You are an expert at summarizing long articles. Proceed to summarize the following text: 
the scale size of galaxies is one of the fundamental parameters to elucidate the history of galaxy formation and evolution . the change of size and stellar - mass relations over cosmic time would pose strong constraints on models of galaxy evolution . the observational relations between galaxy size and stellar mass have been studied in the local universe , based on the sloan digital sky survey ( shen et al . 2003 ; bernardi et al . 2011 ) . using rest - frame optical bands , which presumably trace the distribution of stellar mass in galaxies , many studies have investigated galaxy sizes at higher redshift as a function of stellar mass for massive galaxies ( @xmath16 m@xmath7 ) . for example , the relations for galaxies at @xmath17 were studied for late - type galaxies ( barden et al . 2005 ) and for early - type galaxies ( mcintosh et al . 2005 ; trujillo , ferreras , & de la rosa 2011 ) . damjanov et al . ( 2009 ) and mancini et al . ( 2010 ) gave size - mass relations of massive galaxies ( @xmath18 m@xmath7 ) at @xmath19 . williams et al . ( 2010 ) studied the relation with large samples of galaxies at @xmath20 . for higher redshifts to @xmath10 , size - mass relations have been obtained for galaxies with @xmath21 m@xmath7 ( e.g. , franx et al . 2008 ; nagy et al . 2011 ; cassata et al . 2011 ) . many studies have corroborated that massive galaxies at high redshifts were much smaller than local galaxies with comparable mass ( e.g. , daddi et al . 2005 ; trujillo et al . 2006 , 2007 ; toft et al . 2007 ; zirm et al . 2007 ; cimatti et al . 2008 ; buitrago et al . 2008 ; van dokkum et al . 2008 , 2009 , 2010 ; akiyama et al . 2008 ; damjanov et al . 2009 ; carrasco et al . 2010 ; cassata et al . 2010 ; szomoru et al . 2010 ; van der wel 2011 ; cassata et al . 2011 ) . at a fixed stellar mass , spheroidal galaxies were significantly more compact at high redshift and evolved with rapid increase of the effective radius by a factor @xmath224 or even larger from @xmath23 ( e.g. , buitrago et al . 2008 ; carrasco et al . 2010 ) and by a factor @xmath222 from @xmath11 ( e.g. , van der wel et al . 2008 ; trujillo et al . 2011 ) . the finding of compact massive galaxies with a high stellar velocity dispersion also supports their existence ( van dokkum 2009 ; van de sande 2011 ) . it contrasts with the absence of such compact massive galaxies in the local universe , though several candidates have been found at @xmath24 ( stockton et al . 2010 ) and in the local universe ( trujillo et al . 2009 ; valentinuzzi et al . the findings demonstrate that massive galaxies have increased their size dramatically since @xmath25 in a different manner from the evolution of less massive galaxies . however , other studies have reached contradictory conclusions . there is significant disagreement between the results of different studies . barden et al . ( 2005 ) found weak or no evolution in the relation between stellar mass and effective disc size for galaxies with @xmath26 m@xmath7 since @xmath11 . for early - type galaxies at @xmath11 , mcintosh et al . ( 2005 ) showed that luminosity - size and stellar mass size relations evolve in a manner that is consistent with a completely passive evolution of the red early - type galaxy population . it is also shown that not all high - redshift early - type galaxies were compact and underwent dramatic size evolution ( e.g. , toft et al . 2007 ; zirm et al . 2007 ; saracco et al . 2009 , 2011 ; mancini et al . 2010 ; stott et al , 2011 ) . from the study of surface brightness in rest - frame @xmath27 and @xmath28 bands at @xmath29 , ichikawa et al . ( 2010 ) gave another evidence for no conspicuous evolution in galaxy sizes . as many previous studies show , the size evolution of galaxies are still controversial . any systematic errors in the observation or analyses could bias results towards such a significant evolution ( e.g. , mancini et al . 2010 ; hopkins et a. 2009b ; bouwens et al . 2004 ) . the origin of the discrepancy could be ascribed to redshift effects that more distant galaxies look more compact due to the difficulty of measuring envelopes at low surface density . the light from the outer portion of high - redshift galaxies is apt to be hidden in noise for low @xmath30 observations . as the consequence , effective radii and total luminosity ( or stellar mass ) would be underestimated . on the other hand , very deep observations ( e.g. , szomoru et al . 2010 ; cassata et al . 2010 ; law et al . 2012 ) or stacking methods to enhance the faint envelope of galaxies ( e.g. , zirm et al . 2007 ; van dokkum et al . 2008 , 2010 ; van der wel et al . 2008 ) have claimed that it is not the case . how significantly have the sizes of less - massive normal galaxies evolved from the early universe to the current epoch ? in this context , we look into the evolution of stellar - mass and size scaling relations on the basis of half- and 90 percent - light encircles , focusing on less massive galaxies ( @xmath31 m@xmath7 ) at @xmath1 , using a deep @xmath4-selected galaxy catalogue . we infer that the outer radius is more influenced by merging effect than star formation or central activity . in  2 , we describe the catalogue we used , which is among the deepest in the @xmath4 band to date . the depth is crucial for studying galaxies of low - surface brightness or galaxies which are dimmed due to the cosmological expansion at high redshift to measure the radius at faint outskirt of galaxies . the data analysis and the result for the size and stellar - mass relation are detailed in  3 and  4 . the results are discussed in  5 . ichikawa et al . ( 2010 ) studied the evolution of surface brightness of galaxies at @xmath29 in rest - frame @xmath27 and @xmath28 bands with the same data as the present study . we will discuss the consistency of the present result with their study .    throughout this paper , we assume @xmath32 , @xmath33 , and @xmath34 km s@xmath35 mpc@xmath35 . we use the ab magnitude system ( oke & gunn 1983 ; fukugita et al . we use the @xmath4-band selected catalogue of the moircs deep survey ( mods ) in the goods  north region ( kajisawa et al . 