document: recent investigations of the large scale distribution of galaxies in the sloan digital sky survey ( sdss ; @xcite ) have revealed a complex relationship between the properties of galaxies , ( such as color , luminosity , surface brightness , and concentration ) and their environments ( @xcite ) . 
   these and other investigations using the sdss ( @xcite ) and the two - degree field galaxy redshift survey ( @xcite ) have found that galaxy clustering is a function both of star formation history and of luminosity . for low luminosity galaxies , clustering is a strong function of color , while for luminous galaxies clustering is a strong function of luminosity . for red galaxies , 
   clustering is a non - monotonic function of luminosity , peaking at both high and low luminosities . although galaxy clustering correlates also with surface brightness and concentration , @xcite and @xcite show that galaxy environment is independent of these properties at fixed color and luminosity . 
   thus , color and luminosity  measures of star formation history  appear to have a more fundamental relationship with environment than do surface brightness and concentration  measures of the distribution of stars within the galaxy . 
   some of the investigations above have explored the scale dependence of these relationships . 
   studies of the correlation function , such as @xcite and @xcite , can address this question , but do not address directly whether the density on large scales is related to galaxy properties _ independent _ of the relationships with density on small scales . 
   if only the _ masses _ of the host halos of galaxies strongly affect their properties , then we expect no such independent relationship between galaxy properties and the large scale density field . 
   thus , it is important to examine this issue in order to test the assumptions of the `` halo model '' description of galaxy formation and of semi - analytic models that depend only on the properties of the host halo ( _ e.g. _ , @xcite ) . 
   recent studies of this question have come to conflicting conclusions . 
   for example , @xcite have concluded from their analysis of sdss and 2dfgrs galaxies that the equivalent width of h@xmath4 is a function of environment measured on scales of 1.1 @xmath2 mpc and 5.5 @xmath2 mpc independently of each other . on the other hand , @xcite find that at fixed density at scales of 1 @xmath2 mpc , the distribution of d4000 ( a measure of the age of the stellar population ) is not a strong function of density on larger scales . 
   here we address the dependence on scale of the relative bias of sdss galaxies . 
   section [ data ] describes our data set . 
   section [ results ] explores how the relationship between the color , luminosity , and environments of galaxies depends on scale . 
   section [ bluefrac ] resolves the discrepancy noted in the previous paragraph between @xcite and @xcite , finding that only small scales are important to the recent star formation history of galaxies . 
   section [ summary ] summarizes the results .    where necessary 
   , we have assumed cosmological parameters @xmath5 , @xmath6 , and @xmath7 km s@xmath8 mpc@xmath8 with @xmath9 . 
   the sdss is taking @xmath10 ccd imaging of @xmath11 of the northern galactic sky , and , from that imaging , selecting @xmath12 targets for spectroscopy , most of them galaxies with @xmath13 ( e.g. , * ? ? ? 
   * ; * ? ? ? 
   * ; * ? ? ? 
   automated software performs all of the data processing : astrometry @xcite ; source identification , deblending and photometry @xcite ; photometricity determination @xcite ; calibration @xcite ; spectroscopic target selection @xcite ; spectroscopic fiber placement @xcite ; and spectroscopic data reduction . 
   an automated pipeline called idlspec2d measures the redshifts and classifies the reduced spectra ( schlegel et al . 
   , in preparation ) . 
   the spectroscopy has small incompletenesses coming primarily from ( 1 ) galaxies missed because of mechanical spectrograph constraints ( 6  percent ; * ? ? ? 
   * ) , which leads to a slight under - representation of high - density regions , and ( 2 ) spectra in which the redshift is either incorrect or impossible to determine ( @xmath14  percent ) . 
   in addition , there are some galaxies ( @xmath15  percent ) blotted out by bright galactic stars , but this incompleteness should be uncorrelated with galaxy properties .      for the purposes of computing large - scale structure and galaxy property statistics , we have assembled a subsample of sdss galaxies known as the nyu value added galaxy catalog ( nyu - vagc ; @xcite ) . 
   one of the products of that catalog is a low redshift catalog . 
   here we use the version of that catalog corresponding to the sdss data release 2 ( dr2 ) . 
   the low redshift catalog has a number of important features which are useful in the study of low luminosity galaxies . 
   most importantly :    1 . 
   we have checked by eye all of the images and spectra of low luminosity ( @xmath16 ) or low redshift ( @xmath17 ) galaxies in the nyu - vagc . 
   most significantly , we have trimmed those which are `` flecks '' incorrectly deblended out of bright galaxies ; for some of these cases , we have been able to replace the photometric measurements with the measurements of the parents . for a full description of our checks , 
   see @xcite . 
