Mislav
Baloković

The model tables available here were computed with a new Monte Carlo radiative transfer code BORUS, presented in my Ph.D. thesis, Baloković et al. (2018), and Baloković et al. (2019). Clicking the model name below will open its description, basic instructions, and links to files. I plan to provide models with a range of different geometries and physical assumptions in the future. If you let me know that you are interested in using these models for modeling of AGN spectra, I can get back to you with any updates.

Assumptions relevant to all model tables available below, unless explicitly specified otherwise: (1) the X-ray source is at the geometric center and emits a spectrum that is either a phenomenological cutoff power law (CPL), i.e. F(E) ~ E^-Γ exp(-E/E_cut), or a more realistic coronal continuum (nthComp, as represented in Xspec); (2) gas is assumed to be cold and neutral; (3) Compton scattering neglects the internal structure of the atomic scatterers, so that the Compton shoulder would be comparable to older models which employed such a simplification; (4) fluorescent line emission and the reprocessed continuum are calculated self-consistently; (5) tables represent only the reprocessed component, so the line-of-sight component can be added separately in Xspec (see the example .xcm files below).

• Uniform Density Sphere, CPL Intrinsic Continuum: borus01

  The scattering medium is assumed to be a sphere of uniform density with an X-ray source at the center. Elemental abundances are equal to those in the Sun, except for iron, which can be varied via the relative abundance parameter (A_Fe). Note that the line-of-sight component (absorbed by N_H,los) can have a different column density than the column density of the torus (N_H,tor) in order to account for clouds passing in/out of the line of sight. The model is similar to, and broader than, the sphere model of Brightman & Nandra (2011). It has additional free parameters, additional chemical elements included, calculation extending to higher energies, and line-of-sight component separated out.

  • current table version:
        borus01_v161215a.fits -- with log(N_H,los) as parameter
        borus01_v161215b.fits -- with N_H,los as parameter
  • example .xcm files:
        borus01_NHtied.xcm -- N_H,tor and N_H,los assumed equal
        borus01_NHuntied.xcm -- N_H,tor independent of N_H,los
  • free parameters:
        1 = photon index, Γ = 1.6--2.4
        2 = high-energy cutoff, E_cut/keV = 50--500
        3 = column density, log(N_H,tor/cm^-2) = 22.0--25.0
        4 = iron abundance, A_Fe/A_Fe,Sun = 0.1--10
        5 = redshift
        6 = normalization of the intrinsic spectrum (photons s^-1cm^-2keV^-1 at 1 keV)

   

• Uniform Density Sphere, nthComp Intrinsic Continuum: borus11

  This model is equivalent to the borus01 model described above, except for the different intrinsic continuum, which is represented by the nthcomp model here instead of the phenomenological CPL. This model was first presented in Baloković et al. (2019).

  • current table version:
        borus11_v190815a.fits
  • example .xcm files:
        borus11_NHtied.xcm -- N_H,tor and N_H,los assumed equal
        borus11_NHuntied.xcm -- N_H,tor independent of N_H,los
  • free parameters:
        1 = low-energy photon index, Γ = 1.6--2.4
        2 = coronal electron temperature, kT_e/keV = 5--500
        3 = column density, log(N_H,tor/cm^-2) = 22.0--25.75
        4 = iron abundance, A_Fe/A_Fe,Sun = 0.1--10
        5 = redshift
        6 = normalization of the intrinsic spectrum (photons s^-1cm^-2keV^-1 at 1 keV)

   

• Uniform Density Sphere with Polar Cutouts, CPL Intrinsic Continuum: borus02

  

  The reprocessing medium is assumed to be a sphere with conical cutouts at both poles, approximating a torus with variable covering factor. Half-opening angle of the polar cutouts, θ_tor, measured from the symmetry axis toward the equator, ranges from zero (full covering, equivalent to the borus01 model above) to 83^o (corresponding to disk-like 10% covering). Note that the covering factor is just the cosine of θ_tor. Gas is assumed to be uniformly distributed, with elemental abundances of the Sun, except for the abundance of iron, which is a variable parameter. The line-of-sight component (intrinsic continuum absorbed by N_H,los) can have a different column density than the average column density of the torus (N_H,tor) in order to account for clouds passing in/out of the line of sight. Unless this model is used for fitting a large quantity of broadband X-ray data, fitting for all model parameters is not recommended.

