You are an expert at summarizing long articles. Proceed to summarize the following text: 
unlike stars , galaxies show diverse shapes . the belief that the difference in appearance reflects the generic character has motivated morphological classification of galaxies . since the 1920s the simple scheme suggested by hubble ( hubble 1926 ) based on single band images of bright galaxies has been widely adopted . the essence of hubble s scheme and its elaborations ( de vaucouleurs 1991 ; kormendy 1979 ; de vaucouleurs 1959 ; sandage 1961 ) is to divide galaxies into early and late types . the early types are further divided into ellipticals and lenticulars , and the late types into spirals ( unbarred and barred ) and irregulars . any one who looks directly into galaxy images immediately realize that shapes of galaxies are much more diverse than this , but also that the simple hubble sequence catches the major features of galaxy morphology . as unprecedentedly large sets of digital images of galaxies such as the sloan digital sky survey ( sdss , full details of the sdss are available at http://www.sdss.org . york 2000 ) data are available , time is ripe for understanding the origin of morphology of galaxies . in order to find the accurate relationship of galaxy morphology with other physical properties it is required to define morphological types more objectively and to use morphology subsets as homogeneous as possible . the endeavors to develop an objective , automatic and highly successful morphology classifier applicable to large libraries of digital images have resulted in various schemes ( yamauchi 2005 ; blanton 2003@xmath4 ; abraham , van den bergh , & nair 2003 ; strateva 2001 ; shimasaku 2001 ; abraham 1996 ; doi , fukugita , & okamura 1993 ) . this work further advances this topic . the philosophy of our morphological classification is to develop a scheme applicable down to the faint magnitude limit ( @xmath5 where @xmath6 is the petrosian magnitude after galactic extinction correction ) of the spectroscopic sample of the sdss using only photometric information . the fundamental features of galaxy morphology still useful for galaxies near the faint limit are the surface brightness and color profiles . their mean levels are measured by mean surface brightness and integrated color . their radial variation scaled to a characteristic size can be measured by the sersic or concentration index , and color gradient , for example . therefore , in principle , the morphology classification of galaxies should be made at least in 4-dimensional parameter space . the surface brightness at long wavelength bands represents the stellar mass distribution , and the color tells about the recent star formation history . a difficulty in dividing galaxies into early and late types using the surface brightness profile alone lies in the fact that most spirals consist of both bulge and disk . there is an unavoidable confusion between the bulge - only and the bulge - plus - disk systems when only the surface brightness information in a single band is used for classification . contamination in the early and late type subsets separated by using the concentration index , for example , is typically about 20% ( yamauchi 2005 ; shimasaku 2001 ) . the surface texture is of limited usage because it is sensitive to seeing and is simply lost for small faint galaxies ( @xmath7 in the case of sdss ; yamauchi 2005 ) . on the other hand , the information in color reveals the additional generic difference between early and late type galaxies which have experienced different star formation histories . strateva ( 2001 ) has found that the integrated ( observer frame ) @xmath8 color ( asterisks are attached to the sdss photometry based on the photometric equations used through the early data release ) of the sdss main galaxies ( stauss 2002 ) shows a bimodal distribution . however , they have shown that , when divided at @xmath9 , the early ( e / s0/sa ) and late type ( sb / sc / irr ) subsets have significant contaminations reaching about 30% for a sample with visually identified morphological types . in this paper we extend their work by incorporating color gradient and the concentration index as additional dimensions of the classification parameter space . we use a training set of 1982 galaxies to quantify the performance of our morphology classification scheme . the training set consists of two samples . the first contains @xmath10 sdss galaxies with @xmath11 after galactic extinction correction whose morphological types are assigned by the authors based on the color images retrieved by the sdss image list tool ( http://cas.sdss.org/astro/en/tools/chart/list.asp ) . galaxies are divided into six types : e / s0 ( smooth brightness and color profile ) , s0 ( disk with features , but no spiral arm ) , ae ( e or s0 with abnormal brightness or color distribution ) , s ( spiral arm , disk with dust lane ) , as ( spirals with large