document: x - ray reflection off the surface of cold disks in active galactic nuclei ( agn ) and galactic black holes ( gbhs ) has been an active field of research since the work of @xcite . in early studies , 
   the illuminated material was assumed to be cold and non - ionized @xcite . 
   it was soon realized , however , that photoionization of the disk can have a great impact on both the reflected continuum and the iron fluorescence lines . 
   detailed calculations were then carried out by @xcite and @xcite . however , in all of these papers , the density of the illuminated material was assumed to be constant along the vertical direction . 
   this assumption applies only to the simplest version of radiation - dominated shakura - sunyaev disks @xcite , and only for the portion where viscous dissipation is the dominating heating process . for the surface layers , 
   however , photoionization and compton scattering are the major heating sources . 
   therefore the approximation of constant density is not appropriate . 
   moreover , thermal instability allows the coexistence of gas at different phases . 
   these different phases have very different temperatures , and hence different densities to keep the gas in pressure balance . 
   recently @xcite relaxed the simplifying assumption of constant gas density . 
   they determined the gas density from hydrostatic balance solved simultaneously with ionization balance and radiative transfer . 
   they made an important observation that the thomson depth of the hot coronal layer can have great influence on the x - ray reprocessing produced by the deeper , and much cooler disk . in order to simplify the calculation of the vertical structure , though , they ignored thermal conduction and the effects of transition layers between the different stable phases . 
   a discontinuous change in temperature was allowed whenever an unstable phase was encountered . 
   they argued that such transition layers are of little importance because their thomson depths are negligibly small . 
   however , without taking into account the role of thermal conduction , their method of connecting two different stable layers is rather _ 
   ad hoc_. moreover , even though the thomson depths of these transition layers are small , it does not guarantee that the x - ray emission and reflection from such layers are negligible . 
   because the temperature regime where the transition layers exist is not encountered in the stable phases , some of the most important lines can have appreciable emissivity only in these layers . 
   also , since resonance line scattering has much larger cross section than thomson scattering , the optical depths in resonance lines can be significant .    including thermal conduction in the self - consistent solution of the vertical structure presents a serious numerical challenge . 
   the difficulties are due to the coupling between hydrostatic balance , radiative transfer and heat conduction . 
   @xcite first studied the phase equilibrium of a gas heated by cosmic rays and cooled by radiation . 
   they found that taking into account heat conduction in the boundary layer allows one to obtain a unique solution of the stable equilibrium . 
   @xcite calculated the full temperature profile for a compton - heated corona , and @xcite calculated the static conditions of the plasma for different forms of heating and cooling . 
   but they did not include much discussion of the spectroscopic signatures resulting from the derived vertical structure .    in this paper 
   , we first calculate the temperature structure in the layers above the accretion disk , then calculate the emission lines via radiative recombination ( rr ) and reflection due to resonance line scattering from the derived layers . 
   certain illuminating continua spectra allow more than two stable phases to coexist , with two transition layers connected by an intermediate stable layer . 
   for the transition layer , since the thomson depth is small , the ionizing continuum can be treated as constant ; and since its geometric thickness is smaller than the pressure scale height , the pressure can be treated as constant as well . 
   we can thus obtain semi - analytic solution of the temperature profile by taking into account thermal conduction . for the intermediate stable layer , 
   its thickness is determined by the condition of hydrostatic equilibrium . in our model 
   , the normally incident continuum has a power - law spectrum with an energy index of @xmath0 . 
   we also assume a plane - parallel geometry and that the resonance line scattering is isotropic . 
   the structure of this paper is as follows : in  [ sec_structure ] we discuss the existence of the thermal instability and compute the thermal ionization structure of the transition layers ; in  [ sec_spectrum ] we calculate the recombination emission lines and the reflection due to resonance line scattering ; in  [ sec_summary ] we summarize the important points of the calculations , the validity of various approximations made in the calculations , and the detectability of the recombination emission and reflection lines . 
