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understanding when and how massive galaxies form is one of the most outstanding problems in cosmology and galaxy formation .
galaxies are predicted in cold dark matter based models of structure formation to form gradually with time through the merging of smaller systems ( e.g , .
cole et al .
2001 ) . while there is some evidence for this process , in terms of galaxies ( e.g. , patton et al . 2002 ; conselice et al .
2003 ; bridge et al .
2007 ) , many details are still lacking . alternatively ,
massive galaxies , which are mostly ellipticals in today s universe ( e.g. , conselice 2006a ) , may have formed very rapidly in ` monolithic ' collapses .    a such , massive galaxies are the dominant test - bed for galaxy models , and understanding their evolution observationally is an important goal .
most massive galaxies at @xmath7 are red and passively evolving , yet star formation and merging activity have been seen in ellipticals from @xmath8 to @xmath1 ( stanford et al . 2004 ; lin et al . 2004 ; teplitz et al . 2006 ; conselice et al .
2007a , b ) - thus it is unclear when or how massive galaxies finally assembled .
we must study this process at high redshift since the ages of stars in nearby galaxies can not reveal their entire formation history , as the assembly of mass is likely decoupled from the formation of stars ( e.g. , conselice 2006b ; trujillo et al .
2007 ) .
observational evidence suggests that passively evolving massive galaxies exist at @xmath1 , and likely at even early times , at @xmath9 ( daddi et al .
2004 ; saracco et al . 2005
; bundy et al . 2006 ; conselice et al .
recent claims also exist for the establishment of the full massive galaxy population by @xmath1 ( e.g. , drory et al . 2005 ; bundy et al .
however , what is not yet clear is if number densities measured in these surveys are able to rule out evolution at @xmath7 after considering uncertainties in measuring stellar masses , number densities , and cosmic variance .    on the other hand , at @xmath10
it appears that there are significantly fewer massive galaxies than at @xmath3 ( e.g. , drory et al . 2005 ) .
observationally , the most massive galaxies at @xmath10 are undergoing major mergers , which are able to construct the stellar masses of massive galaxies rapidly ( conselice 2006b ; conselice et al .
the situation at @xmath3 is not as clear , with observations inconclusive on whether there is evolution in the massive galaxy population at @xmath7 ( e.g. , brown et al . 2006 ) .
we argue here that by using a stellar mass selected sample of galaxies the number and mass densities of massive galaxies are consistent , within their errors , with no evolution at @xmath3 , yet there is observable evolution when examining in detail the physical processes occurring within these galaxies . up to 50% of galaxies with m@xmath0
are undergoing star formation at @xmath1 , and roughly one major merger occurs within these systems at @xmath11 .
we assume throughout a standard cosmology of h@xmath12 km s@xmath13 mpc@xmath13 , and @xmath14 .
the most basic method for calculating the evolution of galaxies is measuring how their number densities and integrated stellar mass densities change as a function of time .
recent work on measuring densities suggests that within the measurement uncertainties galaxies with stellar masses m@xmath0 , are largely in place at @xmath1 ( bundy et al .
2005 , 2006 ) .
figure  1 shows the most up to date version of how the number and mass densities of galaxies with stellar masses m@xmath15 and @xmath16  @xmath17  m@xmath18 evolve out to @xmath19 , as seen in the 1.5 deg@xmath20 palomar observatory wide - field infrared survey ( powir ; conselice et al . 2007a ; conselice et al .
2008b ) covering the deep2 fields
( davis et al . 2007 ) from conselice et al . ( 2007b ) using a chabrier imf .
the number density evolution of these massive galaxies shows that statistically there is very little to no evolution at @xmath7 for the m@xmath0 systems .
this appears to support the idea that nearly all massive galaxies are present by @xmath1 ( e.g. , bundy et al .
2006 ) .
however , as can be seen within the observational errors of figure  1 , there is potentially evolution in number densities for m@xmath0 selected galaxies between @xmath21 .
galaxies with m@xmath0 show an increase in number densities between @xmath22 to 0.4 of a factor of 2.7@xmath23 .
this is however significant only at the @xmath24 level , considering all uncertainties ( conselice et al .
a similar result is found for the mass densities of galaxies with m@xmath0 , and it is impossible to rule out that massive galaxies with m@xmath0 are all in place at @xmath25 ( conselice et al .
however , as for the star - formation downsizing described in e.g. , bundy et al .
( 2006 ) there is also a stellar mass downsizing , such that lower mass galaxies are formed after higher mass ones .
the number densities of systems with @xmath16 @xmath17 m@xmath26 increases by a factor of 2.2@xmath27 between @xmath28 and @xmath29 , a result significant at @xmath30 4  @xmath31 . just as for the most massive systems , this evolution occurs completely at @xmath32 ( conselice et al .