2009 , hereafter k09 ; kajisawa et al . 2011 , k11 ) , which are based on our imaging observations in @xmath36 bands with moircs ( suzuki et al . 2008 ) and archived data . four moircs pointings cover 70 percent of the goods  north region ( 103 arcmin@xmath37 , hereafter referred as ` wide ' field ) . one of the four pointings , which includes hdf - n ( williams et al . 1996 ) , is the ultra - deep field of mods ( 28 arcmin@xmath37 , ` deep ' field ) . as the accuracy of background subtraction was highly demanded for the study of faint end of galaxies , the background was scrutinized and carefully subtracted ( see k11 for the details ) . the surface brightness limit was extensively examined in k11 . the typical @xmath38 surface brightness fluctuations in one arcsec diameter were found to be @xmath2227 mag arcsec@xmath39 and @xmath2227.5 mag arcsec@xmath39 in @xmath4 band for the wide and deep fields respectively . these are @xmath40 mag deeper than those of previous studies in @xmath4 band . the depth is crucial for the study of low surface brightness features at the outskirts of galaxies because of the strong dependence of cosmological dimming of surface brightness on redshift .    for the total magnitude @xmath41 in @xmath4 band , we use mag_auto obtained by sextractor ( bertin & arnouts 1996 ) . the @xmath42-percent completeness of the catalogue is @xmath43 in the wide field and @xmath2226 mag in the deep field . we exclude fainter galaxies from the present analysis . the fwhms of the final stacked images are 0.46 arcsec for the deep image and 0.530.60 arcsec for the wide image . the numbers of galaxies are 3555 and 6063 , respectively .    to obtain the stellar mass of mods samples , k09 performed sed fitting of the multiband photometry ( @xmath44 , 3.6 @xmath45 m , 4.5 @xmath45 m , and 5.8 @xmath45 m ) with population synthesis models . we adopt the results with galaxev templates ( bruzual & charlot 2003 ) and the salpeter initial mass function ( see k09 for more details ) . the stellar masses ( @xmath0 ) are obtained from the best - fit stellar mass - to - luminosity ratio in @xmath4 band and scaled with the @xmath4-band flux . a detailed comparison between different mass estimators is given in k09 . in the present analysis , the near - infrared data ( 3.6@xmath45 m ) of spitzer / irac are available for most of the sample galaxies ( 96 percent ) , so that sed fitting is reasonably reliable for the photometry at rest-@xmath27 ( @xmath46 m ) out to redshift @xmath223 . we assume that the size of the stellar system in galaxies is represented by the size measured on @xmath4-band images , which are the rest - frame optical to near - infrared wavelengths at @xmath29 . the difference of the sizes between optical and infrared light is discussed in  4 .    in the present catalogue , 209 galaxies are identified as x - ray sources . among them , 61 sources are massive galaxies emitting hard x - rays with @xmath47 m@xmath7 at @xmath48 ( yamada et al . . one would expect galaxies with agn emission to have smaller half - light radius . considering possible effects on the size and mass estimates , we discard x - ray sources in what follows . as the definition of galaxy size , most previous studies have used the scale length ( @xmath49 ) , obtained by fitting the srsic profile ( srsic 1968 ) to galaxy images . the accuracy of the scale length strongly depends on image quality and depth of observations . for bright galaxies , reliable galaxy sizes can be measured from ground - based data ( trujillo et al . 2006 ; franx et al . 2008 ; williams et al . 2010 ) . on the other hand , it is crucial to take an accurate measure of the profile for small objects near the resolution limit . in fact , konishi et al . ( 2011 ) applied two dimensional fitting for the present sample to obtain srsic indexes with a single component for a morphological study of mods galaxies . however , they found that reliable fitting was successful only for comparatively massive galaxies ( @xmath26 m@xmath7 ) at @xmath11 and very bright galaxies ( @xmath50 ) at higher redshift . the resolution of fwhm @xmath51 arcsec like the present sample would not allow reliable fitting with srsic profile to fainter galaxies . srsic parameters are sometimes degenerated between @xmath52 and @xmath49 , which depends on the surface - brightness limit of the images ( e.g. , mancini et al . 2010 ; stott et al . 2011 ) , so that the reliable fitting would be difficult for faint galaxies . moreover high - redshift galaxies exhibit a wide range of disturbed morphologies ( e.g. , kajisawa & yamada 2001 ) . therefore , the fitting for less massive galaxies at high redshift could also be strongly influenced by their more amorphous features in the shape . in addition , we must take into account that we are observing a mix of galaxy morphologies . as such , we define the half - light radius ( @xmath53 ) as the radius of a circular aperture , which encircles half the @xmath4-band light emitted from galaxies . as we here focus not just on massive ( or bright ) galaxies , but also on less massive galaxies up to @xmath10 , we prefer @xmath54 to @xmath49 for the study of the structural parameters . if a galaxy profile extends to infinity , @xmath49 encloses half the flux in the srsic profile . however , as galaxies are supposed to have an edge at several times the scale length , @xmath49 does not always mean half - light radius . therefore , in general , @xmath53 is smaller than @xmath49 . in the same way , we define 90 percent - light radius @xmath55 . the 90-percent radius will give us more information at outer region of galaxies , where the size would be more influenced by merging effect . @xmath53 and @xmath56 are obtained by sextractor with phot_fluxfrac=0.5 and 0.9    figure [ fig - kvsr50 ] shows @xmath53 versus @xmath41 for all objects in mods . mods catalogue lists many spectroscopically confirmed stars , which are also plotted in fig . [ fig - kvsr50 ] . as few spectroscopic data were available for stars fainter than @xmath57 in the present region , we examined the reliability of @xmath54 using artificial stars . the artefacts were convolved with a moffat point spread function ( @xmath58 and fwhm=0.5 arcsec in the deep field and 0.6 arcsec in the wide field ) , and then buried in images as noisy as those of the deep and wide fields . sextractor was applied to the artefacts in the same manner as for the mods catalogue . the results are plotted in fig . [ fig - kvsr50 ] . the location of stars gives a clear boundary of unresolved galaxies . we define galaxies smaller than @xmath59 in the wide field @xmath60 in the deep field as unresolved galaxies . we first study the reliability of the galaxy size . seeing and background noise strongly affect the observed @xmath54 and @xmath55 , especially for faint or small galaxies . to examine the effect on the size estimate , we generated mock galaxies with a 1/4-law or exponential profile extending to 3 times scale length . the images are then convolved with a moffat point spread function ( @xmath58 and fwhm=0.5 arcsec in the deep field and 0.6 arcsec in the wide field ) , and buried in the simulated noise image . the galaxies were randomly generated with various magnitudes and effective radii or scale lengths , and analyzed with sextractor in the same manner as for the mods galaxies . the results are shown in fig . [ fig - mockr90r50 ] . seeing and noise seriously change the observed radii specifically for galaxies with a 1/4-law profile . the observed @xmath53 is significantly smaller than the intrinsic values in general . the effect is stronger for fainter 1/4-law galaxies , whereas the effect is much smaller for exponential galaxies . the apparent smaller size than the intrinsic size would be due to the fact that the faint and large envelope of 1/4-law galaxies is hidden in background noise . we should be aware of this effect if the observation is not deep enough for early - type galaxies ( see also hopkins et al . 2009b ; mancini et al . the effect will be discussed in more detail in the following section . it is noted that williams et al . ( 2010 ) claimed no systematic effects on @xmath49 for @xmath61 , using the shallower mods images . the radii , @xmath53 and @xmath56 , for small galaxies are affected by smearing due to seeing effect and the effect depends on galaxy morphology and size . therefore , we obtained eq . 1 to correct the size effect by fitting the deviation of the size as shown in fig . [ fig - mockr90r50 ] ( dash line ) . however , it is hard to examine the shapes of the present small or high-@xmath28 galaxies , so that we do not correct the effect which depends on morphology . @xmath62    we adopt @xmath63 and 0.35 arcsec for @xmath53 and @xmath56 , respectively . the size errors for mock galaxies are depicted in fig . [ fig - comparionsize ] as a function of observed magnitude . we should take into account that much smaller values are obtained for the size of 1/4-law galaxies . figure [ fig - comparionmag ] is the difference between intrinsic and observed magnitudes . at the faint limit , observed magnitudes are fainter by @xmath64 mag for 1/4-law galaxies , while the effect is much smaller for exponential galaxies . these results suggest that shallower observations tend to more underestimate size and flux ( therefore , stellar mass ) . we discuss later the influence on the results due to the systematic errors .              using photometric ( or spectroscopic , if available ) redshift data , @xmath53 and @xmath56 in arcsec are converted to the physical size in kpc ( @xmath2 and @xmath3 ) . the photo-@xmath28 accuracy of the present sample is reasonably good , @xmath65 ( @xmath66 ) ( k11 ) , so that we expect no serious influence on our result due to the photo-@xmath28 error . we will confirm this later using galaxies with spectroscopic redshifts . the results for @xmath2 and @xmath3 are shown in figs . [ fig - massvsr50 ] and [ fig - massvsr90 ] as a function of the stellar mass of galaxies for different redshift bins . the unresolved galaxies are displayed in another figure ( fig . [ fig - r50reject ] ) for reference . the results of effective radius ( @xmath49 ) for local galaxies by shen et al . ( 2003 ) are also shown in fig . [ fig - massvsr50 ] for comparison . size - mass relations for star - forming galaxies are consistent with that of late - type galaxies by shen et al . ( 2003 ) , although our definition of half - light radius is different from that of shen et al . it should be noted that it would be difficult to discuss the consistency for massive early - type galaxies because of the small number of such galaxies in our sample .    since our image quality is not high enough for classifying the galaxies into morphological classes at high redshifts , we divided the samples into quiescent and star - forming galaxy groups using a two - color diagnostic plot of rest - frame @xmath67 and @xmath68 colors ( williams et al . 2009 ) . the adopted selection criteria for quiescent galaxies are as follows : @xmath69 where @xmath67 and @xmath68 in the rest frame were obtained with the sed model fit to galaxies . the offset , @xmath70 , is 0.69 , 0.59 , and 0.49 for @xmath71 , @xmath72 , and @xmath73 , respectively . for @xmath74 galaxies , we applied the offset for @xmath75 . therefore the selection would be less reliable ( see williams et al . 2009 ) , though the number of such galaxies is very small . additional criteria of @xmath76 and @xmath77 are required for quiescent galaxies at all redshifts to prevent contamination from unobscured and dusty star - forming galaxies , respectively . the small differences in the slope and offset of the regression lines in different redshift bins in figs . [ fig - massvsr50 ] and [ fig - massvsr90 ] would imply a universal relation between the stellar mass and size of galaxies , irrelevant to redshift . in this context , we plot the stellar - mass surface density ( smsd ) , which is defined as @xmath78 , in a single redshift bin as a function of stellar mass for all galaxies at @xmath79 ( figs . [ fig - sd50all ] and [ fig - sd90all ] ) . the figures are essentially equivalent to the size - mass distribution . however , we can easily identify very compact or low - surface brightness galaxies in the figures , if they exist . for example , galaxies as compact ( or diffuse ) as 3 times smaller ( larger ) in size than the average should be located at @xmath221.0 dex above ( below ) the average . such low surface brightness galaxies can be recognized at @xmath9 m@xmath7 in fig . [ fig - sd90all ] .    