Editing EBL Dec OP313

The source OP 313 is located at a redshift of 0.997 and then is a very good target for EBL constraints.

We use 2 EBL models : 

* Dominguez et al, 2011 https://arxiv.org/abs/1007.1459
* Saldana-Lopez, 2021 https://arxiv.org/abs/2012.03035


=== Methods ===

For this calculation, I use the Fermi-LAT data analysed using the same GTI as LST-1 (more details here : https://www.lst1.iac.es/wiki/index.php/Fermi_LAT_Main_OP313)

Data were fitted using the SummedLikelihood tools from Mireia (need a ref) which allows to make a joint Fermi-LAT/LST fit

The EBL is scaled with a factor alpha. alpha=0 means no EBL and alpha = 1 means the EBL model reproduce perfectly our data.

Different Model were used in the case : Power-Law, Log-Parabola, Power-Law with an exponential cut-off, Log-Parabola with an exponential cut-off.


=== Results === 

This plot presents the scan over different values of alpha from 0 to 2 and for the different models. 

[[File:EBL_alphaScan_saldan.png|thumb|centre|400px|Alpha scan with the EBL model Saldana-Lopez 2021]]

The more concervative model is the Log-Parabola with an exponential cut-off. This will be used for the calculation.

 alpha = 0.50 - 0.50 +0.25

=== Different Check ===

==== Parameters Values === 

For each value of alpha (for the Log-Parabola with an exponential cut-off model) I plotted the SED and the parameters evolution

[[File:LogParabola_ExpCutOff_saldana.png|thumb|centre|400px|Alpha scan  EBL SEDs]]


[[File:LogParabola_ExpCutOff_saldana_scan.png|thumb|centre|400px|Alpha scan  EBL Parameters]]

==== EBL model ====

I checked the difference with Dominguez et al, 2011 model for different spectral shape. No big difference found.


[[File:EBL_checkModel.png|thumb|centre|400px|Alpha scan  EBL model Saldana-Lopez 2021 and Dominguez et al, 2011]]

==== Systematics ====


I mimics the energy biais of the LST data using this gammapy tutorial https://github.com/bkhelifi/CTAO-CTAC_Meeting_Granada_2023/blob/main/Crab_simulations_systematic_errors_Solution.ipynb

Above 70 GeV I have introduce a biais of + or - 15 %

[[File:EBL_sys.png|thumb|centre|400px|Alpha scan  EBL model Saldana-Lopez 2021 for a energy biais of 15%]]