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Freeman, P. E., Doe, S., & Siemiginowska, A. 2001, in ASP Conf. Ser., Vol. 238, Astronomical Data Analysis Software and Systems X, eds. F. R. Harnden, Jr., F. A. Primini, & H. E. Payne (San Francisco: ASP), 483
New Elements of Sherpa, CIAO's Modeling and Fitting Tool
P. E. Freeman, S. Doe, A. Siemiginowska
Harvard-Smithsonian Center for Astrophysics MS-81, 60 Garden Street,
Cambridge, MA 02138
Abstract:
We describe enhancements made to Sherpa
for the CIAO 2.0 release, concentrating upon those
that enable a user to: (1) analyze Chandra X-ray Observatory grating
data with wavelength- or energy-space models;
(2) simultaneously fit background and source datasets; and
(3) estimate and visualize confidence intervals and regions.
We also list enhancements that we plan to make to Sherpa
for future CIAO releases.
Sherpa is the modeling and fitting tool of the
Chandra Interactive Analysis of Observations (CIAO) software package
(Doe et al. 1998 and references therein).
We have developed it with the primary goal that a user should be able to
take
full advantage of Chandra's unprecedented observational capabilities
and be able to analyze data in up to four dimensions
(energy
or wavelength
, time
, and spatial location
) with a wide variety of models, optimization methods, and
fit statistics. The enhancements that we have made to Sherpa
for the CIAO 2.0 release, described below,
represent major steps towards this goal.
Chandra grating data are most naturally analyzed in
wavelength space, while XSPEC line models such as
xsraymond are defined in energy space.1 Sherpa now allows one to define models in either space, while
using either
grating Ancillary Response Files (gARFs) or Response Matrix Files (gRMFs)
or both. The ANALYSIS command allows
one to switch between spaces.2One can also now apply filters defined in wavelength or energy space to
single datasets, groups of datasets, or to allsets. See Figure
1.
Figure 1:
Best-fit of a normalized Gaussian function to an emission line observed
in four first-order HEG and MEG Chandra grating spectra of Capella.
The amplitude, full-width at half-maximum, and position values are
linked between datasets. The identify function of GUIDE
indicates that line is most likely due to
the Si XIII 2
1 transition at 6.7403 Å.
![\begin{figure}
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Standard processing of Chandra grating data includes the
extraction of background spectra, dubbed ``up" and ``down,"
from either side of the source extraction region.
One can either fit both spectra simultaneously with the source spectrum
(see below), or SUBTRACT both from the source spectrum.
This S-lang-based extension to Sherpa assists the fitting of atomic
lines and differential emission measure (DEM).
For more information, see Doe, Noble, & Smith (2001) and
http://asc.harvard.edu/ciao/download/doc/guide_doc.ps.
One can save and restore a Sherpa session
using a Model Descriptor List (MDL) file, which records
information about input datasets, and filter and model definitions.
One example of its usefulness is in DEM fitting,
where the input data are MDL-stored line fluxes and flux errors.3
Previous versions of Sherpa allowed the user to input
background data with the commands BACK or READ BACK,
but these data could only be subtracted from the source data.
Sherpa now allows the simultaneous
analysis of one (or two) background dataset(s)
for every source dataset that is read in.
A background model is fit directly to the background
data, and is also extrapolated to the source region, where it is added
to the source model before convolution.
Rescaling for different extraction region
sizes is done using the values of the BACKSCAL keyword,
set in the header of the PHA files containing source and
background data, using the commands SETDATA and SETBACK.
Sherpa contains many new methods that one can use to estimate
confidence intervals or visualize confidence regions for best-fit
model parameters. Note that these methods are strictly valid,
i.e., provide 1
confidence intervals that actually
contain 68.3% of the
integrated probability, when (1) the
or
(log-likelihood) surface in parameter
space is approximately shaped like a multi-dimensional
paraboloid, and (2)
the best-fit point is sufficiently far from parameter space boundaries.
