Propagating fluctuations in the mass accretion rate of a precessing flow as a power spectral model for black hole binaries
This model and description are due to Adam Ingram.
The power spectrum of black hole binaries (BHBs) in the rise to outburst generally consists of a quasi-periodic oscillation (QPO) and additional band limited noise. This can be phenomenologically modelled using a number of broad Lorentzians for the band limited noise and a narrow Lorentzian for each harmonic of the QPO. Here, we assume a physical origin for this variability in a truncated disc / hot inner flow geometry. Mass accretion rate fluctuations are generated everywhere in the flow (primarily) at the local viscous frequency and propagate inwards towards the black hole. We also assume that the entire flow is precessing due to frame-dragging (Lense-Thirring precession), which gives rise to a QPO. The key assumption is the surface density profile as this sets the precession (and therefore QPO) frequency but also, by mass conservation, sets the viscous frequency as a function of radius. Further details of the model, propfluc, are included in Ingram & Done (2011), particularly in the appendix. This version of the model is calculated analytically using the formalism of Ingram & van der Klis (2013) and is consequently a lot faster than the original model.
We assume that the surface density is given by a smoothly broken power law, consistent with the results of general relativistic magneto hydrodynamic (GRMHD) simulations. The break occurs at the bending wave radius, rbw, with the power law dependence on radius parametrised by zeta for r>>rbw and by lambda for r<<rbw. The sharpness of the break is given by another parameter, kappa. The QPO frequency is calculated self-consistently and the power spectrum of the QPO is represented by Lorentzians centred at f_QPO, 2f_QPO, 3f_QPO and 1/2f_QPO to represent the 1st, 2nd, 3rd and sub harmonics respectively.
There is some extra functionality to this version of the model. Parameters 15 and 16 are respectively `hard' and `soft' band emissivity indices (gamma_h and gamma_s). Parameter 20 (mode) specifies whether the output is the hard band power spectrum (mode=1), soft band power spectrum (mode=2) or the time lag between the two energy bands (mode=3). If gamma_h > gamma_s, the model predicts hard lags. Note, if mode=1, gamma_s should be fixed and if mode=2, gamma_h should be fixed (to anything, the fit is insensitive to the parameter). Parameter 21 (conv) specifies whether the QPO signal is added to the broad band noise signal (conv=0) or multiplied with it (conv=1). The latter is more physically motivated (Ingram & van der Klis 2013). Handy tips for working with the model are provided in Rapisarda, Ingram & van der Klis (2014).
As this is a model for the power spectrum (or lag spectrum if mode=3)
rather than the spectral energy distribution, the process for loading
the data into XSPEC is slightly different. First of all, a power
spectrum can easily be created from a light curve using powspec
from the XRONOS
package (for example). The power spectrum will then typically be
written in the form
Parameters in propfluc:
Download the tar file propfluc.tar. If you are using this without any other models in xspec12 then untar this in a clean directory, fire up xspec12 and type @load. The model should then be set up. Otherwise, build it as normal with other local models.
Keith Arnaud, Lab. for High Energy Astrophysics, NASA/Goddard Space Flight Center
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Last modified: Tuesday, 16-Sep-2014 15:06:15 EDT