in contrast , massive and compact galaxies are rare in the present sample . it is noted that most of massive galaxies with @xmath80 m@xmath7 should be resolved in all redshift bins of the deep field . we conjecture that very compact galaxies coalesce in the unresolved galaxies in fig . [ fig - r50reject ] . since the strong correlations of @xmath2 and @xmath3 with @xmath0 in figs . [ fig - massvsr50 ] and [ fig - massvsr90 ] are suggested , we obtain the least square fit between the size and mass of the galaxies with a linear regression , @xmath81 where @xmath82 is 50 for half light radius or 90 for 90% light radius and @xmath83 is the radius at @xmath84 m@xmath7 . @xmath85 is 10 for all and star - forming galaxies , while @xmath86 for quiescent galaxies because the quiescent galaxies with @xmath87 m@xmath7 were not observed at @xmath88 and their @xmath89 is statistically less robust due to the small numbers of the sample in narrow mass ranges at high redshits . we note that quiescent galaxies are located on average below the regression lines in all redshift bins , though the offset is smaller for @xmath3 than for @xmath2 . the fact suggests that quiescent galaxies are more compact than star - forming galaxies at a give mass . the best - fit slopes ( @xmath90 and @xmath91 ) and offsets ( @xmath92 and @xmath93 ) of the regression analysis with mean errors for all , quiescent galaxies ( qsg ) , and star - galaxies ( sfg ) are summarized in table 1 . the dispersion , @xmath94 , of the linear fit is listed in the sixth and last columns . as the exclusion of unresolved sources could biases the results towards larger radii , we obtained in table 2 the least - squares fit with the unresolved galaxies in fig.[fig - r50reject ] . we depict the evolution of the slope and offset as a function of redshift in fig . [ fig - a_evolution ] . while the slope for the quiescent galaxies are a little steeper than those for star - forming galaxies , the figure indicates that the slopes remain within @xmath95 and offsets do not significantly change from @xmath10 to @xmath12 , irrespective of the sample selection except the quiescent population at @xmath96 where the statistical error is very large .    for smsd in figs . [ fig - sd50all ] and [ fig - sd90all ] , we define the regression as @xmath97 where @xmath98 is smsd at @xmath99 m@xmath7 . the results are shown in table 3 . ccrcccrccc & & & @xmath2 & & & & @xmath3 & + redshift & sample & @xmath100 & @xmath90 & @xmath101 & @xmath94 & @xmath100 & @xmath91 & @xmath102 & @xmath94 + & & & & ( kpc ) & & & & ( kpc ) & + @xmath103 & all & 5259 & @xmath104 & @xmath105 & 0.130 & 5236 & @xmath106 & @xmath107 & 0.148 + & qsg & 408 & @xmath108 & @xmath109 & 0.110 & 408 & @xmath110 & @xmath111 & 0.099 + & sfg & 4851 & @xmath112 & @xmath113 & 0.129 & 4828 & @xmath114 & @xmath115 & 0.151 +   + @xmath116 & all & 543 & @xmath117 & @xmath118 & 0.133 & 542 & @xmath119 & @xmath120 & 0.168 + & qsg & 28 & @xmath121 & @xmath122 & 0.098 & 28 & @xmath123 & @xmath124 & 0.100 + & sfg & 515 & @xmath125 & @xmath126 & 0.133 & 514 & @xmath127 & @xmath128 & 0.170 + @xmath129 & all & 717 & @xmath130 & @xmath131 & 0.119 & 714 & @xmath132 & @xmath133 & 0.124 + & qsg & 70 & @xmath134 & @xmath135 & 0.126 & 70 & @xmath136 & @xmath137 & 0.107 + & sfg & 647 & @xmath138 & @xmath139 & 0.113 & 644 & @xmath140 & @xmath141 & 0.124 + @xmath142 & all & 1083 & @xmath143 & @xmath144 & 0.123 & 1079 & @xmath145 & @xmath146 & 0.151 + & qsg & 134 & @xmath147 & @xmath148 & 0.104 & 134 & @xmath149 & @xmath150 & 0.095 + & sfg & 949 & @xmath151 & @xmath152 & 0.121 & 945 & @xmath153 & @xmath154 & 0.156 + @xmath155 & all & 888 & @xmath156 & @xmath157 & 0.130 & 885 & @xmath158 & @xmath159 & 0.124 + & qsg & 83 & @xmath160 & @xmath161 & 0.105 & 83 & @xmath162 & @xmath163 & 0.085 + & sfg & 805 & @xmath140 & @xmath164 & 0.128 & 802 & @xmath165 & @xmath166 & 0.125 + @xmath167 & all & 519 & @xmath168 & @xmath169 & 0.127 & 514 & @xmath170 & @xmath171 & 0.161 + & qsg & 32 & @xmath172 & @xmath173 & 0.089 & 32 & @xmath174 & @xmath175 & 0.079 + & sfg & 487 & @xmath127 & @xmath176 & 0.127 & 482 & @xmath177 & @xmath178 & 0.165 + @xmath179 & all & 555 & @xmath180 & @xmath181 & 0.128 & 554 & @xmath182 & @xmath183 & 0.128 + & qsg & 28 & @xmath184 & @xmath185 & 0.121 & 28 & @xmath186 & @xmath187 & 0.094 + & sfg & 527 & @xmath188 & @xmath189 & 0.124 & 526 & @xmath190 & @xmath191 & 0.128 + @xmath192 & all & 700 & @xmath193 & @xmath194 & 0.121 & 696 & @xmath195 & @xmath196 & 0.146 + & qsg & 27 & @xmath197 & @xmath198 & 0.109 & 27 & @xmath199 & @xmath200 & 0.097 + & sfg & 673 & @xmath201 & @xmath202 & 0.119 & 669 & @xmath203 & @xmath204 & 0.147 + @xmath205 & all & 254 & @xmath206 & @xmath207 & 0.130 & 252 & @xmath208 & @xmath209 & 0.166 + & qsg & 6 & @xmath210 & @xmath211 & 0.040 & 6 & @xmath212 & @xmath213 & 0.035 + & sfg & 248 & @xmath214 & @xmath215 & 0.129 & 246 & @xmath216 & @xmath217 & 0.167 +    ccrcccrccc & & & @xmath2 & & & & @xmath3 & + redshift & sample & @xmath100 & @xmath90 & @xmath101 & @xmath94 & @xmath100 & @xmath91 & @xmath102 & @xmath94 + & & & & ( kpc ) & & & & ( kpc ) & + @xmath103 & all & 6532 & @xmath218 & @xmath219 & 0.161 & 6502 & @xmath220 & @xmath221 & 0.161 + & qsg & 445 & @xmath222 & @xmath223 & 0.116 & 445 & @xmath224 & @xmath225 & 0.108 + & sfg & 6087 & @xmath226 & @xmath227 & 0.162 & 6057 & @xmath228 & @xmath229 & 0.164 +   + @xmath116 & all & 646 & @xmath230 & @xmath231 & 0.156 & 645 & @xmath232 & @xmath233 & 0.181 + & qsg & 31 & @xmath234 & @xmath235 & 0.129 & 31 & @xmath236 & @xmath237 & 0.124 + & sfg & 615 & @xmath238 & @xmath239 & 0.156 & 614 & @xmath232 & @xmath240 & 0.183 + @xmath129 & all & 858 & @xmath241 & @xmath242 & 0.136 & 855 & @xmath243 & @xmath244 & 0.134 + & qsg & 73 & @xmath245 & @xmath246 & 0.127 & 73 & @xmath247 & @xmath248 & 0.111 + & sfg & 785 & @xmath249 & @xmath250 & 0.133 & 782 & @xmath251 & @xmath252 & 0.135 + @xmath142 & all & 1313 & @xmath253 & @xmath254 & 0.155 & 1308 & @xmath255 & @xmath256 & 0.161 + & qsg & 141 & @xmath257 & @xmath258 & 0.102 & 141 & @xmath259 & @xmath260 & 0.094 + & sfg & 1172 & @xmath261 & @xmath262 & 0.157 & 1167 & @xmath263 & @xmath264 & 0.166 + @xmath155 & all & 1082 & @xmath265 & @xmath266 & 0.164 & 1077 & @xmath253 & @xmath267 & 0.146 + & qsg & 88 & @xmath268 & @xmath269 & 0.103 & 88 & @xmath270 & @xmath271 & 0.084 + & sfg & 994 & @xmath272 & @xmath273 & 0.164 & 989 & @xmath274 & @xmath264 & 0.148 + @xmath167 & all & 675 & @xmath275 & @xmath276 & 0.159 & 668 & @xmath277 & @xmath278 & 0.176 + & qsg & 35 & @xmath279 & @xmath280 & 0.111 & 35 & @xmath281 & @xmath282 & 0.091 + & sfg & 640 & @xmath283 & @xmath284 & 0.160 & 633 & @xmath285 & @xmath286 & 0.179 + @xmath179 & all & 685 & @xmath287 & @xmath288 & 0.174 & 684 & @xmath289 & @xmath290 & 0.139 + & qsg & 36 & @xmath291 & @xmath292 & 0.128 & 36 & @xmath293 & @xmath294 & 0.120 + & sfg & 649 & @xmath295 & @xmath296 & 0.171 & 648 & @xmath297 & @xmath298 & 0.138 + @xmath192 & all & 923 & @xmath299 & @xmath300 & 0.152 & 918 & @xmath301 & @xmath302 & 0.156 + & qsg & 32 & @xmath303 & @xmath304 & 0.103 & 32 & @xmath305 & @xmath306 & 0.094 + & sfg & 891 & @xmath307 & @xmath308 & 0.151 & 886 & @xmath309 & @xmath310 & 0.157 + @xmath205 & all & 350 & @xmath311 & @xmath312 & 0.150 & 347 & @xmath313 & @xmath314 & 0.175 + & qsg & 9 & @xmath315 & @xmath316 & 0.097 & 9 & @xmath317 & @xmath318 & 0.109 + & sfg & 341 & @xmath319 & @xmath320 & 0.149 & 338 & @xmath321 & @xmath322 & 0.176 +    ccrccrccccc & & & @xmath2 & & & & @xmath3 & + selection@xmath323 & sample & n & @xmath324 & @xmath325 & @xmath94 & n & @xmath326 & @xmath327 & @xmath94 + & & & & ( @xmath328 kpc@xmath39 ) & & & & ( @xmath328 kpc@xmath39 ) & +    @xmath329 & all & 5259 & @xmath330 & @xmath331 & 0.26 & 5236 & @xmath332 & @xmath333 & 0.30 + & qsg & 408 & @xmath334 & @xmath335 & 0.22 & 408 & @xmath336 & @xmath337 & 0.20 + & sfg & 4851 & @xmath338 & @xmath339 & 0.26 & 4828 & @xmath340 & @xmath341 & 0.30 + with unresolved galaxies & all & 6532 & @xmath342 & @xmath343 & 0.32 & 6502 & @xmath344 & @xmath345 & 0.32 + & qsg & 445 & @xmath346 & @xmath347 & 0.23 & 445 & @xmath336 & @xmath348 & 0.22 + & sfg & 6087 & @xmath349 & @xmath350 & 0.32 & 6057 & @xmath342 & @xmath351 & 0.33 + @xmath352 & & 3980 & @xmath353 & @xmath354 & 0.25 & 3972 & @xmath355 & @xmath333 & 0.28 + @xmath356 & & 2378 & @xmath357 & @xmath358 & 0.25 & 2378 & @xmath359 & @xmath333 & 0.23 + spectroscopic redshift & & 1610 & @xmath360 & @xmath361 & 0.24 & 1610 & @xmath362 & @xmath363 & 0.22 +      the errors in stellar mass mainly originated from sed fitting and photometric errors of the observations . in the course of @xmath364 fitting to obtain the best sed model with various parameters ( e.g. , star - formation time scale , photometric redshift for galaxies with no spectroscopic redshift available , age , extinction , and metallicity ) , the probability distributions of stellar mass can be calculated , where the photometry and photometric - redshift errors are included . the error for the observed smsd is dominated by the error for the stellar mass . see more details for the error estimate in k09 and ichikawa et al . ( 2010 )    the size and magnitude errors in accordance with galaxy magnitude have been examined using mock galaxies ( figs . [ fig - comparionsize ] and [ fig - comparionmag ] ) . if all galaxies have a shape of 1/4-law , the error would be significant . recalling the size error due to the morphology strongly depends on magnitude , we examine the effect by confining the sample to bright galaxies , where the systematic error becomes smaller . we selected the samples with the magnitude limits , @xmath365 ( 23 ) , 25(24 ) , 26(25 ) for the deep ( wide ) fields , then obtained the regression lines again . the results are compared in table 3 . it should be noted that the section does not change the result . one would be concerned about the reliance on photometric redshift estimates for high redshift galaxies ( e.g. , mosleh et al . 2011 ) . in order to examine the error , we selected only the galaxies with spectroscopic redshift available and compared the result with the photo-@xmath28 sample . although the spectroscopic samples are limited to lower redshift , the result does not change our conclusion ( table 3 ) .                    due to possible color gradients in galaxies , it would be best to use images of the same rest - frame band with comparable @xmath30 for measuring the size of galaxies at all redshifts . nevertheless , we used the radius of galaxies measured on @xmath4-band image , because it is deepest among the images we used and because it is the rest - frame optical or longer band at @xmath29 . if the central region of galaxies are younger ( bluer ) than the outer region , the mass - weighted radius could be larger than the luminosity - weighted radius . if it is older ( redder ) , the result would be vice versa . star forming galaxies sometimes show strong morphological variation between observed wavelengths . bond , gawiser & koekemoer ( 2011 ) reported that this was not generically accompanied by a large difference in half - light radius . barden et al . ( 2005 ) measured the disk scale lengths of local galaxies in various bands . the average size is about 10 percent larger in @xmath27 band than in @xmath4 band . on the other hand , macarthur & courteau ( 2003 ) showed the contrary result that the distribution of disc scale lengths was a decreasing trend with increasing wavelengths ( see also cassata et al . 2010 for early - type galaxies at @xmath366 ) .    