Deproject is a Sherpa extension package
to facilitate deprojection of two-dimensional annular X-ray spectra to recover
the three-dimensional source properties. For typical thermal models this would
include the radial temperature and density profiles. This basic method has been
used extensively for X-ray cluster analysis and is the basis for the XSPEC
model projct. The deproject module brings this functionality to
Sherpa as a Python module that is straightforward to use and understand.
The basic physical assumption of deproject is that the extended source
emissivity is constant and optically thin within spherical shells whose radii
correspond to the annuli used to extract the specta. Given this assumption one
constructs a model for each annular spectrum that is a linear volume-weighted
combination of shell models.
Version 0.2 of deproject is limited to circular annuli.
Further documentation is available at https://deproject.readthedocs.io/
The deproject module is released under the
BSD 2-Clause license,
available as the file LICENSE in the source distribution.
The installation assumes that you are installing deproject into
the CIAO environment (CIAO 4.14 or
later), since this is the easiest way to get the XSPEC models along
with Sherpa. The standalone Sherpa
version can be used, but in this case you will need to build Sherpa
with XSPEC support.
The following Python packages are required:
For Standalone Sherpa or CIAO versions newer than CIAO 4.14,
you should be able to install deproject with the command:
pip3 install deproject
The installation requires pip version 19 or higher, but as that was released in early 2019 it should be available.
The installation documentation describes how to build a development version from the GitHub repository.
If you have a set of X-ray PHA spectra called src<n>.pi, where <n> is
an integer representing the annulus number, and the files contain the
XFLT0001 to XFLT0005 header keywords used by the
XSPEC projct model,
then a
Deproject object
can be created using the
deproject_from_xflt
helper routine with the commands:
>>> from deproject import deproject_from_xflt
>>> from astropy import units as u
>>> dep = deproject_from_xflt('src*.pi', 0.492 * u.arcsec)
where, in this example, the XFLT0001 and XFLT0002 keywords,
which specify the inner and outer radii of the annulus, are in
ACIS pixels, and so need to be multiplied by 0.492 arcseconds to
convert to an angle (the second parameter).
This will automatically load the spectra into separate Sherpa datasets,
which can be fitted individually, but it is generally easier to use
the object returned by deproject_from_xflt. For instance, the
following will set the data range to be fit for each spectra and ensure
that the background is subtracted before fitting:
>>> dep.ignore(None, 0.5) >>> dep.ignore(7.0, None) >>> dep.subtract()
Sherpa functions are used to change the statistic and optimiser:
>>> from sherpa.astro import ui
>>> ui.set_stat('chi2xspecvar')
>>> ui.set_method('levmar')
The data can be fit, and errors estimated for all the parameter, using the onion-skin deprojection approach, with the following commands:
>>> onion = dep.fit() >>> errs = dep.conf()
The return value includes the density (and errors, if appropriate), as an Astropy Quantity.
>>> print(onion['density'])
print(onion['density'])
density
1 / cm3
--------------------
0.1100953546292787
0.07736622021374819
0.04164827967805805
0.03630168106524076
0.025221797991301052
0.021845331641349316
...
0.012396857131392835
0.01336640115325031
0.012303975980575187
0.013631563529090736
0.013996131292837352
0.010843683594144967
0.023067220584935984
Length = 20 rows
The on-line documentation
contains more information, including creating the Deproject object
directly (without the need for the XFLTxxxx keywords).