ReadMe File for XSPEC Models xskdline, xskdconv (c) Kris Beckwith & Chris Done, May 2005 If you use these models, please cite: Beckwith & Done 2004MNRAS.352..353B Beckwith & Done 2005MNRAS.tmp..357B INTRODUCTION This model calculates the line profile from a Keplerian Accretion disk around both Schwarzschild & Kerr (arbitrary spin) black holes. For bug reports, feature requests, etc. please contact k.r.c.beckwith_at_durham.ac.uk. It requires the use of an extensive set of transfer functions, which must be downloaded from the XSPEC website. Each of the XXXX.zip files contain a transfer function for a given black hole spin. All of the zip files MUST be unzipped in within the directory: $LHEASOFT/../spectral/xspec/manager/XSKDLINE/ The model can be used in two distinct forms within XSPEC: 1) As an additive model, called using one of a) XSPEC>mo kdline0 b) XSPEC>mo kdline1 2) As a convolution model, called using one of (e.g.) a) XSPEC>mo kdconv0*compps b) XSPEC>mo kdconv1*compps Each of these forms can be run in two distinct modes (denoted by kdlineN,kdconvN; where N is either 0 or 1): Mode 0 (kdline0,kdconv0): The accretion disk is assumed to extend down to the marginally stable orbit for a particular black hole spin. The value of the spin parameter is determined by inversion of Rms(a) (see e.g. Bardeen, Press & Teulkolsky, 1974). The model can be used to fit to the value of Rms & hence determine a, which is displayed by setting: XSPEC>chatter 12 Mode 1 (kdline1,kdconv1): The model does not assume that the disk extends down to the innermost stable orbit. Instead, the line profile is calculated by specifying the black hole spin, a; the inner (Rmin) & outer (Rmax) edges of the disk; along with inclination, etc. Due to the method used by XSPEC to perform spectral fitting, the radii are c set in units such that Rms(a) = 1, Rout = 100. Unless the user is certain of what they are doing, it is STRONGLY advised that the spectral fit is started using the default settings of the model. Upon the completion of a fitting procedure, the user can determine the values of the radii in units of GMc^{-2} by setting: XSPEC>chatter 12 PARAMETERS kdline0 --------------------------------------------------------------------------- --------------------------------------------------------------------------- Model: kdline0<1> Model Fit Model Component Parameter Unit Value par par comp 1 1 1 kdline0 Energy 1.00000 frozen 2 2 1 kdline0 Rms(G) 6.00000 +/- 0.00000 3 3 1 kdline0 Rout(G) 100.000 +/- 0.00000 4 4 1 kdline0 Incl deg 30.0000 +/- 0.00000 5 5 1 kdline0 Index 3.00000 +/- 0.00000 6 6 1 kdline0 F(r) 1.00000 frozen 7 7 1 kdline0 G(m) 0.00000 frozen 8 8 1 kdline0 norm 1.00000 +/- 0.00000 --------------------------------------------------------------------------- --------------------------------------------------------------------------- 1: Energy Rest frame energy of the line 2: Rms The location of the innermost stable orbit in units of GMc^{-2}. This parameter can lie in the range 1.0 -> 6.0 & is used to determine the black hole spin, by inversion of Rms=Rms(a) 3: Rout The location of the outer edge of the disc in units of GMc^{-2} 4: Incl The inclination of the observer relative to the spin axis of the black hole in Degrees, in the range 1 (face-on) -> 89 (edge-on), measured in degrees. 5: Index Index of radial power law used to generate the line, taken in the form r^{-index} 6: F(r) Specifies the type of radial emissivity, current options: 0: No dependence, F(r) = constant 1: Power law depence (see above) 2: Zero Torque IBC (Page & Thorne, 1974) 7: G(m) Specifies the type of angular emissivity, current options: 0: Optically thick, constant, G(m) = cons. 1: Optically thin, limb brightened, G(m) \propto 1/m 2: Optically thick, limb darkened, G(m) \propto (1+(2.06*m))/2.06 3: G(m) \propto m*log(1+m^{-1}) For more info, see Beckwith & Done (2004) kdline1 --------------------------------------------------------------------------- --------------------------------------------------------------------------- Model: kdline1<1> Model Fit Model Component Parameter Unit Value par par comp 1 1 1 kdline1 Energy 1.00000 frozen 2 2 1 kdline1 Spin 0.00000 +/- 0.00000 3 3 1 kdline1 Rin 1.00000 +/- 0.00000 4 4 1 kdline1 Rout 100.000 +/- 0.00000 5 5 1 kdline1 Incl deg 30.0000 +/- 0.00000 6 6 1 kdline1 Index 3.00000 +/- 0.00000 7 7 1 kdline1 F(r) 1.00000 frozen 8 8 1 kdline1 G(m) 0.00000 frozen 9 9 1 kdline1 norm 1.00000 +/- 0.00000 --------------------------------------------------------------------------- --------------------------------------------------------------------------- 1: Energy Rest frame energy of the line 2: Spin Black hole spin, in range 0 (Schwarzschild) to 1 (Extreme Kerr) 3: Rmin Location of inner edge of accretion disk, in the range 1 to 100 The units of this parameter are as described above 4: Rmax Location of outer edge of accretion disk, in the range 1 to 100 The units of this parameter are as described above 5: Incl The inclination of the observer relative to the spin axis of the black hole in Degrees, in the range 1 (face-on) -> 89 (edge-on), measured in degrees. 