FOV spectrum and image

last updated: 2023/06/12

Source: MCXC J0106.8+0103

Observation ID: 0762870601
SAS Version: 19.0.0

Python version: 3

csh is used

Everything you need in this tutorial is in: spectrum.zip .

You work in the main folder spectrum, there are several subfolders:

1. src - the source code is found there

2. log - an empty folder for you to put the log files. When you run the script in src, this is automatically done.

3. command - the subcommands for the src/FOV_imgspec.csh with comments.

4. InputFiles - the good ccd lists for mos1(goodccdlist_mos1.dat) and mos2(goodccdlist_mos2.dat) are put.

5. esas_products - this is the folder I work on. The content is the same as the main folder but with all the files needed for and created by this chapter. Since the files are two big to be uploaded for the folders full_spectrum_mos1/mos2/pn , I only provide a list of the files produced in this chapter( filesproduced.txt ).

If you successfully work out the previous chapters, then you may just download the source code .

(Remember to set your browser Tex-Encoding as unicode if some characters in this page is not probably displayed.)

Here are the subsections of this part:

Source spectrum and image production ( mos_spectrum and mos_back )

Making background image in sky coordinate( rot-im-det-sky and esky2det )

Production of “Rate” image ( comb and bin_image )

Plotting radial profile using combined and non-combined exposure

Appendix - Error calculation of surface brightness profile.

Discussion:

1.Background counts of image vs spectrum

2.Should the particle background be divided by vignetting-corrected exposure?

FOV spectrum and image production

Whenever you produce any spectrum, make sure you create a new folder and work there. There are many intermediate files which are overwritten when a new spectrum is produced, but not all. Two examples are mos2S002.rmf and mos2S002.arf . If you produce spectrum A first and you forget to delete these two files, when you produce a new spectrum B, these two files are considered under spectrum B. Also, sometimes the background spectrum cannot be produced successfully. This happens often for pn (i.e. pnS003-back.pi ) and you need the intermediate files to produce the background spectrum, or else you have to start from pn_spectrum again, so keep them well in a separate folder.

I put all the subcommands of mos-filter and pn-filter in

command/FOV_imgspec_mos1.csh command/FOV_imgspec_mos2.csh
command/FOV_imgspec_pn.csh

I added comments to each subcommand. You can just extract any subcommand and run it. In the folder InputFiles , I already put the “good” ccd chips in a list called goodccdlist_mos1.dat and goodccdlist_mos2.dat (These are the results of Anomalous CCD Check ) , when you produce spectra of mos1 and mos2 , this file would be read automatically.

Here are what you need for this part:

mos2S002-clean.fits, mos2S002-cheese.fits, mos2S002-bkg_region-det.fits, mos2S002-bkg_region-sky.fits,
mos1S001-clean.fits, mos1S001-cheese.fits, mos1S001-bkg_region-det.fits, mos1S001-bkg_region-sky.fits,
pnS003-clean.fits, pnS003-clean-oot.fits, pnS003-cheese.fits, pnS003-bkg_region-det.fits, pnS003-bkg_region-sky.fits,
and ccf.cif.

Now open three separate windows under the main folder, and run the following concurrently:

source bin/FOV_imgspec.csh mos1S001 400 2300 path_to_caldb

source bin/FOV_imgspec.csh mos2S002 400 2300 path_to_caldb

source bin/FOV_imgspec.csh pnS003 400 2300 path_to_caldb

You have to enter 4 arguments: 1: the full name* of the ccd, 2: lower limit of the energy (in eV) for the image you want to produce, 3: upper limit of the energy and 4: path to calibration data, i.e. where the fwc and other data is stored. Of course, for the energies and path to calibration data, you can modify the script and just put the values there.

*full name of the ccd is not necessarily mos1S001,mos2S002 or pnS003. Sometimes instead of “S”, it can be “U”, and it can be mos1S002, mos2S003 , pnS004 or something else.

For each of the ccd, a separate folder ( full_spectrum_mos2/mos1/pn ) is created and every process takes place in that folder. The file command.csh is updated all the time whenever a new process takes place. I rename it to FOV_imgspec_mos2(/mos1/pn).csh at the end of the whole process. The log files are in log/pn-spectra.log and mos-spectra_mos1(/mos2).log .We will use this file later. Now wait for a few hours (for my side mos1 takes the longest time ~10 hours, mos2 and pn ~ 6) for everything to finish to get all the stuff you need for this chapter, then you can go on with the rest. Note that I rename the files in the script.

Source spectrum and image production

To produce the spectrum and image, run the following, input the path of the calibration files in caldb :

mos-spectra prefix=2S002 caldb=path_to_caldb region=nonfile mask=1 elow=400 ehigh=2300 ccd1=1 ccd2=1 ccd3=1 ccd4=1 ccd5=0 ccd6=1 ccd7=1

pn-spectra prefix=S003 caldb=path_to_caldb region=nonfile mask=1 elow=1 ehigh=1 quad1=1 quad2=1 quad3=1 quad4=1

Now we want the whole FOV, so for the keyword region , just set nonfile . If mask=1 , mos-spectra will look for; mos2S002-bkg_region-det.fits and mos2S002-bkg_region-sky.fits (the same for mos1 and pn ) to make the spectrum and image with point sources masked. If these files are not present, spectrum and image would be produced with no mask. You can check log/mos-spectra-mos2.log to see whether the files are produced with them. It is written at the beginning. For mos1 and mos2, remember in the first chapter Filtering for Soft Protons , we find ccd5 of mos2 in anomaly. Set ccd5=0 would disable this ccd. For pn-spectra , just set all quad=1 .

