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a ubiquitous feature of the optical / uv emission from type 1 seyfert galaxies ( sy1s ) is the highly correlated variability of the continuum flux across a wide range of wavelengths ( e.g. , peterson et al . 1998 ) . when this behavior was first observed during the 19891990 broad line region reverberation mapping campaign for ngc  5548 ( peterson et al.1991 ; clavel et al .  1991 ) , it was immediately recognized that the upper limits for the relative lags between the optical and uv wavebands were too small for the variability to have been mediated by hydrodynamic processes in the putative accretion disk  the differences in the characteristic radii for the emission in the respective wavebands were too large . in fact , the upper limits for the interband lags of @xmath0days required signal speeds of @xmath1 which could not have occurred within the disk itself . this fact and the observation that the optical / uv continuum became bluer as the flux increased led to the conclusion that the continuum variations were due to thermal reprocessing in the disk of higher energy radiation produced by a single varying source , such as the x - ray source posited to exist at the disk s inner regions , near the central black hole ( krolik et al . 1991 ; courvoisier & clavel 1991 ; collin - souffrin 1991 ) . subsequent observations of other sy1s showed that highly correlated broad band optical / uv variability is generic to these objects ( e.g. , courvoisier & clavel 1991 ) . recently , the thermal reprocessing picture has been challenged by simultaneous optical , uv , and x - ray observations of sy1s . the first object so observed was ngc  7469 by the iue and rxte satellites over @xmath2days in 1997 ( nandra et al . although the uv and x - ray light curves showed some similar variability characteristics both in amplitude and time scales , these light curves were not nearly as well correlated as would be expected if the uv emission was due to thermal reprocessing . naively , the variations in the uv should follow those in the x - rays with some characteristic time delay , but the maxima in the uv light curves preceded similarly shaped maxima in the x - ray light curve by @xmath3days , while minima in both light curves occurred nearly simultaneously . the 1998 observations of ngc 3516 by hst , asca , and rxte seem to be equally troubling for the thermal reprocessing model ( edelson et al.2000 ) . these observations consisted of intensive monitoring in optical , uv , and x - ray bands over 3  days and so were able to probe correlations on far shorter time scales than any previous set of observations . the x - rays showed very strong variations ( @xmath4% peak - to - peak ) , while the changes in the optical continuum were much smaller ( @xmath5% ) . because of the accurate relative photometry afforded by the hst / stis ccds , the measurement uncertainties were sufficiently small to reveal significant variability that was strongly correlated across the optical bands . hence , the original motivation for the thermal reprocessing model was still present , but as for ngc 7469 , the x - ray and optical flux variations were not strongly correlated on any relevant time scale .    more recently , nandra et al .  ( 2000 ) have re - examined the 1997 observations of ngc  7469 and found that while the relatively narrow band 210kev x - ray flux was nt well - correlated with the uv flux the spectral index of the x - ray emission was . this led them to suggest that the uv emission is actually correlated with the _ bolometric _ x - ray flux . in this letter , we expand upon that idea and describe what is required for the multiwaveband phenomenology exhibited by ngc 3516 to be due to disk thermal reprocessing in the context of a thermal comptonization model for the x - ray emission . most of the important details of the model are described in zdziarski , lubiski , & smith ( 1999 ; hereafter zls ) which the interested reader is encouraged to consult . we will proceed by summarizing the significant features and results from that work . this model was proposed by zls to explain the apparent correlation between the x - ray spectral index , @xmath6 , and the relative magnitude , @xmath7 , of the so - called compton reflection hump seen in the hard x - ray spectra of sy1s and x - ray binaries . zls argued that this correlation results from the reprocessing and comptonizing interactions between the disk and the hot plasma believed to produce the x - ray continuum . expanding upon the work of previous authors ( e.g. , poutanen , krolik , & ryde 1997 ; zdziarski et al . 