   2 .   for galaxies which were shredded in the target version of the deblending , 
   the spectra are often many arcseconds away from the nominal centers of the galaxy in the latest version of the photometric reductions . 
   we have used the new version of the deblending to decide whether these ( otherwise non - matched spectra ) should be associated with the galaxy in the best version . 
   we have estimated the distance to low redshift objects using the @xcite model of the local velocity field ( using @xmath18 ) , and propagated the uncertainties in distance into uncertainties in absolute magnitude .    for the purposes of our analysis below , we have matched this sample to the results of @xcite , who measured emission line fluxs and equivalent widths for all of the sdss spectra . 
   below , we use their results for the h@xmath4 equivalent width . 
   the range of distances we include is @xmath19 @xmath2 mpc , making the sample volume limited for galaxies with @xmath20 . 
   the total completeness - weighted effective area of the sample , excluding areas close to tycho stars , is 2220.9 square degrees . 
   the catalog contains 28,089 galaxies . @xcite 
   have investigated the luminosity function , surface brightness selection effects , and galaxy properties in this sample . 
   we will be studying the environments of galaxies as a function of their luminosity and color below . to give a sense of the morphological properties of galaxies with various luminosities and colors , figure [ color_mag ] 
   shows galaxies randomly selected in bins of color and luminosity . each image is 40 @xmath2 kpc on a side . 
   red , high luminosity galaxies are classic giant ellipticals . 
   lower luminosity red galaxies tend to be more flattened and less concentrated . 
   blue , high luminosity galaxies have well - defined spiral structure and dust lanes . 
   lower luminosity blue galaxies have less well - defined bulges and fewer spiral features .      in order to evaluate the environments of galaxies in our sample , we perform the following procedure .    first , for each given galaxy in the sample , we count the number of other galaxies @xmath21 with @xmath22 outside a projected radius of 10 @xmath2 kpc and within some outer radius @xmath23 , which we will vary below , and within @xmath24 km s@xmath8 in the redshift direction . 
   this trace catalog is volume - limited within @xmath25 . in order to make a more direct comparison to @xcite 
   , we will also use a trace catalog containing only galaxies with @xmath26 . 
   second , we calculate the mean expected number of galaxies in that volume as : @xmath27 where @xmath28 is the sampling fraction of galaxies in the right ascension ( @xmath4 ) and declination ( @xmath29 ) direction of each point within the volume . 
   we perform this integral using a monte carlo approach , distributing random points inside the volume with a density modulated by the sampling fraction @xmath28 .    in order to calculate the mean density around galaxies in various classes 
   , we will simply calculate : @xmath30 as the density with respect to the mean . 
   when one calculates the mean density around galaxies , it is necessary to have a fair sample of the universe . for the most luminous galaxies in our sample ( @xmath31 ) the sample is volume - limited out to our redshift limit of @xmath32 and constitutes the equivalent of a 60 @xmath2 mpc radius sphere , which constitutes a fair sample for many purposes ( @xmath33cdm predicts a variance in such a sphere to be about 0.13 ) . 
   however , the lower luminosity galaxies can only be seen in the fraction of this volume which is nearby , and below a certain luminosity the sample is no longer fair . 
   for example , consider figure [ check_rho_converge ] , which shows the cumulative mean density around galaxies with @xmath34 in spheres of larger and larger radius around the milky way . 
   the mean overdensity does not converge until a volume which corresponds to approximately @xmath35 . 
   thus , it is not really safe to evaluate the mean density around galaxies that are too low luminosity to be observed out that far in redshift , which is to say , less luminous than @xmath36 .    however , for the moment let us consider figure [ biden_all ] . 