  The model is similar to, and broader than, the torus model of Brightman & Nandra (2011), also known as BNtorus in the literature. borus02 has additional free parameters (E_cut, A_Fe), additional chemical elements included, calculation extending to higher energies and line-of-sight component separated out -- allowing its application to a wider array of different AGN types. Also, note that the torus model is now known not to be correct (Liu & Li 2015, Paltani & Ricci 2017, Baloković et al. 2018, Buchner et al. 2019), so its replacement with borus02 is recommended even if additional features are not required. A manual describing the details of the model and its usage in modeling X-ray spectra will become available in the near future. Simple examples of model setup in Xspec are given below. Please see Baloković et al. (2018) for examples of using this model for parameter constraints.

  Due to the limited photon statistics of the calculated spectra, the tables available below are not recommended for use on the highest-quality CCD-based soft X-ray data, or grating spectra. The smoothness of the model spectra is sufficient for NuSTAR data (FWHM~400 eV) and medium-quality CCD-based data (FWHM~140 eV). Ongoing calculations will improve the statistical quality, so that future versions of these tables will be sufficient for spectra with high energy resolution enabled by X-ray calorimeters on XRISM and Athena (FWHM below 10 eV).

  
  • latest set of Xspec model tables:
        borus02_v170323a.fits -- table with C_tor = cos(θ_tor) and cos(θ_inc) as parameters
        borus02_v170323b.fits -- table with C_tor = cos(θ_tor) and θ_inc as parameters
        borus02_v170323c.fits -- table with θ_tor and θ_inc as parameters 
        borus02_v170323k.fits -- same as table "a", but only the reprocessed continuum
        borus02_v170323l.fits -- same as table "a", but only the reprocessed lines
  • free parameters:
        1 = photon index, Γ = 1.4--2.6
        2 = high-energy cutoff, E_cut/keV = 20--2000
        3 = torus column density, log₁₀(N_H,tor/cm^-2) = 22.0--25.5
        4 = torus covering factor, C_tor = cos(θ_tor) = 0.1--1.0, or θ_tor/deg. = 0--84
        5 = cosine of inclination, cos(θ_inc) = 0.05--0.95, or θ_inc/deg. = 19--87
        6 = relative abundance of iron, A_Fe/A_Fe,Sun = 0.01--10.0
        7 = redshift
        8 = normalization of the intrinsic spectrum (photons s^-1cm^-2keV^-1 at 1 keV)
    
  • example Xspec .xcm files:
        NOTE: The files below assume that the abundance of iron is Solar. For non-unity A_Fe/A_Fe,Sun, the line-of-sight absorption component
          would need to be replaced with one having a free A_Fe/A_Fe,Sun parameter, e.g. vphabs or tbabs.
        borus02_afe1_abscont.xcm -- l.o.s. + reprocessed components, N_H,tor independent of N_H,los
      borus02_afe1_abscont_NHlinked.xcm -- l.o.s. + reprocessed components, N_H,tor equal to N_H,los

   

  Comparison of the borus02 model to other publicly available models for X-ray reprocessing in AGN tori, in terms of assumed geometry and model parameters. From Baloković et al. (2018).

   

• Uniform Density Sphere with Polar Cutouts, nthComp Intrinsic Continuum: borus12

  This model is equivalent to the borus02 model described above in all features except for the different intrinsic continuum, which is represented by the nthcomp model here instead of the phenomenological CPL. This model was first presented in Baloković et al. (2019); please refer to this paper and .xcm files below for examples of application to broadband X-ray data.

