INTEGRAL Reference Catalog: Models

INTEGRAL General Reference Catalog: Models

Every source in the INTEGRAL Reference Catalog has a Spectral Energy Distribution (SED) model with parameters such as column density, photon index, and normalization. These models are used to determine instrumental counting rates.

We use values from the literature when available. For example, sources from the ASCA catalog came with a model, parameters and a normalization. In other cases, we assign default models and parameters depending on the source type, and then offer a normalization.

These values can be adjusted to reflect INTEGRAL observations that have been made public.

The table below lists the default models and parameters for sources in the INTEGRAL Reference Catalog. Details of the models are given after the table. Click here to return to the Catalog page.

Source Type	SED Model	N_H ·10²² [cm⁻²]	Γ₁	Γ₂	E_cut [keV]	E_fold [keV]	E_break [keV]
X-ray Binaries
LMXB	wabs∗cutoff	1.0	1.7	−	5	−	−
LMXB with hardtail	wabs∗(cutoff + powerlaw)	1.0	1.7	2.5	10	−	−
HMXB	wabs∗highecut∗powerlaw	1.0	1.0	−	10	15	−
AGN
Seyfert I	wabs∗cutoff	1.0	1.7	−	100	−	−
Seyfert II	wabs∗cutoff	10.0	1.7	−	100	−	−
Blazar	wabs∗cutoff	1.0	1.7	−	100	−	−
Quasar	wabs∗cutoff	1.0	1.7	−	100	−	−
Radio Pulsars
Radio Pulsar	wabs∗powerlaw	1.0	2.0	−	−	−	−
Unidentified
X-band detection	wabs∗cutoff	1.0	1.7	−	10	−	−
COMPTEL detection	wabs∗bknpower	100.0	−1.5	2.1	−	−	1000
EGRET detection	wabs∗bknpower	100.0	−1.5	2.1	−	−	10000

The equations governing the models used in the catalog are:

powerlaw : simple photon power-law, typically due to synchrotron radiation.
S(E) = A(E/E_o)^Γ
cutoff : power-law with a high-energy exponential cutoff.
S(E) = A(E/E_o)^Γ · e^−E/E_cut
bknpower : broken power-law.

S(E) = { A(E/E_o)^Γ₁ E < E_break

A·E_break^{(Γ₂ &minus Γ₁)} · (E/E_o)^Γ₂ E > E_break
wabs : photoelectric absorption using Wisconsin cross-sections.
m(E) = e^{−N_H · σ(E)}
highecut : high-energy cutoff.

m(E) = { e^{(E_cut − E)/E_fold} E > E_cut

1 E < E_cut

E : energy [keV]
E_o : reference energy [keV] (1 keV in XSPEC)
E_cut : exponential cutoff energy [keV]
E_fold : exponential folding energy [keV]
E_break : break energy [keV]
Γ₁ : photon index for E < E_break
Γ₂ : photon index for E > E_break
N_H : column density of hydrogen [10²²atoms·cm⁻²]
S(E) : monochromatic flux at energy E [ph·cm⁻²·s⁻¹]
A = S(E_o) : normalization at 1 keV (F_obs / F_comp) [ph·cm⁻²·s⁻¹·keV⁻¹]
m(E) : multiplicative flux coefficient of S(E) at energy E
σ(E) : photoelectric cross section (excluding Thompson scattering)

In the HTML format, the model parameters column can be read as follows:

wabs∗powerlaw: N_H, Γ, A
wabs∗cutoff: N_H, Γ, E_cut, A
wabs∗(cutoff + powerlaw): N_H, Γ₁, E_cut, A₁, Γ₂, A₂
wabs∗highecut∗powerlaw: N_H, Γ, E_cut, E_fold, A
wabs∗bknpower: N_H, Γ₁, E_break, Γ₂, A

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