A spectrum in the whole energy range is produced. Images in the energy range that you enter are produced. I choose 0.4-2.3 keV here because it is the soft band luminosity, a quantity I need to do my analysis. I will explain more about the choice of energy in the chapter (Luminosity Calculation) , where I will show you how to calculate luminosities.

Here are the brief steps for mos-spectra:
1.Production of spectrum in the field of interest, the relevant rmf and arf files using mos2S002-clean.fits.
2.Production of spectrum of individual ccd chips using mos2S002-clean. fits(I skip mos1 and pn from now on)
3. Production of spectrum of individual ccd chip corners using mos2S002-clean.fits
4. Production of spectrum of individual ccd chips using FWC data
5. Production of spectrum of individual ccd chip corners using FWC data
6. Production of image, exposure map and mask (not the cheese mask here) in the energy range of interest
7. Production of image of individual ccd chips using FWC data

For pn , the same is repeated with the oot file (i.e. pnS003-clean-oot.fits ).

Here are the details:
1.Production of spectrum in the field of interest, the relevant rmf and arf files using mos2S002-clean.fits.

To produce the whole FOV spectrum mos2S002-obj.pi :

evselect table=mos2S002-clean.fits:EVENTS withfilteredset=yes expression='(PATTERN<=12)&&(FLAG == 0)&&!((DETX,DETY) in BOX(-6560,13180,6590,6600,0))&&region(mos2S002-bkg_region-det.fits)&&(((DETX,DETY) IN circle(-61,-228,17085))||((DETX,DETY) IN box(14.375,-16567.6,5552.62,795.625,0)))' filtertype=expression keepfilteroutput=no updateexposure=yes filterexposure=yes withspectrumset=yes spectrumset=mos2S002-obj.pi energycolumn=PI spectralbinsize=5 withspecranges=yes specchannelmin=0 specchannelmax=11999

The expression is the most important. Pay attention to those involving coordinate selection. “A&&B” means overlapping area of A and B, and “A||B” means A+B (overlapping and non-overlapping area are both included), “!” means exclusion. So for the above:

(((DETX,DETY) IN circle(-61,-228,17085))||((DETX,DETY) IN box(14.375,-16567.6,5552.62,795.625,0)))&&!((DETX,DETY) in BOX(-6560,13180,6590,6600,0))

means circle(-61,-228,17085)+ box(14.375,-16567.6,5552.62,795.625,0) (they together mean the exposed FOV) but excludes BOX(-6560,13180,6590,6600,0)

BOX(-6560,13180,6590,6600,0) corresponds to ccd5. You can extract an image using each of the circle or box in the expression to learn better. “ region(mos2S002-bkg_region-det.fits)” is the mask used. Finally,you extract a spectrum using this expression called mos2S002-obj.pi.

Now you open mos2S002-obj.pi to take a look at the header of the first extension SPECTRUM, look for SLCTEXPR , it is the selection expression that you enter. Explore some other keywords in the header yourself. Also check for the data of this extension, it only has two columns, counts and channel . Just make a plot directly with x=channel and y=counts, you plot the spectrum already!

fv mos2S002-obj.pi &

Fig1. mos2S002-obj.pi plotted using fv.

By the way, for image data, in case you forget what expression you use when you produce them, always check the header.

Here are the spectra of all ccd chips, including the anomalous ccd5. Here again you see at low energies, it has higher counts.

Fig 2. Spectrum of individual ccd chips of mos2 . Figure is produced with a.pltspec() of src/spectrum_script.py

To produce the above only takes a few seconds. But we also need to extract the solid angle for spectral fit. You do the following so that the keyword “ backscale ” (the solid angle) would be added to the header. The unit is in square pixels. This process sometimes takes hours.

backscale spectrumset=mos2S002-obj.pi badpixlocation=mos2S002-clean.fits withbadpixcorr=yes

Now let’s check the value:

fkeyprint mos2S002-obj.pi+1 backscal

It is 714232892 square pixels. For the spectrum, 1 pixel = 0.05 arcsecs. So 714232892 would be 714232892*(0.05/60.)**2 = 496 square arcmins. You need this value in the spectral fit.

