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Ginga Specific Software: Program SPF

Purpose

Program spf performs multi-instrument spectral fitting.

General Parameters

Spf requires two general parameters. The QX parameter system is used to read these parameters.

SPF_NSTEPS The maximum number of iterations taken.
SPF_NAME The root name for all output.

Data Parameters

Spf requires up to six data parameters. The QX parameter system is used to read these parameters.

SPF_NFILES The number of data files to be fit.
SPF_PFILES(SPF_NFILES) The names of the input data files.
SPF_DFILES(SPF_NFILES) The names of the input response matrix files.
SPF_SYSERR(SPF_NFILES) The systematic error applied to the input files.
SPF_ARMASK(J) 1 to fit EXOSAT Argon detector ident channel (J), 0 to omit.
SPF_XEMASK(J) 1 to fit EXOSAT Xenon detector ident channel (J), 0 to omit.

Model Parameters

Spf requires four model parameters. The QX parameter system is used to read these parameters.

SPF_MODEL The model expression (see model expressions).
SPF_P(I) Initial value of parameter I.
SPF_PE(I) Trial step for parameter I (if zero then the parameter is fixed).
SPF_REDSHIFT The redshift to be used in the calculation of the source spectrum.

Statistics Parameters

Spf requires three statistics parameters. The QX parameter system is used to read these parameters.

SPF_CONFIDENCE Confidence level for error calculation (zero for no errors, 0.9 for 90% etc.).
SPF_NOINTEREST Number of "uninteresting" parameters to be used in statistical calculations.
SPF_GRID Do a confidence contour grid (Y/N)?

Grid Parameters

If SPF_GRID=Yes then Spf requires eight grid parameters. The QX parameter system is used to read these parameters.

SPF_XPAR Parameter index for grid X-axis.
SPF_NX The number of X values to use in grid.
SPF_XLO Lower limit on X for the grid.
SPF_XHI Upper limit on X for the grid.
SPF_YPAR Parameter index for grid Y-axis.
SPF_NY The number of Y values to use in grid.
SPF_YLO Lower limit on Y for the grid.
SPF_YHI Upper limit on Y for the grid.

Functions available for use in parameter SPF_MODEL

PLAW(i, j) Simple power-law photon spectrum.
A(E) = p(i) × E(-p(j)) dE
.
Where parameter:
  1. Power law normalisation at 1 keV (in units of photons sec-14 cm-2 keV-1.
  2. Power-law index (photon).
BKNP(i, j, k, l) Broken power-law.
For Ebr > 1.0 keV:
A(E) = p(i) × E(-p(j)) dE for E < Ebr
A(E) = p(i) × Ebr(-(p(j)-p(k))) × E(-p(k)) for E > Ebr
For Ebr < 1.0 keV:
A(E) = p(i) × Ebr(-(p(k)-p(j))) × E(-p(j)) for E < Ebr
A(E) = p(i) × E(-p(k)) for E > Ebr
Where parameter:
  1. Power law normalisation at 1 keV (in units of photons sec-1 cm-2 keV-1.
  2. Power-law index (photon) for E < Ebr.
  3. Power-law index (photon) for E > Ebr.
  4. Break energy, Ebr.
HENC(i, j) High-energy cut-off (exponential).
M(E) = e((p(i)-E) × p(j)).
Where parameter:
  1. Cut-off energy in units of keV.
  2. Cut-off rate in units of keV-1.
BREM(i, j) Thermal bremsstrahlung spectrum.
A(E) = p(i) × G × e(-E/p(j)) / E dE.
G is the Born approximation to the Gaunt factor.

Where parameter:
  1. Bremsstrahlung normalisation (equal to 3.01 × 10-15 × S × T-½ / (4 × pi × D²), with
    S = emission measure = [integral] Ne² dV (cm-3); T = p(j); D = distance to source (cm)).
  2. Bremsstrahlung temperature in units of keV.
COMP(i, j) Comptonisation factor for bremsstrahlung using the prescription of Lamb & Sandford (1979 MNRAS 188, p155).