   the vertical structure of an x - ray illuminated disk at rest is governed by the equations of hydrostatic equilibrium and of energy conservation @xmath1 in the first equation , @xmath2 is the force density due to gravity and radiation pressure . 
   the dependence of the force on the plasma density is included explicitly through the hydrogen density @xmath3 . in the second equation , 
   a time independent state is assumed , @xmath4 is the thermal conductivity , and @xmath5 is the net heating rate depending on the gas state and the incident flux @xmath6 ( differential in energy ) . 
   we neglect the effects of magnetic field and adopt the spitzer conductivity appropriate for a fully ionized plasma , @xmath7 erg @xmath8 s@xmath9 k@xmath9 @xcite . we have used the classical heat flux , @xmath10 , in equation ( [ eq_transition ] ) because the electron mean free path is short compared to the temperature height scale . 
   since the continuum flux may change along the vertical height , in principle , the above two equations must be supplemented by an equation for radiative transfer . 
   a self - consistent solution of such equations is difficult to obtain . in the following , 
   we invoke a few physically motivated approximations , which make the problem tractable . 
   first , in thermally stable regions , the gas temperature is slowly varying , the heat conduction term in the energy balance equation can be neglected . 
   therefore , the temperature can be determined locally with the condition @xmath11 . 
   it is well known @xcite that the dependence of @xmath12 on the gas pressure @xmath13 and the illuminating continuum @xmath6 can be expressed in the form of @xmath14 , where @xmath15 is the electron density , @xmath16 is the net cooling rate per unit volume , and @xmath17 is an ionization parameter defined by @xmath18 where @xmath19 is the total flux of the continuum , and @xmath20 is the speed of light . in figure [ fig_scurve ] , we show the local energy equilibrium curve @xmath21 versus @xmath17 , at @xmath22 calculated with the photoionization code xstar @xcite . 
   these curves are commonly referred to as `` s curves '' due to their appearance . 
   the illuminating continuum is assumed to be a power law with energy index @xmath0 . 
   the solid line labeled with `` s - curve 1 '' corresponds to a low energy cutoff at 1 ev and a high energy cutoff at 150 kev , while the dashed line `` s - curve 2 '' corresponds to a high energy cutoff at 200 kev . 
   the choice of such incident spectra is based on their common appearance in many agns and gbhcs . 
   the region is thermally `` unstable '' where the `` s - curve '' has a negative slope , and `` stable '' where the slope is positive , as indicated in figure [ fig_scurve ] . in the thermally unstable regions , we have @xmath23 where the derivative is taken while the energy balance is satisfied , i.e. , @xmath24 . 
   this condition was shown @xcite to be equivalent to the instability condition discovered by @xcite @xmath25        the thermal instability allows the gas to coexist at different phases . 
   the gas temperature may change by orders of magnitude over a geometric thin region whenever an unstable phase separates two stable ones . 
   this results in enormous temperature gradients and heat conduction . 
   therefore the heat conduction in the energy balance equation should be included in such transition layers between stable phases . 
   on the other hand , the thicknesses of these transition layers are usually smaller than the pressure scale height , so one can safely treat the gas pressure as constant in these regions . moreover , the continuum radiative transfer can be neglected because the compton optical depth is found to be small . 
   the vertical structure of the transition regions is then solely determined by the energy balance equation with heat conduction . 
   the thomson optical depth @xmath26 of such regions is readily estimated by @xmath27 where @xmath28 is the thomson scattering cross section . 
   the transition layer solution is not arbitrary under the steady - state conditions , i.e. , where there is no mass exchange between the two stable phases which the transition layer connects . 
   a similar problem in the context of interstellar gas heated by cosmic rays was well studied by @xcite . 