To produce the rmf file, which contains information about channel to energy conversion, in image called detmap.ds is first produced:

evselect table=mos2S002-clean.fits:EVENTS withfilteredset=yes filtertype=expression expression='(PATTERN<=12)&&(FLAG == 0)&&(((DETX,DETY) IN circle(-61,-228,17085))||((DETX,DETY) IN box(14.375,-16567.6,5552.62,795.625,0)))&&!((DETX,DETY) in BOX(-6560,13180,6590,6600,0))&&region(mos2S002-bkg_region-det.fits)' imagebinning='imageSize' imagedatatype='Int32' imageset=detmap.ds squarepixels=yes ignorelegallimits=no withxranges=yes withyranges=yes xcolumn='DETX' ximagesize=120 ximagemax=19500 ximagemin=-19499 ycolumn='DETY' yimagesize=120 yimagemax=19500 yimagemin=-19499 updateexposure=yes filterexposure=yes

then the rmf mos2S002.rmf is produced:

rmfgen format=var rmfset=mos2S002.rmf spectrumset=mos2S002-obj.pi threshold=1.0e-6 detmaptype=dataset detmaparray=detmap.ds

You can now open mos2S002.rmf:

fv mos2S002.rmf &

See the second extension EBOUNDS. You see there are altogether 2400 channels and each channel corresponds to a particular energy range, with range = 5 keV. The mid energy of the first channel is 2.5keV, and the last 11.9975 keV.

and the exact detmap.ds is produced again for the arf file:

then the arf:

arfgen arfset=mos2S002.arf spectrumset=mos2S002-obj.pi withrmfset=yes rmfset=mos2S002.rmf extendedsource=yes modelee=no withbadpixcorr=no detmaptype=dataset detmaparray=detmap.ds badpixlocation=mos2S002-clean.fits modelootcorr=no

Now open mos2S002.arf and plot it with x=energy_lo or enery_hi , y=specresp :

fv mos2S002.arf &

mos2S002.arf is basically the effective area curve. You see mos2 is most sensitive in the low energy range, ~ 1 – 5 keV. When you do spectral analysis, this has to be taken into account. This is the average effective area for the FOV. Later you will see there is difference in on-axis and off-axis positions.

Fig 3. mos2S002-arf.pi plotted using fv.

2.Production of spectrum of individual ccds using mos2S002-clean.fits . I use ccd2 as an example here:

evselect table=mos2S002-clean.fits:EVENTS withfilteredset=yes expression='(PATTERN<=12)&&(FLAG == 0)&&(((DETX,DETY) IN circle(-61,-228,17085))||((DETX,DETY) IN box(14.375,-16567.6,5552.62,795.625,0)))&&((DETX,DETY) IN BOX(6580,-13530,6620,6640,0))&&!((DETX,DETY) in BOX(-6560,13180,6590,6600,0))&&region(mos2S002-bkg_region-det.fits)' filtertype=expression keepfilteroutput=no updateexposure=yes filterexposure=yes withspectrumset=yes spectrumset=mos2S002-2obj.pi energycolumn=PI spectralbinsize=5 withspecranges=yes specchannelmin=0 specchannelmax=11999

Here BOX(6580,-13530,6620,6640,0)) corresponds to ccd2. This expression for area extraction is a little bit redundant… If you just keep this box and leave out the rest, you actually get the same result, or you can even use (CCRNR=2) instead. You can test it yourself to understand better.

Again for the next step you calculate the solid angle:

backscale spectrumset=mos2S002-2obj.pi badpixlocation=mos2S002-clean.fits withbadpixcorr=yes

4. Production of spectrum of individual ccd chip corners using mos2S002-clean.fits

This is for the production of particle background (i.e. mos2S002-back.pi ) in mos_back (to be carried out in the next part):

evselect table=mos2S002-corn.fits:EVENTS withfilteredset=yes expression='((DETX,DETY) IN BOX(6580,-13530,6620,6640,0))' filtertype=expression keepfilteroutput=no withspectrumset=yes spectrumset=mos2S002-2oc.pi energycolumn=PI spectralbinsize=5 withspecranges=yes specchannelmin=0 specchannelmax=11999

again the box is ccd2.

And then backscale:

backscale spectrumset=mos2S002-2oc.pi useodfatt=no badpixlocation=mos2S002-clean.fits withbadpixcorr=yes ignoreoutoffov=no

These spectra are called “oc”, e.g. mos2S002-2oc.pi for chip2
Here are all the corner spectra (Note that chip 1 has no corner):

Fig.4 spectrum of individual ccd chip corner. Figure is produced with a.pltspec() of src/spectrum_script.py

4. Production of spectrum of individual ccd chips using FWC data

Again this step is for mos_back . You can take a look at the FWC data called mos2-fwc.fits.gz. in the calibration folder. It is in the same format as mos2S002-clean. fits, but the data is taken with the filter wheel closed. It is a collection of different observations so there are a lot of counts:

evselect table=mos2-fwc.fits.gz:EVENTS withfilteredset=yes expression='(FLAG == 0)&&(((DETX,DETY) IN circle(-61,-228,17085))||((DETX,DETY) IN box(14.375,-16567.6,5552.62,795.625,0)))&&((DETX,DETY) IN BOX(6580,-13530,6620,6640,0))&&!((DETX,DETY) in BOX(-6560,13180,6590,6600,0))&&region(mos2S002-bkg_region-det.fits)' withspectrumset=yes keepfilteroutput=no updateexposure=yes filterexposure=yes spectrumset=mos2S002-2ff.pi energycolumn=PI spectralbinsize=5 withspecranges=yes specchannelmin=0 specchannelmax=11999

backscale spectrumset=mos2S002-2ff.pi badpixlocation=mos2S002-clean.fits withbadpixcorr=yes

These spectra are called “ff”, e.g. mos2S002-2ff.pi . Here are all the ff spectra:

Fig. 5. Spectrum of individual ccd chip using the fwc data. Figure is produced with a.pltspec() of src/spectrum_script.py

5. Production of spectrum of individual ccd corners using FWC data

These files are called “fc”,e.g. mos2S002-2fc.pi

evselect table =mos2-fwc.fits.gz:EVENTS withfilteredset=yes expression='(PATTERN<=12)&&(FLAG == 65536)&&((DETX,DETY) IN BOX(6580,-13530,6620,6640,0))&&!(((DETX,DETY) IN CIRCLE(435,1006,17100))||((DETX,DETY) IN CIRCLE(-34,68,17700))||((DETX,DETY) IN BOX(-20,-17000,6500,500,0))||((DETX,DETY) IN BOX(5880,-20500,7500,1500,10))||((DETX,DETY) IN BOX(-5920,-20500,7500,1500,350))||((DETX,DETY) IN BOX(-20,-20000,5500,500,0)))' filtertype=expression keepfilteroutput=no withspectrumset=yes spectrumset=mos2S002-2fc.pi energycolumn=PI spectralbinsize=5 withspecranges=yes specchannelmin=0 specchannelmax=11999

backscale spectrumset=mos2S002-2fc.pi useodfatt=no badpixlocation=mos2S002-clean.fits withbadpixcorr=yes ignoreoutoffov=no

Fig. 6 Spectrum of individual ccd chip corner using the fwc data. Figure is produced with a.pltspec() of src/spectrum_script.py

6. Production of image, exposure map and mask of the source in the energy range of interest

These are done using mos2S002-clean.fits which would be used to produce the “rate image”, i.e. surface brightness profile.

#image mos2S002-obj-im-400-2300.fits in [0.4-2.3]keV

evselect table=mos2S002-clean.fits:EVENTS withfilteredset=yes expression='(PATTERN<=12)&&(FLAG == 0) &&((CCDNR == 1)||(CCDNR == 2)||(CCDNR == 3)||(CCDNR == 4)||(CCDNR == 6)||(CCDNR == 7))&&region(mos2S002-bkg_region-sky.fits)&&(PI in [400:2300])&&(((DETX,DETY) IN circle(-61,-228,17085))||((DETX,DETY) IN box(14.375,-16567.6,5552.62,795.625,0)))' filtertype=expression imagebinning='imageSize' imagedatatype='Int32' imageset=mos2S002-obj-im-400-2300.fits squarepixels=yes withxranges=yes withyranges=yes xcolumn='X' ximagesize=900 ximagemax=48400 ximagemin=3401 ycolumn='Y' yimagesize=900 yimagemax=48400 yimagemin=3401 updateexposure=yes filterexposure=yes ignorelegallimits=yes

# exposure map ( mos2S002-exp-im-400-2300.fits ) in [0.4-2.3] keV

eexpmap attitudeset=atthk.fits eventset=mos2S002-clean.fits:EVENTS expimageset=mos2S002-exp-im-400-2300.fits imageset=mos2S002-obj-im-400-2300.fits pimax=2300 pimin=400 withdetcoords=no

#mask( mos2S002-mask-im-400-2300.fits ) in [0.4-2.3] keV

emask detmaskset=mos2S002-mask-im-400-2300.fits expimageset=mos2S002-exp-im-400-2300.fits threshold1=0.1 threshold2=0.5

7. Production of image of individual ccd chips using FWC data

I believe these are used to produce the background particle image mos2S002-back-im-det-400-2300.fits (a product of mos_back ). We will soon talk more on this in the next part mos_back .

#image of ccd2 ( mos2S002-im2-400-2300.fits ) in [0.4-2.3] keV

evselect table=mos2-fwc.fits.gz:EVENTS withfilteredset=yes expression='((DETX,DETY) IN BOX(6580,-13530,6620,6640,0))&&!((DETX,DETY) in BOX(-6560,13180,6590,6600,0))&&region(mos2S002-bkg_region-det.fits)&&(FLAG == 0)&&(PI in [400:2300])&&(((DETX,DETY) IN circle(-61,-228,17085))||((DETX,DETY) IN box(14.375,-16567.6,5552.62,795.625,0)))' imagebinning='imageSize' imagedatatype='Int32' imageset=mos2S002-im2-400-2300.fits squarepixels=yes withxranges=yes withyranges=yes xcolumn='DETX' ximagesize=780 ximagemax=19500 ximagemin=-19499 ycolumn='DETY' yimagesize=780 yimagemax=19500 yimagemin=-19499 updateexposure=yes filterexposure=yes ignorelegallimits=yes

mos_back

The production of the source spectrum is actually simple. What is more complicated is the production of the particle background which you have to subtract from the source spectrum. Finally you will produce a background spectrum, mos2S002-back.pi , and two background images mos2S002-back-im-det-400-2300.fits (in detector coordinate) and mos2S002-back-im-sky-400-2300.fits (in sky coordinate).

