed in strong, short-lived bursts, mostly at z>1.

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arXiv2011

CANDELS: Constraining the AGN-Merger Connection with Host Morphologies at z~2

Using HST/WFC3 imaging taken as part of the Cosmic Assembly Near-infrared Deep Extragalactic Legacy Survey (CANDELS), we examine the role that major galaxy mergers play in triggering active galactic nuclei (AGN) activity at z~2. Our sample consists of 72 moderate-luminosity (Lx ~ 1E42-1E44 erg/s) AGN at 1.5<z<2.5 that are selected using the 4 Msec Chandra observations in the Chandra Deep Field South, the deepest X-ray observations to date. Employing visual classifications, we have analyzed the rest-frame optical morphologies of the AGN host galaxies and compared them to a mass-matched control sample of 216 non-active galaxies at the same redshift. We find that most of the AGN reside in disk galaxies (51.4%), while a smaller percentage are found in spheroids (27.8%). Roughly 16.7% of the AGN hosts have highly disturbed morphologies and appear to be involved in a major merger or interaction, while most of the hosts (55.6%) appear relatively relaxed and undisturbed. These fractions are statistically consistent with the fraction of control galaxies that show similar morphological disturbances. These results suggest that the hosts of moderate-luminosity AGN are no more likely to be involved in an ongoing merger or interaction relative to non-active galaxies of similar mass at z~2. The high disk fraction observed among the AGN hosts also appears to be at odds with predictions that merger-driven accretion should be the dominant AGN fueling mode at z~2, even at moderate X-ray luminosities. Although we cannot rule out that minor mergers are responsible for triggering these systems, the presence of a large population of relatively undisturbed disk-like hosts suggests that secular processes play a greater role in fueling AGN activity at z~2 than previously thought.

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arXiv2011

The relative abundance of compact and normal massive early-type galaxies and its evolution from redshift z~2 to the present

We report on the evolution of the number density and size of early-type galaxies from z~2 to z~0. We select a sample of 563 massive (M>10^{10} Msun), passively evolving (SSFR<10^{-2} Gyr^{-1}) and morphologically spheroidal galaxies at 0 1.2 and z<1.2, respectively). We measure a significant evolution of the mass-size relation of early-type galaxies, with the fractional increment that is almost independent on the stellar mass. Early-type galaxies (ETGs) formed at z>1 appear to be preferentially small, and the evolution of the mass-size relation at z<1 is driven by both the continuous size growth of the compact galaxies and the appearance of new ETGs with large sizes. We also find that the number density of all passive early-type galaxies increases rapidly, by a factor of 5, from z~2 to z~1, and then more mildly by another factor of 1.5 from z~1 to z~0. We interpret these results as the evidence that the bulk of the ETGs are formed at 1<z<3 through a mechanism that leaves very compact remnants. At z<1 the compact ETGs grow gradually in size, becoming normal size galaxies, and at the same time new ETGs with normal-large sizes are formed.

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arXiv2011

Discovery Of Cold, Pristine Gas Possibly Accreting Onto An Overdensity Of Star-Forming Galaxies At Redshift z ~ 1.6

We report the discovery of large amounts of cold (T ~ 10^4 K), chemically young gas in an overdensity of galaxies at redshift z ~ 1.6 in the Great Observatories Origins Deep Survey southern field (GOODS-S). The gas is identified thanks to the ultra-strong Mg II absorption features it imprints in the rest-frame UV spectra of galaxies in the background of the overdensity. There is no evidence that the optically-thick gas is part of any massive galaxy (i.e. M_star > 4x10^9 M_sun), but rather is associated with the overdensity; less massive and fainter galaxies (25.5 < z_850 < 27.5 mag) have too large an impact parameter to be causing ultra-strong absorption systems, based on our knowledge of such systems. The lack of corresponding Fe II absorption features, not detected even in co-added spectra, suggests that the gas is chemically more pristine than the ISM and outflows of star-forming galaxies at similar redshift, including those in the overdensity itself, and comparable to the most metal-poor stars in the Milky Way halo. A crude estimate of the projected covering factor of the high-column density gas (N_H >~ 10^20 cm-2) based on the observed fraction of galaxies with ultra-strong absorbers is C_F ~ 0.04. A broad, continuum absorption profile extending to the red of the interstellar Mg II absorption line by <~ 2000 km/s is possibly detected in two independent co-added spectra of galaxies of the overdensity, consistent with a large-scale infall motion of the gas onto the overdensity and its galaxies. Overall, these findings provides the first tentative evidence of accretion of cold, chemically young gas onto galaxies at high redshift, possibly feeding their star formation activity. The fact that the galaxies are members of a large structure, as opposed to field galaxies, might play a significant role in our ability to detect the accreting gas.