Where parameter:
  1. Comptonisation temperature in units of keV.
  2. Comptonisation optical depth.
BBOD(i, j) Black-body spectrum.
A(E) = p(i) × E2/(e (E/p(j))-1) dE.
Where parameter:
  1. Black-body normalisation (equal to 7.865 × 1030 × Abb / (D²), with Abb = emitting area (cm-2); D = distance to the source (cm)).
  2. Black-body temperature in units of keV.
RSMT(i, j, k) Raymond & Smith emission spectrum.

Where parameter:
  1. Raymond & Smith normalisation (equal to 1.0 × 10-13 × S / (4 × pi × D²), with
    S = emission measure = [integral] Ne² dV (cm-3); D = distance (cm)).
  2. Plasma temperature in K.
  3. 13 elemental abundances relative to Solar.
MEWE(i, j, k) Mewe & Gronenschild emission spectrum.

Where parameter:
  1. Mewe & Gronenschild normalisation.
  2. Plasma temperature in K.
  3. 15 elemental abundances relative to Solar.
ABSO(i) Photoelectric absorption by interstellar medium using Morris & McCammon cross-sections.
M(E) = e(-p(i) × [sigma] (E)),
with [sigma] (E) = photoelectric cross-section.

Where parameter:
  1. Equivalent hydrogen column in units of 1021 cm-2 (not affected by redshift).
ABSI(i) As ABSO, but redshifted.

Where parameter:
  1. Equivalent hydrogen column in units of 1021 cm-2 (affected by redshift).
IRCO(i) Cold iron absorption (7.11 keV edge).
For E < 7.11 keV:
M(E) < 1.0
For E > 7.11 keV:
M(E) < e(-0.0012 × p(i) × (7.11 / E) 3.11 )
Where parameter:
  1. Cold iron column in units of 1016.52 cm-2, so that the equivalent hydrogen column is in units of 1021 (assumes an Fe/H abundance ratio of 107.52 × 10-12
IRHE(i) He-like iron absorption (8.85 keV edge).
For E < 8.85 keV:
M(E) < 1.0
For E > 8.85 keV:
M(E) < e(-0.0011 × p(i) × (8.85 / E) 3.15 )
Where parameter:
  1. He-like iron column in units of 1016.52 cm-2, so that the equivalent hydrogen column is in units of 1021 (assumes an Fe/H abundance ratio of 107.52 × 10-12
IRHY(i) H-like iron absorption (9.29 keV edge).
For E < 9.29 keV:
M(E) < 1.0
For E > 9.29 keV:
M(E) < e(-0.0011 × p(i) × (9.29 / E) 3.16 )
Where parameter:
  1. He-like iron column in units of 1016.52 cm-2, so that the equivalent hydrogen column is in units of 1021 (assumes an Fe/H abundance ratio of 107.52 × 10-12
KEDG(i, j) K absorption edge (see Tucker p243-244).
For E < p(i):
M(E) < 1.0
For E > p(i):
M(E) < e(-([sigma]th × p(j) × (p(i) / E)s ), with [sigma]th = threshold cross-section and
s = 2 × (Zeff)0.14.
Where parameter:
  1. Absorption edge energy in units of keV. Edge column density in units of 1016.52 cm-2, so that the equivalent hydrogen column is in units of 1021 (assumes an Fe/H abundance ratio of 107.52 × 10-12
GTRA(i) Scattering by interstellar grains.
M(E) = e(-(p(i) / E)2).
Where parameter:
  1. Energy (in units of keV) at which non-scattered fraction is e-1 (not affected by redshift).
GSCA(i) Complementary to GTRA.

Where parameter:
  1. Energy (in units of keV) at which non-scattered fraction is e-1 (not affected by redshift).
LINE(i, j) Narrow Gaussian line (intrinsic width < 0.1 keV).

Where parameter:
  1. Line energy in units of keV.
  2. Line flux in units of photons cm-2 sec-1.
BLIN(i, j, k) Broad Gaussian line.

Where parameter:
  1. Line energy in units of keV.
  2. Line flux in units of photons cm-2 sec-1.
  3. Root mean square width of the line in units of keV.
CFRA(i) Partial covering fraction absorption.

Where parameter:
  1. (1 / covered fraction) - 1.
UFRA(i) Complementary to CFRA.