  • latest set of Xspec model tables:
        borus12_v190815a.fits -- table with C_tor = cos(θ_tor) and cos(θ_inc) as parameters
  • free parameters:
        1 = photon index, Γ = 1.4--2.6
        2 = coronal electron temperature, kT_e/keV = 5--500
        3 = torus column density, log₁₀(N_H,tor/cm^-2) = 22.0--25.75
        4 = torus covering factor, C_tor = cos(θ_tor) = 0.1--1.0 (corresponding to θ_tor/deg. = 0--84)
        5 = cosine of inclination, cos(θ_inc) = 0.05--0.95 (corresponding to θ_inc/deg. = 19--87)
        6 = relative abundance of iron, A_Fe/A_Fe,Sun = 0.01--10.0
        7 = redshift
        8 = normalization of the intrinsic spectrum (photons s^-1cm^-2keV^-1 at 1 keV)
    
  • example Xspec .xcm files:
        borus12_ngc5506_model1.xcm -- spectral model for NGC 5506 with relativistic disk reflection, from Baloković et al. (2019)
        borus12_ngc5506_model2.xcm -- spectral model for NGC 5506 without relativistic disk reflection, from Baloković et al. (2019)

Graphics I made for illustrative purposes in papers and presentation slides. If they are useful for your presentations, any credit would be appreciated. Note that some versions have been published in journals, which should therefore be referenced accordingly. Most of the material was created and edited using Gimp, TinkerCad and LibreOffice.

• Approximate Torus Geometry with a Variable Covering Factor

  Simplified toroidal geometry, a uniform sphere with symmetric polar cutouts, as adopted in Brightman & Nandra (2011) and Baloković et al. (in prep.; see the borus02 model above). The data plotted in the figure on the right are results from the spectral modeling presented in Brightman et al. (2015). The sample consists of 10 Compton-thick AGN observed with NuSTAR. It is not meant to be complete or representative; it just illustrates that with NuSTAR data it is possible to estimate covering factors of individual AGN, complementary to previous work done on AGN populations.

   

• Multi-wavelength Constraints on AGN Geometry (3D Model of IRAS 09104+4109)

  Sketch of multi-wavelength spectral components observable in the obscured hyper-luminous quasar IRAS 09104+4109 in the framework of the classical Unified Model of AGN. I made the sketch on the left for Figure 5 in Farrah et al. (2016), where we modeled multi-wavelength data and found that it can be self-consistently explained if the half-opening angle of the torus is roughly 40o, and the viewing angle is just 5-10o larger (measured from the axis of symmetry). The figure on the right is a zoomed-out version of the same 3D model without the spectral component labels.

   

Selected figures from my published papers (adapted for better legibility in presentations), and the data behind some of them.

• Mrk 421: Distribution of Fractional Variability Amplitude in Quiescence

  Fractional variability amplitude (as defined in Vaughan et al., 2003 and Poutanen et al., 2008) as a function of the spectral band for the blazar Mrk 421 in the quiescent period January--March 2013. Vertical error bars show the statistical uncertainty, while horizontal error bars show the energy band covered. Two different computations are shown: 1) using the complete light curves acquired in the campaign (open symbols; data), and 2) using only the data taken within narrow windows centered on the coordinated NuSTAR and VHE observations (filled symbols; data). Because of low flux in the Fermi/LAT band, light curve could not be computed on the short timescale of NuSTAR and VHE observations. Published as Figure 9 in Baloković et al. (2016).

   

Scripts I wrote for my own work, that could potentially be useful to others.

• Energy Binning Above a Minimum SNR per Bin: snrgrppha

  This NuSTAR-specific Python script can be used instead of the usual energy binning of "20 counts per bin" using grppha (part of HEAsoft), which does not take into account the background spectrum. snrgrppha will calculate signal-to-noise ratio (SNR) per bin taking the background spectrum into account. Starting from the low-energy end of the bandpass, it will place bin borders so that each bin exceeds the user-specified SNR threshold. For the highest-energy bin, which is typically background-dominated, SNR will be calculated and printed on the screen, but will not be included by default (channels will be marked as bad). The user can override this by running with the --heaccept flag, in which case the minimum SNR will likely be determined by the highest-energy bin.

  • Python code (version 150913):
        snrgrppha
  • examples of usage:
        $> snrgrppha fpma_src.pha 3.0 -- SNR > 3.0, highest-energy bin excluded
        $> snrgrppha fpma_src.pha 5.0 --heaccept -- SNR > 5.0, highest-energy bin included
        The output file is always named snrgrp.pha; rename files to avoid overwriting.
  • requirements:
        pylab, pyfits, grppha