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Generate a spectral energy distribution

Now you will learn how to produce a spectral energy distribution (aka SED) for the blazar PG 1553+113. A SED is simply a plot of flux or luminosity as a function of energy or wavelength. SEDs can teach you a lot about the physical processes responsible for the emission in the source.

By following this tutorial, you will reproduce an old result from the LAT collaboration. You will be able to compare the results of your analysis with those published in that paper.

In our previous likelihood fit, we have obtained a fit of the source parameters to the global data (all energies and times) but we have not computed flux points to be plotted as a spectrum. To do so you have to run the analysis for each of the energy bins for which you want to generate a spectral point. If this sounds a bit complicated, this is because it is in fact a bit so. Fortunately, our friend Enrico can automate the SED-generation process!

Copy files generated in the previous activity

First, let’s copy some files that we generated in the previous tutorial. In the terminal, type the following commands to create a directory that will hold the results from this analysis:

cd ~/LAT_day02
mkdir sed
cd sed
cp ~/flux/pg1553.conf ~/flux/events.txt . # copy previously generated conf. file and events list

Customize configuration file

Let’s teach Enrico that it now needs to get SED points instead of doing only a global likelihood analysis. For this purpose, we need to change a few fields in the configuration file. Here are the instructions.

  1. Open the configuration file pg1553.conf with a text editor.
  2. Change only the following fields in the file:

out = /home/fermi/LAT_day02/sed
(directory that will hold the output)

[file]
	event = events.txt
	xml = /home/fermi/LAT_day02/sed/PG1553_PowerLaw2_model.xml
	… 

[Ebin]
	NumEnergyBins = 7
	…

Generate source model

You will generate now the XML file with the source model for your analysis:

enrico_xml pg1553.conf

Compute SED points

You will use the enrico_sed tool again. This is how it works. It will first run a global fit and if the option [Ebin] -> NumEnergyBins in the configuration file 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 maximum likelihood fit run by the enrico_sed tool. If the TS found in any of the energy time bins is below [Ebin] -> TSEnergyBins then an upper limit is computed.

Now type in the terminal:

enrico_sed pg1553.conf

You will need a very good patience now. It is unlikely that you will finish this analysis over the duration of the hands-on activity (unless you are a relative of The Flash). In my case, this analysis took about 3 hours running on a 2015 MacBook under the VM. Your patience will be rewarded.

Plot the SED

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 the SED plot.

[fermi@localhost sed]$ enrico_plot_sed pg1553.conf 
[Message]: Save Ebin results in 
[Message]: Reading /home/fermi/day02/sed/Ebin7/PG1553_0.conf
[Message]: Energy bins results
Energy =  177.0
E**2. dN/dE =  1.08234529418e-11  +  1.8669187668e-12  -  1.8669187668e-12
[Message]: Reading /home/fermi/day02/sed/Ebin7/PG1553_1.conf
[Message]: Energy bins results
Energy =  556.0
E**2. dN/dE =  1.2966909576e-11  +  1.1563884279e-12  -  1.1563884279e-12
[Message]: Reading /home/fermi/day02/sed/Ebin7/PG1553_2.conf
[Message]: Energy bins results
Energy =  1745.0
E**2. dN/dE =  2.11215785539e-11  +  1.61963497302e-12  -  1.61963497302e-12
[Message]: Reading /home/fermi/day02/sed/Ebin7/PG1553_3.conf
[Message]: Energy bins results
Energy =  5477.0
E**2. dN/dE =  3.68410595707e-11  +  3.02001119251e-12  -  3.02001119251e-12
[Message]: Reading /home/fermi/day02/sed/Ebin7/PG1553_4.conf
[Message]: Energy bins results
Energy =  17190.0
E**2. dN/dE =  6.7988682993e-11  +  8.2282031554e-12  -  8.2282031554e-12
[Message]: Reading /home/fermi/day02/sed/Ebin7/PG1553_5.conf
[Message]: Energy bins results
Energy =  53954.0
E**2. dN/dE =  8.0641835618e-11  +  1.60158118073e-11  -  1.60158118073e-11
[Message]: Reading /home/fermi/day02/sed/Ebin7/PG1553_6.conf
[Message]: Energy bins results
Energy =  169338.0
E**2. dN/dE =  4.08989208649e-11  +  1.45252100068e-11  -  1.45252100068e-11
Info in <TCanvas::SaveSource>: C++ Macro file: /home/fermi/day02/sed/Spectrum/SED_PG1553_PowerLaw2.C has been generated
Info in <TCanvas::Print>: eps file /home/fermi/day02/sed/Spectrum/SED_PG1553_PowerLaw2.eps has been created

Exercise 1: SED plot

Open the file ./Spectrum/SED_PG1553_PowerLaw2.png and inspect this plot.

  1. Is the measured SED consistent with the power-law model as we chose?
  2. Compare your result with Figure 1 of Abdo et al. 2010 ApJ—the result published by the LAT Collaboration using the first few months of observations of the telescope. Are the SEDs consistent with each other?
  3. Do you notice anything funny going on with your fit? Remember that you fitted a power-law model. Pay attention to the highest energies measured.

Exercise 2: counts spectrum

Open the file ./Spectrum/SED_PG1553_PowerLaw2_CountsPlot.png and inspect this plot. Notice the contribution of our dear blazar compared to all the other sources. Why do you think this count spectrum is different compared to the SED plot we saw before? (e.g. why is it not a perfect power-law extending to lower energies as we should expect?)

Next: generating a light curve.

Solutions to exercises.