1998 ) , zls noted that the @xmath7-@xmath6 correlation could arise in a geometry in which the comptonizing plasma occupies a spherical region of radius @xmath8 centered on the black hole . the accretion disk has an inner radius @xmath9 which penetrates this sphere at its equator by varying amounts . this varying penetration could be due to changes in @xmath8 , @xmath9 , or both . smaller values of @xmath10 result in a larger fraction of the x - ray photons from the sphere being intercepted by the disk . the covering factor , @xmath7 , for compton reflection and thermal reprocessing is larger , and a larger fraction of the disk soft photons re - enter the plasma precipitating additional cooling via compton losses and thereby reducing the temperature of the plasma . this results in a softer x - ray spectrum and a larger value for the photon index @xmath6 . enforcing energy balance under the assumption that the disk emits only reprocessed radiation , zls derived a @xmath7-@xmath6 relation which looks very similar to the observed correlations . we follow zls by assuming that the region of comptonizing plasma is homogeneous and optically thin and that we can neglect internal viscous dissipation in the disk , at least initially . reprocessing of incident x - rays by a razor - thin disk then gives a radial effective temperature distribution @xmath11^{1/4}. \label{t(r)}\ ] ] here @xmath12 is the total luminosity of the comptonizing plasma , @xmath13 is the stefan - boltzmann constant , and @xmath14 is the disk albedo . the dimensionless function @xmath15 is given by eq . 1 of zls .    assuming local blackbody emission and that the optical portion of the observed spectrum originates at large radii , we may use the asymptotic form @xmath16 in eq . [ t(r ) ] to obtain the disk spectrum @xmath17 where @xmath18 , @xmath19^{1/4}$ ] , and @xmath20 is the photon energy . neglecting variations in the disk albedo and assuming that @xmath9 is fixed on the time scales of interest , a constant optical flux implies a constant value of @xmath21 . in the presence of variations of the x - ray luminosity , this requires @xmath22 .    for @xmath23 , i.e. , at higher frequencies , it turns out that the large radius limit of @xmath15 is a surprisingly good approximation for evaluating the disk spectrum since it enters as the 1/4-power in @xmath24 , and at @xmath25 , the function takes the value @xmath26 ( zls ) , and we have @xmath27 . hence , for @xmath28 , adopting the asymptotic form for @xmath15 throughout and setting @xmath22 , all @xmath8-dependence drops out of eq . [ fopt ] , and in this approximation , the resulting disk spectrum has a constant shape and magnitude for different values of @xmath8 . the exact expression for @xmath15 flattens for @xmath29 , so when @xmath30 , the disk spectrum predicted by the full calculation will be somewhat softer , but not appreciably at the wavelengths which have actually been observed . given the x - ray luminosity @xmath12 , we estimate the x - ray spectrum produced by thermal comptonization in the sphere . for this we use a second result from zls which relates the amplification factor for comptonization , @xmath31 , to the ratio @xmath10 ( zls , eq .  2 ) . following zls , we use the empirical result of beloborodov ( 1999a ) which gives the x - ray spectral index as a function of @xmath31 : @xmath32 . to determine the overall magnitude of the x - ray spectrum , we use another empirical result of beloborodov ( 1999a ) to estimate the temperature of the comptonizing plasma , @xmath33 , where the compton parameter is given by @xmath34 and @xmath35 . we assume a typical value for the thomson depth , @xmath36 , and solve the preceding equations to find the electron temperature @xmath37 . we model the x - ray continuum as a power - law with an exponential roll - over , @xmath38 , where the cut - off energy is taken to be @xmath39 appropriate for a thomson depth @xmath40 . the normalization , @xmath41 , of the x - ray spectrum is given by @xmath42 for @xmath43 , the precise value of the minimum photon energy is not very important so we have set it at a nominal value of @xmath44kev . we have computed thermal comptonization and disk reprocessing spectra in this model for ngc 3516 . the x - ray luminosity @xmath12 is found by fitting the disk spectrum to the mean optical fluxes measured by hst ( edelson et al . we fix the disk inner radius at @xmath45 cm and plot the resulting spectral energy distributions ( seds ) in figure  [ seds ] for values of the sphere radius in the range @xmath46@xmath47 cm ( solid curves ) . as claimed , the calculated disk spectrum is strikingly constant , with only relatively small variations in the bluer parts of the spectrum . for comparison , we plot the mean fluxes measured by hst . given the crudeness of this model , the quality of the fit is satisfactory even for the uv flux . since the uv flux was only monitored over a significantly shorter period than the optical data due to saa passages . in addition , the uv data point , at @xmath48 , is in a part of the spectrum which may be contaminated by the broad wings of the siiv emission line ( see edelson et al . 2000 , fig .  3 ) . unfortunately , similar contamination problems may exist for the optical data as well ( see edelson et al . 2000 , fig .  4 ) . ] since we have thus far neglected local viscous dissipation in the disk , the black hole mass does not enter into the calculation of the disk emission . however , the value of the disk inner radius can , in principle , be constrained by the optical and uv data . the dashed curve in figure  [ seds ] is the sed obtained for @xmath49 cm . this shows that while the disk spectrum is relatively insensitive to factor @xmath5 changes in @xmath8 for a given optical flux , comparably sized changes in @xmath9 produce strong color variations in the uv . therefore , in order to account for the uv flux , the disk inner radius can not be too much larger than @xmath50 cm . for a central black hole mass of @xmath51m@xmath52(e.g . , edelson & nandra 1999 ) , this value for the disk inner radius is roughly consistent with innermost radius implied by asca observations of the broad fek@xmath53 emission line ( nandra et al.1999 ) . despite the fact that the optical / uv continuum barely changes as a function of @xmath8 , the x - ray spectrum varies drastically . in the 210kev band in particular , the flux changes by factors of @xmath54 for the spectra shown . to relate this result more concretely to the x - ray observations of ngc  3516 , we plot in figure  [ gamma_vs_flux ] the x - ray spectral index versus 210kev flux for a family of curves corresponding to different optical fluxes with the position on any given curve being parameterized by the value of @xmath8 . we propose that the hst / asca / rxte monitoring observations of ngc 3516 can be explained in this model by changes in @xmath8 and accompanying changes in @xmath12 so that @xmath22 is approximately maintained , and the source takes a path in the @xmath6-@xmath55 plane which lies nearly along a curve of constant optical flux . any significant variations in the optical / uv continuum will correspond to deviations from the constant flux curve and therefore from the @xmath22 relation . furthermore , the changes associated with such departures will be broad band and will show the same color variations that have been previously associated with thermal reprocessing .    for comparison , we have plotted in figure  [ gamma_vs_flux ] values of @xmath6 and @xmath55 which we have obtained from fitting the publicly archived rxte ngc 3516 data for the observations in question . although this simple model overpredicts the x - ray flux by a factor @xmath3 for the observed range of spectral indices , the correlation of spectral index and flux given by the model is strikingly similar to that of the data . the flux discrepancy could be reduced somewhat by selecting a smaller value for the thomson depth @xmath56 since for a given spectral index ( and @xmath57-parameter ) that will imply a larger value of @xmath37 and more of the x - ray luminosity can be `` hidden '' at higher energies . alternatively , a large reduction can be obtained by including contributions to the disk emission from local viscous dissipation . this corresponds to adding a term @xmath58 inside the square brackets in the expression for the disk temperature ( eq .  [ t(r ) ] ) where @xmath59 for a maximal kerr metric and @xmath60 for a schwarzschild metric . since the viscous dissipation term is independent of @xmath8 , it acts essentially as a constant offset for the required value of the x - ray luminosity , and @xmath22 is still needed to maintain a constant optical flux . in order to match the observed x - ray fluxes , roughly 1/4 of the total disk luminosity must be due to thermal reprocessing with the remaining 3/4 being due to viscous dissipation . assuming @xmath61m@xmath52  and @xmath59 , we have solved for the energy balance condition and find that an accretion rate of @xmath62m@xmath52  yr@xmath63 is required to match the mean x - ray flux . this solution is plotted as the thick solid curve in figure  [ gamma_vs_flux ] . although the energy balance condition we have used only restricts the properties of the comptonizing plasma , _ global _ energy balance is roughly satisfied by this solution . the bolometric x - ray luminosity which gives the observed mean x - ray flux and spectral index is @xmath64erg  s@xmath63 , while the above accretion rate implies a disk luminosity of @xmath65erg  s@xmath63 due solely to viscous dissipation . for a disk extending all the way to @xmath59 ( rather than being truncated at @xmath8 ) , the total implied luminosity is @xmath66erg  s@xmath63 , and we have @xmath67 this would be expected if the accretion luminosity that would otherwise emerge as local black body emission from the inner regions of the untruncated disk were instead partitioned to the heating of the comptonizing plasma . we note that we have arbitrarily set the thomson depth to @xmath36 in computing this solution . by fine tuning the values of @xmath56 and @xmath68 , we find that we can satisfy the global energy balance condition arbitrarily well while simultaneously matching the observed mean x - ray flux , spectral index and optical continuum levels . the fact that an approximately constant optical / uv continuum can in principle result from thermal reprocessing of a highly variable x - ray flux is connected with the fact that the radial distribution of the flux incident upon the disk is well approximated by a power - law , even very close to the innermost disk radius . as we showed above , the constant flux constraint , in conjunction with the assumed constancy of the disk inner radius and disk albedo , causes the radius of the comptonizing sphere to drop out of the integral describing the disk spectrum . however , this constraint does not demand that the shape of the incident flux distribution be a power - law . the only requirement is that the relevant physical parameters affecting the incident flux can be considered independently from the expression which describes the _ shape _ of the distribution . for example , consider the model proposed by beloborodov ( 1999b ) in which the comptonizing medium consists of a blob of plasma which is at some height @xmath69 above the disk . the blob moves with mildly relativistic velocities either vertically away from or towards the underlying accretion disk , and the effective reflection fraction is controlled by relativistic aberration of the flux from the blob . using the formulae in beloborodov ( 1999b ) , the radial distribution of the flux incident upon the disk is given by @xmath70,\ ] ] where @xmath71 is the blob velocity in units of @xmath72 , @xmath73 , and @xmath74 is the disk radius in units of the blob height . for the range of blob velocities required by this model to reproduce the observed @xmath7-@xmath6 correlation , @xmath750.7 , the factor in the square brackets which gives the shape of the flux distribution is largely insensitive to the exact value of @xmath71 . therefore , since the lower limit of the radial flux integral can be taken to be zero ( cf . eq .  [ fopt ] ) , a nearly constant optical flux in this model can be obtained if @xmath76 . although neither of the aforementioned models offer any reason for the luminosity scalings which seem to be required by the ngc 3516 observations , any plausible explanation would still have to contend with why ngc 7469 and probably other sy1s violate it . therefore , we will not attempt to posit a physically motivated rationale for the specific relationship between x - ray luminosity and geometry required for any particular object , but a cursory examination of the important time scales may provide some insights . for ngc 3516 , the typical variability time scale exhibited by the 210 kev light curve is @xmath7730ks ( edelson et al . assuming a radial thomson depth @xmath36 and @xmath28 , the cooling time is very short : @xmath78s , where @xmath79 is the total number of electrons in the sphere with mean temperature @xmath80k . unfortunately , the thermal expansion time for a sphere of this size is fairly long , approximately @xmath81ks . this assumes that the protons and the electrons are at the same temperature . if we have a two - temperature plasma in which the protons possess a virial temperature of @xmath82k , then the expansion time scale is reduced substantially . alternatively , this could also be achieved if we have a pair plasma instead . we have assumed for simplicity that the thermal emission from the disk is locally blackbody . detailed modeling of bare disk atmospheres appropriate for sy1s indicates that this is a moderately reasonable approximation in the optical , but significant deviations can occur at higher frequencies ( e.g. , hubeny et al . 