AGN SED tool

SSC/EC Simulator User Guide
author: andrea.tramacere@unige.ch

• Tramacere A. et al. 2011
  
• Tramacere A. et al 2009
  
• Massaro E. et. al 2006
  

In the following is given a brief description of what blazars are, of the physical processes reproduced by the SED tool, and a user guide to the use of the web interface. To have a deeper understanding of the numerical code and of its physical implications we remand the reader to the references listed above.

Content:

Blazars objects are Active Galactic Nuclei (AGNs) characterized by a polarised and highly variable non-thermal continuum emission extending from radio to γ-rays. In the most accepted scenario, this radiation i s produced within a relativistic jet that originates in the central engine and points close to our line of sight. Since the relativisti c outflow moves with a bulk Lorentz factor (Γ) and is observed at small angles (θ ≃ 1/Γ ), the emitted fluxes are affected by a beaming factor δ = 1/(Γ(1 − βcos θ )) . To model the emission processes we assume to have a plasma of leptons (e+/-) distributed in a one-zone homogeneous emitting region. This emitting is assumed to have a spherical geometry, and an entangled magnetic fie lds. The electron are accelerated to relativistic energies (through shock firs order, or stochastic second order acceleration), and their energy distribution is described by an analytical law. These accelerated electrons interact with the entangled magnetic field, and emit synchrotron radiation. In the case of synchrotron self Compton model (SSC)(Jones et al. 1974) the seed photons for the Inverse Compton (IC) process are the synchrotron photons produced by the same population of relativistic electrons. In the case of external radiation Compton (ERC) scenario (Sikora et al. 1994), the seed photons for the IC process are typically UV photons generated by the accretion disk surrounding the black hole, and reflected toward the jet by the Broad Line Region (BLR) within a typical distance from the accretion disk of the order of one pc. If the emission occurs at larger distances, the external radiation is likely to be provided by a dusty torus (DT) (Sikora et al. 2002). In this case the photon field is typically peaked at IR frequencies.






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This forms is used to input parameters concerning the emitting region properties. These parameters are listed in the following :

1. R: the size of the spherical emitting region in cm
2. B: the intensity of the entangled magnetic field (expressed in Gauss) within the emitting region with size R
3. z: the redshift of the host galaxy
4. Γ: the Bulk Lorentz factor of the emitting region
5. θ: the Jet viewing angle

the corresponding beaming factor of the jet will be :δ = 1/(Γ(1 − βcos θ )).

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This forms is used to input parameters concerning the emitting electron distribution. Before describing the various options, we give a caveat on the normalization of the electron energy distribution function. The analytical law f(γ), expressing the differential electron distribution function, is defined over the energy interval [γ_min, γ_max], and is normalized to unity through the constant K:


in this way, by defining the differential electron distribution function n(γ) as:


the numerical value N will provide, by definition, the number of emitting particles per unit volume expressed in #/cm³:

• power-law:
  a power law function, defin as:
  
  
  f(\gamma)=\gamma^{-p}
  • p = spectral index
  
  
• pl+exp cutoff:
  power law function plus an exponential cutoff, definided as :
  
  
  f(\gamma)=\gamma^{-p} exp(-\gamma/\gamma_{cut})
  • p = spectral index
  • γ_cut = cut off energy

• log-par:
  a log-parabolic funtion defined as :
  
  
  f(\gamma)=(\gamma/\gamma_0)^{-(s+r\log(\gamma/\gamma_0))}
  • γ₀ = reference energy
  • s = spectral index at the reference energy γ₀
  • r = spectral curvature

for further references see: Massaro E. et al. 2004.

• log-par+pl:
  a log-parabolic funtion plus a power-law low energy branch, defined as:
  
  
  f(\gamma)=(\gamma/\gamma_0)^{-s}, \gamma \leq\gamma_0
  f(\gamma)=(\gamma/\gamma_0)^{-(s+r\log(\gamma/\gamma_0))}, \gamma >\gamma_0

• γ₀ = energy at which pl turns int log-par
• s = spectral index at the reference energy γ₀
• r = spectral curvature
  

• log-par Ep:
  a log-parabolic function, described in terms of peak energy and peak curvature, defined as :
  
  
  f(\gamma)=10^{-(r\log(\gamma/\gamma_p)^2)}
  • γ_p = energy at which pl turns int log-par
  • r = spectral curvature

for further references see:Tramacere A. et al 2009, Tramacere A. et al. 2007

• broken pl:
  
  a broken power law function, defined as:
  
  f(\gamma)=(\gamma)^{-p}, \gamma\leq \gamma_{break} \\
  f(\gamma)=(\gamma)^{-p1}, \gamma> \gamma_{break} \\
  • p = low energy spectral index
    
  • γ_break = break energy
    
  • p₁ = high energy spectral index
    

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The Emission scenario form description

The user has the possibility to choose among different scenarios, using the drop-down menus, and filling the resulting forms.