6: Index Index of radial power law used to generate the line, taken in the form r^{-index} 7: F(r) Specifies the type of radial emissivity, current options: 0: No dependence, F(r) = constant 1: Power law depence (see above) 2: Zero Torque IBC (Page & Thorne, 1974) 8: G(m) Specifies the type of angular emissivity, current options: 0: Optically thick, constant, G(m) = cons. 1: Optically thin, limb brightened, G(m) \propto 1/m 2: Optically thick, limb darkened, G(m) \propto (1+(2.06*m))/2.06 3: G(m) \propto m*log(1+m^{-1}) For more info, see Beckwith & Done (2004) kdconv0 --------------------------------------------------------------------------- --------------------------------------------------------------------------- Model: kdconv0<1> Model Fit Model Component Parameter Unit Value par par comp 1 1 1 kdconv0 Rms(G) 6.00000 +/- 0.00000 2 2 1 kdconv0 Rout(G) 100.000 +/- 0.00000 3 3 1 kdconv0 Incl deg 30.0000 +/- 0.00000 4 4 1 kdconv0 Index 3.00000 +/- 0.00000 5 5 1 kdconv0 F(r) 1.00000 frozen 6 6 1 kdconv0 G(m) 0.00000 frozen --------------------------------------------------------------------------- --------------------------------------------------------------------------- 1: Rms The location of the innermost stable orbit in units of GMc^{-2}. This parameter can lie in the range 1.0 -> 6.0 & is used to determine the black hole spin, by inversion of Rms=Rms(a) 2: Rout The location of the outer edge of the disc in units of GMc^{-2} 3: Incl The inclination of the observer relative to the spin axis of the black hole in Degrees, in the range 1 (face-on) -> 89 (edge-on), measured in degrees. 4: Index Index of radial power law used to generate the line, taken in the form r^{-index} 5: F(r) Specifies the type of radial emissivity, current options: 0: No dependence, F(r) = constant 1: Power law depence (see above) 2: Zero Torque IBC (Page & Thorne, 1974) 6: G(m) Specifies the type of angular emissivity, current options: 0: Optically thick, constant, G(m) = cons. 1: Optically thin, limb brightened, G(m) \propto 1/m 2: Optically thick, limb darkened, G(m) \propto (1+(2.06*m))/2.06 3: G(m) \propto m*log(1+m^{-1}) For more info, see Beckwith & Done (2004) kdconv1 --------------------------------------------------------------------------- --------------------------------------------------------------------------- Model: kdconv1<1> Model Fit Model Component Parameter Unit Value par par comp 1 1 1 kdconv1 Spin 0.00000 +/- 0.00000 2 2 1 kdconv1 Rin(G) 1.00000 +/- 0.00000 3 3 1 kdconv1 Rout(G) 100.000 +/- 0.00000 4 4 1 kdconv1 Incl deg 30.0000 +/- 0.00000 5 5 1 kdconv1 Index 3.00000 +/- 0.00000 6 6 1 kdconv1 F(r) 1.00000 frozen 7 7 1 kdconv1 G(m) 0.00000 frozen --------------------------------------------------------------------------- --------------------------------------------------------------------------- 1: Spin Black hole spin, in range 0 (Schwarzschild) to 1 (Extreme Kerr) 2: Rmin Location of inner edge of accretion disk, in the range 1 to 100 The units of this parameter are as described above 3: Rmax Location of outer edge of accretion disk, in the range 1 to 100 The units of this parameter are as described above 4: Incl The inclination of the observer relative to the spin axis of the black hole in Degrees, in the range 1 (face-on) -> 89 (edge-on), measured in degrees. 5: Index Index of radial power law used to generate the line, taken in the form r^{-index} 6: F(r) Specifies the type of radial emissivity, current options: 0: No dependence, F(r) = constant 1: Power law depence (see above) 2: Zero Torque IBC (Page & Thorne, 1974) 7: G(m) Specifies the type of angular emissivity, current options: 0: Optically thick, constant, G(m) = cons. 1: Optically thin, limb brightened, G(m) \propto 1/m 2: Optically thick, limb darkened, G(m) \propto (1+(2.06*m))/2.06 3: G(m) \propto m*log(1+m^{-1}) For more info, see Beckwith & Done (2004)