to investigate the effect of the color gradient , we compare the 90 present - light radius of galaxies measured on the nearest rest - frame @xmath27 band for each redshift bin . the sizes of the present samples were obtained on acs @xmath367 , @xmath28 , and moircs @xmath368 , @xmath369 bands and compared with that of @xmath4 band in fig . [ fig - r90vsacs ] . we used acs images binned to 0.117 arcsec per pixel , keeping the original image resolution . [ fig - r90vsacs ] demonstrates that the sizes of acs in @xmath367 and @xmath28 bands are systematically @xmath370 percent smaller than that in @xmath4 band . the convolution of the acs @xmath367-band image with psf and seeing enhances low surface brightness details . if the acs images are convolved with a gaussian ( fwhm=2 pixel , 0.234 arcsec ) , the difference is decreased to @xmath2215 percent . as the convolution enhances the galaxy edge of low surface brightness , it tends to give a larger galaxy size ( see also fig . 7 of mancini et al . it should be noted that the @xmath368 and @xmath369 images gives larger image size for smaller galaxies . the size strongly depends on the depth and the seeing size . although we have found the universal relation between @xmath0 and smsd ( or size ) , which does not depend strongly on redshift , we have good reason to expect offsets from the relation for some galaxy populations ( e.g. , massive compact galaxies ) in certain mass and redshift ranges . the regression analysis could be more weighted on the numerous less massive populations . therefore , it is likely that there are small ( but not highly significant ) offsets between galaxy populations . the small offsets would account for the size evolution of such populations . using the @xmath0@xmath371 relation obtained for the galaxies at @xmath372 ( tables 1 and 2 ) as a reference , we examined the deviation of the median size of galaxies in the mass and redshift bins from the reference . the evolution of the massive ( @xmath47m@xmath7 ) quiescent galaxies , defined in a @xmath67 and @xmath68 diagram ( williams et al . 2010 ) , is also obtained . ( we use median values to avoid unreasonable contributions from outliers with large deviation . ) we show the results in fig . [ fig - r_evolution ] , where unresolved galaxies are included . in addition , the median values of @xmath15 , which represent a sort of _ compactness _ of galaxies , are depicted in the figure to see the evolution of the compactness as a function of redshift . we note that the result with resolved galaxies are in good agreement with that with unresolved galaxies . using the deepest @xmath4-band image , we obtained scaling relations between stellar - mass ( @xmath0 ) and size ( or equivalently smsd ) as a function of redshift for galaxies at @xmath1 in a wide mass range of @xmath373 m@xmath7 . we defined the radii encircling half- ( @xmath2 ) and 90 percent - light ( @xmath3 ) in a circular aperture . the depth was found to be crucial for proper measure of the size and mass for less massive galaxies dimmed due to cosmic expansion . we conclude that there is no strong evidence for the size evolution at a given mass over the redshift range , irrespective of galaxy populations ( star - forming , quiescent ) . the size - mass relation ( @xmath374 ) have a universal slope ( @xmath375 ) and small offsets ( @xmath8 percent ) . in other words , as galaxies grow in mass through star formation or merging process , their sizes evolve in such a way that galaxies in general move along the scaling relation . the universal relation demonstrates that the stellar mass in galaxies with the same stellar mass was built up on average in a similar manner over cosmic times . the trend is insensitive to the stellar populations . our result is comparable with the @xmath376 found by shen et al . ( 2003 ) for low - mass galaxies ( @xmath377 m@xmath7 ) . on the other hand , it is in contrast to the steeper relation for massive galaxies obtained by previous studies ( e.g. , shen 2003 ; bernardi et al . the scaling relations are much tighter ( @xmath3780.17 dex ) than those ( @xmath3790.5 dex ) of previous studies in the local universe ( e.g. , shen et al . 2003 ) or at high redshifts ( e.g. , franx et al . 2008 ) . the weak growth of the galaxy size , irrelevant to galaxy mass , is in disagreement with the scenario that more massive galaxies rapidly changed their sizes . if massive high-@xmath28 galaxies are several times smaller than local galaxies with comparable mass , they should be located well above the stellar mass vs. smsd relations . several candidates of such compact galaxies with @xmath380 possibly coalesce as unresolved galaxies in figs . [ fig - sd50all ] and [ fig - sd90all ] . however , such galaxies are found to be few . our finding is in contrast with the previous results for quiescent early - type massive galaxies ( e.g. , zirm et al . 2007 ; williams et al . 2010 ) . with regard to smsd , the average smsds in @xmath2 for our sample galaxies with @xmath26 m@xmath7 are found not to evolve with redshift ( log @xmath381  8.70 ) . the average smsd for all galaxies at @xmath382 is @xmath383 , which is very consistent with the result , @xmath384 , for disk galaxies with @xmath26 obtained by barden et al ( 2005 ) , though our sample could be a mixture of disk and elliptical galaxies . however , due to small volume of the present study , the results could be subject to statistical uncertainties . the weak size evolution presented in the present study is reconciled with the surface brightness ( sb ) evolution . ichikawa et al . ( 2010 ) presented a universal linear correlation between the stellar mass and sb in rest - frame @xmath27 and @xmath28 bands for galaxies at @xmath1 , using the same sample as the present study . the correlation has a nearly constant slope , independent of redshift and color of galaxies in the rest-@xmath28 frame . in contrast , sb shows a strong dependence on redshift for a given stellar mass . it evolves as @xmath385 . the increase in the luminosity with redshift is estimated by using the expected luminosity evolution from a single burst at @xmath386 for massive galaxies ( @xmath26 ) and constant star formation for blue samples ( @xmath387 ) for less massive galaxies . the redshift dependence of sb evolution is well explained by the pure luminosity evolution of galaxies out to @xmath10 without the need of the size evolution , which supports the results for young early - type galaxies ( e.g. , saracco et al . 