   the greyscale and contours show the mean density relative to the mean as a function of color and luminosity , using a projected radius of @xmath37 @xmath2 mpc . 
   the mean is calculated in a sliding box with the width shown . 
   if the sliding box contains fewer than 20 galaxies , the result is ignored and colored pure white . here 
   we show the results for the entire sample . 
   our statistical uncertainties are well - behaved down to about @xmath38 , but we are likely to be cosmic variance limited for @xmath39 , as indicated by the solid vertical line . 
   thus , the apparent decline in the mean overdensity for red galaxies lower luminosity than @xmath40 is probably spurious . despite that limitation , 
   we note that there is a strong relationship between environment and color even at @xmath41 . 
   we note in passing that we can still use the variation of the density within @xmath42 to study the properties of galaxies as a function of density down to low luminosity . 
   just because the _ mean _ density of galaxies in that volume has not converged does _ not _ imply that there is insufficient variation of density to study the variation of galaxy properties with environment .    for our fair sample of galaxies with @xmath43 , 
   figure [ biden_scales ] shows the dependence of overdensity on luminosity and color for six different projected radii : 0.2 , 0.5 , 1 , 2 , 4 , and 6 @xmath2 mpc . 
   we only show results for @xmath44 , for which we have a fair sample . 
   obviously , the density contrast decreases with scale ; on the other hand , the qualitative form of the plot does not change . 
   our results remain similar to those shown in @xcite and @xcite . 
   the results here demonstrate that the environments of low luminosity , red galaxies do continue to become denser as absolute magnitude increases down to absolute magnitudes of @xmath45 ( about two magnitudes less luminous than explored by our previous work ) . 
   figure [ biden_ratios ] shows the ratio of the overdensity @xmath29 at each scale relative to that at the largest scale of @xmath46 @xmath2 mpc . this ratio is a measure of the steepness of the cross - correlation between galaxies of a given color and absolute magnitude with _ all _ galaxies in our volume - limited sample ( @xmath47 ) . 
   interestingly , the contours in steepness are qualitatively similar to the contours in overdensity in figure [ biden_scales ] . 
   this similarity implies that for each class of galaxy , the strength of the correlation on large scales always is associated with a _ steeper _ correlation function . 
   another way of looking at similar results is to ask , as a function of environment , what fraction of galaxies are blue . 
   we split the sample into `` red '' and `` blue '' galaxies using the following , luminosity - dependent cut : @xmath48 blue galaxies thus have @xmath49 . 
   we then sort all the galaxies with @xmath50 into bins of density on three different scales : @xmath51 , @xmath52 , and @xmath53 @xmath2 mpc . in each bin 
   we calculate the fraction of blue galaxies . 
   figure [ lowz_fracblue ] shows this blue fraction as a function of density . in all cases , the blue fraction declines as a function of density , as one would expect based on figure [ biden_scales ] above , and from the astronomical literature ( a highly abridged list of relevant work would include @xcite ) . 
   if we divide the sample into bins of luminosity , we find that higher luminosities have smaller blue fractions ( of course ) but that the dependence of blue fraction on density does not change . 
   the question naturally arises : _ which _ scales are important to the process of galaxy formation ? 
   is the local environment within 0.5 @xmath2 mpc the only important consideration ? or is the larger scale environment also important ? 
   for example , consider figure [ denvden ] , which shows the conditional dependence of the three density estimators at the three scales on each other . the diagonal plots simply show the distribution within our sample of each density estimator . 
   the off - diagonal plots show the conditional distribution of the quantity on the @xmath54-axis given the quantity on the @xmath55-axis . as an example 
   , the lower right panel shows @xmath56 shows the fraction of blue galaxies as a function of two density estimates : one with @xmath51 @xmath2 mpc and one with @xmath57 @xmath2 mpc . in this case 
   it is clear that the blue fraction is a function of both densities . 
   that is , even at a fixed density on scales of @xmath37 @xmath2 mpc , the density outside that radius matters to the blue fraction ; in addition , at a fixed density on scales of @xmath52 @xmath2 mpc , the distribution of galaxies within that radius appears to affect the blue fraction as well .    on the other hand , 
   consider figure [ lowz_fracblue2_1.0 - 6.0 ] , which is the same as figure [ lowz_fracblue2_0.5 - 1.0 ] , but now showing the densities at scales of @xmath57 and @xmath53 @xmath2 mpc . in figure 
   [ lowz_fracblue2_1.0 - 6.0 ] the contours are vertical , indicating that the density between @xmath52 and @xmath53 @xmath2 mpc has very little effect on galaxy properties . at a fixed value of the density at the smaller scale , 
   the larger scale environment appears to be of little importance . 
