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the basic picture of galaxy formation and evolution in the cosmological context can be explained in the standard @xmath1 cold dark matter ( cdm ) cosmology .
particularly , large scale clustering properties and formation and evolution of dark matter halos can reliably be predicted by the theory of gravity .
however , in order to obtain the full picture of cosmological galaxy formation , we must solve complicated processes of baryonic physics , such as gas cooling , star formation , feedback , galaxy mergers , and so on .
one of the key observables about galaxies that must be explained by the theory of cosmological galaxy formation is the luminosity functions ( lfs ) and their evolution .
compared with the shape of dark matter halo mass function predicted by the @xmath1cdm cosmology , the observed galaxy lfs have two remarkable features : flatter faint - end slopes and sharp exponential cut - off at the luminous / massive end ( see benson et al .
2003 and references therein ) , which must be explained by some baryonic processes .
a widely accepted solution to achieve a flat faint end is supernova feedback , i.e. , energy input into the interstellar medium by supernova explosions to suppress star formation in small galaxies .
however , the problem is not yet completely solved at the quantitative level .
in fact , unreasonably high efficiency of supernova feedback to remove cold interstellar gas in dwarf galaxies is necessary in many existing theoretical models to reproduce the observed flat faint ends , and such an extreme supernova feedback tends to produce discrepancies with observations other than luminosity function shapes ( nagashima & yoshii 2004 , hereafter ny04 ; nagashima et al .
2005 ; bower et al .
2006 , 2012 ; guo et al .
2011 ; wang , weinmann & neistein 2012 ; mutch , poole & croton 2013 ; puchwein & springel 2013 ; hopkins et al .
these results imply that another physical effect may also be taking an important role to produce the observed flat faint end slopes .    for the massive end ,
a popular solution to suppress the formation of too massive galaxies is the feedback by active galactic nuclei ( agns ; e.g. , bower et al .
2006 ; croton et al .
2006 ; menci et al .
2008 ; somerville et al . 2008 ; guo et al . 2011 ) .
the agn feedback can also explain the observed trends of the early appearance of massive and quiescent galaxies at high redshifts , and downsizing of star - forming galaxies from high to low redshifts , which are apparently in contradiction with the simple expectation in the @xmath1cdm universe ( e.g. , bower et al .
2006 ; somerville et al .
2008 ) . however , there are large uncertainties about the physics of agn feedback both in theoretically and observationally .
the current success in explaining the observed trends by this process is based on rather phenomenological modelings including highly uncertain parameters , and further studies are required to confirm the quantitative influence of this process on galaxy evolution .
therefore it is still worth to explore yet other physical effects working to shape galaxy lfs , which is the aim of this paper .
it is reasonable to expect that such an effect would be manifested in the scaling laws about star formation efficiency .
the relation between the surface densities of star formation rate ( sfr ) and gas ( @xmath2-@xmath3 ) has been a subject of intensive research .
it is popular to fit this relation by a power - law ( so - called kennicutt - schmidt law , kennicutt 1998 ) , but recent observations indicate a cut - off around the total ( i.e. , + h@xmath4 ) gas density of @xmath5 , under which sfr is suppressed and not well correlated with gas density .
this threshold gas density for sfr can be interpreted as a result of less efficient formation of cold molecular gas under the threshold , while the star formation efficiency ( sfe ) from molecular gas is rather universal in many different environments ( wong & blitz 2002 ; kennicutt et al .
2007 ; bigiel et al . 2008 , 2010 ; leroy et al . 2008
; blanc et al . 2009 ; heiderman et al . 2010 ; lada et al .
2010 , schruba et al . 2011
; see kennicutt & evans 2012 and schruba 2013 for reviews ) .
a likely physical origin of the suppression of h@xmath4 formation under the threshold is radiative feedback by uv photons produced by young massive stars ( schaye 2004 ; krumholz , mckee & tumlinson 2008 , 2009 ; mckee & krumholz 2010 ; hopkins et al . 2013 ) .
the formation of h@xmath4 is driven by collisionally excited metal line cooling and molecule formation on dust grain surfaces , which should be balanced with molecule dissociations by uv photons and grain photoelectric heating , both of which are energetically supplied by uv radiation field . if a region in a galaxy is optically thick to uv radiation field by dust grains , self - shielding of uv radiation would accelerate h@xmath4 formation .
this implies that the more fundamental threshold about star formation is not the total gas surface density but dust opacity . for a typical dust - to - gas ratio ,
the observationally indicated threshold in @xmath3 is close to the value at which the effective dust opacity @xmath6 becomes of order unity , where @xmath6 is averaged over wavelength with a weight of the heating radiation energy spectrum ( totani et al .