2011 ) and for disk galaxies at @xmath388 ( barden et al . 2005 ) .    nevertheless , there are some populations having a small offset from the universal scaling relation . we see more or less evolution in the size and compactness for such populations as a function of redshift in fig . [ fig - r_evolution ] . the figure suggests a moderate increase of 3050 percent for @xmath2 and @xmath3 for less massive galaxies ( @xmath9 m@xmath7 ) from @xmath10 to @xmath11 , while the sizes remains unchanged or slightly decrease towards @xmath12 . for massive galaxies ( @xmath13 m@xmath7 ) , the evolution is @xmath14 percent in @xmath3 from @xmath10 to @xmath12 , though that in @xmath2 is weaker . @xmath3 evolved as @xmath389 , it is noted that trujillo et al . ( 2006 ) , using the ground - based @xmath4-band data comparable with our depth , but in a smaller region ( 6.3 arcmin@xmath37 ) , concluded that there was no evidence for significant evolution for the size - mass relation and that there was small increase ( 29 percent ) since @xmath390 for the most massive bin @xmath391 m@xmath7 . in our sample , the average @xmath2 for the most massive bin of @xmath392@xmath393 m@xmath7 is larger by @xmath394 percent at @xmath12 than at @xmath390 , which is in good agreement with the result of trujillo et al . ( 2006 ) , whereas it is much weaker than those of other studies for galaxies of similar mass ( e.g. , franx et al . 2008 ; buitrago et al . 2008 ; van der wel et al . 2009 ; williams et al . 2010 ) . using new deep wfc3 data , cassata et al . ( 2011 ) and law et al . ( 2012 ) have given new evidences of compact galaxies at high - z . although the data in @xmath369 band is shallower by 1 mag arcsec@xmath39 than our @xmath4-band data , their conclusion would be robust . it would be possible that the compact galaxies are mingled in unresolved galaxies of the present sample or that the difference of the definition for half - right radius ( @xmath395 and @xmath53 ) gives the contradict result .    the ratio , @xmath15 , in fig . [ fig - r_evolution ] would give a clue to understanding the evolution of the compactness of galaxies . while middle and low mass galaxies shows no evolution in the compactness , the galaxies in the most massive bin are more compact at higher redshift . recalling weaker evolution in @xmath2 than in @xmath3 , we infer that the compactness evolution is ascribed mainly to the expansion of the outer rim of massive galaxies . in other words , at a given mass , massive galaxies in the local universe are more influenced by mergers or star formation at the outer envelopes than those at high redshifts . it would be worth noting that the galaxies in the massive bin of the deep field are complete in sampling over the present redshift range and their @xmath2 and @xmath3 are well resolved in the present psf . however , the present observation samples a comparatively small volume and therefore , the results could be subject to statistical uncertainties for massive galaxies of low number density due to field variances .    the size evolution is often used to advocate the merging processes in the hierarchical paradigm of galaxy formation and evolution . minor dry merger is a plausible mechanism for weak size evolution ( e.g. , guo & white 2008 ; bezanson et al . 2009 ; naab , johansson , & ostriker 2009 ; hopkins et al . 2010 ) . in that the size evolution is stronger in massive galaxies , our findings are qualitatively in agreement with previous studies based on simulations ( e.g. , boylan - kolchin , ma , & quataert 2006 ; hopkins et al . naab et al . ( 2009 ) showed that minor mergers or the accretion of relatively low - mass satellites may be the main driver for the late evolution of sizes of massive early - type galaxies . somerville et al . ( 2008 ) showed based on a cdm model of disc formation with @xmath26 m@xmath7 that the average size of discs at fixed stellar mass was about 50 percent larger than that at @xmath10 . the predicted evolution in the mean size at a fixed stellar mass since @xmath11 is about @xmath396 percent , which is comparable with our observations . the newly accreted small galaxies preferentially populate the outer region of massive galaxies . the small size growth of the present result is plausibly accounted for by minor mergers or the accretion of relatively low - mass satellites ( e.g. , naab et al . 2009 ; hopkins et al . naab et al . ( 2009 ) and fan et al . ( 2010 ) showed the fractional variation of the gravitational radius of the main galaxy after @xmath100 minor - merger events with @xmath374 as @xmath397 where @xmath398 and @xmath399 are final and initial galaxy sizes , @xmath400 is the fractional ratio of merging galaxy to the main galaxy . it takes @xmath221 ( @xmath223 ) minor - merger events with @xmath401 to increase the radius by @xmath402 ( @xmath403 ) percent for massive galaxies since @xmath10 , provided that the merger mass ratio is 1:10 . it would not be unreasonable that massive galaxies experienced such a small number of minor merging since @xmath4043 ( e.g. , bundy et al . 2009 ; lpez - sanjuan et al . 2011 ) . deep observations will be important in constraining the exact amount ( or lack thereof ) and distribution of merging galaxies , and how galaxies built up with redshift . in this context , our finding demonstrates that minor mergers in massive system built up an envelope of lower surface density materials . deeper imaging observations in a wider filed with high spatial resolution and consistent analyses from the local universe to high redshift will give constraints on the compactness and the amount of low - surface brightness material at the outer envelope as a function of redshift to improve our understanding of galaxy formation . this work has been supported in part by a grant - in - aid for scientific research ( 21244012 ) of the ministry of education , culture , sports , science and technology in japan . we thank ramsey lundock for careful reading of the manuscript . mods catalogue has been accomplished by moircs builders . we owe the present study to their dedicated efforts .    99 akiyama m. , minowa y. , kobayashi n. , ohta k. , ando m. , and iwata i. 2008 , apjs . , 175 , 1 barden a. , et al . 