   we follow their procedure here and define @xmath29 , in order to rewrite equation ( [ eq_transition ] ) in the form : @xmath30 a steady - state requires vanishing heat flux at both boundaries of the transition layer , or @xmath31 where @xmath32 and @xmath33 are the temperatures of the two stable phases which are connected by a transition layer . 
   this condition determines a unique ionization parameter @xmath17 for the transition layer in question , and the integration of equation ( [ eq_dy2 ] ) along the vertical height gives the detailed temperature profile as a function of optical depth . 
   if the disk does not realize the steady - state solution , there are additional enthalpy terms in equation ( [ eq_transition ] ) which require that there be mass flow through the transition region 
   i.e. the cool material in the disk evaporates , or the hot material in the corona condenses @xcite . 
   physically , this corresponds to a movement of the transition layer up or down through the vertical disk structure . 
   however , since the density increases monotonically toward the center of the disk , this `` motion '' stops where the transition layer reaches the steady state value of @xmath17 . 
   thus , in the absence of disk winds or continuous condensation from a disk corona , the steady state solution should generally be obtained . 
   there is a complication for the `` s - curves '' shown in figure [ fig_scurve ] , because in each curve there exist two unstable regions and therefore there should be two transition layers . for `` s curve 1 '' , 
   condition [ eq_y2 ] can be met for both transition layers with resulting ionization parameters @xmath34 , where @xmath35 and @xmath36 are associated with the transition layer which connects to the lowest temperature phase and highest temperature phase , respectively . for `` s curve 2 '' 
   , the resulting ionization parameters for two transition layers , however , satisfy @xmath37 . 
   such a situation is unphysical , where the ionization parameter of the upper transition layer is smaller than that of the lower one , because in the context of accretion disks , the upper layer receives more ionizing flux and has lower pressure . 
   so in practice , for `` s curve 2 '' the intermediate stable region is skipped and a transition layer connects the lowest temperature phase to the highest temperature phase directly . 
   the ionization parameter of this transition layer is determined the same way by applying equation ( [ eq_y2 ] ) . 
   there is then an intermediate stable layer , of nearly uniform temperature , in between these two transition layers for `` s curve 1 '' , as indicated with bc in figure [ fig_scurve ] . 
   the thickness of the intermediate layer should in principle be obtained by solving the coupled equations of hydrostatic equilibrium , energy balance , and radiative transfer . however , unlike the stable phase at the disk base or that of the corona , which may be compton thick , this intermediate stable layer is generally optically thin , because its optical depth is restricted by the difference between @xmath35 and @xmath36 . 
   furthermore , the temperature in this layer is slowly varying , and therefore heat conduction can be neglected . 
   we shall make another approximation that the variation of the force density @xmath2 in the hydrostatic equation can also be neglected . 
   this may not be a good approximation . 
   however , since our main purpose is to investigate qualitatively the effects of an intermediate stable layer , such a simplifying procedure does capture the proper scaling relations of the problem , and has the advantage of less specific model dependence . 
   writing equation ( [ eq_hydro ] ) in a dimensionless form and parameterizing the force factor by a dimensionless parameter @xmath38 , we obtain @xmath39 the parameter a defined here is identical to the gravity parameter in @xcite in the absence of radiation pressure . 
   the integration of this equation from @xmath35 to @xmath36 gives the thomson depth of the intermediate stable layer . 
   assuming radiation pressure can be neglected , the force factor at a given radius @xmath40 of the disk can be estimated as @xmath41 where @xmath42 is the luminosity of the continuum source in units of the eddington limit , @xmath43 is the half thickness of the disk at radius @xmath40 , @xmath44 is the mass of the central source , @xmath45 is the proton mass , and @xmath46 is the eddington luminosity . in this estimate , we have assumed that @xmath47 . 
   this gives @xmath48 the value : @xmath49 for a typical thin disk , as those present in agn and black hole binaries , one expects @xmath50 . if the luminosity is sub eddington , @xmath51 as in most agns , @xmath48 is of order unity . 
