XSPEC User's Guide

8
R ( I, J)
D
EJ
EJ
1
E
R( I, E)
dE
XSPEC reads both the energy ranges, E
J
, and the response matrix RD
(, I J ) from
a response file in a compressed format that only stores non-zero elements. XSPEC also
includes an option to use an auxiliary response file, which contains an array A(J)that is
multiplied into R (, I J ) as follows:
D
J
E
J1
R ( I, J) R ( I, J) A ( J)
D D D
This array is designed to represent the efficiency of the detector with the response
file representing a normalized Redistribution Matrix Function, or RMF. Conventionally,
the response is in units of cm 2 .
M(E): The Model Spectrum
The model spectrum, M ( E ), is calculated within XSPEC using the energy ranges
defined by the response file :
EJ
MD( J) M( E)
dE
and is in units of photons cm -2 s -1 . XSPEC allows the construction of composite
models consisting of additive components representing X-ray sources (e.g., power-laws,
blackbodys, and so forth), multiplicative components, which modify additive components
by an energy-dependent factor (e.g., photoelectric absorption, edges, ...). Convolution and
mixing models can then perform sophisticated operations on the result. Models are
defined in algebraic notation.
For example, the following expression:
EJ
1
phabs (power + phabs (bbody))
defines an absorbed blackbody, phabs(bbody), added to a power-law, power. The
result then is modified by another absorption component, phabs. For a list of available
models, see Chapter 6.
Fits and Confidence Intervals
Once data have been read in and a model defined, XSPEC uses a fitting algorithm
to find the best-fit values of the model parameter. The default is a modified Levenberg-
Marquardt algorithm (based on CURFIT from Bevington, 1969). The algorithm used is
local rather than global, so be aware that it is possible for the fitting process to get stuck
in a local minimum and not find the global best-fit. The process also goes much faster
(and is more likely to find the true minimum) if the initial model parameters are set to
sensible values.
The Levenberg-Marquardt algorithm relies on XSPEC calculating the 2 nd
derivatives of the fit statistic with respect to the model parameters. By default these are
calculated analytically, with the assumption that the 2 nd derivatives of the model itself
D