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arXiv2011

Color and Stellar Population Gradients in Passively Evolving Galaxies at z~2 from HST/WFC3 Deep Imaging in the Hubble Ultra Deep Field

We report the detection of color gradients in six massive (stellar mass > 10^{10} M_{sun}) and passively evolving (specific SFR < 10^{-11}/yr) galaxies at redshift 1.3<z<2.5 identified in the HUDF using HST ACS and WFC3/IR images. After matching different PSFs, we obtain color maps and multi-band optical/near-IR photometry (BVizYJH) in concentric annuli, from the smallest resolved radial (~1.7 kpc) up to several times the H-band effective radius. We find that the inner regions of these galaxies have redder rest-frame UV--optical colors than the outer parts. The slopes of the color gradients mildly depend on the overall dust obscuration and rest-frame (U-V) color, with more obscured or redder galaxies having steeper color gradients. The z~2 color gradients are also steeper than those of local early-types. The gradient of a single parameter (age, extinction or metallicity) cannot fully explain the observed color gradients. Fitting spatially resolved HST seven-band photometry to stellar population synthesis models, we find that, regardless of assumptions for metallicity gradient, the redder inner regions of the galaxies have slightly higher dust obscuration than the bluer outer regions, although the magnitude depends on the assumed extinction law. The derived age gradient depends on the assumptions for metallicity gradient. We discuss the implications of a number of assumptions for metallicity gradient on the formation and evolution of these galaxies. We find that the evolution of the mass--size relationship from z~2 to z~0 cannot be driven by in--situ extended star formation, implying that accretion or merger is mostly responsible for the evolution. The lack of a correlation between color gradient and stellar mass argues against the metallicity gradient predicted by the monolithic collapse, which would require significant major mergers to evolve into the one observed at z~0. (Abridged)

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arXiv2010

A Detailed Study of Photometric Redshifts for GOODS-South Galaxies

We use the deepest and the most comprehensive photometric data currently available for GOODS-South galaxies to measure their photometric redshifts. The photometry includes VLT/VIMOS (U-band), HST/ACS (F435W, F606W, F775W, and F850LP bands), VLT/ISAAC (J-, H-, and Ks-bands), and four Spitzer/IRAC channels (3.6, 4.5, 5.8, and 8.0 micron). The catalog is selected in the z-band (F850LP) and photometry in each band is carried out using the recently completed TFIT algorithm, which performs PSF matched photometry uniformly across different instruments and filters, despite large variations in PSFs and pixel scales. Photometric redshifts are derived using the GOODZ code, which is based on the template fitting method using priors. The code also implements "training" of the template SED set, using available spectroscopic redshifts in order to minimize systematic differences between the templates and the SEDs of the observed galaxies. Our final catalog covers an area of 153 sq. arcmin and includes photometric redshifts for a total of 32,505 objects. The scatter between our estimated photometric and spectroscopic redshifts is sigma=0.040 with 3.7% outliers to the full z-band depth of our catalog, decreasing to sigma=0.039 and 2.1% outliers at a magnitude limit m(z)<24.5. This is consistent with the best results previously published for GOODS-S galaxies, however, the present catalog is the deepest yet available and provides photometric redshifts for significantly more objects to deeper flux limits and higher redshifts than earlier works. Furthermore, we show that the photometric redshifts estimated here for galaxies selected as dropouts are consistent with those expected based on the Lyman break technique.

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arXiv2010

The Morphology of Passively Evolving Galaxies at z ~ 2 from HST/WFC3 Deep Imaging in the Hubble Ultradeep Field

We present near-IR images, obtained with the Hubble Space Telescope (HST) and the WFC3/IR camera, of six passive and massive galaxies at redshift 1.3<z<2.4 (SSFR<10^{-2} Gyr^{-1}; stellar mass M~10^{11} M_{sun}), selected from the Great Observatories Origins Deep Survey (GOODS). These images, which have a spatial resolution of ~1.5 kpc, provide the deepest view of the optical rest-frame morphology of such systems to date. We find that the light profile of these galaxies is regular and well described by a Sersic model with index typical of today's spheroids. Their size, however, is generally much smaller than today's early types of similar stellar mass, with four out of six galaxies having r_e ~ 1 kpc or less, in quantitative agreement with previous similar measures made at rest-frame UV wavelengths. The images reach limiting surface brightness mu~26.5 mag arcsec^{-2} in the F160W bandpass; yet, there is no evidence of a faint halo in the galaxies of our sample, even in their stacked image. We also find that these galaxies have very weak "morphological k-correction" between the rest-frame UV (from the ACS z-band), and the rest--frame optical (WFC3 H-band): the Sersic index, physical size and overall morphology are independent or only mildly dependent on the wavelength, within the errors.