2011 ) .
therefore it is physically reasonable to expect that a galaxy - scale mean value of @xmath6 has an important role in galaxy formation and evolution .
a further observational support to this picture comes from infrared observations .
the relations between dust temperature , galaxy size , and infrared luminosity of @xmath71,000 nearby star - forming galaxies indicate that almost all of them are in the optically thick regime , and the distribution of dust opacity estimated by gas - phase metal column density suddenly drops around @xmath8 , indicating less efficient formation of galaxies at @xmath9 ( totani et al .
2011 ) .
the purpose of this paper is to investigate the effect of the radiative feedback depend on dust opacity , on cosmological galaxy formation and evolution particularly about the shape of galaxy luminosity functions .
the theory of structure formation in the universe predicts that the mean surface density @xmath10 of dark halos with mass @xmath11 and size @xmath12 nearly scales as @xmath13 , indicating higher gas surface density and dust opacity at higher redshifts in more massive objects , and hence more efficient star formation .
this may have a favorable effect to explain observations , in a similar way to the feedbacks by supernovae and agns .    to investigate the effect quantitatively
, we use a semi - analytic model ( sam ) of cosmological galaxy formation , _ the mitaka model _ ( ny04 ) .
this is a model similar to general sams , in which formation and evolution of dark matter halos are solved analytically or calculated by n - body simulations , while complicated baryonic processes are treated phenomenologically ( for reviews , see baugh 2006 ; benson 2010 ) . in general
, sams has many adjustable parameters and the effects of complicated physical processes on the lfs are degenerate ( e.g. , neistein & weinmann 2010 ) ; therefore a set of best - fit parameters may not be a quantitatively correct description of real galaxy formation .
it should be noted that the most important aim of this work is to examine the qualitative effects of the new feedback on luminosity functions .    in most of the sams ,
the star formation rate is simply proportional to cold gas mass , and the star formation time scale is modeled as a simple function of the dynamical time scale of galaxy disks or dm halos ( e.g. , cole et al .
2000 ; ny04 ) . some models ( e.g. , kauffmann 1996 ; croton et al .
2006 ; somerville et al . 2008 ; lagos et al . 2011 ; wang et al .
2012 ) incorporated the threshold of gas surface density below which star formation activity is significantly suppressed . in the models of kauffmann ( 1996 ) , croton et al .
( 2006 ) , and lagos et al .
( 2011 ) , they introduced the threshold of gas surface density motivated by the toomre stability criterion on a galactic scale ( toomre 1964 ) . in this scenario the threshold of gas surface density increases with redshift , and hence the threshold effect should be systematically different in the cosmological context from the threshold by dust opacity considered in this paper .
furthermore , some recent observations indicate that star formation are controlled by the physical state of local interstellar gas , rather than the dynamical state of an entire galaxy ( e.g. , leroy et al .
2008 ; lada et al .
2010 ) .    in other models , such as somerville et al .
( 2008 ) , a critical gas surface density threshold for star formation is introduced motivated from the observations of the @xmath2-@xmath3 relation ; however , to our knowledge there are no sams that consider a feedback depending on dust surface density rather than gas density .
recently krumholz & dekel ( 2012 ) incorporated a star formation law which depends on gas surface density and gas metallicity , and discussed average evolution of typical galaxies without calculating detailed merger histories of dark halos .
the relation between the luminosity function shapes and the dust opacity threshold of star formation has not yet been discussed in previous studies .
this paper is organized as follows . in section [ sec :
model ] , we will describe our model particularly focusing on the modelings of star formation and feedback .
in section [ sec : results ] , we show the results of our model , and section [ sec : gasmodel ] is devoted for discussion . we will summarize our work in section [ sec : summary ] . in this work ,
the cosmological parameters of @xmath14 , @xmath15 , and @xmath16 are adopted , and all magnitudes are expressed in the ab system .
we present a new version of a semi - analytic model of cosmological galaxy formation , incorporating a star formation law with a feedback depending on the galaxy - scale mean dust opacity and metallicity , motivated by recent observations of star formation in nearby galaxies and theoretical considerations . 
 this new model is used to investigate the effect of such a feedback on shaping the galaxy luminosity function and its evolution . 
 star formation activity is significantly suppressed in dwarf galaxies by the new feedback effect , and the faint - end slope of local luminosity functions can be reproduced with a reasonable strength of supernova feedback , which is in contrast to the previous models that require a rather extreme strength of supernova feedback . 
 our model can also reproduce the early appearance of massive galaxies manifested in the bright - end of high redshift @xmath0-band luminosity functions . 
 though some of the previous models also succeeded in reproducing this , they assumed a star formation law depending on the galaxy - scale dynamical time , which is not supported by observations . 
 we argue that the feedback depending on dust opacity ( or metal column density ) is essential , rather than that simply depending on gas column density , to get these results .    
 -.45 in    galaxies : evolution  galaxies : formation  cosmology : theory .