2007b ) . taken as a whole
, we calculate that the scenario whereby the stellar mass and number densities of massive galaxies does not evolve between @xmath33 to @xmath34 can be rejected at @xmath35 @xmath31 confidence . through a careful analysis of number densities
it does not appear that high mass galaxy formation , with the possible exception of m@xmath0 systems , is complete by @xmath33 .
there could be a factor of @xmath36 evolution in the mass and number densities for massive galaxies at @xmath7 due to measurement uncertainties .
we note that the millennium simulation underpredicts the densities of these massive galaxies by a large factor ( figure  1 ) , demonstrating how difficult it is to model these systems .
one way to understand the star formation history of massive galaxies is to examine their position on color - magnitude diagrams .
conselice et al .
( 2007b ) find that 35@xmath44% of galaxies with m@xmath0 at @xmath1 are blue in color and not on the red sequence , and thus must be undergoing unobscured star formation .
previous studies have examined the increase in the amount of stellar mass on the red - sequence , finding as much as a factor of two increase since @xmath1 ( faber et al .
2007 ; brown et al . 2007 )
. however , this increase is due to galaxies appearing on the red - sequence , which were previously blue , and not due to in - situ growth on the red - sequence itself due to e.g. , dry mergers .
this can be seen through massive galaxies gradually moving onto the red - sequence with time , as the number of blue massive galaxies declines at @xmath7 ( e.g. , bundy et al .
2006 ; conselice et al .
2007b ) .    quantifying the ongoing rate of star formation in massive galaxy samples can be done in several ways , including rest - frame uv emission , emission line fluxes , and spitzer mips 24@xmath37 m data
. a surprisingly higher fraction of massive galaxies are detected in the mid - infrared compared with the fraction which are blue .
conselice et al .
( 2007b ) find that @xmath3840% of the m@xmath0 systems at @xmath39 are detected in 24@xmath37 m mips data after removing those systems which are detected by chandra .
a total of 37@xmath40% of the systems at m@xmath0 are detected at 24 @xmath37 m , with an average star formation rate of 70 yr@xmath13 .
conselice et al .
( 2007b ) find , similar to previous studies utilising ir star formation indicators , a decline with redshift in star formation occurring within the massive galaxy population . for systems with m@xmath0 the star formation rate declines as @xmath41 , and for systems with @xmath17 m@xmath42 @xmath17 as @xmath43 .
the overall decline in the entire galaxy population s star formation history can be parameterised as @xmath44 .
it appears that while the @xmath17 m@xmath42 @xmath17 galaxies have a similar decline as the overall field , the highest mass galaxies decline at a faster rate .
the number and mass densities of the most massive galaxies are significantly lower at @xmath9 than at lower redshifts . while the star formation rate in these massive galaxies may be low ( e.g. , krick et al .
2006 ) , mergers are likely the major method for forming these galaxies . examining the structural cas and other parameters ( conselice et al .
2000,2002 ; conselice 2003 ; ravindranath et al .
2006 ) for galaxies at @xmath45 reveals that mergers produce the rapid growth in massive galaxies at @xmath46 ( conselice et al .
2003 , 2005 ; conselice 2006b ; conselice et al .
2008a ) .
what is not yet clear is the role mergers play in massive galaxy formation at @xmath3 , particularly dry mergers that are not easily identifiable through structure .
one method of measuring the amount of merging is by examining changes in the number and mass densities of galaxies as a function of time after accounting for growth due to star formation ( figure  2 ; conselice et al .
conselice et al .
( 2007b ) find that 12% of galaxies with  @xmath17  m@xmath47  merge between @xmath48 , and enter the higher mass bin . at @xmath49
this merger fraction drops to 8% .
this is consistent with the cas merger fractions ( e.g. , conselice et al .
2003 ) for the same galaxies , and previous published results using smaller galaxy samples ( e.g. , conselice et al . 2003
; lin et al . 2004 ; bridge et al . 2007 ) .
this corresponds to a merger rate giving n@xmath50 mergers for m@xmath0 systems at @xmath39 , roughly doubling the mass of these galaxies during this time .
while massive galaxies can be identified up to @xmath51 using deep nir imaging , the evolution of these galaxies is difficult to measure within a factor of 2 - 3 using simply luminosity or mass functions . by examining the change in the mass function , and through structural parameters and mips 24 @xmath37 m and [ oii ] line emission
we show that massive galaxies are still undergoing some evolution , with at least as much as a factor of two increase in stellar mass at @xmath11 from star formation and merging .
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observing massive galaxies at various redshifts is one of the most straightforward and direct approaches towards understanding galaxy formation . 
 there is now largely a consensus that the massive galaxy ( m@xmath0 ) population is fully formed by @xmath1 , based on mass and luminosity functions . 
 however , we argue that the latest data can only rule out number and mass density evolution of a factor of @xmath2 at @xmath3 . 
 we furthermore show that the star formation history of m@xmath0 galaxies reveals that 40@xmath45% of galaxies with m@xmath0 at @xmath1 are undergoing star formation that effectively doubles their stellar mass between @xmath5 . 
 these massive galaxies also undergo 0.9@xmath6 major mergers during this same time period .