   @xcite found that these contours were not vertical when he looked at the fraction of galaxies for which the h@xmath4 equivalent width was @xmath58  . 
   their result appears in conflict with that of the previous paragraph . 
   on the other hand , the emission lines measure a more recent star formation rate than does the color ; it is possible in principle that the more recent star formation rate depends more strongly on large - scale environment . to rule out this possibility , 
   figure [ lowz_frachalpha2_1.0 - 6.0 ] shows the same result as figure [ lowz_fracblue2_1.0 - 6.0 ] , but now showing the fraction of galaxies with h@xmath4 equivalent widths ( as measured by @xcite ) greater than 4  . 
   again , for strong emission line fraction as for the blue fraction , the smaller scales are important , but the 6 @xmath2 mpc scales are not , in contradiction with @xcite . 
   why , then , did @xcite conclude that large scales _ were _ important ? 
   there are a number of differences between our study and theirs . 
   first , their contouring method differs ; instead of measuring the blue fraction in bins of fixed size , at each point they measure the star - forming fraction among the nearest 500 galaxies in the plane of @xmath59 and @xmath60 . we have found that this procedure creates a _ slight _ bias in the contouring in the sense that near the edges of the distribution vertical contours will become diagonal . 
   however , this effect is not strong enough to explain the differences between our results and those of @xcite . 
   second , to estimate the density in their sample they used a spherical gaussian filter , whereas here we use the overdensity in cones . 
   we have not investigated what effect this difference has . 
   finally , they use tracer galaxies with a considerably lower mean density than ours . 
   their effective absolute magnitude limit is @xmath61 ; such galaxies have a mean density of @xmath62 @xmath63 mpc@xmath64 . 
   our tracers ( @xmath22 ) have a mean density of @xmath65 @xmath63 mpc@xmath64 , almost six times higher . 
   figure [ lowz_frachalpha2_m-20.5_1.0 - 6.0 ] shows our results when we restrict our tracer sample to @xmath61 . 
   the contours in this figure are very diagonal , similar to the results of @xcite . 
   this result suggests that one of two possible mechanisms are causing the differences between our results and those of @xcite . 
   first , the higher luminosity galaxies with @xmath61 might be yielding fundamentally different information about the density field than our lower luminosity tracers . 
   second , the lower mean density of the galaxies with @xmath61 might be effectively introducing `` noise '' in the measurement on small scales . 
   remember that the large scale and small scale densities are intrinsically correlated . 
   so if the small scale measurement is noisy enough , the higher signal - to - noise ratio large scale measurement could actually be adding extra information about the environment on _ small _ scales . 
   such an effect would make the contours in figure [ lowz_frachalpha2_m-20.5_1.0 - 6.0 ] diagonal . 
   we have performed a simple test to distinguish these possibilities , which is to remake figure [ lowz_frachalpha2_1.0 - 6.0 ] using the low luminosity tracers ( @xmath66 ) but subsampling them to the same mean density as the high luminosity tracers ( @xmath67 ) . this test yields diagonal contours , meaning one can understand the diagonal contours of figure [ lowz_frachalpha2_m-20.5_1.0 - 6.0 ] and of @xcite as simply reflecting the low signal - to - noise ratio of the density estimates . 
   we explore the relative bias between galaxies as a function of scale , finding the following .    1 .   the dependence of mean environment on color persists to the lowest luminosities we explore ( @xmath68 ) . 
   red , low luminosity galaxies tend to be in overdense regions , down at least to @xmath69 . 
   this result extends those found by @xcite and @xcite towards lower luminosities by about 2 magnitudes . 
   3 .   at any given point of color and luminosity , a correlation function with a stronger amplitude implies correlation function with a steeper slope . 