The confidence interval is determined for
each parameter in turn by varying its value
while holding the values of all other parameters at their
best-fit values. While fast, UNCERTAINTY will underestimate a
parameter's interval if it is correlated with other parameters.
One can visualize spaces with INTERVAL-UNCERTAINTY and
REGION-UNCERTAINTY.
Figure 2:
Examples of parameter space visualization.
Left: A plot showing the Cash statistic as a function of power-law
slope, generated using INTERVAL-PROJECTION. Right:
contour plot showing 1, 2, and 3
confidence regions for the
power-law amplitude and slope, generated using
REGION-PROJECTION. The central cross indicates the best-fit point.
![\begin{figure}
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The confidence interval is determined for each parameter in turn
while allowing the values of all other parameters
to float to new best-fit values.
One can visualize spaces with INTERVAL-PROJECTION and
REGION-PROJECTION (see Figure 2).
The confidence interval for each parameter is determined
using the diagonal terms of the covariance matrix.
While fast, it cannot be used to visualize parameter spaces.
Below we list other enhancements to Sherpa made
for the CIAO 2.0 release.
- We have extensively retooled the algorithms for the
optimization methods POWELL, SIMPLEX, and
LEVENBERG-MARQUARDT to make them more robust.
- The parameter value guessing algorithm now takes into account
the exposure time and ARF if PHA spectral data are input.
- One can use ARFs and RMFs with different photon-space binning.
- One can simulate one-dimensional spectra with FAKEIT.
- One can define two-dimensional spatial models
in either image coordinates or in the World Coordinate System (WCS).
- New models other than ngauss and delta
include a broken power law ( bpl), one- and
two-dimensional constants ( const and const2d),
a two-dimensional delta function ( delta2d),
a phenomenological photoionization edge model ( edge),
and a line broadening model ( linebroad).
- One can set preferences in a .sherparc
file in the home directory.
Sherpa does not yet treat photon ``pile-up," which can markedly affect
the fitting of energy spectra of strong sources observed by either
Chandra or XMM. Another Chandra-specific enhancement
would be the ability to convolve data with analytic functions specified in
Fits Embedded Function (FEF) files (Rots et al. 2001),
rather than a response matrix, which could
markedly decrease the time needed to analyze grating spectra.
Currently, Sherpa cannot apply exposure maps in spatial analysis, nor
can it calculate the fluxes in two dimensions. Also,
the current Sherpa requirement that a one-to-one mapping exist
between each background bin and source bin must be waived so that, e.g.,
one can define differently sized source and background regions in an
image.
Enhancements to be made include adding
model comparison tests, correlation analysis and non-parametric fitting,
and support for Bayesian analyses (e.g., specification of the prior and
credible interval/region estimation).
Acknowledgments
This project is supported by the Chandra X-ray
Center under NASA contract NAS8-39073.
References
Doe, S., Noble, M., & Smith, R. 2001, this volume, 310
Doe, S., Ljungberg, M., Siemiginowska, A., & Joye, W. 1998,
in ASP Conf. Ser., Vol. 145, Astronomical Data Analysis
Software and Systems VII, ed. R. Albrecht, R. N. Hook, &
H. A. Bushouse
(San Francisco: ASP), 157
Rots, A., McDowell, J., Wise, M., He, H., & Freeman, P. 2001,
this volume, 479
Footnotes
- ... space.1
-
Models in the XSPEC v.10 library are available to users of CIAO 2.0,
while the v.11 library will be available starting with CIAO 2.1.
- ... spaces.2
-
The reader will find
more information about ANALYSIS, as well as all other Sherpa
commands, at
http://asc.harvard.edu/ciao/documents_manuals.html.
- ... errors.3
-
Flux errors are easily estimated for three Sherpa models for which
the amplitude is equal to the flux: the normalized Gaussian ( ngauss);
the delta function ( delta); and the Lorentzian ( lorentz).
© Copyright 2001 Astronomical Society of the Pacific, 390 Ashton Avenue, San Francisco, California 94112, USA
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