   however , since the disk surface may not be normal to the continuum radiation , @xmath19 may be only a fraction of the value assumed above , which increases @xmath48 by one or two orders of magnitude . 
   on the other hand , as the source approaches the eddington limit , @xmath48 may become smaller than 1 . 
   therefore , we expect @xmath48 to be in the range of 0.1  10 . the exceptional cases of much smaller and larger @xmath48 are discussed in 
   [ sec_summary ] . 
   the temperature profiles and optical depths of the transition layers and possible intermediate stable layer are shown in figures [ fig_transition ] . 
   three labeled curves in solid lines correspond to `` s - curve 1 '' ( in figure [ fig_scurve ] ) with different values of the force factors @xmath48 = 10 , 1 , and 0.1 , respectively . 
   the dashed curve corresponds to `` s - curve 2 '' , where there is no intermediate stable layer . 
   for each of the solid curves , three layers are clearly seen , with two transition layers being connected by an intermediate stable layer , as illustrated for the case of @xmath52 . 
   the smaller @xmath48 produces a more extended intermediate stable layer as expected . 
   because the stable phase with the lowest temperature is almost neutral , and the stable phase at the highest temperature is almost fully ionized , they are not efficient in generating x - ray line emission , except for iron fluorescence lines from the neutral material . only the transition layers and the intermediate stable layer are expected to emit discrete lines in the soft x - ray band . in a photoionized plasma , 
   the temperature is too low for collisional excitation to be an important line formation process . 
   instead , radiative recombination ( rr ) followed by cascades dominates the line emission . 
   the flux of a particular line can be written as @xmath53 where @xmath54 is the density of the ion before recombination , @xmath55 is the line energy , and @xmath56 is the line emissivity defined as in @xcite .    in ionization equilibrium where the ionization rate is equal to the recombination rate , we have @xmath57 , where @xmath58 is the recombination coefficient of ion @xmath59 , @xmath60 is the number density of ion @xmath61 , @xmath6 is again the monochromatic incident flux ( differential in energy ) , and @xmath62 is the photoionization cross section of ion @xmath61 . defining the branching ratio @xmath63 , equation ( [ flux_emission ] ) can be rewritten as : @xmath64 where @xmath65 is the fractional abundance of ion @xmath61 with respect to the electron density . 
   as indicated , @xmath66 and @xmath67 depend only on temperature @xmath21 and ionization parameter @xmath17 , which are both functions of optical depth @xmath68 . for convenience 
   , we further define the `` emission equivalent width '' @xmath69 . 
   then if @xmath70 , which depends only on the shape of the incident continuum , @xmath71 can be written as : @xmath72    therefore the emission equivalent width @xmath71 is independent of the density of the medium and the incident flux . 
   it is a unique function of the structure deduced in section [ sec_structure ] . 
   all other variables depend only on @xmath21 and @xmath17 . 
   the numerical values of @xmath73 were provided by d. liedahl ( private communication ) , and were calculated using the models described in @xcite . 
   the values of @xmath74 were computed using xstar @xcite .    in figure 
   [ fig_emission ] , we plot the spectra of the recombination emission within the 0.5  1.5 kev band with a spectral resolution @xmath75 ev , which is close to the spectral resolution of the grating spectrometers on _ chandra _ and _ xmm - newton_. the top panel corresponds to the case without an intermediate stable layer , and the bottom panels corresponds to the case with an intermediate layer for @xmath76 and 0.1 , respectively . for clarity , from top to bottom , 
   the flux in each panel is multiplied by a factor indicated in each panel . 
   it appears that the existence of an intermediate stable layer enhances the emission in this energy band . 
   this is not surprising since the ions that are responsible for these lines have peak abundances at temperatures close to that of the intermediate stable layer . in all cases , 
   the equivalent widths ( ews ) of the emission lines are less than 1.0 ev , with respect to the ionizing continuum . 