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arXiv2009

Structural Properties of Central Galaxies in Groups and Clusters

Using a representative sample of 911 central galaxies (CENs) from the SDSS DR4 group catalogue, we study how the structure of the most massive members in groups and clusters depend on (1) galaxy stellar mass (Mstar), (2) dark matter halo mass of the host group (Mhalo), and (3) their halo-centric position. We establish and thoroughly test a GALFIT-based pipeline to fit 2D Sersic models to SDSS data. We find that the fitting results are most sensitive to the background sky level determination and strongly recommend using the SDSS global value. We find that uncertainties in the background translate into a strong covariance between the total magnitude, half-light size (r50), and Sersic index (n), especially for bright/massive galaxies. We find that n depends strongly on Mstar for CENs, but only weakly or not at all on Mhalo. Less (more) massive CENs tend to be disk (spheroid)-like over the full Mhalo range. Likewise, there is a clear r50-Mstar relation for CENs, with separate slopes for disks and spheroids. When comparing CENs with satellite galaxies (SATs), we find that low mass (<10e10.75 Msun/h^2) SATs have larger median n than CENs of similar Mstar. Low mass, late-type SATs have moderately smaller r50 than late-type CENs of the same Mstar. However, we find no size differences between spheroid-like CENs and SATs, and no structural differences between CENs and SATs matched in both mass and colour. The similarity of massive SATs and CENs shows that this distinction has no significant impact on the structure of spheroids. We conclude that Mstar is the most fundamental property determining the basic structure of a galaxy. The lack of a clear n-Mhalo relation rules out a distinct group mass for producing spheroids, and the responsible morphological transformation processes must occur at the centres of groups spanning a wide range of masses. (abridged)

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arXiv2008

Environmental Effects on Satellite Galaxies: The Link Between Concentration, Size and Colour Profile

Using the SDSS DR4 group catalogue of Yang et al. (2007), we investigate sizes, concentrations, colour gradients and surface brightness profiles of central and satellite galaxies. We compare central and satellite galaxies at fixed stellar mass, in order to disentangle environmental from stellar mass dependencies. Early and late type galaxies are defined according to concentration. We find that at fixed stellar mass, late type satellite galaxies have smaller radii and larger concentrations than late type central galaxies. No such differences are found for early-type galaxies. We have also constructed surface brightness and colour profiles for the central and satellite galaxies in our sample. We find that late-type satellite galaxies have a lower surface brightness and redder colours than late-type central galaxies. We show that all observed differences between satellite and central galaxies can be explained by a simple fading model, in which the star formation in the disk decreases over timescales of 2-3 Gyr after a galaxy becomes a satellite. Processes that induce strong morphological changes (e.g. harassment) and processes that strip the galaxy of its entire ISM need not to be invoked in order to explain the environmental dependencies we find.

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arXiv2008

STAGES: the Space Telescope A901/2 Galaxy Evolution Survey

We present an overview of the Space Telescope A901/2 Galaxy Evolution Survey (STAGES). STAGES is a multiwavelength project designed to probe physical drivers of galaxy evolution across a wide range of environments and luminosity. A complex multi-cluster system at z~0.165 has been the subject of an 80-orbit F606W HST/ACS mosaic covering the full 0.5x0.5 (~5x5 Mpc^2) span of the supercluster. Extensive multiwavelength observations with XMM-Newton, GALEX, Spitzer, 2dF, GMRT, and the 17-band COMBO-17 photometric redshift survey complement the HST imaging. Our survey goals include simultaneously linking galaxy morphology with other observables such as age, star-formation rate, nuclear activity, and stellar mass. In addition, with the multiwavelength dataset and new high resolution mass maps from gravitational lensing, we are able to disentangle the large-scale structure of the system. By examining all aspects of environment we will be able to evaluate the relative importance of the dark matter halos, the local galaxy density, and the hot X-ray gas in driving galaxy transformation. This paper describes the HST imaging, data reduction, and creation of a master catalogue. We perform Sersic fitting on the HST images and conduct associated simulations to quantify completeness. In addition, we present the COMBO-17 photometric redshift catalogue and estimates of stellar masses and star-formation rates for this field. We define galaxy and cluster sample selection criteria which will be the basis for forthcoming science analyses, and present a compilation of notable objects in the field. Finally, we describe the further multiwavelength observations and announce public access to the data and catalogues.