From my interpretation, the background spectrum ( mos2S002-back.pi ) depends on 1) the corner spectra of own own observation (e.g. mos2S002-2oc.pi ), 2) FWC spectra in the same area as the source ( mos2S002-2ff.pi ) , 3) FWC corner spectra( mos2S002-2fc.pi ) and 4) qdp data in the calibration folder ( mos2-qpb.fits.gz). For particle background image (mos2S002-back-im-det-400-2300.fits), it depends on the fwc images ( mos2S002-im2-400-2300.fits ) extracted in mos-spectra . If any of the files are missing, mos2_back cannot be run successfully.

Now let’s run mos_back:

mos_back prefix=2S002 caldb=path_to_calib_data diag=0 elow=400 ehigh=2300 ccd1=1 ccd2=1 ccd3=1 ccd4=1 ccd5=0 ccd6=1 ccd7=1 >& log/mos2_mos_back.log

After running mos_back , you see a file called mos2S002-aug.qdp . Let’s open it:

qpd mos2S002-aug.qdp

PGPLOT file/type: /xw

Fig. 7 mos2S002-aug.qdp

The data in red is from the file mos2-qpb.fits.gz of the calibration data. Just open it and you see it has columns of “ HARD ” and “ RATE ”. The green cross is from our corner data with rate = (number of events in [0.3-10 keV])/(exposure) and hard =(number_of_events_in[2.5-5.0keV])/(number_of_events_in[0.40.8keV]). You can see these from the header of extension 0 of the file.

You can also see the corner rate and hardness of different ccd chips in log/mos2_back.log (I added some comments to this file but I am not able to decode everything in it). Now we can check by producing the relevant files of ccd2:

evselect table=mos2S002-corn.fits:EVENTS withfilteredset=yes expression='(PATTERN<=12)&&((FLAG & 0x766a0f63)==0)&&(CCDNR==2)&&(PI in [300:10000])' filtertype=expression filteredset=temp_events_mos2ccd2_0.3-10.fits keepfilteroutput=yes updateexposure=yes filterexposure=yes

evselect table=mos2S002-corn.fits:EVENTS withfilteredset=yes expression='(PATTERN<=12)&&((FLAG & 0x766a0f63)==0)&&((CCDNR==2))&&(PI in [400:800])' filtertype=expression filteredset=temp_events_mos2ccd2_0.4-0.8.fits keepfilteroutput=yes updateexposure=yes filterexposure=yes

evselect table=mos2S002-corn.fits:EVENTS withfilteredset=yes expression='(PATTERN<=12)&&((FLAG & 0x766a0f63)==0)&&((CCDNR==2))&&(PI in [2500:5000])' filtertype=expression filteredset=temp_events_mos2ccd2_2.5-5.0.fits keepfilteroutput=yes updateexposure=yes filterexposure=yes

Now open the above the files and calculate the hardness ratio and rate yourself. You find they have the same values as in log/mos2_mos_back.log

Since the corner files do not have enough data, they are augmented by data from mos2-qpb.fits.gz with similar hardness and rate. I believe those chosen are represented by white +. Finally, if you want to reproduce this image using python, run in src/spectrum_script.py :

a.qdpplot("mos2-qpb.fits.gz",["2","3","4","6","7"])

Fig 8. Reproduction of mos2S002-aug.qdp.

I don’t have the white + here as I don’t know the exact criteria how they are chosen, and this plot is somewhat different from mos2S002-aug.qdp probably due to different selection criteria used in both plots.

Finally, scroll to almost the bottom of log/mos2_mos_back.log and I think this is where mos2S002-back-im-det-400-2300.fits is produced .

I put the numbers in Table 1:

image	(A)Average non-zero value of FWC image	(B)Total number of counts in image	(C)FWC image scaling	C*S
mos2S002-im1-400-2300.fits	2.53404617	141478.531	1.23124784E-02	1741.95129
mos2S002-im2-400-2300.fits	2.59940314	101057.000	1.23224957E-02	1245.27441
mos2S002-im3-400-2300.fits	2.40861535	103355.812	1.21821780E-02	1259.09888
mos2S002-im4-400-2300.fits	2.49437261	89094.0000	1.16151366E-02	1034.83899
mos2S002-im6-400-2300.fits	2.47978711	110477.000	1.18284747E-02	1306.77441
mos2S002-im7-400-2300.fits	2.50920081	97893.5078	1.16683478E-02	1142.25549
Sum:				7730.19347

(A) The average non-zero value of FWC image = the total number of counts divided the number of non-zero pixels. Since this is from the calibration file; mos2-fwc.fits.gz , the value is source independent.

(B) Total number of counts in image. Again this is from the calibration file mos2-fwc.fits.gz , the value is source independent.

(C) FWC image scaling is related to the data exposure/fwc data exposure, i.e. exposure of [ mos2S002-1obj.pi/; mos2S002-im1-400-2300.fits ]

Now let’s extract the exposure:

fkeyprint mos2S002-im1-400-2300.fits+0 EXPOSURE

fkeyprint mos2S002-1obj.pi+1 EXPOSURE

exposure for mos2S002-im1-400-2300.fits: 1.91E+06s

exposure for mos2S002-1obj.pi: 2.70E+04s

So the ratio is 0.014, and it is basically the same for all ccds. Compare with the official value ~ 0.012, this is a little bit bigger. I guess the difference comes from the renormalization factor, as indicated in De Luca & Modelndi (2004) (Section 3.6), which "account for the different intensities of the NXB in the sky fields and in the closed observations due to the non-simultaneity of the measurement". And finally for the sum: 7730.19347, it is roughly the same as the total counts in mos2S002-back-im-det-400-2300.fits ,which is 7584.76758.

