A New Method for Characterizing Unresolved Point Sources: applications to Fermi Gamma-Ray Data Ben Safdi Massachusetts Institute of Technology 2015 B.S., S. Lee, M. Lisanti, and B.S., S. Lee, M. Lisanti, T. Slatyer, W. Xue [1412.6099 and 1506.05124]
Multi-messenger approach to astrophysical neutrinos
Multi-messenger approach to astrophysical neutrinos % & '()%*'+,-.'/0 & '1! '12! 3!" $!" # " 45 6&7"8 Fermi IGRB!')<=='>=<?@21* (/-9:;- IceCube HE ν s connected to lower-energy Fermi γ s % & '()%*'+,-.'/0 & '1! '12! 3!" $!" # 45 6&7!8 predicted IGRB: star forming galaxies no atten. ) # *01)2*+,-.*34 # *5! *56! /!" '!" ( 78 9#:$!"!!" "!"!!" #!" $!" %!" &!" ' )*+,-./ 1404.1189
Multi-messenger approach to astrophysical neutrinos % & '()%*'+,-.'/0 & '1! '12! 3 % & '()%*'+,-.'/0 & '1! '12! 3!" $!" #!" $!" # " Fermi IGRB!')<=='>=<?@21* 45 6&7"8 (/-9:;- 45 6&7!8 predicted IGRB: star forming galaxies no atten. IceCube HE ν s connected to lower-energy Fermi γ s Ex: pp in star-forming galaxies both ν s and γ s as secondaries ) # *01)2*+,-.*34 # *5! *56! /!" '!" ( 78 9#:$!"!!" "!"!!" #!" $!" %!" &!" ' )*+,-./ 1404.1189
Multi-messenger approach to astrophysical neutrinos % & '()%*'+,-.'/0 & '1! '12! 3 % & '()%*'+,-.'/0 & '1! '12! 3!" $!" #!" $!" # " Fermi IGRB!')<=='>=<?@21* 45 6&7"8 (/-9:;- 45 6&7!8 predicted IGRB: star forming galaxies no atten. IceCube HE ν s connected to lower-energy Fermi γ s Ex: pp in star-forming galaxies both ν s and γ s as secondaries ν and γ spectral index = source spectra index = Γ ) # *01)2*+,-.*34 # *5! *56! /!" '!" ( 78 9#:$!"!!" "!"!!" #!" $!" %!" &!" ' )*+,-./ 1404.1189
Multi-messenger approach to astrophysical neutrinos % & '()%*'+,-.'/0 & '1! '12! 3 % & '()%*'+,-.'/0 & '1! '12! 3 ) # *01)2*+,-.*34 # *5! *56! /!" $!" #!" $!" #!" '!" ( " Fermi IGRB!')<=='>=<?@21* 45 6&7"8 (/-9:;- 45 6&7!8 predicted IGRB: star forming galaxies no atten. 78 9#:$ IceCube HE ν s connected to lower-energy Fermi γ s Ex: pp in star-forming galaxies both ν s and γ s as secondaries ν and γ spectral index = source spectra index = Γ Star-forming galaxies faint but numerous: contribute to isotropic gamma-ray background (IGRB)!"!!" "!"!!" #!" $!" %!" &!" ' )*+,-./ 1404.1189
Multi-messenger approach to astrophysical neutrinos Import to understand contributions from unresolved PSs (e.g., blazars) to IGRB to constrain diffuse contributions (e.g., star-forming galaxies)
PSs important for gamma-ray signals of DM Import to understand contributions from unresolved PSs to gamma-ray background to constrain contributions from dark matter (DM)
The Fermi Large-Area Telescope (LAT) 0902.1089 Fermi (NASA) 1406.0507
The Fermi Gamma-Ray Sky Data taken from August 4, 2008 to December 5, 2013 HEALPIX nside = 128 (N pix = 196, 608) Mollweide view 0 35
The Fermi Gamma-Ray Sky Model from August 4, 2008 to December 5, 2013 HEALPIX nside = 128 (N pix = 196, 608) Mollweide view 0 35
GeV Excess: Inner Galaxy 8 20 0.5-1 GeV residual 20 20 1-3 GeV residual 12 10 0-10 15 10 5 10-6 counts/cm 2 /s/sr 10 0-10 10 8 6 4 2 10-6 counts/cm 2 /s/sr -20 20 10 0-10 -20 0-20 20 10 0-10 -20 0-2 20 3-10 GeV residual 4 20 10-50 GeV residual 1.5 10 0-10 3 2 1 10-6 counts/cm 2 /s/sr 10 0-10 1.0 0.5 10-6 counts/cm 2 /s/sr -20 20 10 0-10 -20 0-20 20 10 0-10 -20 0.0 (Daylan et al.) FIG. 7: Intensity maps (in galactic coordinates) after subtracting the point source model and best-fit Galactic di use model,