   the strongest lines are the hydrogen - like and helium - like lines of oxygen , with ews approaching several tenths of an ev . 
   hydrogen - like and helium - like lines from iron outside the plotted energy band are somewhat stronger , with ews reaching a few ev . we note that our low equivalent width values conflicts with those derived by @xcite , who found some lines with equivalent widths as high as 30 ev . 
   however , since they did not consider the appropriate locations for the transition regions in @xmath17-space , their intermediate stable layer subtended a much larger optical depth than we find here . 
   naturally with a thicker layer , they found larger equivalent widths . 
   emission from rr is not the only line formation process in the transition layers and the intermediate stable layer . due to very large cross sections in resonance line scattering , the reflected flux in these lines 
   may be significant . with the computed thermal and ionization structure , 
   the column density in each ion and the optical depth in all resonance lines can be calculated straightforwardly . 
   the cross sections for resonance line scattering depend on the line broadening . 
   we assume thermal doppler effects as the only mechanism . 
   although the gas temperature is a function of depth , we calculate the line width for a temperature where the abundance of each ion peaks as an average , and assume that the resonance scattering cross sections are uniform along the vertical direction . in terms of absorption oscillator strength @xmath77 
   , this cross section of the resonance line scattering @xmath78 can be written as @xmath79 where @xmath80 is the electron mass , @xmath81 is the electron charge , @xmath82 is the wavelength of the line and @xmath83 is the average line width in wavelength . under the assumption of thermal doppler broadening , @xmath84 where @xmath85 is the temperature at which the ion abundance peaks , and @xmath86 is the ion mass . the resonance scattering optical depth @xmath87 for a line from ion @xmath59 can be estimated as @xmath88 where @xmath89 is the column density of the ion .    the radiative transfer in the line is a complicated issue @xcite . 
   a full treatment is beyond the scope of this work . 
   however , since we are only interested in a reasonable estimate of the reflected line flux , a simple approach may be adopted . 
   we assume the resonance line scattering is isotropic and conservative and neglect the polarization dependence 
   . under such conditions , the reflection and transmission contributions by a plane - parallel slab of finite optical depth @xmath90 have been solved by @xcite . for normal incident flux @xmath19 , 
   the angle dependent reflectivity is @xmath91 where @xmath92 , @xmath93 is the reflectivity at @xmath94 , @xmath95 is the reflected intensity , @xmath19 is the incident flux , and @xmath96 is the scattering function defined as @xmath97 where @xmath98 and @xmath99 are two functions that satisfy the following integral equations : @xmath100d\mu^{\prime } \nonumber \\ y(\mu)&= & e^{-\tau /\mu}+\frac{\mu}{2}\int_{0}^{1}\frac{1}{\mu-\mu^{\prime}}[y(\mu)x(\mu^{\prime})-x(\mu)y(\mu^{\prime})]d\mu^{\prime}.\end{aligned}\ ] ] the solutions of these equations may be obtained by an iterative method with the starting point @xmath101 and @xmath102 . the angle integrated reflectivity @xmath103 can be calculated as @xmath104 and is shown in figure [ fig_totref ] as a function of the resonance scattering optical depth @xmath87 . 
   the reflected flux in a line can be written as @xmath105 where @xmath106 is the line width in energy . 
   similarly to the `` emission equivalent width '' @xmath71 , we define a `` reflection equivalent width '' @xmath107 , which results in : @xmath108    this `` reflection equivalent width '' from our numerical results is a few tenths of an ev for strong resonance lines , similar to that of the recombination emission lines .    in figure 
   [ fig_reflection ] , we plot the spectra of the resonantly scattered lines in the energy band 0.5  1.5 kev with a spectral resolution @xmath75 ev . 
   the top panel corresponds to the case without an intermediate stable layer , and the bottom panels corresponds to the case with an intermediate layer for @xmath76 and 0.1 , respectively . for clarity , from top to bottom , the flux in each panel is multiplied by a factor of 100 . 