   4 .   in regions of a given overdensity on small scales ( @xmath70 @xmath2 mpc ) , the overdensity on large scales ( @xmath46 @xmath2 mpc ) does not appear to relate to the recent star formation history of the galaxies . 
   the last point above deserves elaboration . 
   first , it contradicts the results of @xcite . 
   we have found that their results are probably due to the low mean density of the tracers they used . 
   this explanation underscores the importance of taking care when using low signal - to - noise quantities . 
   galaxy environments are difficult to measure , in the sense we use tracers that do not necessarily trace the `` environment '' perfectly , meaning neither with low noise nor necessarily in an unbiased manner . 
   we claim here that our higher density of tracers marks an improvement over previous work , but it is worth noting the limitations of assuming that the local galaxy density fairly and adequately represents whatever elements of the environment affect galaxy formation . 
   second , if the galaxy density field is an adequate representation of the environment , the result has important implications regarding the physics of galaxy formation . in simulations 
   whose initial conditions are constrained by cosmic microwave background observations and galaxy large - scale structure observations , virialized dark matter halos do not extend to sizes much larger than @xmath71@xmath72 @xmath2 mpc . 
   thus , our results are consistent with the notion that only the masses of the host halos of the galaxies we observe are strongly affecting the star formation of the galaxies . 
   in addition , @xcite find that only the star formation histories , not the azimuthally - averaged structural parameters , are directly related to environment . 
   for these reasons , it is likely that we can understand the process of galaxy formation by only considering the properties of the host dark matter halos . 
   our results therefore encourage the `` halo model '' description of galaxy formation and the pursuit of semi - analytic models which depend only on the properties of the host halo ( _ e.g. _ , @xcite ) . 
   thanks to eric bell and george lake for useful discussions during this work . thanks 
   to guinevere kauffmann for encouraging us to pursue this question . 
   thanks to christy tremonti and jarle brinchmann for the public distribution of their measurements of sdss spectra . 
   funding for the creation and distribution of the sdss has been provided by the alfred p. sloan foundation , the participating institutions , the national aeronautics and space administration , the national science foundation , the u.s . 
   department of energy , the japanese monbukagakusho , and the max planck society . 
   the sdss web site is http://www.sdss.org/.    the sdss is managed by the astrophysical research consortium ( arc ) for the participating institutions . 
   the participating institutions are the university of chicago , fermilab , the institute for advanced study , the japan participation group , the johns hopkins university , los alamos national laboratory , the max - planck - institute for astronomy ( mpia ) , the max - planck - institute for astrophysics ( mpa ) , new mexico state university , university of pittsburgh , princeton university , the united states naval observatory , and the university of washington .          , m. , eke , v. , miller , c. , lewis , i. , bower , r. , couch , w. , nichol , r. , bland - hawthorn , j. , baldry , i.  k. , baugh , c. , bridges , t. , cannon , r. , cole , s. , colless , m. , collins , c. , cross , n. , dalton , g. , de propris , r. , driver , s.  p. , efstathiou , g. , ellis , r.  s. , frenk , c.  s. , glazebrook , k. , gomez , p. , gray , a. , hawkins , e. , jackson , c. , lahav , o. , lumsden , s. , maddox , s. , madgwick , d. , norberg , p. , peacock , j.  a. , percival , w. , peterson , b.  a. , sutherland , w. , & taylor , k. 2004 , , 348 , 1355
summary: we investigate the relationship between the colors , luminosities , and environments of galaxies in the sloan digital sky survey spectroscopic sample , using environmental measurements on scales ranging from @xmath0 to @xmath1 @xmath2 mpc . 
   we find : ( 1 ) that the relationship between color and environment persists even to the lowest luminosities we probe ( @xmath3 ) ; ( 2 ) at luminosities and colors for which the galaxy correlation function has a large amplitude , it also has a steep slope ; and ( 3 ) in regions of a given overdensity on small scales ( 1 @xmath2 mpc ) , the overdensity on large scales ( 6 @xmath2 mpc ) does not appear to relate to the recent star formation history of the galaxies . of these results , the last has the most immediate application to galaxy formation theory . in particular 
   , it lends support to the notion that a galaxy s properties are related only to the mass of its host dark matter halo , and not to the larger scale environment .