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that early - type galaxies form a well - defined color magnitude relation ( cmr ) was first recognized by @xcite .
extensive studies by @xcite and @xcite compared the cmr of nine galaxy clusters and of field galaxies .
they found them to be astonishingly similar . in combination with other studies comparing the cmr for e and s0 , within clusters , groups and the field @xcite a high degree of universality
was shown for the relation .
the cmr is typically explained by an increase of mean stellar metallicity with increasing galaxy mass as the dominant effect .
the common underlying idea is that more massive galaxies have deeper potential wells , which can retain metal - enriched stellar ejecta more effectively and subsequently recycle the enriched gas into new stars .
another factor could be a variable integrated galactic initial mass function , with more massive stars in more massive galaxies , and thus a more substantial enrichment ( e.g.  ) .
an alternative explanation was given with a change of the mean age ( see e.g. @xcite , and some observational support for it in @xcite ) .
the question of which explanation to favor is not totally settled yet due to the ambiguity introduced by the age - metallicity degeneracy . but
data from clusters at higher redshift show that the cmr is in place ever since , favoring the mass - metallicity relation to be the dominant effect .    from early on
, it was discussed whether the universality of the cmr also holds over the whole range of galaxy masses , i.e.  whether dwarf and giant early - type galaxies follow the same cmr .
studies of different clusters show consistency with one common cmr for dwarfs and giants , albeit with a significant increase in the scatter at low luminosities ( @xcite for coma , @xcite for perseus , @xcite and for fornax , @xcite for antlia and for hydra i ) .
more explicitely , @xcite stated that there is a common linear relation .
but his fig .
3 might hint at a change of slope from high to low luminosities , similar to what @xcite suggested .
interestingly , visual examination of the diagrams presented by most of the above - mentioned studies indicates consistency also with a change of slope 
yet linear relations were fitted in most cases ( see , however , @xcite ; see sect .
5 ) . in this letter
we revisit the question of the universality of the cmr for dwarfs and giants .
the sample is based on the virgo cluster catalog ( vcc ; @xcite ) .
all early - type galaxies therein with a certain cluster member status and @xmath4 mag are taken into account , which is the same magnitude limit up to which the vcc was found to be complete .
this translates into @xmath5 mag with our adopted distance modulus of m - m=31.09 mag ( d=16.5 mpc , @xcite ) .
we treat uncertain classifications as in @xcite and exclude possible irregulars .
seven further galaxies are exluded due to their low @xmath6 in @xmath7 and @xmath8 .
the sloan digital sky survey ( sdss ) data release five ( dr5 ) @xcite covers all but six early - type dwarf galaxies of the vcc . since the quality of sky level subtraction of the sdss pipeline is insufficient , we use sky - subtracted images as provided by @xcite , based on a careful subtraction method .
the images were flux - calibrated and corrected for galactic extinction @xcite .    for each galaxy , we determined a 
petrosian semimajor axis " ( @xcite , hereafter petrosian sma , @xmath9 ) , i.e. , we use ellipses instead of circles in the calculation of the petrosian radius ( see , e.g. , @xcite ) .
the total flux in the @xmath10-band was measured within @xmath11 , yielding a value for the half - light semimajor axis , @xmath12 .
this petrosian aperture still misses some flux , which is of particular relevance for the giant galaxies @xcite .
the brightness and the half - light sma were corrected for this missing flux according to @xcite .
axial ratio and position angle were then determined through an isophotal fit at @xmath13 .
colors were measured within the elliptical @xmath10-band half - light aperture for each filter .
errors were estimated from the @xmath6 and calibration uncertainties ( which we estimate to have a _ relative _ effect of 0.1 mag in each band , which is smaller than the absolute values given by sdss ) , as described in @xcite .
our data constitute a very homogeneous set of measurements for galaxies in one cluster , obtained and reduced with the same instrument , setup , and software .
from the five sdss filter bands we choose four representative colors : @xmath0 , mostly sensitive to age ; @xmath1 with the highest @xmath6 ; @xmath2 with the longest wavelength baseline at good @xmath6 ; and @xmath3 , mostly sensitive to metallicity .