distortion in shape ) , i ( irregulars ) . the first three correspond to the early type , and the rest is the late types . the second training set is fukugita s catalog ( in preparation ; see also nakamura 2003 ) listing @xmath12 galaxies with @xmath13 ( after galactic extinction correction ) and with visually identified morphological types from @xmath14 to @xmath15 at half integer steps . among them we use a subset of @xmath16 galaxies that are listed both in the main galaxy and the spectroscopic sample and are not too much contaminated by foreground stars . by comparing the morphological types of @xmath17 galaxies common in our sample and fukugita s catalog , we have found that the early and late types divide at @xmath18 ( @xmath19 and 2 correspond to hubble type s0 and sa , respectively ) in the latter catalog . we use the color versus color gradient space as the major morphology classification tool , and use the concentration index as an auxiliary parameter . in the color - color gradient space spirals tend to separate from the region clustered by ellipticals and lenticulars as majority of spirals exhibit significant color gradient . as a measure of color gradient , we adopt the difference in @xmath20 color of the region with @xmath21 from that of the annulus with @xmath22 , where @xmath23 is the petrosian radius and @xmath20 is a rest frame @xmath24 color @xmath25-corrected to the redshift of 0.1 ( hereafter , @xmath1 means @xmath20 ) , and @xmath25-correction of magnitude and color is calculated based on the study of blanton et al . ( 2003@xmath26 ) . negative color difference means bluer outside . model magnitude is used for color . it is the magnitude calculated from the best - fit model profile obtained by fitting the de vaucouleur and exponential profiles to the galaxy image . we have chosen the @xmath27- and @xmath28-bands to estimate color gradient because they are widely separated in wavelength across the 4,000-@xmath29 break , and have @xmath30 ratios higher than the @xmath31- and @xmath32-bands . choice of other bands results in nosier color gradient estimates at faint magnitudes , or less successful separation of galaxies into early and late types . other measures of color gradient like the linear slope of the radial @xmath1 color profile and the @xmath1 color difference between the region with @xmath33 and the annulus with @xmath34 , are also calculated for comparisons . @xmath35 and @xmath36 are the radii from the center of a galaxy containing 50 and 90% of the pertrosian flux . we have found that the clump of the normal early type galaxies in the color - color gradient space is less tight for the latter measures at fainter magnitudes @xmath37 .    throughout this paper we use ab magnitudes converted from sdss magnitudes . the @xmath27- and @xmath28-band atlas images and basic photometric parameters of individual galaxies are retrieved from the sdss data release 3 ( dr3 ) at princeton ( http://photo.astro.princeton.edu ) . we have generated a big set of sersic model images convolved with the psf of various sizes . these images are used to find a best - fit sersic model with true sersic index and true axis ratio for an observed image of a given size of the psf . the fitting is made at radii larger than @xmath38 to avoid the central region whose profile is much affected by seeing . then the best - fit sersic models in @xmath27- and @xmath28-bands are convolved with the psf of the same size , and the effects of seeing on the concentration index and color difference are estimated . we have confirmed the seeing - corrected concentration index and color difference show no apparent dependence on seeing . we use the elliptical annuli in all our parameter calculations to take into account flattening or inclination of galaxies . the position angle and axis ratio used to define the elliptical annuli and to calculate the radial surface brightness profile are isophotal ones measured from the @xmath28-band image . the petrosian radii in our analysis are usually larger than those in the dr3 catalog which adopted circular annuli . the photometric parameters we use for morphology classification are the @xmath0 color , color difference @xmath39 , and the ( inverse ) concentration index @xmath40 in the @xmath28-band , where @xmath41 . here , the concentration index is used as a complementary parameter to discriminate red disky spirals from early type galaxies . the @xmath28-band image is used to measure the index because the image at longer wavelengths is expected to better represent the stellar mass distribution . all parameters are seeing - corrected as described above . figure  [ fig1 ] shows the distribution of galaxies of this training set in the @xmath0 versus @xmath39 space and in the @xmath0 versus concentration index space . the early ( e / s0 ) and late types ( sa to sd ) determined by visual inspection are marked as circles ( red ) and crosses ( blue ) , respectively . squares ( green ) are irregulars . in our automated scheme classified as early type galaxies are those lying above the boundary lines passing through the points @xmath42 , @xmath43 and @xmath44 in the @xmath0 versus @xmath39 space . they are also required to have @xmath45 . the rest are classified as late types . the completeness of this classification scheme reaches @xmath46 for early types and @xmath47 for late types . the reliabilities are @xmath47 and @xmath48 , respectively . the completeness , @xmath49 , is the fraction of galaxies of a given type that are successfully selected from the original sample by the classification scheme . the reliability , @xmath50 , is the fraction of galaxies of the desired type from the selected subsample . the @xmath51 failure is due to a few red passive spirals , galaxies with companions or foreground stars , and to incorrect visual classification ( for edge - on objects in particular ) . the parameter @xmath40 does only an auxiliary role improving the results by a few percents . we estimate the completeness and reliability of our morphology classification is about @xmath52 near @xmath53 , which is close to the faint end of the spectroscopic sample of the sdss . the performance of our classification scheme slowly degrades at @xmath54 because it becomes harder to measure the color difference and concentration index as the size of galaxies relative to the ccd pixel and the fwhm of the psf decreases . to estimate the performance of our classification scheme at fainter magnitudes we redshift the galaxies in the training sample ( @xmath55 ) with morphological types assigned by us . we calculate the new redshift at which a galaxy appear dimmer by a desired magnitude adopting a cosmology with density parameters @xmath56 and @xmath57 . the reduction factor in angular size is calculated and images are binned down ( giavalisco et al . the resulting images are convolved with the psf in such a way that they have the seeing effects equal to those of the original ones . noises are not added anew . following this procedure we generated three mock morphology samples of @xmath10 galaxies in half magnitude bins from @xmath58 to @xmath59 . the distributions of these redshifted galaxies in the color - color gradient space and in the color - concentration index space are very similar with those of three samples of randomly - drawn @xmath60 sdss galaxies with actual magnitudes in the same bins , thus justifying our procedure . we determine the classification criteria at fainter magnitudes using these redshifted morphology samples . results are summarized in table  [ table1 ] . table 1 says that our classification boundaries in the color - color gradient space hardly change even at magnitudes down to @xmath53 . the only major change is the boundary at the reddest colors ( the line connecting to the point p3 ) . at fainter magnitudes the clump of the normal e / s0 s expands vertically in the color - color gradient space because the measured color - differences have more errors . the classification boundary at the reddest colors has been chosen to include more ellipticals taking into account this fact . we think the @xmath25-correction of color in this reddest color range has been accurately estimated . our @xmath25-correction might have more errors for intermediate - type spirals for which the spectra of the central part of galaxies are less representative of the total color . but in this case our classification is hardly affected because these galaxies are blue , have large color gradients , and are located far from the classification boundaries . inspection of location of galaxies in the color - color gradient space leads us to classification beyond the dichotomous division into early and late types . normal ellipticals and lenticulars are very homogeneous systems whose light is dominated by old population ii stars . they strongly concentrate within a spot centered at @xmath61 in the @xmath0 and @xmath39 plane . dispersion is mainly due to companions or foreground stars . they show very weak but definite color gradient ( , outside is bluer ) . we have discovered a trail of early types containing about 10% of early type galaxies toward the left hand direction @xmath62 from the concentration of normal early types and then upwards . the galaxies in this trail are bluer than normal ones , often show emission lines , and occasionally show star burst activity near the center . they tend to be more centrally concentrated than spirals at the same color . we have found that most @xmath63 galaxies ( dressler & gunn 1983 ) listed in yamauchi & goto ( 2005 ) are located in this trail .    