Cosmological Evolution of the FSRQ Gamma-ray Luminosity Function and Spectra and the Contribution to...

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Cosmological Evolution of the FSRQ Gamma-ray Luminosity Function and Spectra and the Contribution to the Extragalactic Gamma-ray Background Based on Fermi- LAT Observations Jack Singal AAS HEAD Meeting 4/10/13 With: Vahe Petrosian Allan Ko J. Singal, A. Ko, & V. Petrosian, in prep

Transcript of Cosmological Evolution of the FSRQ Gamma-ray Luminosity Function and Spectra and the Contribution to...

Page 1: Cosmological Evolution of the FSRQ Gamma-ray Luminosity Function and Spectra and the Contribution to the Extragalactic Gamma-ray Background Based on Fermi-LAT.

Cosmological Evolution of the FSRQ Gamma-ray Luminosity Function and Spectra and the

Contribution to the Extragalactic Gamma-ray Background Based on

Fermi-LAT Observations

Jack Singal AAS HEAD Meeting4/10/13

With: Vahe PetrosianAllan Ko

J. Singal, A. Ko, & V. Petrosian, in prep

Page 2: Cosmological Evolution of the FSRQ Gamma-ray Luminosity Function and Spectra and the Contribution to the Extragalactic Gamma-ray Background Based on Fermi-LAT.

Context

• The Fermi-LAT catalogs report gamma-ray flux (F100) and photon spectral index (Γ)

• Spectroscopic redshifts for almost all of the Fermi-LAT 1LAC FSRQ blazars have been provided by Shaw et al. (2012, ApJ, 748, 49), providing a sample that is essentially complete only limited by the Fermi-LAT observations.

• Approximately half the blazars observed by the Fermi-LAT in it’s first and second catalogs are Flat Spectrum Radio Quasar (FSRQ) type

• With this - plus redshifts - one can determine the luminosities and would have the relevant information to find the redshift evolutions in Lγ and Γ, as well as the density evolution and the integrated output

• Another analysis has been done by Ajello et al. (2012, ApJ, 751, 108)

• Here we discuss the results of non-parametric methods to get the luminosity and spectral distributions directly from the Fermi-LAT and redshift data

Page 3: Cosmological Evolution of the FSRQ Gamma-ray Luminosity Function and Spectra and the Contribution to the Extragalactic Gamma-ray Background Based on Fermi-LAT.

Why is it not straightforward?The data is truncated! We are missing (many) objects.

Because of the energy dependence of the Fermi-LAT PSF hard spectrum objects can be seen to a lower flux

Also missing low flux high redshift objects

Goal here: Compute directly the luminosity and photon index evolutions, density evolution, local distributions, and integrated output of FSRQs, properly accounting for the truncations, using techniques we’ve developed.

(to get the evolutions and distributions)

Missing these

Fermi-LAT 1LAC blazarsFSRQBL LacUnknown type

Page 4: Cosmological Evolution of the FSRQ Gamma-ray Luminosity Function and Spectra and the Contribution to the Extragalactic Gamma-ray Background Based on Fermi-LAT.

Data and MethodsWe have been using a custom variant of the Kendall Tau test with “associated sets” to access the true intrinsic distributions of populations from flux-limited surveys

Fermi-LAT1 LAC FSRQswith spectro-zs

Techniques explored and extended in :- Singal et al., 2011, ApJ, 743, 104- Singal et al., 2012, ApJ, 753, 45- Singal et al., 2013, ApJ, 764, 43

Page 5: Cosmological Evolution of the FSRQ Gamma-ray Luminosity Function and Spectra and the Contribution to the Extragalactic Gamma-ray Background Based on Fermi-LAT.

Notation: Evolving Luminosity Functions

Parameterize luminosity function in a band :

zgzgLzzL a

a

aaaa

,

aka zzg 1

density evolution

‘local’ luminosity function

Luminosity evolution with redshift, can parameterize

luminosity evolution with redshift

Or, for samples with more high redshift objects

a

a

k

k

a

nz

zzg

11

1

Ψa(La,z) gives # of objects per luminosity per comoving volumeIntegrate dL dz to get total number

Here we have relatively low redshift objects

Page 6: Cosmological Evolution of the FSRQ Gamma-ray Luminosity Function and Spectra and the Contribution to the Extragalactic Gamma-ray Background Based on Fermi-LAT.

Results: Luminosity and Index Evolutions

22 Lcomb

kγ=6.5±0.3, kΓ=0±0.1

aka zzg 1

FSRQ blazars have undergone significant gamma-ray luminosity evolution with redshift, but not photon index evolution

Requires simultaneous determination of best-fit evolutions

τcomb = 1 and 2 contours

Preliminary

Page 7: Cosmological Evolution of the FSRQ Gamma-ray Luminosity Function and Spectra and the Contribution to the Extragalactic Gamma-ray Background Based on Fermi-LAT.

