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when observing a nearby elliptical or bulge of a spiral galaxy , there are two distinct characteristics in the galaxy s surface brightness .
the first is the most obvious : the galaxy is brightest in the center and grows fainter with increasing radius .
the second characteristic is only apparent in good seeing conditions : the surface brightness is clumpy on the scale of the seeing disk . these clumps , which can be a few percent of the mean surface brightness for the nearest galaxies like m  31 and m  32 , arise from poisson statistical fluctuations in the number of stars per seeing disk .
historically , this effect was known as `` incipient resolution . '' in the modern context , they are called surface brightness fluctuations ( sbfs ) .
tonry & schneider ( 1988 ) devised a technique to quantify sbfs and to use them as a distance indicator for undisturbed early - type galaxies . specifically , they proposed using the ratio of the 2@xmath2 moment of the stellar luminosity function ( lf ) to the 1@xmath3 moment as a standard candle : @xmath4 where @xmath5 is the number of stars of type @xmath6 with a luminosity of @xmath7 .
@xmath8 has units of luminosity and is expressed in astronomer s units as @xmath9 and @xmath10 , the absolute and apparent sbf magnitude , respectively .
since @xmath9 is an intrinsic property of the lf , sbfs can be useful for studying the stellar populations of early - type galaxies .
the potential parameter space to explore is very large , since the `` age '' and `` metallicity '' of the stars can be a complex combination of formation epoch and subsequent history ( e.g. , kaufmann , in this volume ) .
sbfs provide data _ unique _ from the integrated light / spectra of these galaxies . because of their @xmath11 dependence , sbfs are very sensitive probes of the most luminous stars , the cool red giant stars ( figure  1 ) .
modeling these stars interior structure and emergent spectra is very challenging .
also , since bright rgb and agb stars evolve quickly , only a handful of each are present in any star cluster in the milky way or magellanic clouds .
therefore , sbf measurements , which arise from the stellar population of entire galaxies , provide one of the best observational tests of our current understanding of these stars .
recent observational and theoretical advances make now a ripe time to revisit and expand sbf stellar population studies .
past modeling ( tonry et al .  1990 ; buzzoni 1993 ; worthey 1993 ) used the previous generation of evolutionary tracks ( vandenberg or revised yale isochrones ) based on older stellar opacities . the optical sbf dataset has been expanded and improved considerably ( tonry et al .
1997 ) , and a growing body of ir data has widened the spectral coverage .
figure  2 presents @xmath12-band sbf data for fornax cluster ellipticals from liu et al .
( 1999b ) and jensen et al .
( 1998 ) .
fornax is appealing since it is close enough to have a cepheid distance measured with hst ( silbermann et al .
1999 ) and is compact on the sky , implying the galaxies basically lie at the same distance .
predictions from bruzual & charlot ( 1998 ) single - burst models are overplotted ; these use padova evolutionary tracks , stellar spectra of lejeune et al.(1997 ) , and a semi - empirical agb prescription ( charlot & bruzual 1991 ) .
( see bruzual , in this volume . )
the good agreement between data and models means the lifetimes , luminosities , and colors of the bright rgb and agb stars are roughly correct , or else multiple errors are cancelling each other out ( e.g. , charlot et al .
1996 ) .
the bc98 models agree worse with the @xmath13-band empirical sbf calibration ( tonry et al .
1997 ) than with the @xmath12-band data , which has lead us to revise the most evolved stars in the models ( liu et al .
this illustrates the usefulness of sbf tests .
although the models agree reasonably well with integrated colors of elliptical galaxies and local group globular clusters , it is the sbf comparison which reveals possible weaknesses in the modeling of the most luminous stars .
in old populations , @xmath9 is expected to be very metal - dependent , since it strongly tracks the rgb and agb , whose colors are governed by metallicity ( frogel et al .
1983 ) . therefore , sbf data are potentially very useful in characterizing the stellar content of ellipticals .
broad - band colors are degenerate in age and metallicity , with changes of @xmath14 preserving the color ( worthey 1994 [ w94 ] ; worthey , this volume ) .
absorption line indices can be more age- or metal - sensitive , e.g. , @xmath15 and @xmath16 are age - sensitive ( @xmath17 ) and mg@xmath18 and c@xmath184668 are metal - sensitive ( @xmath19 ) . in comparison ,
ir sbf magnitudes are predicted by the bc98 and w94 models to have in old populations .
this suggests ir sbf data combined with balmer absorption indices could effectively disentangle age and metallicity effects in ellipticals .
developing accurate models is critical for measuring distances to galaxies from sbfs .
optical / ir sbf distances can be measured to @xmath20  km / s and therefore to obtain @xmath21 , but accurate distances rely on accurate @xmath12-corrections to account for the redshifting of the galaxy spectrum .
moreover , models can guide us to better observations .
for instance , @xmath13-band sbf distances use the @xmath22 integrated galaxy color to account for stellar population variations from galaxy to galaxy ( tonry et al .
both the bc98 and w94 models suggest that @xmath23 or @xmath24 colors , which are more metallicity - driven , would lead to a better correction , reducing the scatter by @xmath2550% .
the wider spectral ranges of these colors also lead to greater tolerance of errors in photometry or reddening than @xmath22 .
finally , accurate models could provide a purely theoretical calibration for sbf distances , independent of any cepheid calibration .
buzzoni , a. 1993 , , 275 , 433 bruzual , g. & charlot , s. 1998 , in preparation ( bc98 ) charlot , s. & bruzual , c. 1991 , , 367 , 126 charlot , s. , worthey , g. , & bressan , a. 1996 , , 457 , 625 frogel , j. a. , cohen , j. g. , & persson , s. e. 1983 , , 275 , 773 jensen , j. b. , tonry , j. l. , & luppino , g. a.  1998 , , 505 , 111 lejeune , th . ,
cuisinier , f. , & buser , r.  1997 , , 125 , 229 liu , m. c. , charlot , s. , & graham , j. r. 1999a , in preparation liu , m. c. , graham , j. r. , & charlot , s. 1999b , in preparation silbermann , n. a. et al .  1999 , , 515 , 1 tonry , j. l. & schneider , p. 1988
, , 96 , 807 tonry , j. l. , ajhar , e. a. , & luppino , g.  1990 , , 100 , 1416 tonry , j. l. , blakeslee , j. p. , ajhar , e. a. , & dressler , a.  1997 , 475 , 399 worthey , g. 1993 , , 409 , 530 ; erratum 1993 , apj , 418 , 947 worthey , g. 1994 , , 95 , 107 ( w94 )
we are using optical / ir surface brightness fluctuations ( sbfs ) to validate the latest stellar population synthesis models and to understand the stellar populations of ellipticals . 
 integrated light and spectra measure only the first moment of the stellar luminosity function ( @xmath0 ) . since sbfs 
 also depend on the second moment ( @xmath1 ) , they provide novel information , in particular about the reddest , most luminous rgb and agb stars , which are the most difficult stars to model . 
 sbfs can also provide useful new constraints on the age / metallicity of unresolved stellar populations in ellipticals . 
 finally , developing accurate stellar population models benefits several aspects of sbf distance measurements to galaxies .    
 -1 in to appear in , + eds .  
 i.  hubeny , s.  heap , & r.  cornett ( asp conf .  
 series ) , 1999