Spectral analysis
Spectroscopy is a complex art, because there are many different mechanisms
by which an object can produce electromagnetic radiation. Each mechanism
has a characteristic spectrum either in the form of line or continuum emission
and generally the observed spectrum is a result of more then one mechanism.
Extracting scientific information from the observed spectrum requires detailed
understanding of the instrument used to record the spectrum
as well as through understanding of various emission mechanisms and physical
conditions giving rise to the radiation.
For example, let's consider an observed spectrum and examine
each part of it.
Above is an X-ray spectrum, made using data from the
ASCA
satellite, of a
supernova
remnant known as Cas-A. The X-axis shows the range of energy of radiation
and the Y-axis shows the intensity of the radiation being emitted by the
SNR at each energy. In X-ray range, the energy of the radiation is typically
measured in units keV, or kilo-electron Volts.
This spectrum consists of many emission lines superimposed over a continuum
emission. First task in spectral analysis is to quantify the observed spectrum
i.e. to measure position, strength, width of individual lines and to measure
precise shape of the continuum. This information is then used to extract
science out of the observed spectrum. For example, each element has
a unique line emission pattern extending over a range of electromagnetic
band. Emission lines in X-ray range are typically due to highly ionized
elements present in astrophysical plasma. Thus presence of a line at particular
position or energy in the observed spectrum indicates the presence of corresponding
element in the X-ray source. Strength and width of the line also gives indication
of the temperature and
density
of that element in the source. Variation in the position, strength or
width of the line indicates possible velocities fields.
However, line emission ceases to be the dominant cooling mechanism of
astrophysical
plasmas
for temperatures exceeding 1 keV and hence X-ray spectra are primarily
characterized by their continua. The simplest of these are the featureless
power laws produced by the interaction of power law distributions of cosmic
ray
electrons
with ambient
magnetic fields
. The Crab
nebula
, for example, is a prime example of such a source, called a synchrotron
source. Almost as simple, is the blackbody spectrum, which originates in
a completely thermalized body. Such spectra are seen, for example,
in X-ray bursts of
neutron stars
or black hole candidates with very hot accretion disk.
When we use a X-ray spectrometer to determine the spectrum of a source,
what the spectrometer obtains is not the actual spectrum. The raw data are
a convolution of the actual input photon spectrum with the response function
of the spectrometer. In X-ray detectors there is a finite probability that
an incident photon with certain energy will be detected as having some other
energy, determined by the type of detector and physics of X-ray interaction.
The detector response matrix basically gives the probability that an incoming
photon of energy E will be detected in channel I. Deconvolution of the observed
spectrum with the detector response matrix, to determine the true incident
spectrum, is most often not possible.
The conventional approach is to assume some model for the input spectrum
so that it can be characterized by a limited number of adjustable parameters.
Then to convolve the assumed model spectrum with the detector response and
to adjust the model parameter so that the convolved spectrum matches with
the observed spectrum. This is known as model fitting of the observed spectrum.
Confidence with which we can say that the best fit parameters really
describes the input spectrum depends on the statistics of the actual fitting
process. However, this method requires that we have some a priori knowledge
of the actual spectral form.
A software package called XSPEC is available as a part of HEAsoft
to carry out this process. XSPEC is a mission independent spectral analysis
package. It can read X-ray spectrum, which is generally stored in a FITS file
with extension ".pha", along with other necessary information such as background
during the observation and detector response matrix. It has many pre-defined
models and which can be used to fit the observed spectrum. XSPEC also gives
statistical uncertainties on the best fit model parameters as well as the
confidence limit on the best fit model. For detail information on spectral
analysis and XSPEC package please consult the
XSPEC User's Guide
. In our excersise of spectral analysis we shall use XSPEC to analyse observed
spectrum from few X-ray pulsar sources.
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