# Spectrum¶

In this tutorial we will perform a full likelihood analysis of the AGN PG1553+113. We will use the same dataset already used in the official Fermi/LAT collaboration likelihood tutorial as well as in the enrico tutorial, so that you can check your results and have additional information by consulting the two other webpages. The results from the analysis of this dataset were published in Abdo, A. A. et al. 2010, ApJ, 708, 1310.

## A note on directory structure¶

In order to avoid confusions, it is always best to provide absolute paths for all the files in the analysis. In this tutorial we will assume that you have extracted the fermi-hero.tar.gz data tarball to the home directory of your user (here, as an example, we use the username hero), so that the directory structure looks like this:

$cd /home/hero/fermi-hero$ ls
excercises  solutions  spacecraft.fits
$ls excercises/spectrum/ L120405112547B0489E7F68_PH00.fits  To start the tutorial, change directory to /home/hero/fermi-hero/excercises/spectrum. ## Make a config file¶ enrico uses configuration files to run analysis (for a full description see the enrico documentation on the configuration files). You can use the enrico_config tool to quickly make a config file called pg1553.conf. It will ask you for the required options and copy the rest from a default config file enrico/data/config/default.conf: $ enrico_config pg1553.conf
Please provide the following required options [default] :
Output directory [~/fermi-hero/excercises/spectrum] :
Target Name : PG1553+113
Right Ascension: 238.92935
Declination: 11.190102
Options are : PowerLaw, PowerLaw2, LogParabola, PLExpCutoff
Spectral Model [PowerLaw] : PowerLaw2
ROI Size [15] : 15
FT2 file [] : ~/fermi-hero/spacecraft.fits
FT1 list of files [] : ~/fermi-hero/excercises/spectrum/L120405112547B0489E7F68_PH00.fits
tag [LAT_Analysis] : spectrum
Start time [239557418] : 239557417
End time [334165418] : 256970880
Emin [100] : 200
Emax [300000] :


Note :

• Always give the full path for the files
• We used the PowerLaw2 model as in the Fermi tutorial.
• Time is give in MET
• Energy is given in MeV
• ROI size is given in degrees

Now you can edit this config file by hand to make further adjustments.

## Generate a source model xml file¶

The Fermi Science Tools base their likelihood analysis on a source model written in xml format. Often, this model is complicated to generate. You can run enrico_xml to make such model of the sky and store it into a xml file which will be used for the analysis. The options for this step are provided in the config file. For the enrico_xml tool, the relevant options are in the [space] and [target] sections. The out file is given by [file]/xml.

This tool automatically adds the following sources to the xml source model file:

• your target source.
• The galactic (GalDiffModel) and isotropic (IsoDiffModel) diffuse components that are the dominant background sources in most LAT analysis.
• All the LAT sources from the two-year catalog (2FGL) that are inside the ROI. The spectral parameters of the sources within 3 degrees of our source are left free so they can be fit simultaneously with our source, whereas those further away are fixed to their catalog values.
$enrico_xml pg1553.conf use the default location of the catalog use the default catalog Use the catalog : /CATALOG_PATH/gll_psc_v08.fit Add 24 source(s) in the ROI of 15.0 degrees 3 source(s) have free parameters inside 3.0 degrees 0 source(s) is (are) extended write the Xml file in /home/hero/fermi-hero/excercises/spectrum/PG1553+113_PowerLaw2_model.xml  You can explore the PG1553+113_PowerLaw2_model.xml output file with a text editor, where you will find a source xml environment for each of the sources. Additionally, the Science Tools provide the modeleditor command, which allows you to modify the model from a GUI. Tip You can find more information about the different spectral models available and their parameters at the source model definitions for gtlike and a few examples of model definitions in XML format webpages. ## Run global fit¶ The gtlike tool finds the best-fit parameters by minimizing a likelihood function. Before running gtlike, the user must generate some intermediary files by using different tools. With enrico, all those steps are merged in one tool. enrico_sed will execute the following steps for you with the options you have selected in pg1553.conf: 1. gtselect: Perform event selection. 2. gtmktime: Perform time selection based on spacecraft file. 3. gtbin: Compute a counts cube map from the selected data. A counts cube map is a collection of counts maps for different energies. 4. gtltcube: Perform the calculation of the livetime cube. This is the most computationally intensive step, taking. 5. gtexpcube2: Use the previously generated livetime cube and apply it to your ROI to obtain an exposure cube. 6. gtsrcmaps: Create model counts maps for each of the sources in the source model catalog. This is used to speed up the likelihood calculation of gtlike. From all the preliminary fits files generated in the previous steps, enrico is ready to run the likelihood minimisation routine that will result in the best-fit parameters for our source of interest with the tool gtlike. To run the global fit just call: $ enrico_sed pg1553.conf


Warning

Computationally intensive! enrico_sed takes a long time to execute and requires significant amounts of RAM memory. As an example, in my 2011 i5 laptop the gtltcube step took 20 minutes and the gtsrcmaps took 10 minutes to run.

