Документ взят из кэша поисковой машины. Адрес оригинального документа : http://hea.iki.rssi.ru/conf/hea2010/Presentations/23_posters/Malyshev.pdf Дата изменения: Wed Jan 26 13:25:08 2011 Дата индексирования: Tue Oct 2 01:08:42 2012 Кодировка: Поисковые слова: п п п п п п п п п п п п п п п п п п п

- Fermi

arxiv: 1007.4556 : Ilias Cholis Jo Bovy

CCPP, NYU

HEA, , 2010


Spherical harmonics of gamma-rays and DM annihilation

Dmitry Malyshev, NYU

Motivation
DM annihilation at high latitudes is a large scale small amplitude signal: ``Fourier transform'' is a tool of choice for such signals

Advantages of spherical harmonics decomposition for large scale structure searches:
1. Don't need to worry about pixelation: for sufficiently many pixels, low L modes are independent of the pixel size. 2. Linear operations on data, no information loss 3. Data separation: low L modes are dominated by the large scale structure while high L modes are dominated by the noise
2


Spherical harmonics of gamma-rays and DM annihilation

Dmitry Malyshev, NYU

What we did:
1. Use 13 months of Fermi LAT data (http://fermi.gsfc.nasa.gov/ssc/data/) 2. Mask the Galactic plane below 10 degrees in latitude 3. Use a low energy bin (around 2.5 GeV) as an astrophysical template. 4. Compare the case of a two-template model (isotropic + astro) with the three template models (istropic + astro + extra) where for the extra template we try i) NFW DM decay r-1 r-2 ii) NFW DM annihilation iii) a profile that follows the mass distribution in the stellar halo r-3 (Juric et al (ApJ 673, 864), Bell et al (ApJ 680, 295)) of the Milky way

3


Spherical harmonics of gamma-rays and DM annihilation

Dmitry Malyshev, NYU

Gamma-ray data in a 9.5 GeV bin

Photon counts in pixels
4


Spherical harmonics of gamma-rays and DM annihilation

Dmitry Malyshev, NYU

Templates
Astrophysics template is given by the data in a 2.5 GeV bin

NFW DM annihilation template

5


Spherical harmonics of gamma-rays and DM annihilation

Dmitry Malyshev, NYU

Angular power spectrum for Fermi data
in an energy bin with central energy 9.45 GeV
The statistical variance of harmonic decomposition Large scale structure coefficients in the presence of point sources is m times Point sources larger than the variance in the Poisson statistics case. of photons from point sources. It is equal to the ratio of a plateau in Cl 's for medium l 's to the Poisson noise level

m is the average number

Poisson noise (PSF)
6


Spherical harmonics of gamma-rays and DM annihilation

Dmitry Malyshev, NYU

Fitting the alm's in an energy bin
Two templates model Three templates model

2 /dof = 23.6/14

2 /dof = 12.9/13

The isotropic component is non-trivial due to the spherical decomposition in a window

7


Spherical harmonics of gamma-rays and DM annihilation

Dmitry Malyshev, NYU

Two template residual

The residual is in sigma values = (data - model) / sqrt(model) astro + isotropic template fitting

8


Spherical harmonics of gamma-rays and DM annihilation

Dmitry Malyshev, NYU

Three template residual

The residual is in sigma values = (data - model) / sqrt(model) astro + isotropic + DM template fitting

The difference is subtle: the model with DM template has much better large scale behavior while the change near the GC is almost invisible.

9


Spherical harmonics of gamma-rays and DM annihilation

Dmitry Malyshev, NYU

Global template fitting
In this plot we fit the three templates globally to all energy bins assuming a power-law dependence on the energy F E -n

The best fit values of the indices are: galactic: 3.1 DM: 2.0 isotropic: 1.8 The fitting is subtle since the ``astro'' template includes isotropic, galactic and DM fluxes at E0
10


Spherical harmonics of gamma-rays and DM annihilation

Dmitry Malyshev, NYU

Conclusions
1. Spherical harmonics are a natural choice for fitting the large scale structures in gamma-rays. It is a linear procedure, that avoids many difficulties associated with coordinate space fitting (e.g., the need to smear photons, upgrading / degrading of templates to fit to the same pixelation etc.) 2. The calculation of chi^2 and the fitting procedure are simple. The data is conveniently separated into low L modes (relevant for the fitting) and high L modes (dominated by the noise). 3. We observe that adding an extra spherical template significantly reduces 2 the . NFW DM annihilation and a stellar halo profile have a slightly 2 than NFW DM decay. better

11


Spherical harmonics of gamma-rays and DM annihilation

Dmitry Malyshev, NYU

Dark matter and astrophysics may look like twins: they are hard to distinguish.

Diane Arbus, Identical Twins (1967)

12