GeV Excess: Spectrum (from Wei Xue)
GeV Excess: Spectrum (from Wei Xue)
Pulsars: Spectrum Millisecond pulsar spectrum similar to excess (from 61 millisecond pulsars and 36 globular clusters) (Cholis, Hooper, Linden)
Astrophysical Scenarios Can we use the Fermi data to differentiate between smooth and unresolved PS emission?
Photon Statistics: DM vs. Point Sources dark matter only point sources only 5 0
Photon Statistics: DM vs. Point Sources diffuse + dark matter diffuse + point sources 15 0
Photon Statistics: Point Sources p (p) k = probability of finding k photons in pixel p
Photon Statistics: Point Sources = probability of finding k photons in pixel p Generating function: p (p) k P (p) (t) = k=0 p (p) k tk p (p) k = 1 k! d k P (p) dt k t=0
Photon Statistics: Point Sources = probability of finding k photons in pixel p Generating function: p (p) k P (p) (t) = k=0 p (p) k tk p (p) k = 1 k! d k P (p) dt k t=0 Point sources: [ ] P (p) (t) = exp x p m(t m 1), x p m = m=1 ds dn (p) ds S m m! e S
Photon Statistics: Point Sources = probability of finding k photons in pixel p Generating function: p (p) k P (p) (t) = k=0 p (p) k tk p (p) k = 1 k! Point sources: [ ] P (p) (t) = exp x p m(t m 1), x p m = ds m=1 Source-count: dn (p) ds = Ap d k P (p) dt k dn (p) ds t=0 ( ) n1 S, S S b S b ( ) n2 S, S < S b S b S is average number of photon counts S m m! e S
Photon Statistics: Point Sources = probability of finding k photons in pixel p Generating function: p (p) k P (p) (t) = k=0 p (p) k tk p (p) k = 1 k! Point sources: [ ] P (p) (t) = exp x p m(t m 1), x p m = ds m=1 Source-count: dn (p) ds = Ap d k P (p) dt k dn (p) ds t=0 ( ) n1 S, S S b S b ( ) n2 S, S < S b S b S is average number of photon counts A p follow a spatial template S m m! e S
Photon Statistics: Point Sources = probability of finding k photons in pixel p Generating function: p (p) k P (p) (t) = k=0 p (p) k tk p (p) k = 1 k! Point sources: [ ] P (p) (t) = exp x p m(t m 1), x p m = ds m=1 Source-count: dn (p) ds = Ap d k P (p) dt k dn (p) ds t=0 ( ) n1 S, S S b S b ( ) n2 S, S < S b S is average number of photon counts A p follow a spatial template x p m is expected number of m-photon sources S b S m m! e S
Photon Statistics: Point Sources = probability of finding k photons in pixel p Generating function: p (p) k P (p) (t) = k=0 p (p) k tk p (p) k = 1 k! Point sources: [ ] P (p) (t) = exp x p m(t m 1), x p m = ds m=1 Source-count: dn (p) ds = Ap d k P (p) dt k dn (p) ds t=0 ( ) n1 S, S S b S b ( ) n2 S, S < S b S is average number of photon counts A p follow a spatial template x p m is expected number of m-photon sources Straightforward modification to include PSF (Malyshev & Hogg) S b S m m! e S
Non-Poissonian template fit (NPTF) data set d (counts in each pixel {n p })
Non-Poissonian template fit (NPTF) data set d (counts in each pixel {n p }) model M with parameters θ
Non-Poissonian template fit (NPTF) data set d (counts in each pixel {n p }) model M with parameters θ The likelihood function: p(d θ, M) = pixels p p (p) n p (θ)
