Reltrans model flavours

Reltrans is not just a single model, but is a library of different model flavours that have slightly different physics. This page lists all the available models, briefly describes their differences, and lists their input parameters.

Note

This page might not be fully comprehensive currently as this documentation is under development.

Models

Note

reltrans is a library of spectral timing models which means that all variants of the model include parameters related to which spectral timing product the model returns. These include:

• fmin and fmax: these two parameters define the frequency range of the cross-spectrum to be evaluated. Setting both of these values to 0 will cause the model to always return the time-averaged spectrum.

• ReIm: this parameter flags the model to output different timing products or components of the cross-spectrum.

  • 0: The time-averaged spectrum.

  • 1: Real part of the cross spectrum.

  • 2: Imaginary part of the cross spectrum.

  • 3: Modulus of the cross spectrum.

  • 4: Lag-energy spectrum.

  • 5: Modulus of the folded cross spectrum.

  • 6: Lag-energy spectrum calculated from the folded cross spectrum.

reltransDCp

reltransDCp can be considered the “default” version of the lastest reltrans release. It assumes that the disk is illuminated by an nthcomp spectrum with electron temperature kTe, and the disk density is a parameter. This means that it uses the xillverDCp tables.

Parameters:

Parameter number	Name	Description
1	h	height of the corona from the blackhole
2	a	spin
3	inc	inclination
4	rin	inner radius of the disk
5	rout	outer radius of the disk
6	z	redshift
7	Gamma	slope
8	logxi	ionisation
9	Afe	iron abundance
10	logNe	disk density
11	kTe	electron temperature of the corona
12	nH	galactic absorption
13	boost	reflection spectrum normalisation
14	Mass	mass of the black hole
15	fmin	minimum frequency of cross spectrum
16	fmax	maximum frequency of cross spectrum
17	ReIm	flag for outputs
18	phiA	phase shift of the reference band
19	phiAB	phase difference between the pivoting and normalisation of the illuminating variability
20	g	ratio of the normalisation between the pivoting and normalisation of the illuminating variability
21	RESP	the number of instrument responses used

reltransPL

reltransPL is identical to reltransDCP except that it assumes that the disk is illuminated by an exponentially cut-off powerlaw spectrum, and the disk density is hardwired to $10^{15}~cm^{-3}$. This means that it uses the xillver tables.

Parameters:

Parameter number	Name	Description
1	h	height of the corona from the blackhole
2	a	spin
3	inc	inclination
4	rin	inner radius of the disk
5	rout	outer radius of the disk
6	z	redshift
7	Gamma	slope
8	logxi	ionisation
9	Afe	iron abundance
10	Ecut	observed exponential cut off energy
11	nH	galactic absorption
12	boost	reflection spectrum normalisation
13	Mass	mass of the black hole
14	fmin	minimum frequency of cross spectrum
15	fmax	maximum frequency of cross spectrum
16	ReIm	flag for outputs
17	phiA	phase shift of the reference band
18	phiAB	phase difference between the pivoting and normalisation of the illuminating variability
19	g	ratio of the normalisation between the pivoting and normalisation of the illuminating variability
20	RESP	the number of instrument responses used

rtransDbl

reltransDbl is identical to reltransDCP except that it assumes that there are 2 illuminating sources.

Parameters:

Parameter number	Name	Description
1	h1	height of the first corona from the blackhole
2	h2	height of the second corona from the blackhole
3	a	spin
4	inc	inclination
5	rin	inner radius of the disk
6	rout	outer radius of the disk
7	z	redshift
8	Gamma	slope
9	logxi	ionisation
10	Afe	iron abundance
11	logNe	disk density
12	kTe	electron temperature of the corona
13	eta_0	Time-averaged normalization ratio C1 / C2 between the two lampposts and sets continuum cutoff and disk disk ionization
14	eta	Fourier frequency dependent normalization ratio C1(νc)/ C2(νc)
15	beta_p	propagation speed delay between the two lampposts if they are coherent (0 if incoherent)
16	nH	galactic absorption
17	boost	reflection spectrum normalisation
18	Mass	mass of the black hole
19	fmin	minimum frequency of cross spectrum
20	fmax	maximum frequency of cross spectrum
21	ReIm	flag for outputs
22	phiA	phase shift of the reference band of the bottom lamppost
23	phiAB1	phase difference between the pivoting and normalisation of the illuminating variability for the bottom lamppost
24	g1	ratio of the normalisation between the pivoting and normalisation of the illuminating variability of the bottom lamppost
25	phiAB2	phase difference between the pivoting and normalisation of the illuminating variability for the top lampost
26	g2	ratio of the normalisation between the pivoting and normalisation of the illuminating variability of the top lamppost
27	RESP	the number of instrument responses used

rtdist

rtdist is a variant of reltransDCp. It self-consistently calculates the disk ionisation by calculating the geometric relationship between the observer, source of illuminating spectrum and the disk, thus logxi is not a parameter of this model flavour, since it has been replaced by the distance between the observer and the source. It also features a change to the previous boost normalisation factor for the reflection spectrum. The source is no longer assumed to be isotropic. Instead, the angular dependence is specified by the parameters b1, b2 and qboost (referred to as as boost but defined differently from other reltrans flavours). b1 and b2 are linear and quadratic coefficients of the \(\text{mu}= \cos(\theta)\) dependence and qboost skews the relation where \(qboost = \frac{I(\text{mu}=-1)}{I(\text{mu}=1)}\). The disk scale height also has become a free parameter.

For a comprehensive explanation of the model, please see the model paper: https://ui.adsabs.harvard.edu/abs/2022MNRAS.509..619I/abstract.

Note

IMPORTANT!

If you are using rtdist in reltrans, the xspec norm parameter must be frozen to 1 as Anorm replaces xspec norm’s function.

• For the DC component, the xspec norm parameter must be frozen to norm=1.

• For the lag spectrum, the xspec norm parameter must (as usual) be frozen to norm=1.

• For the Re/Im/amp spectra, the xspec norm becomes the average power in that frequency range in squared fractional rms units (this is the case if the data really is the cross-spectrum and not the complex covariance).

The reason for this is that Anorm is A0 from the RELTRANS 2.0 paper. Previously, A0 was input as the norm parameter of the DC component. Now we need A0 for all calls because we use it to calculate logxi(r). It is therefore its own model parameter. The model therefore already multiplies the DC component by Anorm and the AC components by Anorm^2 before sending then to xspec.

Note

\(h/r > 0\) is currently not used in the calculation of mu_e and mu_i. These are the cosines of the angles between the incident/emitted ray and the z-axis, NOT the disc normal. This may have implications when inferring information about the geometry of the disk.

Parameters:

Parameter number	Name	Description
1	h	height of the corona from the blackhole
2	a	spin
3	inc	inclination
4	rin	inner radius of the disk
5	rout	outer radius of the disk
6	z	redshift
7	Gamma	slope
8	Dkpc	Distance to source in kpc
9	Afe	iron abundance
10	logNe	disk density
11	kTe	electron temperature of the corona
12	nH	galactic absorption
13	boost	reflection spectrum normalisation
14	Mass	mass of the black hole
15	honr	scale height of the disk
16	b1	emissivity parameter
17	b2	emissivity parameter
18	fmin	minimum frequency of cross spectrum
19	fmax	maximum frequency of cross spectrum
20	ReIm	flag for outputs
21	phiA	phase shift of the reference band
22	phiAB	phase difference between the pivoting and normalisation of the illuminating variability
23	g	ratio of the normalisation between the pivoting and normalisation of the illuminating variability
24	Anorm	normalisation of the model
25	RESP	the number of instrument responses used

Simulators

We also include a number of simulators for the different reltrans model flavours. These are explicitly for simulating the timing products that reltrans computes. This results in additional coherence, rms variability and time exposure parameters. See Environmental variables for additional parameters pertaining to the simulation such as seeding the simulation. There is no simulator for the reltransPL.

simrelt

simrelt is the simulator for the reltransDCp model.