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arXiv2007

Ongoing Assembly of Massive Galaxies by Major Merging in Large Groups and Clusters from the SDSS

We investigate the incidence of major mergers creating >10e11 Msun galaxies in present-day groups and clusters more massive than 2.5e13 Msun. We identify 38 pairs of massive galaxies with mutual tidal interaction signatures selected from >5000 galaxies with >5e10 Msun that reside in 845 such groups. We fit the images of each galaxy pair as the line-of-sight projection of symmetric models and identify mergers by the presence of residual asymmetries around each progenitor, such as off-center isophotes, broad tidal tails, and dynamical friction wakes. At the resolution and sensitivity of the SDSS, such mergers are found in 16% of high-mass, galaxy-galaxy pairs with magnitude differences of <1.5 and <30 kpc projected separations. We find that 90% of these mergers have nearly equal-mass progenitors with red-sequence colors and centrally-concentrated morphologies, the hallmarks of dissipationless merger simulations. Mergers at group centers are more common than between 2 satellites, but both are morphologically indistinguishable and we tentatively conclude that the latter are likely located at the dynamical centers of recently accreted subhalos. The frequency of central and satellite merging diminishes with group mass consistent with dynamical friction expectations. Based on reasonable assumptions, the centers of these massive halos are growing in stellar mass by 1-9% per Gyr, on average. Compared to all LRG-LRG mergers, we find a 2-9 times higher rate for their merging when restricted to these dense environments. Our results imply that the massive end of the galaxy population continues to evolve hierarchically at a measurable level, and that the centers of massive groups are the preferred environment for merger-driven galaxy assembly. (abridged)

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arXiv2006

The Alignment between the Distribution of Satellites and the Orientation of their Central Galaxy

We use galaxy groups selected from the Sloan Digital Sky Survey to examine the alignment between the orientation of the central galaxy (defined as the brightest group member) and the distribution of satellite galaxies. By construction, we therefore only address the alignment on scales smaller than the halo virial radius. We find a highly significant alignment of satellites with the major axis of their central galaxy. This is in qualitative agreement with the recent study of Brainerd (2005), but inconsistent with several previous studies who detected a preferential minor axis alignment. The alignment strength in our sample is strongest between red central galaxies and red satellites. On the contrary, the satellite distribution in systems with a blue central galaxy is consistent with isotropic. We also find that the alignment strength is stronger in more massive haloes and at smaller projected radii from the central galaxy. In addition, there is a weak indication that fainter (relative to the central galaxy) satellites are more strongly aligned. We present a detailed comparison with previous studies, and discuss the implications of our findings for galaxy formation.

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arXiv2004

Spatial Locality of Galaxy Correlation Function in Phase Space: Samples from the 2MASS Extended Source Catalog

We analyze the statistical properties and dynamical implications of galaxy distributions in phase space for samples selected from the 2MASS Extended Source Catalog. The galaxy distribution is decomposed into modes $δ({\bf k, x})$ which describe the number density perturbations of galaxies in phase space cell given by scale band $\bf k$ to ${\bf k}+Δ{\bf k}$ and spatial range $\bf x$ to ${\bf x}+Δ{\bf x}$. In the nonlinear regime, $δ({\bf k, x})$ is highly non-Gaussian. We find, however, that the correlations between $δ({\bf k, x})$ and $δ({\bf k', x'})$ are always very weak if the spatial ranges (${\bf x}$, ${\bf x}+Δ{\bf x}$) and (${\bf x'}$, ${\bf x'}+Δ{\bf x'}$) don't overlap. This feature is due to the fact that the spatial locality of the initial perturbations is memorized during hierarchical clustering. The highly spatial locality of the 2MASS galaxy correlations is a strong evidence for the initial perturbations of the cosmic mass field being spatially localized, and therefore, consistent with a Gaussian initial perturbations on scales as small as about 0.1 h$^{-1}$ Mpc. Moreover, the 2MASS galaxy spatial locality indicates that the relationship between density perturbations of galaxies and the underlying dark matter should be localized in phase space. That is, for a structure consisting of perturbations on scales from $k$ to $ k+Δ{k}$, the nonlocal range in the relation between galaxies and dark matter should {\it not} be larger than $|{Δ{\bf x}}|=2π/|Δ{\bf k}|$. The stochasticity and nonlocality of the bias relation between galaxies and dark matter fields should be no more than the allowed range given by the uncertainty relation $|{Δ{\bf x}|| Δ{\bf k}}|=2π$.

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