2005 , apj , 635 , 959 bernardi m. , roche n. , shankar f. , steth , r.  k. , 2011 , mnras , 412 , l6 bertin e. , arnouts s. 1996 , a&as , 117 , 393 bezanson r. , van dokkum p.  g. , tal t. , marchesini d. , kriek m. , franx m. , coppi p. , apj . , 697 , 1290 bond n.  a. , gawiser e. , koekemoer a.  m. , 2011 , apj , 729 , 48 bouwens r.  j. , illingworth g.  d. , blakeslee j.  p. , broadhurst t.  j. , franx m. , 2004 , apj , 611 , l1 boylan - kolchin m. , ma c - p . , quataert e. , 2006 , mnras , 369 , 1081 bruzual g. , charlot s. 2003 , mnras , 344 , 1000 buitrago f. , trujillo i. , conselice c.  j. , bouwens r.  j. , dickinson m. , yan h. , 2008 , apj , 687 , l61 bundy k. , fukugita m. , ellis r.  s. , targett t.  a. , belli s. , kodama t. , apj , 697 , 1369 carrasco e.  r. , conselice c.  j. , trujillo i. , 2010 , mnras , 405 , 2253 cassata p. , et al . , 2010 , apj , 714 , l79 cassata p. , et al . , 2011 , apj , 743 , 96 cimatti a. , et al . 2008 , a&a , 482 , 21 daddi e. , et al . 2005 , apj , 626 , 680 damjanov i. , et al . , 2009 , apj , 695 , 101 fan l. , lapi a. , de zotti g. , danese l , 2008 , apj , 689 , l101 fan l. , lapi a. , bressan a. , bernardi m. , de zotti g. , danese l , 2010 , apj , 718 , 1460 fontana a. , et al . 2009 , a&a , 501 , 15 franx m. , van dokkum p.  g. , schreiber m.  f. , wuyts s. , labb , toft s. , 2008 , apj , 688 , 770 fukugita m. , ichikawa t. , gunn j.  e. , doi m. , shimasaku k. , schneider d.  p. 1996 , aj , 111 , 1748 guo q. white s.  d.  m. , 2008 , mnras , 384 , 2 hopkins p.  f. , hernquist , l. , cox t.  j. , keres , d. , wuyts s. , 2009 , apj , 691 , 1424 hopkins p.  f. , bundy k. , murray n. , quataert e. , lauer t.  r. , and ma , c - p . , 2009 , mnras , 398 , 898 hopkins p.  f. , bundy k. , hernquist l. , wuyts s. , cox t.  j. , mnras , 401 , 1099 ichikawa t. , kajisawa m. , yamada t. , akiyama m. , yoshikawa t. , onodera m. , konishi m. , 2010 , apj . , 709 , 741 kajisawa m. , et al . , 2009 , apj , 702 , 1393 kajisawa m. , et al . , 2011 , pasj , 63 , s379 kajisawa m. , yamada t. , 2001 , pasj , 53 , 833 konishi m. , et al . , 2011 , pasj , 63 , s363 law , d.  r. , steidel , d.  c. , shapley , a.  e. , nagy , s.  r. , reddy , n.  a. , erb , d.  k. , 2012 , apj , 745 , 85 lpez - sanjuan c. , et al . 2011 , a&a , 530 , a20 macarthur l.  a. , courteau s. , 2003 , apj , 582 , 689 . mancini c. , et al . , 2010 , mnras , 401 , 933 mcintosh d. , et al . , 2005 , apj , 632 , 191 mosleh m. , williams r.  j. , franx m. , kriek , m. , 2011 , apj , 727 , 5 naab t. , johansson p.  h. , ostriker j.  p. , 2009 , apj , 699 , l178 nagy s.  r. , law d.  r. , shapley a.  e. , steidel c.  c. , 2011 , apj , 735 , 19l oke j.  b. , gunn j.  e. 1983 , apj , 266 , 713 saracco p. , longhetti m. , andreon s. , 2011 , mnras , 392 , 718 saracco p. , longhetti m. , gargiulo a. , 2011 , mnras , 412 , 2707 srsic j .- 1968 , atlas de galaxias australes ( cordoba : obs . astron . ) somerville r.  s. , et al . 2008 , apj , 672 , 776 szomoru d. , 2010 , apj.,714 , l244 stott j.  p. , collins c.  a. , burke c. , hamilton - morris v. , smith g.  p. , 2011 , mnras , 414 , 445 shen s. , mo h.  j. , white s.  d.  m. , blanton m.  r. , kauffmann g. , voges w. , brinkmann j. , csabai i. , 2003 , mnras , 343 , 978 stockton a. , shih h - y . , larson k. , 2010 , apj , 709 , l58 suzuki r. , et al . 2008 , pasj , 60 , 1347 toft s. , et al . , 2007 , apj , 671 , 285 trujillo i. , et al . 2006 , apj , 650 , 18 trujillo i. , conselice c.  j. , bundy k. , cooper m.  c. , eisenhardt p. , ellis r.  s. 2007 , mnras , 382 , 109 trujillo i. , cenarro a.  j. , de lorenzo - cceres a. , vazdekis a. , , de la rosa i.  g. , cava a. , apj . , 692 , l118 trujillo i. , ferreras i. , de la rosa i.  g. , 2011 , mnras , 415 , 3903 valentinuzzi t. et al . 2010 , apj , 712 , 1232 van der wel a. , bell e.  f. , van den bosch f.  c. , gallazzi a , rix h - w . , 2009 , apj . , 698 , 1232 van der wel a. , holden b.  p. , zirm a.  w. , franx m. , rettura a. , illingworth g.  d. , ford h.  c. , 2008 , apj , 688 , 48 van der wel a. , et al . , 2011 , apj , 730 , 38 van de sande j. , et al . 2011 , apj , 736 , l9 van dokkum p.  g. , et al . , 2008 , apj , 677 , l5 van dokkum p.  g. , kriek m. , franx m. , 2009 , nat , 460 , 717 van dokkum p.  g. , et al . , 2010 , apj , 709 , 1018 williams r.  e. , et al . 1996 , aj , 112 , 1335 williams r.  j. , quadri r.  f. , franx m. , van dokkum p. , toft s. , kriek m. , labb i. , 2010 , apj , 713 , 738 yamada t. , et al . , 2009 , apj , 699 , 1354 zirm a.  w. , et al . , 2007 , apj , 656 , 66
we present scaling relations between stellar - mass ( @xmath0 ) and the size of galaxies at @xmath1 for half- ( @xmath2 ) and 90 percent - light ( @xmath3 ) radii , using a deep @xmath4-band selected catalogue taken with the subaru telescope and moircs in the goods - north region . 
 the logarithmic slope @xmath5 is independent of redshift in a wide mass range of @xmath6 m@xmath7 , irrespective of galaxy populations ( star - forming , quiescent ) . the offset change is @xmath8 percent . 
 provided that optical light in the rest frame traces the stellar mass of galaxies , the universal relation demonstrates that the stellar mass was built up in galaxies over their cosmic histories in a similar manner on average irrelevant to galaxy mass . 
 the small offset in each stellar mass bin from the universal relation shows weak size evolution at a given mass . there is a moderate increase of 3050 percent for @xmath2 and @xmath3 for less massive galaxies ( @xmath9 m@xmath7 ) from @xmath10 to @xmath11 , 
 while the sizes remains unchanged or slightly decrease towards @xmath12 . for massive galaxies ( @xmath13 m@xmath7 ) , the evolution is @xmath14 % increase in @xmath3 from @xmath10 to @xmath12 , though that in @xmath2 is weaker . 
 the evolution of compactness factor , @xmath15 , which becomes smaller at lower redshift , is suggestive of minor merging effect in the outer envelope of massive galaxies . 
 [ firstpage ]    galaxies : evolution  galaxies : fundamental parameters  galaxies : high - redshift  infrared : galaxies .