on the other hand , a spiral branch is extended downward of the cluster of normal early types . sa type spirals often start to have star forming zones at the outskirt of disk . their integrated color is still dominated by the red light from their bulges , but they begin to show color gradient . as the star formation activity becomes stronger , color gradient increases first and then starts to decrease as the star forming region expands toward the center . very late type spirals and most irregulars at the upper left corner are very blue and have inverted color gradient ( , center is bluer ) since they usually show strong star burst near the center . the spiral branch meets the trail of early types there . the major advantage of morphology classification in the color - color gradients space is that the blue early type galaxies are separated from the spiral galaxies because the former tend to have nearly constant color profile or bluer cores while the latter tend to have red bulge plus blue disk structure . the spiral branch is a sequence of locality of star formation activity and cold gas and dust concentration as illustrated in fig . the position of a spiral along the branch has a strong correlation with its morphological subclass as shown in fig . [ fig3 ] . after making early - late type division , one can further divide galaxies into subclasses based on their location along the early and late type branches . for example , late type galaxies can be divided into @xmath64 , @xmath65 , and @xmath66 subclasses which group galaxies lying above the line @xmath67 , between this line and the line @xmath68 , and left of the latter line , respectively . these subclasses roughly correspond to sa - sb , sb - sc , and sc - sd / irr , respectively . dispersion of the spiral branch is partly due to internal extinction which tends to make @xmath0 and @xmath69 increase . dependences of @xmath0 and @xmath69 on axis ratio of galaxies indicate that the effects of internal extinction are strongest for intermediate type spirals . our new morphology classification scheme takes into account history and locality of star formation as well as stellar mass distribution . it is easy to implement the scheme for multi - band surveys with wide spectrum coverage . we expect that the strong concentration of early types and the general shape of the spiral branch in the color versus color gradient space are still maintained for galaxies at high redshifts . any change in their location and shape will be colorful evidence for evolution of star formation activity and cold gas infall into galaxies with different morphology . cbp thanks michael vogeley for collaboration on parts of this work and for invitation to drexel university when this work was started . we also thank yasushi suto for suggesting us to use fukugita et al.s catalog . we thank the anonymous referee for helpful comments . this work is supported by the korea science and engineering foundation ( kosef ) through the astrophysical research center for the structure and evolution of cosmos ( arcsec ) . abraham , r. g. , 1996 , , 107 , 1 abraham , r. g. , van den bergh , s. , & nair , p. a. 2003 , , 588 , 218 blanton , m. r. , 2003@xmath4 , , 594 , 186 blanton , m. r. , 2003@xmath26 , , 125 , 2348 de vaucouleurs , g. 1959 , handbuch der physik , 53 , 275 de vaucouleurs , g. , 1991 , in third reference catalogue of bright galaxies , ( new york : springer ) doi , m. , fukugita , m. , & okamura , s. 1993 , , 264 , 832 dressler , a. , & gunn , j. e. 1983 , , 270 , 7 giavalisco , m. , livio , m. , bohlin , r. c. , macchetto , f. d. , & stecher , t. p. 1996 , aj , 112 , 369 hubble , e. p. 1926 , , 64 , 321 kormendy , j. a. 1979 , , 227 , 714 nakamura , o. , 2003 , , 125 , 1682 sandage , a. 1961 , in the hubble atlas of galaxies ( washington : carnegie institution ) shimasaku , k. , 2001 , , 122 , 1238 stoughton , c. , 2002 , , 123 , 485 strateva , i. , 2001 , , 122 , 1861 strauss , m. a. 2002 , , 124 , 1810 yamauchi , c. , & goto , t. 2005 , , 359 , 1557 yamauchi , c. , 2005 , ( in press ) york , d. , 2000 , , 120 , 1579        the three points , @xmath70 , @xmath71 , and @xmath72 , define the lines dividing the sdss galaxies into the early and late types in the @xmath73 versus @xmath74 plane . the early types are also required to have @xmath75 .
we have found the @xmath0 color versus @xmath1 color gradient space can be used for highly successful morphology classification of galaxies in the sloan digital sky survey . in this 
 space galaxies form early and late type branches well - separated from each other . 
 the location of galaxies along the branches reflects the degree and locality of star formation activity , and monotonically corresponds to the sequence of morphological subclasses . 
 when the concentration index is used together , the completeness and reliability of classification reaches about 91% for a training set of sdss galaxies brighter than @xmath2 . at faintest magnitudes ( @xmath3 ) of the sdss spectroscopic sample , 
 the performance still remains at about 88% . 
 the new classification scheme will help us find accurate relations of galaxy morphology with spatial and temporal environments , and help one understand the origin of morphology of galaxies .