   we see that the equivalent widths of the reflected lines are notably enhanced when there is an intermediate stable layer , but not as significantly as for the recombination emission lines . 
   this is because the optical depths of many strong lines become much larger than unity , and the reflection is saturated . 
   if there are broadening mechanisms other than thermal doppler effects , such as turbulent velocity , the reflected intensity can be further enhanced .      in order to gain a crude idea of the relative importance of recombination emission and reflection from the transition layers and intermediate stable layer 
   , we compare them to the `` hump '' produced by compton scattering off a cold surface @xcite . 
   we use the greens function obtained by @xcite to calculate the compton reflection . 
   this method was verified to be accurate with a monte carlo procedure by @xcite . in figure 
   [ fig_spectrum ] , we show the combined spectra including recombination emission and reflection lines from resonance line scattering , and the compton reflection `` hump '' . 
   we now summarize the most important conclusions that can be drawn from the calculations presented in this paper . 
   we also discuss the detectability of the predicted line features .    1 .   the unique ionization parameters that characterize the steady - state solutions of the transition layers depend on the shape of the `` s - curve '' . 
   we have shown that two power - law illuminating spectra with different high energy cutoffs produce very different temperature profiles . 
   the harder spectrum only allows one transition layer even though there are two unstable branches in the `` s - curve '' , while the softer one allows two separate transition layers connected by an intermediate stable layer . 
   this is due to the fact that the ionization parameter of the upper transition layer must be larger than that of the lower one , if they are to exist separately in a disk environment . 
   the harder spectrum produces a turnover point of the upper branch of the `` s - curve '' at smaller @xmath17 . 
   therefore the transition layer due to the upper unstable region joins the lower one smoothly without allowing the intermediate stable region to form . 
   the turnover of the upper `` s - curve '' represents the point where compton heating starts to overwhelm bremsstrahlung . 
   the ionization parameter at which this point occurs is related to the compton temperature of the continuum , @xmath109 @xcite . 
   a harder spectrum has larger @xmath110 , therefore the intermediate stable layer tends to disappear for hard incident spectra . 
   although the thomson depths of the transition layers and possible intermediate stable layer are generally negligible , the x - ray emission lines from them may comprise the main observable line features , because the temperatures of these layers are inaccessible to the stable phases , and thus some of the important lines can have appreciable emissivity only in these layers . 
   due to the much larger cross sections for resonance line scattering , reflection due to resonance lines off such transition layers is also important . 
   the strengths of reflected lines are at least comparable with those of the recombination emission lines when there is no intermediate stable layer . 
   because the appearance of the reflected line spectrum is different from that of the recombination emission spectrum , high resolution spectroscopic observations should be able to distinguish these mechanisms . 
   3 .   the justification of the assumption that the ionizing continuum does not scatter in the intermediate layer depends on the magnitude of the parameter @xmath48 . 
   the thomson depth of this layer @xmath68 is given by : @xmath111 for the power - law continuum with high energy cutoff at 150 kev ( `` s curve 1 '' ) , @xmath112 and @xmath113 from our numerical results . 
   therefore , @xmath114 . 
   @xmath68 is much less than unity as long as @xmath48 is greater than 0.1 . for smaller @xmath48 
   , however , another effect comes into play . 
   @xcite showed that the thomson depth of the coronal layer ( the stable phase with highest temperature ) exceeds unity when the gravity parameter ( identical to @xmath48 defined here when the radiation pressure is neglected ) is @xmath115 0.01 . 
   therefore not much ionizing flux can penetrate this layer , and the reprocessing in the deeper and cooler layers can be neglected completely . as @xmath48 becomes much larger than 10 , 
   the thickness of the intermediate stable layer is negligible compared to the transition layers . 
   therefore , its presence may be ignored . 
   since the recombination rate must equal the photoionization rate in the irradiated gas , recombination radiation is also a form of reflection 
   i.e. the line equivalent widths are independent of the incident flux . 
   they depend only on the structure ( @xmath116 ) deduced from the hydrostatic and energy balance equations . 
   the detectability of these recombination emission and reflection lines depends on whether the primary continuum is viewed directly . 
   when the ionizing continuum is in direct view , our results show that the ews of the strongest lines in the 0.5  1.5 kev band are at most a few tenths of an ev , slightly larger when there is an intermediate stable layer . 