• Synch drop-down:sets the synchrotron emission
  
  
  • yes = synchrotron emission is computed
  • Self-ab= synchrotron self absorption is computed
  • no = synchrotron emission is not computed

• IC drop-down: sets the inverse Compton (SSC) emission
  
  
  • yes = IC emission of synchrotron photons (SSC) is computed
  • no = IC emission of synchrotron photons (SSC) is not computed

• EC drop-down: sets the External emission
  
  
  • BLR = computation of EC emission disk seed photons reprocessed by the Broad Line Region (BLR)(read the caveat ont accretion disk paramters)
    
    • L_disk = disk luminosity in erg/s
    • dist BLR disk = Radius of the BLR in cm
    • τ_BLR = fraction of diks luminosity reflected by the BLR
    • T_disk= peak disk temperature in Kelvin
  
  
  • Dust = computation of IC emission of seed disk seed photon originating in the dusty torus
    • L_disk = disk luminosity in erg/s
    • dist TORUS disk = radius of the dusty torus
    • τ_DT= fraction of diks luminosity re-emitted by the torus in the infrared
      
    • T dust= dust temperature in Kelvin
      
      
  • Dust+BLR = computation of EC emission both for BLR and Dust
    

Caveat on accretion diks parameters

To model the accretion disk we follow the approach of Ghisellini et al. 2009. In the following we explain how to link the input parameters (L_disk,T_disk), to the Black Hole (BH) mass, to the accretion efficiency, and to the accretion rate. We start from the relation expressing the accretion disk temperature as a funciont of the distance (R) from the BH, as function of the accretion efficiency ε, of the Schwarzschild radius (R_S), and of the disk luminosity (L_disk):

this function peaks at R4R_S, with a temperature T_disk, hence we can derive R_S as :



where we use a reference value of ε=0.1. From R_S it is straightforward to derive the BH mass (R_S = 2 GM_BH/c²), and from the relation:


we can derive the accretion rate.

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The Run Model buttom

By clicking on this buttuon the SSC/EC model is computed, according to the paremters inserted in the forms above. The output will be shown in the right frame.

If the "save model" radio button is cheked, after the model computation, at the side of the SED plot will appear a link to save the model file, corresponding to the computation. This file can be uploaded later, using the Upload Menu

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The working area menu description

The user can decide to set a working directory on the remote machine, and a flag, in this way it's possible to store different results organized in directories (path), and in the same directory with different names (flag) :

• "path"
  • the name of the directory to create on the remote machine
    

• "flag"
  • the name for the output files of the current model

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The Upload menu description

By using this meny, the user can upload a spectral energy distribution, or a model file saved fro a previous computation. These two options can be chosen by the following form:

• "Load Data File": The user can upload an SED using an ascii file, with the following format:

• if plot type = "observed"
  • freq = ν_rest
  • flux = ν_obsF_obs

• if plot type = "rest frame"

• freq =ν_obs
• flux = ν_restL_{ν rest}

• "Load Model File": The user can upload a model file where has saved the parameters of a previous computation. To save a Model file, check the "save model radio button" in the Submit menu, and download the corresponding model file using the link that appears close to the SED plot:

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The Plot menu description

The plot menu is used to set plotting options. The output will be shown in the right frame. The "plot type" drop down menu allows to choose betwen :

• "observed"

or

• "rest-frame"
  • frequencies are transformed according to: ν_rest = ν_obs /(1+z)
  • fluxes are transformed to luminosities according to:
    ν_restL_{ν rest} = 4πD²_L ν_obsF_obs
    where D_L is the luminosity distance

There radio buttons allows to select different plotting options:

• "only replot": in this case will be only updated the plot, the SED model will be not updated. For example, you may upload an SED file to plot on top of your model
  
  
• "plot uploaded data": in this case the uploaded SED will be plotted
  
  
• "plot uploaded data": in this case "only" the uploaded SED will be plotted
  
  

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References:

Jones et al. 1974
Ghisellini et al. 2009
Massaro E. et al. 2004
Massaro E. et. al 2006
Sikora et al. 1994
Sikora et al. 2002
Tramacere A. et al. 2007
Tramacere A. et al. 2011
Tramacere A. et al 2009