Dealing with background in XSPEC
When the background requires a different response to the source
Suppose we have a model for the background spectrum which requires a different response to that for the source spectrum. Read in the source and background spectra as separate files :
XSPEC12>data 1:1 source.pha 2:2 back.pha
The source and background files have their own response matrices :
XSPEC12>response 1 source.rsp 2 back.rsp
Set up the model for the source. Here we will take the simple case of an absorbed power-law :
XSPEC12>model phabs(pow)
Input parameter value, delta, min, bot, top, and max values for ...
1 0.001 0 0 100000 1e+06
1:data group 1::phabs:nH>
1 0.01 -3 -2 9 10
2:data group 1::powerlaw:PhoIndex>
1 0.01 0 0 1e+24 1e+24
3:data group 1::powerlaw:norm>
Input parameter value, delta, min, bot, top, and max values for ...
1 0.001 0 0 100000 1e+06
4:data group 2::phabs:nH>
1 0.01 -3 -2 9 10
5:data group 2::powerlaw:PhoIndex>
1 0.01 0 0 1e+24 1e+24
6:data group 2::powerlaw:norm>0 0
Note that we have fixed the normalization of the source model for the background dataset at zero so it doesn't contribute. Now we need to set up the background model for both datasets with its own response matrix.
XSPEC12>response 2:1 back.rsp 2:2 back.rsp
This tells xspec that both these datasets have a second model which must be multiplied by the back.rsp response matrix. We now define the background model to be used. In this case take the simple example of a single power-law
XSPEC12>model 2:myback pow
Input parameter value, delta, min, bot, top, and max values for ...
1 0.01 -3 -2 9 10
1:myback:data group 1::powerlaw:PhoIndex>
1 0.01 0 0 1e+24 1e+24
2:myback:data group 1::powerlaw:norm>
Input parameter value, delta, min, bot, top, and max values for ...
1 0.01 -3 -2 9 10
3:myback:data group 2::powerlaw:PhoIndex>
1 0.01 0 0 1e+24 1e+24
4:myback:data group 2::powerlaw:norm>
We have now set up xspec so that the source data is modeled by a source model multiplied by the source response plus a background model multiplied by the background response and the background data is modeled by the background model multiplied by the background response. The background models fitted to the source and background data are constrained to be the same.
XSPEC12>show model
Current model list:
========================================================================
Model phabs<1>*powerlaw<2> Source No.: 1 Active/On
Model Model Component Parameter Unit Value
par comp
Data group: 1
1 1 phabs nH 10^22 1.0000000 +/- 0.0
2 2 powerlaw PhoIndex 1.0000000 +/- 0.0
3 2 powerlaw norm 1.0000000 +/- 0.0
Data group: 2
4 1 phabs nH 10^22 1.0000000 = 1:phabs[1]:nH
5 2 powerlaw PhoIndex 1.0000000 = 1:powerlaw[2]:PhoIndex
6 2 powerlaw norm 0.0 frozen
________________________________________________________________________
========================================================================
Model myback:powerlaw<1> Source No.: 2 Active/On
Model Model Component Parameter Unit Value
par comp
Data group: 1
1 1 powerlaw PhoIndex 1.0000000 +/- 0.0
2 1 powerlaw norm 1.0000000 +/- 0.0
Data group: 2
3 1 powerlaw PhoIndex 1.0000000 = 1:myback:powerlaw[1]:PhoIndex
4 1 powerlaw norm 1.0000000 = 1:myback:powerlaw[1]:norm
________________________________________________________________________
Including particle background
A particular case of background requiring a different response is particle background. This is assumed to depend on the instrumental response but not on the telescope effective areas. In xspec v11 and earlier a particle background model could be included by appending /b to additive components at the end of the model definition. These components were multiplied by the response file but not the arf. To do the equivalent in the current version of xspec suppose that our source.rsp in the example above can be split into source.rmf, the instrument response, and source.arf, the telescope effective area. To read the data in this case we do the following :
XSPEC12>data 1:1 source.pha 2:2 back.pha XSPEC12>response 1 source.rmf 2 source.rmf XSPEC12>arf 1 source.arf XSPEC12>response 2:1 source.rmf 2:2 source.rmf
We can then define the source and background models in the same way as the previous example.
Simulating a spectrum with particle background
Suppose we don't yet have a background spectrum but want to simulate a dataset which includes the particle background. We need a spectrum file - it doesn't matter what is in it - and the rmf and arf files.
XSPEC12>data test.pha XSPEC12>response source.rmf XSPEC12>arf source.arf XSPEC12>response 2:1 source.rmf
Now define the source and background models and run fakeit eg :
XSPEC12>model phabs(pow)
Input parameter value, delta, min, bot, top, and max values for ...
1 0.001 0 0 100000 1e+06
1:phabs:nH>
1 0.01 -3 -2 9 10
2:powerlaw:PhoIndex>
1 0.01 0 0 1e+24 1e+24
3:powerlaw:norm>
XSPEC12>model 2:myback pow
Input parameter value, delta, min, bot, top, and max values for ...
1 0.01 -3 -2 9 10
1:myback:powerlaw:PhoIndex>
1 0.01 0 0 1e+24 1e+24
2:myback:powerlaw:norm>
XSPEC12>fakeit