If you want to check the (A), (B), exposure ratio and total counts in mos2S002-back-im-det-400-2300.fits , in src/spectrum_script.py, do:

a.checkbkimg("mos2S002",[1,2,3,4,6,7])

Now we check the radial profile of mos1S001-back-im-sky-400-2300.fits mos2S002-back-im-sky-400-2300.fits and pnS003-back-im-sky-400-2300.fits . , with the centre in the central position of the image, i.e. xc=450, yc=450. Since in the table you see there is difference in the average non-zero value in the FWC image, the radial profile is not exactly that flat. The ratio of (minimum bin/maximum bin) for mos1, mos2 and pn are ~ 87%,94% and 84%, respectively.

Fig. 9 profile of mos2S002-back-im-sky-400-2300.fits and mos1 and pn . The ratio of (minimum bin/maximum bin) for mos1, mos2 and pn are ~ 87%,94% and 84%, respectively.

Making background image in sky coordinate

Now we have produced mos2S002-back-im-det-400-2300.fits ,we want to produce the same image in sky coordinate, we do:

rot-im-det-sky prefix=2S002 mask=1 elow=400 ehigh=2300 mode=1 > mos2_rot_det_sky.log

open the log file log/mos2_rot_det_sky.log , you see the central position X,Y =450.91 of the image mos2S002-obj-im-400-2300.fits (in sky coordinate, size=900*900 pixels) in ra and dec are extracted (with values = 16.68 and 1.07) and converted to detector coordinate using esky2det :

esky2det datastyle=user ra=16.685125 dec=1.07061111111111 outunit=det withheader=no calinfostyle=set calinfoset=mos2S002-obj-im-400-2300.fits verbosity=0

The detector coordinate of the same position in X, Y are: 1232.412324, -1633.01633

You can read the ra and dec directly using ds9 or use ecoordconv
:

ecoordconv imageset=mos2S002-obj-im-400-2300.fits x=450.91 y=450.91 coordtype=impix

You see on the screen you get the same ra, dec and detector coordinates:

ecoordconv:Region Centre:

Theta: Phi: 39.214786 2.6544148

X: Y: 25921 25921

DETX: DETY: 1232.4621 -1633.0042

IM_X: IM_Y: 450.91 450.91

RA: DEC: 16.685125 1.0706111

RAWX: RAWY: 356.4802 226.32278

CCD(s): 1 centred on CCD: 1

You use rot_det_sky to produce the final product: mos2S002-back-im-sky-400-2300.fits. The following have to be present for the command to be successfully carried out: mos2S002-obj-im-400-2300.fits,mos2S002-mask-im.fits and mos2S002-back-im-det-400-2300.fits :

rot_det_sky mode=1 prefix=2S002 elow=400 ehigh=2300 detx=1232.412324 dety=-1633.01633 skyx=450.91 skyy=450.91 maskfile=1 clobber=1

And you are done!

Production of “Rate” image

The “rate” image is the one you use to produce the surface brightness profile, which is in units of counts/s/arcmin ² or arcsec ² or whatsoever (The unit of the “official” rate image is counts/s/deg ² ). Remember we did this already in the previous chapter cheese , right? But previously we don’t subtract the particle background, we are going to do it now. Also, pn observes photons 3-4 times that of mos1 and mos2 , if you want to use a “rate” image with mos1, mos2 and pn having the same weighting, you have to use the normalized exposure map (I’ll soon tell you what it is). Here I will show you how to produce these images using ESAS and also by yourself.

Now run:

comb caldb=$SAS_ESAS_CALDB withpartcontrol=1 withsoftcontrol=0 withswcxcontrol=0 elowlist=400 ehighlist=2300 mask=1 prefixlist="1S001" >&log/comb_mos1.log

mv comb-obj-im-400-2300.fits comb-obj-im-400-2300-mos1.fits

mv comb-back-im-sky-400-2300.fits comb-back-im-sky-400-2300-mos1.fits

mv comb-exp-im-400-2300.fits comb-exp-im-400-2300-mos1.fits

comb caldb=$SAS_ESAS_CALDB withpartcontrol=1 withsoftcontrol=0 withswcxcontrol=0 elowlist=400 ehighlist=2300 mask=1 prefixlist="2S002" >& log/comb_mos2.log

mv comb-obj-im-400-2300.fits comb-obj-im-400-2300-mos2.fits

mv comb-back-im-sky-400-2300.fits comb-back-im-sky-400-2300-mos2.fits

mv comb-exp-im-400-2300.fits comb-exp-im-400-2300-mos2.fits

comb caldb=$SAS_ESAS_CALDB withpartcontrol=1 withsoftcontrol=0 withswcxcontrol=0 elowlist=400 ehighlist=2300 mask=1 prefixlist="S003" >& log/comb_pn.log

mv comb-obj-im-400-2300.fits comb-obj-im-400-2300-pn.fits

mv comb-back-im-sky-400-2300.fits comb-back-im-sky-400-2300-pn.fits

mv comb-exp-im-400-2300.fits comb-exp-im-400-2300-pn.fits

The products are comb-obj-im-400-2300.fits , comb-back-im-sky-400-2300.fits and comb-exp-im-400-2300.fits .