Non-Poissonian template fit (NPTF) data set d (counts in each pixel {n p }) model M with parameters θ The likelihood function: p(d θ, M) = pixels p p (p) n p (θ)
The models: templates Fermi p6 diffuse (1) Fermi bubbles (1) 0 40 0 1 Isotropic (1) NFW (1) 0 1.5 0 1.5 Isotropic PS (4) NFW PS (4) 0 1.5 0 1.5
Isotropic point sources Region: mask 30 around plane 0 40 include diffuse, bubbles, isotropic, and isotropic PS
Isotropic point sources: source-count function dn/df [photons 1 cm 2 s deg 2 ] 10 11 10 10 10 9 10 8 10 7 10 6 10 5 10 4 Iso. PS Iso. PS (3FGL masked) 3FGL PS 10 10 3-11 10-10 10-9 10-8 F [photons / cm 2 / s]
Isotropic point sources: intensities 3FGL sources
Isotropic point sources: fluxes 3FGL sources
Isotropic point sources: fluxes 3FGL sources
Isotropic point sources: fluxes 3FGL sources
Region: mask 4 around plane, out to 30 latitude [degrees] counts 50 0 50 0 longitude [degrees] 0 counts 50
NFW point sources: source-count function For ROI out to 10, with 4 around plane masked 0 0 3 5 18 9 2 2 0
NFW point sources: source-count function Prediction: 200 PS s in inner galaxy (large uncertainties) 0 0 3 5 18 9 ~62 ps s make half of excess 2 2 0
NFW point sources: flux fraction For ROI out to 10, with 4 around plane masked posterior probability 0.20 0.15 0.10 0.05 0.00 Point sources masked 0.2 0.1 DM only NFW PS NFW DM 0.0 0 5 10 15 20 fraction of flux [%] 0 5 10 15 20 fraction of flux [%]
Model comparison NFW DM + NFW PS favored over NFW DM with Bayes factor 10 6 (very strong evidence)
Model comparison NFW DM + NFW PS favored over NFW DM with Bayes factor 10 6 (very strong evidence)
Tentative conclusion: GeV excess better fit by point-source emission than smooth (DM) emission
Where are the PSs? log[1 CDF(data; DM model)] 30 20 20 15 10 0 10-10 5-20 -30 30 20 10 0-10 -20-30 0
Summary Many more cross checks of these results
Summary Many more cross checks of these results Validation with Monte-Carlo-generated fake data
Summary Many more cross checks of these results Validation with Monte-Carlo-generated fake data Future: incorporate energy dependence / look at different energy range
Summary Many more cross checks of these results Validation with Monte-Carlo-generated fake data Future: incorporate energy dependence / look at different energy range Future: find the PS s!
Summary Many more cross checks of these results Validation with Monte-Carlo-generated fake data Future: incorporate energy dependence / look at different energy range Future: find the PS s! Future: cross-correlate CDF map with other surveys (IceCube, other wavelengths,...)
Summary Many more cross checks of these results Validation with Monte-Carlo-generated fake data Future: incorporate energy dependence / look at different energy range Future: find the PS s! Future: cross-correlate CDF map with other surveys (IceCube, other wavelengths,...) Future: constrain IceCube scenarios using high-lat results
Summary Many more cross checks of these results Validation with Monte-Carlo-generated fake data Future: incorporate energy dependence / look at different energy range Future: find the PS s! Future: cross-correlate CDF map with other surveys (IceCube, other wavelengths,...) Future: constrain IceCube scenarios using high-lat results Future: potentially use NPTF on IceCube data for PS search
Questions?