Accretion Disk Spectra

Class providing the spectral energy distribution (in \(L_\odot\) Hz\(^{-1}\)) of circumnuclear accretion disks around supermassive black holes, as a function of wavelength. The spectrum depends on the black hole accretion rate and radiative efficiency, and is used to compute AGN contributions to the UV background, photoionization of the IGM, and other radiative effects.

Default implementation: accretionDiskSpectraHopkins2007

Methods

spectrumNode → double precision

Returns the spectrum (in units of \(L_\odot\) Hz\(^{-1}\)) of the accretion disk at the given wavelength (in units of Å) for node.

• type(treeNode) node [inout]

• double precision wavelength [in]

spectrumMassRate → double precision

Returns the spectrum (in units of \(L_\odot\) Hz\(^{-1}\)) of the accretion disk at the given wavelength (in units of Å) for a specified accretion rate, and radiative efficiency.

• double precision accretionRate [in]

• double precision efficiencyRadiative [in]

• double precision wavelength [in]

wavelengths

Return a tabulation of wavelengths at which accretion disk spectra are defined.

• integer wavelengthsCount [out]

• double precision(:) wavelengths [out]

accretionDiskSpectraFile

Accretion disk spectra are computed by interpolating from tabulated data read from a file specified by [fileName]. The tables provide spectral energy distributions as a function of physical parameters, enabling efficient lookup of accretion disk emission across a range of conditions.

Methods

loadFile

Load a file of AGN spectra.

• character(len=*) fileName [in]

Parameters

• [fileName] (string) — The name of a file from which to read tabulated spectra of accretion disks.

accretionDiskSpectraHopkins2007

Accretion disk spectra using the model of Hopkins et al. (2007).

(Default implementation)

Methods

buildFile

Build the tabulation file containing AGN spectra.

Parameters

• [fileName] (string) — The name of a file from which to read tabulated spectra of accretion disks. (inherited from accretionDiskSpectraFile)

accretionDiskSpectraThinDisk

Accretion disk spectra computed intrinsically for a three-component thin-disk AGN SED based on the model of Done et al. (2012) and comprising (1) a multitemperature blackbody disk following the Shakura and Sunyaev (1973) temperature profile, (2) a soft Comptonized warm corona, and (3) a hard Comptonized hot corona extending to hard X-rays. Strict energy closure is enforced: fractions [fractionHot] and [fractionWarm] of the bolometric luminosity are allocated to the hot and warm coronae respectively, with the remainder \((1 - f_\mathrm{hot} - f_\mathrm{warm})\) going to the disk.

The disk temperature normalization is derived self-consistently from energy conservation so that the SED integrates exactly to the bolometric luminosity. Specifically, the disk temperature profile follows that for a Shakura and Sunyaev (1973) disk (their equation 2.6):

\[T^4(x) = T_0^4 x^{-3} (1-x^{-1/2}),\]

where \(x=R/R_\mathrm{ISCO}\). Integrating the thermal emission over the disk from the ISCO to infinity and setting this equal to the disk luminosity gives

\[2 \times 2 \pi R_\mathrm{ISCO}^2 \sigma T_0^4 \int_1^\infty \mathrm{d}x x^{-2} (1-x^{-1/2}) = L_\mathrm{disk},\]

where \(\sigma\) is the Stefan-Boltzmann constant, and the first factor of 2 on the left arises from that fact that the disk has upper and lower surfaces. This results in

\[T_0^4 = \frac{3 L_\mathrm{disk}}{4 \pi \sigma R_\mathrm{ISCO}^2}.\]

The warm and hot corona spectra are power laws with exponential cutoffs, normalized by the upper incomplete gamma function to achieve the same strict closure. This functional form is commonly used to model hot coronae (Fabian et al., 2015), and is used here as a phenomenological model for the warm bump also. The model uses only the thin-disk luminosity, and returns zero outside the thin-disk regime.

Methods

calculationReset

Reset the cached SED.

• type(treeNode) node [inout]

• integer(kind_int8) uniqueID [in]

computeSED

Compute the SED for given BH properties and populate the cache.

• double precision luminosityBolometric [in]

• double precision radiusISCO [in]

• double precision(self%wavelengthcount) sedOut (optional) [out]

Parameters

• [fractionHot] (real; default 0.02d0) — The fraction of the bolometric luminosity allocated to the hot Comptonized corona. Default from: chosen to produce a plausible AGN SED—in reality will depend on viewing angle, geometry, and energy partition.

• [fractionWarm] (real; default 0.05d0) — The fraction of the bolometric luminosity allocated to the warm Comptonized corona. Default from: chosen to produce a plausible AGN SED—in reality will depend on viewing angle, geometry, and energy partition.

• [temperatureHot] (real; default 200.0d0) — The exponential cutoff energy (in keV) of the hot corona power-law spectrum. Default from: (Fabian et al., 2015).

• [temperatureWarm] (real; default 0.2d0) — The exponential cutoff energy (in keV) of the warm corona power-law spectrum. Default from: (Done et al., 2012).

• [spectralIndexHot] (real; default 1.9d0) — The photon spectral index \(\Gamma\) of the hot corona power-law spectrum, so that \(S_\nu \propto \nu^{-\Gamma}\). Default from: (Tortosa et al., 2018).

• [spectralIndexWarm] (real; default 2.6d0) — The photon spectral index \(\Gamma\) of the warm corona power-law spectrum. Default from: (Petrucci et al., 2018).

• [energyMinimumHot] (real; default 0.1d0) — The minimum seed-photon energy (in keV) below which the hot corona spectrum is set to zero. Default from: chosen to restrict the hot component to the X-ray regime where it is typically measured.

• [energyMinimumWarm] (real; default 1.0d-2) — The minimum seed-photon energy (in keV) below which the warm corona spectrum is set to zero. Default from: typical of the UV/EUV disk photons which seed the warm Comptonization, e.g. Done et al. (2012).

• [massBlackHoleFiducial] (real; default 1.0d8) — The fiducial black hole mass (in \(\mathrm{M}_\odot\)) used when spectrumMassRate is called without a specific node (i.e. when only the accretion rate and radiative efficiency are available).

• [spinBlackHoleFiducial] (real; default 0.5d0) — The fiducial dimensionless black hole spin used when spectrumMassRate is called without a specific node.