;

You only get comb-back-im-sky-400-2300.fits if you set withpartcontrol=1 in comb . withsoftcontrol and withswcxcontrol means soft proton and SWCX, respectively. We will deal with them after Spectral Fit .

Here are how the files are produced:

comb-obj-im-400-2300.fits = mos2S002-obj-im-400-2300.fits*mos2S002-cheese.fits

comb-back-im-sky-400-2300.fits = mos2S002-back-im-sky-400-2300.fits*mos2S002-cheese.fits

comb-exp-im-400-2300.fits = mos2S002-exp-im-400-2300.fits*Filter scale factor(1.134)

So what is new is the filter scale factor=1.134. Open log/comb_mos2.log and just search for “filter scale factor”. For mos1 , it is 1.162, pn = 4.3142. It is slightly different for different filters. This filter scale factor is for normalized radial profile which I will soon show you.

Note that for pn, the comb-obj-im-400-2300.fits is produced with the oot scale factor taken into account:

comb-obj-im-400-2300.fits =(pnS003-obj-im-400-2300.fits- pnS003-obj-im-400-2300-oot.fits oot_scale_factor)*pnS003-cheese.fits

In log/comb_pn.log , look for “OOT scale factor”, it is 0.023. Because of the oot , you see there some negative values in comb-obj-im-400-2300.fits , but not mos1 and mos2.

And, finally, to produce the “rate image”, you do:

bin_image thresholdmasking=0.02 detector=1 binning=1 prefix="2S002" elow=400 ehigh=2300 withpartcontrol=yes withsoftcontrol=no withswcxcontrol=no >& log/bin_image-mos2.log

The products are rate-400-2300.fits and sigma-400-2300.fits

This is just:

$rate-400-2300.fits = C * \frac{(mos2S002-obj-im-400-2300.fits) - (mos2S002-back-im-sky-400-2300.fits)}{mos2S002-exp-im-400-2300.fits}$

sigma-400-2300.fits = C * \frac{\sqrt{mos2S002-obj-im-400-2300.fits}}{mos2S002-exp-im-400-2300.fits}

But to use them for radial profile, remember to multiply mos2S002-cheese.fits . In src/spectrum_script.py

a.rateimg("mos2S002-obj-im-400-2300.fits","mos2S002-back-im-sky-400-2300.fits","mos2S002-exp-im-400-2300.fits","mos2S002-cheese.fits","rate_mos2.fits

rate_mos2.fits is the final product. The rate image rate_mos2.fits is corrected for cheese . C is the conversion factor = 2073600 which is the unit conversion of pixel ²to deg ², that means the unit of the rate image is counts/s/deg ². Remember 1 pixel = 2.5 arcsec = 2.5/3600. deg, so 1 deg ² = (3600/2.5) ²= 2073600.

For pn, the rate image is a little bit complicated as you have to deal with the oot. The rate image for pn is produced in this way:

$rate-400-2300.fits = C * \frac{(pnS003-obj-im.fits) - (pnS003-back-im-sky.fits) - (pnS003-obj-im-oot.fits×oot-scale-factor)}{pnS003-exp-im-400-2300.fits}$

where

pnS003-obj-im.fits = pnS003-obj-im-400-2300.fits
pnS003-back-im-sky.fits = pnS003-back-im-sky-400-2300.fits
pnS003-obj-im-oot.fits = pnS003-obj-im-oot-400-2300.fits

if ( (pnS003-obj-im-400-2300.fits - pnS003-obj-im-400-2300.fits*oot_scale_factor ) > 0:

$sigma-400-2300.fits = C * \frac{\sqrt{(pnS003-obj-im-400-2300.fits) - (pnS003-obj-im-400-2300-oot.fits*oot-scale-factor)}}{pnS003-exp-im-400-2300.fits}$

else

sigma-400-2300.fits = 0

In src/spectrum_script.py :

a.rateimgpn("pnS003-obj-im-400-2300.fits","pnS003-obj-im-400-2300-oot.fits","pnS003-back-im-sky-400-2300.fits","pnS003-exp-im-400-2300.fits","pnS003-cheese.fits",0.023,"rate_pn.fits")

Again the rate image rate_pn.fits is corrected for cheese . You can practice by comparing the rate image created using ESAS commands and one created by yourself using the raw products to understand better. Other than python , you can also use farith to create a rate image.

Of course, you don’t need rate-400-2300.fits and sigma-400-2300.fits for the real analyses. I just use the raw products in the code to allow more flexibility for units. Just remember to deal with the oot issue of pn . One thing to note:

comb-obj-im-400-2300-pn.fits = pnS003-obj-im-400-2300.fits - pnS003-obj-im-400-2300-oot.fits*oot_scale_factor

comb-obj-im-400-2300-pn.fits has already been corrected for oot, so I always use the combined image and particle background for surface brightness profile.

