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discovered by the bepposax gamma - ray burst monitor [ 3 ] , grb 970508 is the second gamma - ray burst ( grb ) for which an optical afterglow has been detected ( e.g. , [ 4 ] ) .
transient x - ray , near - infrared , millimeter , and radio emission have also been detected .
grb 970508 is the first grb for which a distance scale has been determined : metzger et al .
[ 1,2 ] report the existence of absorption and emission features in spectra of the optical afterglow taken with the keck ii 10-m telescope @xmath7 2 days and @xmath7 26 days after the grb event .
their identification of these features places grb 970508 at a redshift of @xmath0 .
the lack of a lyman-@xmath1 forest in these spectra further constrains this redshift to be less than @xmath8 2.1 .
consequently , grb 970508 is almost certainly cosmological in origin .
a host galaxy for grb 970508 has not yet been observed .
however , metzger et al . [ 1 ] report that the line emission observed in the keck ii spectra is consistent with constancy between their may 11 and june 5 observations . over this same period
, the continuum emission has faded .
this suggests that a host galaxy of relatively weak continuum emission may be present at the observed redshift of @xmath4 [ 2 ] .
grb afterglows are believed to be described by the relativistic blast - wave model [ 5 - 13 ] .
furthermore , the afterglow of grb 970228 , the only other grb for which sufficient afterglow information is available , has been shown to be compatible with this model [ 14,11,15 - 17,13 ] .
a basic prediction of the relativistic blast - wave model is that after an initial period of increasing optical flux , lasting hours to days , the optical flux of the afterglow will decrease as a power - law of index @xmath9 . during this period of declining optical flux ,
the optical spectrum will be described by a power - law of index @xmath10 ( e.g. , [ 15 ] ) . however , in the case of grb 970508 , @xmath11 [ 18 ] , which is inconsistent with the relativistic blast - wave model .    in  2 ,
i show that the reported grb 970508 optical afterglow measurements , once corrected for galactic absorption , are inconsistent with this prediction of the relativistic blast - wave model unless a second , redshifted source of extinction is introduced .
this second source of extinction may be the yet unobserved host galaxy .
i determine its redshift and i estimate its hydrogen column density along the line of sight .
an observing strategy for future optical afterglow observations is recommended in  3 .
as of 1997 november 3 , @xmath12 70 optical and near - infrared measurements of the grb 970508 afterglow have been reported .
these measurements span @xmath12 80 days , the earliest of which was taken @xmath7 4 hours after the grb event .
although the photometry is generally quite good , with quoted errors that are often less than 0.1 mag , zero - point errors are evident between different observing groups in various bands .
consequently , i consider only the largest self - consistent subset of these data : sokolov et al .
[ 18 ] report 22 optical measurements ( b , v , r@xmath13 , and i@xmath13 bands ) taken with a 6-m telescope between @xmath7 2 days and @xmath7 31 days after the grb event .
all of these measurements were taken after the optical flux had peaked (  1 ) , also @xmath7 2 days after the grb event .
i have corrected these measurements for galactic absorption using the iras 100 @xmath14 m v - band absorption measure of rowan - robinson et al . [
19 ] and the interstellar absorption curve [ 20,21 ] .
the v - band correction is @xmath15 mag .
i use the absorption measure of rowan - robinson et al . , which measures the dust directly , instead of measures of the hydrogen column density , i.e. [ 22 - 24 ] , since the iras 100 @xmath14 m flux about the location of grb 970508 varies significantly on angular scales that are smaller than the scales over which these measures of the hydrogen column density are averaged .
the corrected measurements are plotted in figure 1 .
psfig    the following model is now @xmath16-fitted to these corrected measurements : @xmath17 the first term is the extinction - free prediction of the relativistic blast - wave model (  1 ) .
the second term is the correction that a second , redshifted source of extinction introduces .
it is given by redshifting the interstellar absorption curve and by specifying the magnitude of the extinction , which i parameterize as the v - band absorption magnitude _ at the redshift of the source _
. a constant error of @xmath7 0.07 mag must be added in quadrature to the quoted errors of sokolov et al . [ 18 ] for the model to fit the data ( @xmath19 ) .
this suggests that either the quoted errors are underestimated by a factor @xmath20 , or that the flux is varying by @xmath7 6% on timescales of days .
reichart [ 16 ] noticed possibly related temporal behavior in the light - curve of grb 970228 .    the best fit is : @xmath21 cgs , @xmath22 , @xmath23 mag , and @xmath24 .
the quoted uncertainties are 1 @xmath6 confidence intervals for one interesting parameter .
the best - fit redshift is consistent with the observed redshift of @xmath4 .
furthermore , redshifts greater than @xmath5 are ruled out at the 3 @xmath6 confidence level .
the best - fit v - band absorption magnitude corresponds to a hydrogen column density of @xmath7 4.5 x 10@xmath25 @xmath26 .
the possibility that there is no second source of absorption , i.e. , @xmath27 , is ruled out at the 3.8 @xmath6 confidence level .
using equation ( 1 ) and the best - fit temporal decline power - law index , i have scaled each of the measurements that were fitted to in  2 to its corresponding value for may 11 , just shortly after the optical peak .
these points define the post - peak , time - independent optical spectrum and are plotted in figure 2 .
the best - fit spectrum , as well as the extinction - free , relativistic blast - wave component of this spectrum ( the first term of equation ( 1 ) ) , are also plotted in figure 2 .
a broad absorption feature is apparent in the best - fit spectrum .
this is the ultraviolet absorption feature of the interstellar absorption curve , redshifted into the b band .
had the redshift of grb 970508 been less than @xmath4 , u - band measurements would also have been necessary for this , the only strong feature of the interstellar absorption curve , to have been detected .
consequently , in this type of analysis , different bands most sensitively probe different redshift ranges , depending on whether or not this absorption feature has been redshifted into the band in question . since grbs are generally believed to have redshifts of @xmath28 , self - consistent sets of u- , b- , and v - band measurements should be a goal of future optical afterglow observations .    in this letter ,
i present a method by which redshifts can be determined for grbs that are associated with host galaxies , even if absorption or emission lines are not observable or if spectra of sufficient quality are unattainable .
this method also yields hydrogen column densities along the line of site , which provides valuable information about the distribution of grbs within galaxies . for grb 970508
, i find that the redshift of its host galaxy , or possibly that of an intermediate galaxy , is @xmath3 , which is consistent with the observed redshift of metzger et al .
: @xmath4 .
redshifts greater than @xmath5 are ruled out at the 3 @xmath6 confidence level .
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grb 970508 is the second gamma - ray burst ( grb ) for which an optical afterglow has been detected . 
 it is the first grb for which a distance scale has been determined : absorption and emission features in spectra of the optical afterglow place grb 970508 at a redshift of @xmath0 [ 1,2 ] . 
 the lack of a lyman-@xmath1 forest in these spectra further constrains this redshift to be less than @xmath2 . 
 i show that the spectrum of the optical afterglow of grb 970508 , once corrected for galactic absorption , is inconsistent with the relativistic blast - wave model unless a second , redshifted source of extinction is introduced . 
 this second source of extinction may be the yet unobserved host galaxy . 
 i determine its redshift to be @xmath3 , which is consistent with the observed redshift of @xmath4 . 
 redshifts greater than @xmath5 are ruled out at the 3 @xmath6 confidence level .