The command line output of the likelihood fitting should be similar to the following:

# ************************************************************
# *** SUMMARY:  ***
# ************************************************************
Source  =   PG1553
RA  =   238.929  degrees
Dec =   11.1901  degrees
Start   =   239557417.0   MET (s)
Stop    =   256970880.0   MET (s)
ROI =   15.0  degrees
E min   =   100.0  MeV
E max   =   300000.0  MeV
IRFs    =   P7SOURCE_V6

# ************************************************************
# ***   1     gtlike --- Run likelihood analysis
# ************************************************************

# ************************************************************
# ***   2 Remove all the weak (TS<1) sources
# ************************************************************
delete source :  2FGL J1506.6+0806  with TS =  0.767925309599
delete source :  2FGL J1602.4+2308  with TS =  -1.51036832301
delete source :  2FGL J1625.2-0020  with TS =  -0.595845252567

# ************************************************************
# ***   3 Re-optimize --- False
# ************************************************************

# ************************************************************
# ***   4    Results --- Print results of the fit
# ************************************************************
2FGL J1504.3+1029
Spectrum: LogParabola
0           norm:  1.418e+00  0.000e+00  1.000e-05  1.000e+03 ( 1.000e-10) fixed
1          alpha:  2.147e+00  0.000e+00  5.000e-01  5.000e+00 ( 1.000e+00) fixed
2           beta:  1.237e-01  0.000e+00  5.000e-04  5.000e+00 ( 1.000e+00) fixed
3             Eb:  6.583e+02  0.000e+00  3.000e+01  3.000e+05 ( 1.000e+00) fixed

.
.
.
<< Fit results for all 2FGL sources in ROI >>
.
.
.

2FGL J1650.8+0830
Spectrum: PowerLaw
60     Prefactor:  6.834e-01  0.000e+00  1.000e-05  1.000e+03 ( 1.000e-11) fixed
61         Index: -2.588e+00  0.000e+00 -5.000e+00 -5.000e-01 ( 1.000e+00) fixed
62         Scale:  5.007e+02  0.000e+00  3.000e+01  3.000e+05 ( 1.000e+00) fixed

GalDiffModel
Spectrum: ConstantValue
63         Value:  9.683e-01  1.921e-02  1.000e-02  1.000e+01 ( 1.000e+00)

IsoDiffModel
Spectrum: FileFunction
64    Normalization:  1.048e+00  2.588e-02  1.000e-03  1.000e+03 ( 1.000e+00)

PG1553
Spectrum: PowerLaw2
65      Integral:  7.953e+01  5.898e+00  1.000e-05  1.000e+03 ( 1.000e-09)
66         Index: -1.652e+00  3.260e-02 -5.000e+00 -5.000e-01 ( 1.000e+00)
67    LowerLimit:  1.000e+02  0.000e+00  3.000e+01  3.000e+05 ( 1.000e+00) fixed
68    UpperLimit:  3.000e+05  0.000e+00  3.000e+01  3.000e+05 ( 1.000e+00) fixed

Source Name Npred   TS
2FGL J1504.3+1029   685.605 225.223
2FGL J1505.1+0324   46.157  8.439
2FGL J1506.9+1052   91.375  17.318
2FGL J1512.2+0201   82.526  22.541
2FGL J1516.9+1925   96.264  20.261
2FGL J1540.4+1438   95.445  5.211
2FGL J1546.1+0820   18.329  7.421
2FGL J1548.3+1453   183.234 24.980
2FGL J1549.5+0237   424.594 171.586
2FGL J1550.7+0526   197.593 39.120
2FGL J1551.9+0855   147.204 39.806
2FGL J1553.5+1255   981.741 808.294
2FGL J1607.0+1552   358.437 130.859
2FGL J1608.5+1029   563.097 41.313
2FGL J1612.0+1403   100.888 11.320
2FGL J1624.4+1123   141.388 8.021
GalDiffModel    27825.333   4090.152
IsoDiffModel    22819.444   2049.134
PG1553  1020.913    2189.417

# ************************************************************

Values and (MINOS) errors for PG1553
TS :  2189.41693741
Integral :  79.53 +/-  5.90 [ -5.79, + 6.01 ] 1e-09
Index :  -1.65 +/-  0.03 [ -0.03, + 0.03 ] 1e+00
LowerLimit :  100.00 +/-  0.00  1e+00
UpperLimit :  300000.00 +/-  0.00  1e+00
The covariance matrix is :
[[  3.47835182e+01  -1.46149842e-01]
[ -1.46149842e-01   1.06305680e-03]]

Source Flux  [1.00e+02 MeV, 3.00e+05 MeV] :
2FGL J1551.9+0855   Integral Flux : 1.44e-08 +/-  5.41e-09 ph/cm2/s
2FGL J1553.5+1255   Integral Flux : 8.40e-08 +/-  8.63e-09 ph/cm2/s
GalDiffModel   Integral Flux : 4.68e-04 +/-  9.28e-06 ph/cm2/s
IsoDiffModel   Integral Flux : 2.17e-04 +/-  5.36e-06 ph/cm2/s
PG1553   Integral Flux : 7.95e-08 +/-  5.90e-09 ph/cm2/s