Results: Density Evolution

dzdVdz

zdz

1

jmz

jj

11

Cumulative density evolution σ(z) determined with Lynden-Bell method (1971, MNRAS, 155, 95) modified with associated sets (e.g. Singal et al., 2012, ApJ, 764, 43)

# of objects with redshift less than object j which are in object j’s associated set

Raw data

True density ev.

Page 8: Cosmological Evolution of the FSRQ Gamma-ray Luminosity Function and Spectra and the Contribution to the Extragalactic Gamma-ray Background Based on Fermi-LAT.

Results: ‘Local’ Luminosity Function

zg

LL

'

(With best-fit redshift evolution taken out)

Preliminary

knL

kk

11'

Cumulative lum. fn. Determined by modified Lynden-Bell (1971, MNRAS, 155, 95) modified with associated sets (e.g. Singal et al., 2012, ApJ, 764, 43)

Local cumulative gamma-ray Lum. function

Page 9: Cosmological Evolution of the FSRQ Gamma-ray Luminosity Function and Spectra and the Contribution to the Extragalactic Gamma-ray Background Based on Fermi-LAT.

Results: Photon Index DistributionSince there is no redshift evolution in the photon index, we can use the photon index distribution h(Γ) that we determined for all 1 LAC FSRQs in Singal et al. (2012, ApJ, 753, 45).

knP

kk

11ˆ

Cumulative lum. fn. Determined by modified Lynden-Bell

d

Pdh

ˆˆ

(integral removes correlation with flux)

Observed

Intrinsic

For FSRQsh(Γ) Gaussian:μ=2.52±0.08σ=0.17±0.02

Shows for all 1LAC blazars but we have FSRQs separately as well

Page 10: Cosmological Evolution of the FSRQ Gamma-ray Luminosity Function and Spectra and the Contribution to the Extragalactic Gamma-ray Background Based on Fermi-LAT.

Results: Contribution to the EGBWith the distributions and evolutions we can calculate the total energy output from FSRQs

Integrating ψ(Lγ) by parts gives the dependence on the cumulative lum fn. Φ (Lγ). Then we express in terms of the local luminosity function Φ (Lγ

’). Integrating over all luminosities the surface term is zero and

This allows us to calculate the total directly from the determined distributions (no fitting)

We find that 1.0 (+0.4/-0.1) MeV cm-2 sec-1 sr-1

This can be compared with the total EGB (resolved and unresolved) measured by the Fermi-LAT of 4.72 (+0.63/-0.29) MeV cm-2 sec-1 sr-1

We find that FSRQs in toto account for 22(+10/-4)% of the EGB

Ajello et al. (2012, ApJ, 751, 108) report 21.7(+2.5/-1.7)%

In Singal et al. (2012, ApJ, 753, 45) we calculated that all blazars account for 39-66% of the EGB

Page 11: Cosmological Evolution of the FSRQ Gamma-ray Luminosity Function and Spectra and the Contribution to the Extragalactic Gamma-ray Background Based on Fermi-LAT.

Conclusions• We use well established non-parametric methods to determine the evolutions and distributions of gamma-ray luminosity and photon index directly from Fermi-LAT data for FSRQs.

• FSRQ blazars exhibit strong luminosity evolution with redshift in the gamma-ray band.

• FSRQ blazars do not exhibit redshift evolution of the photon index.

• FSRQ blazars have rapid density evolution, peaking at around redshift 1.

• FSRQ blazars in toto account for 22(+10/-4)% of the EGB.

Further discussion / info: J. Singal, A. Ko, & V. Petrosian, in prep

Page 12: Cosmological Evolution of the FSRQ Gamma-ray Luminosity Function and Spectra and the Contribution to the Extragalactic Gamma-ray Background Based on Fermi-LAT.

In a nutshell: Kendall Tau Test with “Associated Sets”

We determine the correlations in truncated data by the Kendall Tau test modified with the method of ‘associated sets’ (B. Efron, & V. Petrosian, 1992, ApJ, 399, 345 & 1999, JASA, 94, 447)

Example of associated set: Say I wanted to determine the luminosity rank of the red point among all points of a lower redshift

excluded – would not be seen if at redshift of point in question

The associated set is an unbiased set for comparison

Will be more complicated to form associated sets if multiple variables, etc…

(Because of the truncation, the raw rank would be seriously biased)

Techniques explored and extended in :- Singal et al., 2011, ApJ, 743, 104- Singal et al., 2012, ApJ, 764, 43