Where parameter:
  1. (1 / covered fraction) - 1. The same parameter as used in CFRA.
POLY(i, j, k, l) Polytropic gas distribution model.

Where parameter:
  1. Central density.
  2. Central temperature.
  3. Polytropic index.
  4. "beta" parameter.
COMA(i, j, k) Hughes Coma/Polytropic model for on-axis Ginga pointing.

Where parameter:
  1. Normalisation.
  2. Isothermal temperature.
  3. Isothermal radius.
GABS(i, j) Absorption due to Gaussian distribution of absorbers.

Where parameter:
  1. Mean equivalent Hydrogen column density in units of 1021 cm-2.
  2. Gaussian width ([sigma]) of the distribution in units of 1021 cm-2.
LABS(i) Absorption due to power-law distribution of absorbers.

Where parameter:
  1. Index of the power-law distribution.
PABS(i, j) Absorption due to Poissonian distribution of clouds.

Where parameter:
  1. Mean number of absorbing clouds.
  2. Equivalent Hydrogen column density per cloud in units of 1021 cm-2.
PLEM(i, j, k) Power-law distribution of emission measures.

Where parameter:
  1. Normalisation for cool component.
  2. Low temperature for distribution.
  3. High temperature for distribution.
TABn(i, j, n) Table model with n (equal to 0, 1 or 2) parameters.

Where parameter:
  1. Normalisation.
  2. Parameter 1.
  3. Parameter n.

Model Expressions

Model expressions are built using the above functions and the arithmetic operators +, -, * and /, using parentheses as appropriate. For example,

qcl>SPF_MODEL = '(PLAW(1,2) + BBOD(3,4)) * ABSO(5)

The model expression can be expanded to two input lines by terminating the string expression for SPF_MODEL by an & at an appropriate position (i.e. before or after a complete model term) and by setting the parameter SPF_MODEL_& to the remaining terms. For example,

qcl>SPF_MODEL = '(PLAW(1,2) + BBOD(3,4)) &
qcl>SPF_MODEL_& = ' * ABSO(5)

Note that all energies are in rest frame of source except for grain scattering. If the parameter SPF_REDSHIFT > 0 then source spectrum will be appropriately shifted including the intrinsic absorption profile set by function ABSI. The absorption profile imposed by the function ABSO is used on the redshifted result and therefore is appropriate for the column density in our galaxy.

The functions GTRA and GSCA are complementary to each other and use the same parameter. If one is used in an expression then the other should also appear. The same is true for the functions CFRA and UFRA and an example of their use is given below (note that CFRA and UFRA have the same value):

qcl>SPF_MODEL = '(PLAW(1,2) * ((CFRA(3) * ABSO(4)) + UFRA(3)))

Output Files

Spectral results and model files, together with an ASCII file summarising the results.

Output Parameters

Spf returns a large number of output parameters. The QX parameter system is used to store these parameters.

SPF_NAME The root name for all output.
SPF_NPARAM The number of parameters fitted.
SPF_P(SPF_NPARAM) The best-fit values for each parameter.
SPF_PLO(SPF_NPARAM) The lower limit on each parameter (if zero then parameter frozen during the fitting process).
SPF_PHI(SPF_NPARAM) The upper limit on each parameter (if zero then parameter frozen during the fitting process).
SPF_REDCHI The reduced chi-square.
SPF_NFREE The number of free parameters.
SPF_FLUX01_2 The model flux between 0.1 and 2 keV.
SPF_FLUX05_35 The model flux between 0.5 and 3.5 keV.
SPF_FLUX2_6 The model flux between 2 and 6 keV.
SPF_FLUX2_10 The model flux between 2 and 10 keV.
SPF_FLUX10_20 The model flux between 10 and 20 keV.
SPF_FLUX20_30 The model flux between 20 and 30 keV.
SPF_GFILE The name of confidence grid (if present).
SPF_DEL68 Delta chi-square for 68% confidence level.
SPF_DEL90 Delta chi-square for 90% confidence level.
SPF_DEL95 Delta chi-square for 95% confidence level.
SPF_DEL99 Delta chi-square for 99% confidence level.

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