first of all , the impression one can get by examining just the _ black points _ in fig .  1 is that there is not one common linear relation from the faint to the bright galaxies . in all colors
the overall shape appears more like `` s '' shaped .
the brightest ( @xmath14 ) galaxies have almost constant color , i.e.  no correlation between color and brightness ; the very brightest galaxies show a larger scatter .
these were reported before to be _ morphologically _ different from the other galaxies in more detailed studies of the inner light profiles ( e.g. @xcite ) . for the remaining galaxies several descriptions seem to be plausible , ranging from just an offset between two relations with similar slopes up to a curved relation .    with the non - linear shape , it seems not very favorable to fit a straight line .
this would not describe the data well , and there is no theoretical prediction what other function is expected .
so at first , we want to make the overall shape more clearly visible , using continous , overlapping magnitude bins , in which mean and scatter are calculated . in fig .
1 these derived relations are shown with grey lines .
the first impression is confirmed : one common linear relation for dwarfs and giants can not be seen .
moreover , the white histograms showing the galaxy distributions in the bins are clearly peaked towards the bright and the faint end , while they are rather flat at intermediate luminosity .
if the notion of two separate relations with an overlap is correct , this should become evident through an increased scatter about the relation around the intersection , relative to the photometric error .
therefore we calculate the rms of the scatter around the mean in running bins ( clipping one time at 3@xmath15 ) and divide it by the rms of the photometric errors @xmath16 with color @xmath17 and mean color @xmath18 , averaging over the galaxies in the respective bin . here
we exclude des with blue cores , since they are known to have different colors @xcite
. this rms - ratio should be one if the scatter is only due to the measurement errors and larger than one if there is an intrinsic scatter . in fig .  1 we show the cmrs along with the rms - ratio @xmath19 .    indeed , the rms - ratio is enhanced between @xmath20 , indicating an intrinsically increased scatter , which could in principle be explained by a transition between two separate relations .
but the change is steady .
thus also alternative explanations , such as a more varied star formation history with decreasing galaxy mass , seem plausible  although the decrease in the scatter for the faintest dwarfs would still need to be explained .    one can argue about the significance of the rms - ratio increase for the brightest galaxies , since it is just a handful of them  nevertheless , this larger scatter might be related to the absence of a well - defined cmr at the brightest magnitudes .
the numerical galaxy catalog of @xcite is based on a high resolution @xmath21-body simulation in a @xmath22cdm universe @xcite .
the dark - halo merger trees of the @xmath21-body simulation are taken as input for a semi - analytical model ( sam ) of galaxy formation ( here a modified version of the mitaka model , @xcite ) .
the sam models physical processes of galaxy formation and evolution such as gas radiative cooling , star formation , heating by supernova explosions ( supernova feedback ) , mergers of galaxies , population synthesis , and extinction by internal dust and intervening hi clouds .
in particular , the model takes into account the dynamical response to starburst - induced gas removal after gas - rich mergers ( also for cases intermediate between a purely baryonic cloud and a baryonic cloud fully supported by surrounding dark matter as in ) .
the gravitational well is shallower for the dwarf galaxies and thus they suffer a more substantial gas loss than giants .
this process is not only important for the galaxy sizes , but also for their metal enrichment histories .    in the comparison of the cmr of the virgo galaxies with the sam ( fig .
2 ) , the shapes of the distributions are fairly similar , and the model cmr is indeed not well represented by a linear relation . in @xcite we presented an analogous comparison for the scaling relation of radius and brightness and found that the model qualitatively agrees with distribution of the galaxies in that diagram . both the cmr and the relation between size and brightness do not show a linear , nor one common behaviour for dwarfs and giants .
nevertheless , in the framework of the sam both can be explained by the same physical processes , which govern @xmath22cdm structure formation , and thus both can be of cosmological origin ( see also @xcite ) .    beside the good agreement in the overall shape , an offset is observed .
this offset could partly be due to uncertainties of the adopted synthetic stellar population model .