Parameters:

Parameter number	Name	Description
1	h	height of the corona from the blackhole
2	a	spin
3	inc	inclination
4	rin	inner radius of the disk
5	rout	outer radius of the disk
6	z	redshift
7	Gamma	slope
8	logxi	ionisation
9	Afe	iron abundance
10	logNe	disk density
11	kTe	electron temperature of the corona
12	nH	galactic absorption
13	boost	reflection spectrum normalisation
14	Mass	mass of the black hole
15	fmin	minimum frequency of cross spectrum
16	fmax	maximum frequency of cross spectrum
17	coh2	coherence of the simulated signal
18	phiA	phase shift of the reference band
19	phiAB	phase difference between the pivoting and normalisation of the illuminating variability
20	g	ratio of the normalisation between the pivoting and normalisation of the illuminating variability
21	Anorm	assumed flux normalisation of the model
22	Texp	exposure time of observation
23	pow	power averaged over simulated frequency range
24	RESP	the number of instrument responses used

simrtdbl

simrtdbl is the simulator for reltransDbl.

Parameters:

Parameter number	Name	Description
1	h1	height of the first corona from the blackhole
2	h2	height of the second corona from the blackhole
3	a	spin
4	inc	inclination
5	rin	inner radius of the disk
6	rout	outer radius of the disk
7	z	redshift
8	Gamma	slope
9	logxi	ionisation
10	Afe	iron abundance
11	logNe	disk density
12	kTe	electron temperature of the corona
13	eta_0	Time-averaged normalization ratio C1 / C2 between the two lampposts and sets continuum cutoff and disk disk ionization
14	eta	Fourier frequency dependent normalization ratio C1(νc)/ C2(νc)
15	nH	galactic absorption
16	boost	reflection spectrum normalisation
17	Mass	mass of the black hole
18	fmin	minimum frequency of cross spectrum
19	fmax	maximum frequency of cross spectrum
20	coh2	coherence of the simulated signal
21	phiA	phase shift of the reference band of the bottom lamppost
22	phiAB	phase difference between the pivoting and normalisation of the illuminating variability for the bottom lamppost
23	g	ratio of the normalisation between the pivoting and normalisation of the illuminating variability of the bottom lamppost
24	phiAB2	phase difference between the pivoting and normalisation of the illuminating variability for the top lampost
25	g2	ratio of the normalisation between the pivoting and normalisation of the illuminating variability of the top lamppost
26	Texp	exposure time of observation
27	pow	power averaged over simulated frequency range
28	RESP	the number of instrument responses used

simrtdist

simrtdist is the simulator for rtdist.

Parameters:

Parameter number	Name	Description
1	h	height of the corona from the blackhole
2	a	spin
3	inc	inclination
4	rin	inner radius of the disk
5	rout	outer radius of the disk
6	z	redshift
7	Gamma	slope
8	Dkpc	Distance to source in kpc
9	logxi	ionisation
10	Afe	iron abundance
11	logNe	disk density
12	kTe	electron temperature of the corona
13	nH	galactic absorption
14	boost	reflection spectrum normalisation
15	Mass	mass of the black hole
16	b1	emissivity parameter
17	b2	emissivity parameter
18	fmin	minimum frequency of cross spectrum
19	fmax	maximum frequency of cross spectrum
17	coh2	coherence of the simulated signal
20	ReIm	flag for outputs
21	phiA	phase shift of the reference band
22	phiAB	phase difference between the pivoting and normalisation of the illuminating variability
23	g	ratio of the normalisation between the pivoting and normalisation of the illuminating variability
24	Anorm	assumed flux normalisation of the model
25	Texp	exposure time of observation
26	pow	power averaged over simulated frequency range
27	RESP	the number of instrument responses used