Reproducing an input spectrum

marx allows users to specify either a flat input spectrum or to pass in a file. Here, we generate input spectra with the spectral modeling program Sherpa. We run marx to simulate a point source and extract the data from that simulation using CIAO, read it back into Sherpa and fit the simulated data. If everything works well and all detector effects are treated consistently, we should recover the same spectral parameters (up to Poisson noise). On the other hand, if marx and CIAO are inconsistent the fit parameters will deviate from the input parameters.

In the past, this has happened after the release of marx 5.0, which contains some files to describe the ACIS contamination. This contamination changes with time and several CalDB releases had happened before we released marx 5.1. At that time, marx always predicted too many counts at low energies.

The following tests are designed to test consistency with CIAO. Since there is always some uncertainty about the intrinsic spectrum of astrophysical sources, this test is best done with simulated input spectra.

Absorbed powerlaw on ACIS-S

code:Absorbed powerlaw on ACIS-S

This test checks the internal consistency of a marx spectral simulation by simulating a source placed on an back-illuminated chip of ACIS-S. The input spectrum is an absorbed powerlaw.

Spectra and model shown in top of each other. Differences are described in the text.

Data reduced as required to reproduce the marx setup (see Current caveats for MARX) is shown in green, data reduced with standard CIAO setting in orange. The orange error bars are omitted for clarity. In this display, green and orange points should be on top of each other, but the next figure shows that real differences exist when ARF is needed to calculate the flux. Lines show the input model (red, using the ARF of the green data), the best-fit model to the green data (green line) and to the orange data (orange line).

ARFs differ in the range 2-5 keV

ARFs for both extraction methods (some color as above).

Fit results:

Parameter Input MARX special extraction CIAO default extraction
name value value err_down err_up value err_down err_up
a.nH 1.0 1.1 -0.049 0.052 0.99 -0.047 0.049
p.PhoIndex 1.8 1.9 -0.058 0.059 1.8 -0.056 0.057
p.norm 0.001 0.0011 -8e-05 8.8e-05 0.00098 -6.8e-05 7.5e-05

The table shows how the best fit of the simulated and extracted data compares to the parameter values that were used to generate the input spectrum. The two columns compare the fit results using an extraction that takes marx‘s Current caveats for MARX into account and an extraction that just applies CIAO default values.

In a Monte-Carlo simulation we can never expect the fit to hit the input values exactly. In fact, a perfect agreement between input and output numbers would indicate that the random number generator is not random enough. When running this example many times, the average distance should be roughly 1 sigma.

Powerlaw spectrum of an off-axis source

code:Powerlaw spectrum of an off-axis source

Same as above, but for an off-axis source.

Spectra and model shown in top of each other. Differences are described in the text.

Data reduced as required to reproduce the marx setup (see Current caveats for MARX) is shown in green, data reduced with standard CIAO setting in orange. The orange error bars are omitted for clarity. In this display, green and orange points should be on top of each other, but the next figure shows that real differences exist when ARF is needed to calculate the flux. Lines show the input model (red, using the ARF of the green data), the best-fit model to the green data (green line) and to the orange data (orange line).

ARFs differ in the range 2-5 keV

ARFs for both extraction methods (some color as above).

Fit results:

Parameter Input MARX special extraction CIAO default extraction
name value value err_down err_up value err_down err_up
a.nH 1.0 1.0 -0.078 0.082 1.0 -0.078 0.081
p.PhoIndex 1.8 1.8 -0.079 0.08 1.8 -0.079 0.081
p.norm 0.001 0.00097 -9.8e-05 0.00011 0.00099 -0.0001 0.00011

The table shows how the best fit of the simulated and extracted data compares to the parameter values that were used to generate the input spectrum.

See above for a detailed description.

Two thermal components on ACIS-I

code:Two thermal components on ACIS-I

Same as above, but for a front-illuminated ACIS-I chip and using an input spectrum with two thermal components similar to a stellar corona.

Spectra and model shown in top of each other. Differences are described in the text.

Data reduced as required to reproduce the marx setup (see Current caveats for MARX) is shown in green, data reduced with standard CIAO setting in orange. The orange error bars are omitted for clarity. In this display, green and orange points should be on top of each other, but the next figure shows that real differences exist when ARF is needed to calculate the flux. Lines show the input model (red, using the ARF of the green data), the best-fit model to the green data (green line) and to the orange data (orange line).

ARFs differ in the range 2-5 keV

ARFs for both extraction methods (some color as above).

Fit results:

Parameter Input MARX special extraction CIAO default extraction
name value value err_down err_up value err_down err_up
a1.kT 0.7 0.72 -0.039 0.036 0.72 -0.038 0.034
a1.Ne 2.0 1.7 -1.3 1.3 1.8 -1.2 1.3
a1.norm 0.0002 0.0002 -1.3e-05 1.3e-05 0.00021 -1.3e-05 1.3e-05
a2.kT 2.0 2.0 -0.11 0.11 2.0 -0.12 0.12
a2.norm 0.0004 0.00037 -2.1e-05 2.1e-05 0.00038 -2.3e-05 2.3e-05

The table shows how the best fit of the simulated and extracted data compares to the parameter values that were used to generate the input spectrum.

See above for a detailed description.