Blazar SED modeling

The Theoretical Modeling section of mmdc.am computes the broadband SED of a blazar for the parameters you give, within seconds, and fits the models to your own data (Fitting your SED).

Open Theoretical Modeling on mmdc.am

An SSC model. The panel on the right holds the Data card, the model tabs and the parameters.

In short

1. Set the Redshift z in the Data card, and tick EBL absorption if you want it.
2. Choose SSC, EIC or Hadronic.
3. Enter the parameters, or use Run model ▾ → Load example for a tested set (Load example (Mrk 421) for SSC).
4. Press Run model. The SED appears on the plot.

A value outside its range is shown in red with the allowed range; the range of every field is also shown inside it.

The models

The SSC and EIC models are convolutional neural networks (CNNs) trained on the physical models of Bégué, Sahakyan, Dereli Bégué, et al. 2024, ApJ, 963, 71 (SSC) and Sahakyan, Bégué, Casotto, et al. 2024, ApJ, 971, 70 (EIC). They are trained on a leptonic framework that includes synchrotron and inverse Compton emission (from internal and external photon fields), with self-consistent electron cooling and pair creation–annihilation. The physical models and their parameters are described in detail in those two papers. The hadronic model is likewise a neural-network surrogate of its physical model. The trained networks are used with MultiNest (Feroz et al. 2009) to fit your data.

Model	What it describes
SSC, synchrotron self-Compton	Electrons in one spherical blob emit synchrotron photons and up-scatter them by inverse Compton.
EIC, external inverse Compton	As SSC, and the electrons also up-scatter photons from the broad-line region (BLR) and the dusty torus (DT). The SED also includes the thermal emission of the disk, the BLR and the torus.
Hadronic, lepto-hadronic	Protons in the blob add the emission of their interactions, and neutrinos, to the electrons' synchrotron and SSC emission.

The hadronic model also predicts the neutrino flux, drawn as a dashed curve.

Redshift, distance and EBL

• Redshift z (0 < z ≤ 4.99) is required for every run and fit. It is converted to a distance with a flat cosmology, H₀ = 71 km s⁻¹ Mpc⁻¹ and Ω_m = 0.27 (Ned Wright's Cosmology Calculator).
• EBL absorption, when ticked, attenuates the γ-ray emission by the extragalactic background light with model C of Finke, Razzaque & Dermer 2010, ApJ, 712, 238. The optical depths are tabulated every 0.01 in z up to z = 4.99, which is why z is limited to 4.99; z is rounded to the nearest table.

Parameters

All logarithms are base 10. The ranges are those the form accepts for a run; a fit samples slightly different ranges (see Fitting your SED).

SSC

Parameter	Meaning	Range
δ	Doppler factor of the emitting region	3 – 50
log R	comoving radius of the blob [cm]	15 – 18
log B	comoving magnetic field [G]	−3 – 2
p	power-law index of the electrons	1.8 – 5
log γmin	minimum Lorentz factor of the electrons	1.5 – 5
log γmax	cut-off Lorentz factor of the electrons	2 – 8
log Le	electron luminosity [erg s⁻¹]	42 – 48

EIC

The SSC parameters (with slightly different ranges), plus the external photon fields.

Parameter	Meaning	Range
δ	Doppler factor	3 – 50
log R	comoving blob radius [cm]	15 – 18
log B	comoving magnetic field [G]	−3 – 2.5
p	power-law index of the electrons	1.8 – 5
log γmin	minimum Lorentz factor	1.5 – 5
log γmax	cut-off Lorentz factor	2 – 6
log Le	electron luminosity [erg s⁻¹]	42 – 48
log Ld	accretion disk luminosity [erg s⁻¹]	43.5 – 47
log MBH	mass of the central black hole [M⊙]	7 – 10
log νBLR	frequency of the BLR photons [Hz]	fixed at 15.393 (ν = 2.47 × 10¹⁵ Hz)
log νDT	frequency of the dusty torus photons [Hz]	fixed at 13.477 (ν = 3.0 × 10¹³ Hz)

ν_BLR and ν_DT are fixed in the model: the values in their fields are not used, in a run or in a fit (the fields must still hold a value in their range, 14.5–16 and 12.5–14).

Hadronic

Parameter	Meaning	Range
δ	Doppler factor	3.5 – 80
log R	comoving blob radius [cm]	14.5 – 18
log B	comoving magnetic field [G]	−3 – 3.5
pe	power-law index of the electrons	1.75 – 5
log γmin	minimum Lorentz factor of the electrons	1.5 – 2
log γe,max	cut-off Lorentz factor of the electrons	2 – 8
log Le	electron luminosity [erg s⁻¹]	42.5 – 48.5
pp	power-law index of the protons	1.65 – 3.45
log γp,max	cut-off Lorentz factor of the protons	3 – 11
log Lp	proton luminosity [erg s⁻¹]	42 – 52

Compare with data

Upload an SED in the Data card (Upload SED (CSV)) to draw it with the model. The file format is described in Fitting your SED. The upload is optional for a run; it is needed for a fit.

Citing the models

If you use the modeling tools in a publication, please cite (also under ⋯ → Cite):

• Bégué, Sahakyan, Dereli Bégué, et al. 2024, ApJ, 963, 71
• Sahakyan, Bégué, Casotto, et al. 2024, ApJ, 971, 70
• Sahakyan, Vardanyan, Giommi, et al. 2024, AJ, 168, 289 (MMDC)

From Python

The same models are available from Python with the astro-mmdc SDK: see Blazar emission modeling.