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with the discovery of fe  k@xmath0  emission at 6.4  kev  and spectral hardening at 2030  kev  in the x - ray spectra of seyfert  1 galaxies ( pounds et al .
1990 ) , it was a center figure in probing the physics around black holes.ascas observation about the mcg-6 - 30 - 15 s board and skewed profile reveal two important physical mechanisms - the gravitational and the doppler effect.there are also other sources which show board and skewed profile.various explanation and observation about the fe  k@xmath0have been presented ( see fabian 2000,reynolds & nowak 2003 for details.)another intriguing thing is that , the sources always show a x - ray continuum with power - law distribution , till now , there is no convincing explanation about the production of the x - ray continuum .    from both the observational and theoretical side ,
the iron line is expected to be the reflection from the accretion disk .a lot of computational method to compute the iron line profile from the vicinity of black hole has been invited(fanton 1997,bromley 1994,labor 1991),among which the most renowned is the ray - tracing method due to it s efficiency in computing.the differences in the line profiles from source to source have possibly implied variation in the geometry , the view angle , the structure of the bh - accretion disk system.with xmm s high s / n data , it greatly facilitate the astronomical community to study the iron k@xmath0 in agn . in order to model the fe  k@xmath0many detailed calculations about the accretion disk
must be performed.many author have make computation considering the geometry , such as flat , concave , conical , thick.(hartnoll 2002),merloni founded that the inner boundary condition of accretion flows have a significant effect on the profile .
the ionization state and fe abundance in the accretion disk also have been studied by ballantyne 1999,fabian 2002.nayakshins two - layer model in the surface of accretion disk also seems plausible.recent mhd studies have proposed that there may be exist spiral velocities in accretion disk which will brought quasi - humps in the profiles .
however , for simplicity , the disk emissivity is usually assumed to have a power - law profile @xmath1(where @xmath2 is the distance from the center in units of schwarzshild radii),and the index of such power - law is generally assumed to be given by the accretion disc emissitvity index in a standard geometrically thin and optically think disk(shakura sunyaev 1973).the fact that both wilms et al.2001 and miller et al.2002 require a larger value of @xmath0 to fit the line profile has prompted speculation that , in the inner disc disc region , additional energy dissipation must be taking place.the long mcg-6 - 30 - 15 s observation with xmm - newton reported by fabian et al.2002 show that , the strong , skewed iron line is clearly detected and is well characterized by a steep emissity profile within 6gm / c@xmath3 and a flatter profile beyond .
in contrast to explain the steep profile in the non - zero torque theory , which needs a comprehensive study of the mhd in accretion disk.we just make the simplest computation to deduced the flux striking the surface of the disk in the gr scheme , hence see the effects on line profiles , and the result is very useful in accounting for the steep emissivity in the inner part of the disk .
numerical models of reflection spectra from accretion discs began with the simplest case : assuming a static , neutral and constant density slab of material irradiated by a power - law continuum of x - rays .
george & fabian ( 1991 ) and matt , perola & piro ( 1991 ) performed monte - carlo calculations of the reflection spectra in such circumstances , and provided predictions on the equivalent width ( ew ) of fe  k@xmath0  for different reflection geometries.in this paper , we also assume the source is centredly located , static with a power law flux @xmath4,and this assumption is very close to the observation about the x - ray continuum .
the gravitational field of a rotating black hole is described by the kerr metric(we use units c = g=1 ) @xmath5 where @xmath6 @xmath7 @xmath8    we can see that the metric depends only on two parameters , the mass @xmath9 of the black hole and the specific angular momentum @xmath10 . and it is straight forward to formulate that the photo in kerr metric should has the relation in different place.we assume the photo propagate from place@xmath11to place@xmath12 then we can get @xmath13 and due to the invariance in general relativity @xmath14 so we can deduce that @xmath15 notice here , in the photons prorating in the kerr metric , the a is changing , due to the frequency changing.so we can get @xmath16 as we know , in the newtonian space - time the intensity of the flux should not be changed , how ever , eq .  [ intense ] show that the intensity changed due to a factor.the same , we can get @xmath17 where @xmath18is the flux striking the disc in kerr metric , while@xmath19is the fomat in newtonian space - time . in the newtonian space-time.in the model of point like , static source up the black hole
, the flux striking the disk should be @xmath20 in kerr black hole , we know that @xmath21 we set r , a , in unit of m , then@xmath19can have the detailed formula @xmath22 for a non - rotating black hole , we can get @xmath23 when we set r , h in unit of schwichild radii @xmath24,the formula change to @xmath25 from eq .
[ qin ] we can see that the flux striking the accretion disc has a close relation with both the photo index @xmath0 , the accretion rate @xmath26,and the sources location.observations shows that the source x - ray continuum always have a photo index @xmath27 .
when we compute the @xmath18 in this model , we find that in a extremely rotating kerr metric the flux concentrated on only a very small region near the center , while other place left nearly no illumination at all.it is apparently a gr effect.when it comes to the schwchild metric , the power law approximation is also not good to describe the emissivity , but it is rather flatter to the case in kerr metric.we can conclude that the need of steep power law model may due to a rapidly rotating black hole .
our work is invoked by recent report of steep emissity in inner part of accretion disk(fabian 2002).in the observation of mcg-6 - 30 - 15,fabian use a broken emissivity law to model the data , and with good result.however,they assume that the steep emissivity is a result from two reflector in the disk . in our work
we can see that , the steep emissivity may come from the effect of light bending near the center black hole.and the concentrating of flux , will give inner side a rather high ionization parameter,@xmath28 , which may result a line component at @xmath29kev.there are also other sources , such as iras 13224 - 3809(boller 2003),which should induce a steeper emissivity law.the steep emissivity law may be a evidence of a centering rapidly rotating black hole .    in present x - ray study ,
there are lots of uncertainty in modelling the iron lines in agn , the s / n is a big problem to determine the real shape of the line.former observation confirms that there exist many agn which contain board and skew iron line , indicating that the line is produced very near the black hole.however,recent xmm observation show that there does not ubiquitous exist board iron line , instead , a narrow cole at 6.4 kev is present.this has not been included in this paper .    our work show that in the gr effect , the emissity can not be simply regarded as a power law as a function of r , instead , it should be described by various factors such as a , the source s position the photo index.when computed in the gr we find in the kerr metric the large concentration of the flux in the accretion disc , rather left other part of the disk `` empty'',also , the large concentration in flux will undoubtedly invoke the model of ionized disk describe by ross 1999.and our work is only a simplified model to test the gr effects , further work such as the disk motion and density under high illumination which may affect the emissity should be invoked .
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in this paper , we present a simple relativistic approach to analyze the flux striking the disk which is possibly from a source up the black hole.the x - ray source is locate above an accretion disc orbiting around the black hole , this assumption is invoked by recent studies about iron k@xmath0 . we compute and arguing that due to the light bending effect near black hole , the flux striking the disk surface may be very concentrated , which will undoubtable change the disk s ionization state hence change the iron line s ionization state and emissivity.also,our model may explain the steep power law when modelling the lines .