Dark Matter Annihilation in The Galactic Center As Seen by the Fermi Gamma Ray Space Telescope Page: 4 of 21
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where 0 is the difference between the measured and actual directions of the observed gamma ray. The function P68
is the angle within which 68% of the gamma rays are reconstructed, and is well fit (in degrees) by
log1o[P68(E)] = -0.276 - 0.674logo[E7/1 GeV], Ey < 20 GeV
logo[Ps(E7)] = -0.785 - 0.283logo[E/1 GeV], E7 > 20 GeV. (6)
The quantity C appearing in Eq. 5 accounts for the non-gaussianity of the LAT's PSF. We fit this according to [14]
C = 1, 0 < P68
C = 0.735 + 0.265 ( I, 0 > P68. (7)
At angular distances of more than 1-2 from the Galactic Center, the disk component of the emission can be clearly
and easily separated from the other components. For this reason, we begin by studying only the region of the sky with
12 + b2 > 2 . For a given angular annulus, we fit the data to a combination of the three components described above,
and consider one energy bin at a time (distributed logarithmically in energy, with ten bins per decade). For each
combination of energy and distance from the Galactic Center, we find the combination of the following parameters
that yields the best overall chi-square fit: the intensity of the disk emission for l < 0, the intensity of the disk emission
for l > 0 , the width of the disk emission for l < 0 , the width of the disk emission for l > 0 , and the intensity of
the spherically symmetric emission. For simplicity, we fix the intensity of each point source assuming that it has a
power-law spectrum with an index and intensity as described in the Fermi First Source Catalog (the central values
that are quoted). At times, this simplifying choice will not be supported by the data (departures from power-law
behavior are evident for some of the point sources), but this impacts our overall results only slightly.
In Figs. 2-5, we show the angular distribution (meaning with the direction from the Galactic Center) of the (front
converting) events observed by FGST between 9 and 10 degrees away from the Galactic Center in the first 16 energy
bins (300 MeV to 11.94 GeV), and compare this to that predicted for our best-fit model parameters. In each frame,
the emission from the disk is clearly apparent and in some cases emission from individual point sources can be seen
(compare to the point sources between the two circles shown in Fig. 1). The data shown corresponds to that collected
between August 4, 2008 and August 12, 2010.
The most significant discrepancies between our best fit model and the data, as shown in Figs. 2-5 (and also over
other angular ranges), results from our simplistic treatment of point sources. Because we have not allowed the
intensity of the point source contributions to float in this fit, but rather have fixed them to the overall flux and
power-law spectral index listed in the FGST First Source Catalog, there are evident examples in which either brighter
or dimmer point source emission would provide a better fit, relative to that included in our simple model. Notice, for
example, the E. =599-754 MeV and 754-949 MeV frames of Figs. 3-4, at approximately arctan(b/l) 220 - 230 .
Here the spectrum of the responsible nearby point source (clearly identifiable in Fig. 1 as 1FGL J1802.5-3939, located
at l = -7.5581 , b = -8.3935 ) evidently exceeds that predicted by the best fit power-law. If it were not for
considerations of computation time, we could fit for the individual intensities of each point source in each energy
bin. Given that less than 7% of the total gamma ray flux in the inner t15' window is associated with resolved point
sources, this choices does not significantly impact our extraction of the spectral shapes or intensities of the gamma
ray emission from the disk or from the spherically symmetric components.
We have repeated this procedure to derive the spectra of the disk and spherically symmetric components of the
gamma ray emission over various regions of the Inner Galaxy (between 2 and 10 from the Galactic Center). The
results are shown in Figs. 6-8. We find that the emission from the disk has a fairly uniform spectral shape and overall
intensity, varying only slightly along the disk (with l). The spherically symmetric emission also shows no discernible
variation in the spectral shape, but does become steadily brighter as we move closer to the Galactic Center.
The spectra shown in Figs. 6-8 can be easily accounted for with known emission mechanisms. In particular, their
spectral shapes are consistent with being dominated by gamma rays from neutral pion decay, with a smaller but not
insignificant contribution from inverse Compton scattering (a small contribution from Bremsstrahlung may also be
present). In Fig. 9, we show the shapes of the spectra predicted from these emission mechanisms, as calculated using
the publicly available code GALPROP [15]. The solid lines shown in Figs. 6-7 correspond to the predicted spectrum
from pion decay and inverse Compton scattering, with relative normalizations as shown in Fig. 9. This provides a
good overall fit to the observed spectra from the disk. In Fig. 8, the solid line again represents the contribution
from pion decay and inverse Compton scattering, but with a larger fraction of the emission from inverse Compton
scattering (7.15 times larger, relative to the pion component, than in the disk). Again, this provides a good overall
fit to the observed spectra. The greater relative contribution from inverse Compton scattering (or equivalently, the
lesser relative contribution from pion decay) is likely the consequence of lower gas densities away from the Galactic
Disk.
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Hooper, Dan; /Fermilab /Chicago U., Astron. Astrophys. Ctr.; Goodenough, Lisa & U., /New York. Dark Matter Annihilation in The Galactic Center As Seen by the Fermi Gamma Ray Space Telescope, article, October 1, 2010; Batavia, Illinois. (https://digital.library.unt.edu/ark:/67531/metadc1013560/m1/4/: accessed April 24, 2024), University of North Texas Libraries, UNT Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.