   + the signal to noise ratio ( snr ) in such a line can be written as @xmath117 where @xmath118 is the integration time of the observation , @xmath55 is the energy of the line , @xmath119 is the photon flux in the continuum , @xmath120 and @xmath121 are the effective area and resolving power of the instrument , respectively . for a line at @xmath115 1 kev , with @xmath122 , and with hetgs on board _ chandra _ , we have @xmath123 . 
   a typical seyfert 1 galaxy has a flux of @xmath124 erg @xmath125 s@xmath9 in the energy band of 210 kev . assuming a power law with energy index of 1 , 
   the photon flux at 1 kev would be @xmath126 @xmath125 s@xmath9 kev@xmath9 . for a reasonable integration time of 10 ks , we have snr @xmath127 . 
   when the primary continuum is obscured as in seyfert 2 galaxies , the ews of the emission and reflection lines can be orders of magnitude larger , because the continuum at this energy region is absorbed severely , and the snr can be greatly enhanced , making these lines observable . 
   acknowledgment : smk acknowledges several grants from nasa which partially supported this work , mfg acknowledges the support of a chandra fellowship at mit . 
   we wish to thank m. sako , d. savin and e. behar for several useful discussions . 
   the `` s - curves '' produced by two different incident ionizing spectra . 
   the vertical line indicates the unique solution of @xmath17 which satisfies condition [ eq_y2 ] : two solutions for `` s - curve 1 '' , @xmath35 = 2.82 and @xmath36 = 3.14 ; and only one for `` s - curve 2 '' , @xmath17 = 2.22 . ] 
   the temperature profiles of the transition layers and the intermediate stable layer versus thomson optical depth @xmath68 . 
   the solid curves correspond to `` s - curve 1 '' with different force factors @xmath48 , the dashed line corresponds to the `` s - curve 2 '' . ]    the spectra of the emission lines via rr in the transition layers and the intermediate stable layer . 
   the spectral resolution is @xmath128 ev . the top panel corresponds to `` s - curve 2 '' , while bottom panels correspond to `` s - curve 1 '' with different parameter a. ]      the spectra of the reflection lines due to resonance scattering in the transition layers and the intermediate stable layer . 
   the spectral resolution is @xmath75 ev . the top panel corresponds to `` s - curve 2 '' , while bottom panels correspond to `` s - curve 1 '' with different parameter a. ]    the combined spectrum . 
   emission lines via recombination , red  reflection lines due to resonance line scattering , and black  the compton reflection hump . 
   the spectral resolution is @xmath129 ev . the top panel corresponds to `` s - curve 2 '' , while bottom panels correspond to `` s - curve 1 '' with different parameter a. ]
summary: we derive a semi - analytic solution for the structure of conduction - mediated transition layers above an x - ray illuminated accretion disk , and calculate explicitly the x - ray line radiation resulting from both resonance line scattering and radiative recombination in these layers . 
   the vertical thermal structure of the illuminated disk is found to depend on the illuminating continuum : for a hard power law continuum , there are two stable phases connected by a single transition layer ; while for a softer continuum , there may exist three stable phases connected by two separate transition layers , with an intermediate stable layer in between . 
   we show that the structure can be written as a function of the electron scattering optical depth through these layers , which leads to unique predictions of the equivalent width of the resulting line radiation from both recombination cascades and resonance line scattering . 
   we find that resonance line scattering plays an important role , especially for the case where there is no intermediate stable layer .