On the other hand, if you want to use the radial profile of the 3ccds with equal weighting, then you use comb-exp-im-400-2300.fits to produce the rate image. But before we make the radial profile, we first have to decide the centre. Here since the source is a relaxed cluster, we use the emission peak. In src/spectrum_script.py :

imgcomb() #parameters omitted
emissionpeak( ) #parameters omitted

(For the emission peak and the emission-weighted centre, I will talk more in the Chapter Emission Peak vs Emission-weighted Centre )

In imgcomb() , you first combine mos1,mos2 and pn to produce the combined rate image called rate_comb.fits , then use it as the input for the emission peak. rate_comb.fits is first smoothed and searching is performed within a certain area. Sometimes there are random spots with exceptionally high rate, even higher than the cluster centre. Smoothing can avoid picking up such random spots.

The result is written in Centre.txt. It reads like this:

ra,dec = 16.706594 1.0560902

xc,yc(pix in python) = 420 430

detx,dety(mos1) = 160.70728 -402.16132

detx,dety(mos2) = 232.60537 -57.590704

detx,dety(pn) = -86.59832 -89.11581

Plotting radial profile using combined and non-combined exposure

Now let’s make the radial profile using comb-exp-im-400-2300-mos2.fits and mos2S002 -exp-im-400-2300.fits and see the difference. In src/spectrum_script.py :

a.plotradial() #paramters omitted

Fig. 10. Surface brightness profile using the combined exposure, which is the uncombined one*correction_factor. mos1,mos2 and pn have the same weighting.

Fig. 11. Surface brightness profile using the uncombined exposure. mos1,mos2 and pn have different weightings.

So you see if you use comb-exp-im-400-2300-mos2.fits to make the surface brightness profile, all 3 ccds have the same weighting. If this is what you want, use comb-exp-im-400-2300-mos2.fits. If not, use mos2S002 -exp-im-400-2300.fits . After you get the plot, you can proceed with what you want, e.g. fitting. Some people combine the data of all 3 ccds when performing fitting, some don’t. Choose whatever you find suitable.

By the way, you don’t see the errors bars in the surface brightness profiles. They are just too small. They are calculated using the standard error calculation. If you are unfamiliar with it, see the Appendix for “Error calculation of surface brightness profile”.

Discussion:

Background counts of image vs spectrum

Now we have produced the background image mos2S002-back-im-det-400-2300.fits and background spectrum mos2S002-back.pi . The two are produced from different sources (the background image is from the fwc file and the spectrum is also related to the corner spectrum). I check whether they have the same counts in the same energy range. Since we need to first subtract the particle background from the source, correct estimation of the particle background directly affects CXB estimation, and hence the luminosity (You can derive the luminosity using either image data or spectral data).

I extracted the background images of mos1 , mos2 and pn in 1) 0.4-2.3 keV, 2) 0.7-10 keV and 3) 7.0-10.0 keV. The results are summarized in Table 2.

	(Counts in spec/(counts in img) in [0.4-2.3] keV	(Counts in spec/(counts in img) in [0.7-10.0] keV	(Counts in spec/(counts in img) in [7.0-10.0] keV
mos1	~0.5	~1.0	~0.8
mos2	~0.5	~1.0	~0.8
pn	~1.0	~1.3	~2.9

Table 2: Summary of (counts in spectrum)/(counts in image) of different ccds in different energy range.

So for the energy range that a spectrum usually works on, [0.7-10.0] keV, the image and spectrum counts are quite consistent for all ccds, but for the range that the CXB lies in, [0.4-2.3] keV, the counts in image and spectrum are quite different for mos1 and mos2 , but not pn .

As for the range ([7.0-10.0] keV) that mainly proton flares are found, mos1 and mos2 find rather consistent count rates but not pn , which is ~3 times higher.

So how much does the particle background affect the r500 luminosity? The background rate is of the same magnitude as CXB (private study). Lowering the background rate would increase the CXB, but the increase and decrease wouldn’t be offset, as I will show in the Section Luminosity Calculation. I calculated the luminosities with the background image counts halved, and found for dim sources, the change in luminosity is ~20%. However, the current particle background of mos1, mos2 and pn give consistent luminosities across the three ccds, so I guess it is a good estimate.

Should the particle background be divided by vignetting-corrected exposure?

Currently the rate image is calculated this way:

$S (x) = \sum \frac{s o u r c e - b k g}{e x p o s u r e}$

However, the particle background is not affected by vignetting effect. As you can see in Table 1, column A, the counts/pixel is quite steady across different ccd chips, and ccd 1 does not have the highest value. I wonder whether the background should be divided by the vignetting-corrected exposure or vignetting-uncorrected exposure. I tested with vignetting-uncorrected exposure and find the change in luminosity minimal, a few percent at most.

P.S. If you want to produce vignetting-uncorrected exposure, when you do eexpmap , just set “ withvignetting=no”

Appendix

Error calculation of surface brightness profile.

$S (x) = \sum \frac{s o u r c e - b k g}{e x p o s u r e}$

The error for the source is the square of source counts, which is the error for Poisson statistics. Then we apply the formular of error propagation:

$Δ z = \sqrt{{(Δ x)}^{2} + {(Δ y)}^{2} + . . .}$

$Δ S (x) = \sum {(\frac{Δ s o u r c e}{e x p o s u r e})}^{2} = \sum \frac{s o u r c e}{e x p o s u r e^{2}}$