# ************************************************************
# ***   5    PlotSED --- Generate SED plot
# ************************************************************

Decorrelation energy : 2.50e+03 MeV
Diffential flux  at the Decorrelation energy : 2.55e-12 +/-  1.23e-13 ph/cm2/s/MeV
SED value at the Decorrelation energy : 2.56e-11 +/-  1.24e-12 erg/cm2/s

# ************************************************************
# ***   6    gtmodel --- Make model map
# ************************************************************
time -p /data/soft/fermi-st/ScienceTools/bin/gtmodel srcmaps=/home/vzabalza/lat-tut/excercises/spectrum/PG1553_LAT_srcMap.fits srcmdl=/home/vzabalza/lat-tut/excercises/spectrum/PG1553_PowerLaw2_LAT_out.xml outfile=/home/vzabalza/lat-tut/excercises/spectrum/PG1553_LAT_ModelMap.fits irfs="P7SOURCE_V6" expcube=/home/vzabalza/lat-tut/excercises/spectrum/PG1553_LAT_ltCube.fits bexpmap=/home/vzabalza/lat-tut/excercises/spectrum/PG1553_LAT_BinnedMap.fits convol=yes resample=yes rfactor=2 outtype="CMAP" chatter=2 clobber=yes debug=no gui=no mode="ql"
real 35.64
user 32.12
sys 3.50
# ************************************************************

After the fit has converged, enrico prints the best-fit parameters for all the sources in the model file, including our source of interest:

Values and (MINOS) errors for PG1553
TS :  2189.41693741
Integral :  79.53 +/-  5.90 [ -5.79, + 6.01 ] 1e-09
Index :  -1.65 +/-  0.03 [ -0.03, + 0.03 ] 1e+00
LowerLimit :  100.00 +/-  0.00  1e+00
UpperLimit :  300000.00 +/-  0.00  1e+00
The covariance matrix is :
[[  3.47835182e+01  -1.46149842e-01]
[ -1.46149842e-01   1.06305680e-03]]

In addition, it runs the tool gtmodel to generate a counts map from the best-fit model, which is subtracted from our original counts map file to identify any sources that have been imperfectly modeled.

Observed (left, PG1553_LAT_CountMap.fits) and model (right, PG1553_LAT_ModelMap.fits) counts maps.

Residual counts map (PG1553_Residual_Model_cmap.fits) resulting of the substraction of the model map to the observed map. The uniform noise-like appearance and a low peak value of about 3% of the above maps indicate that the model accounts for all the observed emission.

A file with the extension ‘results’ will be produced and where all the results will be stored.

Note

If you want to refit the data because e.g. you changed the xml model, you are not force to regenerate the fits file. Only the gtlike tool should be executed again. You can do this with enrico by changing the option [spectrum]/FitsGeneration from yes to no, and enrico will bypass all the preliminary calculations and perform only the fit.

You can use enrico_testmodel to compute the log(likelihood) of the models PowerLaw, LogParabola and PLExpCutoff. An ascii file is then produced in the Spectrum folder with the value of the log(likelihood) for each model. You can then use the Wilk’s theorem to decide which model best describes the data.

## Compute flux points¶

Warning

The computation of flux points takes very long, so we will not have time to execute it during the tutorial. It is here for information and future reference.

Note that for the above global fit, we have obtained a fit of the source parameters to the data, but we have not computed flux points to be plotted as a spectrum. To do so you should rerun the above analysis for each of the energy ranges for which you want to generate a spectral point. Fortunately, enrico can automate this process!

To compute flux points, the enrico_sed tool will also be used. It will first run a global fit (see previous section) and if the option [Ebin]/NumEnergyBins is greater than 0, at the end of the overall fit, enrico will run NumEnergyBins new analyses by dividing the energy range.

Each analysis is a proper likelihood analysis (it runs gtselect, gtmktime,gtltcube,..., gtlike), run by the same enrico tool than the full energy range analysis. If the TS found in any of the energy time bins is below [Ebin]/TSEnergyBins then an upper limit is computed.

Note

If a bin failed for some reason or the results are not good, you can rerun the analysis of the bin by calling enrico_sed and the config file of the bin (named SOURCE_NumBin.conf and in the subfolder Ebin#).

## Plotting the spectrum¶

Enrico will already have produced several diagnostic plots during the execution of the analysis tools. To plot the final spectrum, we will use the tool enrico_plot_sed, which will use the results from the likelihood fitting to produce an SED plot. If you have not run the spectral point computation routine, enrico_plot_sed will only plot a bowtie of the best-fit model and its uncertainty:

If we have run the enrico_sed tools with [Ebin]/NumEnergyBins larger than 0, the Ebin# directory will be populated with the results of the likelihood analyses of all the energy bins, and will be used to plot the SED containing the flux points:

### Table Of Contents

7. Summary

#### Next topic

Galactic Center High-Energy View