2000 , 2001 ) . this appears to remain true for disks powered exclusively by external x - ray illumination ( sincell & krolik 1997 ) . our treatment of the reprocessed flux in the optical is therefore probably fairly good , but the full seed photon spectrum illuminating the comptonizing plasma will not be very accurate . more detailed modeling of the disk spectrum will likely affect the specific values we deduce for the disk inner radius , x - ray luminosity , and comptonizing sphere radius , but it will not change our general conclusions . the existing simultaneous optical , uv , and x - ray data plus the global energy balance condition ( eq .  [ global_energy_balance ] ) provide just enough information to infer unique values for the five model parameters , @xmath9 , @xmath8 , @xmath37 , @xmath56 , and @xmath68 , required to describe the entire spectral energy distribution . therefore , a crucial test of this general scheme for linking thermal comptonization and thermal reprocessing will be provided by simultaneous optical , uv , and _ broad band _ x - ray monitoring observations which include reliable measurements of the thermal roll - over at energies @xmath83kev . these latter measurements are necessary for making estimates of the x - ray luminosity @xmath12 which can then be compared with the luminosities required by the model . forthcoming _ integral _ observations of sy1s will provide some of the necessary spectral coverage to address this issue , but what is really required is a hard x - ray / soft gamma - ray telescope which can measure the x - ray spectrum and thermal roll - over on time scales comparable to the shortest variability time scales seen from these objects . we thank andzrej zdziarski and the anonymous referee for helpful comments . jc was partially supported by nasa atp grant nag 5 - 7723 during the course of this work . ob acknowledges support from nasa grant nag 5 - 7075 and nsf grant phy 99 - 07949 . this research has made use of data obtained from the high energy astrophysics science archive research center ( heasarc ) , provided by nasa s goddard space flight center . beloborodov , a. m. 1999a , in high energy processes in accreting black holes , eds . j. poutanen and r. svensson , ( san francisco : astronomical society of the pacific ) , 295 beloborodov , a. m. 1999b , apj , 510 , l123 clavel , j. , et al . 1991 , apj , 366 , 64 collin - souffrin , s. 1991 , a&a , 249 , 344 courvoisier , t. j .- , & clavel , j. 1991 , a&a , 248 , 389 edelson , r. e. , & nandra , k. 1999 , 514 , 682 edelson , r. e. , et al . 2000 , apj , 534 , 180 hubeny , i. , agol , e. , blaes , o. , & krolik , j. h. 2000 , apj , 533 , 710 hubeny , i. , blaes , o. , krolik , j. h. , & agol , e. 2001 , apj , in press ( astro - ph/0105507 ) krolik , j. h. et al . 1991 , apj , 371 , 541 nandra , k. , et al . 1998 , apj , 505 , 594 nandra , k. , george , i. m. , mushotzky , r. f. , turner , t. j. , & yaqoob , t. 1999 , apj , 523 , l17 nandra , k. , et al . 2000 , apj , 544 , 734 peterson , b. m. , et al . 1991 , apj , 368 , 119 peterson , b. m. , et al . 1998 , pasp , 110 , 660 poutanen , j. , krolik , j. h. , & ryde , f. 1997 , mnras , 292 , l21 sincell , m. w. , & krolik , j. h. 1997 , apj , 476 , 605 zdziarski , a. a. , et al . 1998 , mnras , 301 , 435 zdziarski , a. a. , lubiski , p. , & smith , d. a. , 1999 , mnras , 303 , l11 ( zls )
we present an application of the thermal comptonization / disk reprocessing model recently proposed by zdziarski , lubiski , & smith . 
 we show that the absence of strong optical variations in the presence of strong concurrent x - ray variations , similar to those found by hst / rxte monitoring observations of ngc 3516 , can be explained by changing the geometry of the comptonizing plasma rather than the accretion disk itself . 
 the total x - ray luminosity of the comptonizing plasma must decrease as its spatial extent increases . 
 in contrast , the disk inner radius must be roughly fixed in order not to produce optical / ultraviolet color variations stronger than observed . by including emission due to internal viscous dissipation in the disk 
 , we can roughly match the optical and x - ray flux levels and variability amplitudes seen from ngc 3516 during the hst / rxte campaign .