vs. @xmath23 ( for which no transformations are needed ) the observed galaxies lie bluewards of the model ones with an smaller absolute offset than in @xmath24 vs. @xmath25 , but the scatter of the observed galaxies is larger due to the lower @xmath6 in the @xmath8-band . ]
furthermore , the relative number of bright galaxies exceeds the observed one and the luminosity function is clearly different , which could possibly be explained with model input physics .
in the literature , there is no consistent view of commonness or distinctness of the color magnitude relation of dwarf and giant early - type galaxies .
some studies find a linear relation over the whole range of brightness , others find a change of slope .
we studied the cmr of virgo cluster early - type galaxies , based on the wealth of sdss imaging data in multiple filter bands .
our main result is that the dwarfs and giants do not follow one common _ linear _ relation .
the appearance in the different colors , from @xmath0 to @xmath3 , is very similar , suggesting that age and metallicity go hand in hand : the cmr at shorter wavelengths is more sensitive to changes in age , while it is more sensitive to changes in metallicity at longer wavelengths .
recent studies indeed claim that a combination of the effects of age , metallicity and also @xmath26-enhancement shape the cmr @xcite .
the most direct comparison with other data is possible with @xcite , who studied early - type galaxies in the virgo cluster with the hubble space telescope s advanced camera for surveys ( acs ) in the acs virgo cluster survey . in their fig .
123 they show the cmr in @xmath27 , using smaller apertures for the color measurements .
for comparison we repeat the plot and indicate galaxies common to both samples with black dots in the symbols ( fig .  3 ) .
we also show their fits ( to their data ) : two linear fits to a brighter and fainter subsample and one parabola for the whole sample .
while a qualitatively good agreement is found , the small offset to bluer colors of our data is likely explained by a combination of the effect of different apertures , the atmosphere , and different physical filters . while we agree with @xcite that the cmr is not linear over the whole range , the faint dwarfs in our sample , which they do not reach ( cf .
3 ) , do not lie on the extrapolation of their parabolic fit , but rather define an overall `` s''-like shape .
furthermore , some of the galaxies that might drag their cmr to the blue side , at their faint end , display blue cores from recent star formation activity @xcite , which we excluded .
we found an increase of the scatter about the cmr at intermediate brightness , visible in fig .  1 through a broadening of the color distributions within the respective magnitude bins .
this confirms the result that dwarfs and giants do _ not _ share one common _ linear _ cmr . for the brighter and fainter galaxies
the scatter is closer to the photometric errors .
@xcite concluded that the cmr is a result of two more fundamental relations : the faber - jackson relation and a relation between color and velocity dispersion .
given the slope change of the faber - jackson relation from giants to dwarfs a change of slope of the cmr would actually be expected .
it is important to emphasize that the curved shape of the cmr , and the possible existence of two adjacent relations does _ not _ necessarily imply different formation scenarios of dwarfs and giants .
this is in accordance with previous claims of no distinction between them ( ) . instead , from the good qualitative agreement of the observed cmr shape with a semi - analytic model ,
we conclude that a common origin within the framework of @xmath22cdm structure formation appears plausible for both giant _ and _ dwarf early types .
a more detailed multiparameter comparison of dwarfs and giants will be communicated in a forthcoming paper .
we thank masahiro nagashima for helpful advice , and the referee for useful comments . we are supported within the framework of the excellence initiative by the german research foundation ( dfg ) through the heidelberg graduate school of fundamental physics ( grant number gsc 129/1 ) .
the study is based on sdss ( http://www.sdss.org/ ) .
in this letter we present a study of the color magnitude relation of 468 early - type galaxies in the virgo cluster with sloan digital sky survey imaging data . 
 the analysis of our homogeneous , model - independent data set reveals that , in all colors ( @xmath0 , @xmath1 , @xmath2 , @xmath3 ) similarly , giant and dwarf early - type galaxies follow a continuous color magnitude relation ( cmr ) that is best described by an s - shape . 
 the magnitude range and quality of our data allows us to clearly confirm that the cmr in virgo is not linear . 
 additionally , we analyze the scatter about the cmr and find that it increases in the intermediate - luminosity regime . 
 nevertheless , despite this observational distinction , we conclude from the similarly shaped cmr of semi - analytic model predictions that dwarfs and giants could be of the same origin .