High-energy tail of the Galactic Center gamma-ray excess

Observations by the Fermi-LAT have uncovered a bright, spherically symmetric excess surrounding the center of the Milky Way Galaxy. The spectrum of the $\gamma$-ray excess peaks sharply at an energy $\sim 2\mathrm{GeV}$, exhibiting a hard spectrum at lower energies, and falls off quickly above an energy $\sim 5\mathrm{GeV}$. The spectrum of the excess above $\sim 10\mathrm{GeV}$ is potentially an important discriminator between different physical models for its origin. We focus our study on observations of the $\gamma$-ray excess at energies exceeding 10 GeV, finding: (1) a statistically significant excess remains in the energy range 9.5–47.5 GeV, which is not degenerate with known diffuse emission templates such as the Fermi bubbles, (2) the radial profile of the excess at high energies remains relatively consistent with data near the spectral peak (3) the data above $\sim 5\mathrm{GeV}$ prefer a slightly greater ellipticity with a major axis oriented perpendicular to the Galactic plane. Using the recently developed non-Poissonian template fit, we find mild evidence for a point-source origin for the high-energy excess, although given the statistical and systematic uncertainties we show that a smooth origin of the high-energy emission cannot be ruled out. We discuss the implication of these findings for pulsar and dark matter models of the $\gamma$-ray excess. Finally we provide a number of updated measurements of the $\gamma$-ray excess, utilizing novel diffuse templates and the Pass 8 data set.

Figure 1

The spectrum of the GCE extracted in the IG (green) and GC (orange) regions over the full energy range (left) and 10–50 GeV (right). This spectrum was determined using the analysis framework outlined in Sec. 2a for the IG and Sec. 2c for the GC. We show the spectrum for the best fit generalized NFW profile, which corresponds to $\gamma =1.14$ for the IG and 1.05 for the GC. A similar figure showing the spectra for identical $\gamma$ values or identical diffuse emission models is shown in Fig. 28. In both cases the flux is normalized to its value at 5° from the plane. In the GC analysis, no flux is observed in several bins, and so we instead show the 90% upper limit. Note the IG and GC analyses differ in their ROI, diffuse modeling and treatment of the point sources. See text for details.

Figure 2

Same as the left panel of Fig. 1, except $\gamma =1.14$ for both the IG and GC analyses. Also, in this case both the IG and GC analyses use the same diffuse mode: p7v6 in the left panel and GALPROP model A in the right panel. Using the same diffuse model in both regions alleviates some of the tension in the overall normalization computed between the two analyses. However, fixing $\gamma =1.14$ in the GC analysis has an almost comparable effect in magnitude on the normalization of the spectrum as changing diffuse model. We further explore this in Appendix pp4.

Figure 3

Preference for adding GCE correlated PSs to our default fit as a function of the minimum energy bin, whilst the maximum is kept at 47.5 GeV. The result for our default analysis is shown in red, whilst varying the disk PS to use a thicker disk template is shown in orange, and changing the diffuse model from p6v11 to p7v6 or model F is shown in purple and khaki respectively. In addition, in blue we shown the median and 90% confidence limits from analyzing a large ensemble of mock data maps assuming both disk and GCE correlated PSs (left) or just a disk PS template (right). Mock data sets were created using the p6v11 diffuse model. See text for details.

Figure 4

Spatial residual in our default ROI for the IG subtracting all templates except (left) or including (right) the GCE template. The data have been smoothed to 2°, but the PS masks have not—these are the masks corresponding to the lowest energy where the PSF is largest, here 9.5 GeV. A number of regions of over and under subtraction are evident in both maps, symptomatic of imperfect background models. Masks are shown in gray. See text for details.

Figure 5

Same as Fig. 4 for the GC analysis, and with all data and models smoothed to 0.25°. The left figure shows the residual when the GCE template is not included, while the right shows the residual after the GCE template is included in the model prediction.

Figure 6

We show the IG preferred variation in $\mathrm{\Delta }\mathrm{TS}$ with energy and inner slope, $\gamma$, of a generalized NFW profile from which we form our GCE template. On the left panel we zoom in to higher energies, and find that the statistical power to discriminate between different values of $\gamma$ is reduced, leading to an opening up of the preferred value. Also in the bin around 15 GeV we notice an increased preference for lower $\gamma$ values.

Figure 7

Same as Fig. 6 for an analysis of the GC ROI. We find results consistent with the IG analysis, though we note that the relatively weak statistical evidence for a GCE component in the energy range 23–38 GeV makes our constraint on the value of $\gamma$ weak at high energies. The left panel is identical to the right, but shown in only the high energy regime.

Figure 8

Preferred axis ratio as a function of energy in the IG. The axis ratio is defined such that values greater than 1 correspond to a stretch perpendicular to the plane, whilst values less than 1 indicate a stretch along the plane. The left panel is identical to the right, but shown in only the high energy regime.

Figure 9

For a fixed axis ratio of 2 we show the IG preference for a stretch along various axes for each of the energy bins, as compared to the quality of fit for no stretch at all. The left panel is identical to the right, but shown in only the high energy regime.

Figure 10

Same as Fig. 8 for an analysis of the GC ROI. We again find results consistent with the IG analysis, including a preference for a GCE profile stretched perpendicularly to the Galactic plane at high $\gamma$-ray energies. The left panel is identical to the right, but shown in only the high energy regime.

Figure 11

The best fit position of the GCE template compared to the dynamical center of the Milky Way Galaxy, as a function of the minimum energy of the GC analysis. A small offset is found, in particular at high energies. However, this result is best understood as demonstrating the degeneracy between the GCE template and the multiple PS degrees of freedom densely clustered around the position of Sgr A*. The three white dots denote the positions of nearby 3FGL point sources (from left to right 3FGL J1746.3-2851c, 3FGL J1745.6-2859c, 3FGL J1745.3-2903c).

Figure 12

The combined spectrum of a pulsar model that includes both prompt emission from pulsars (with a spectrum following that of [75]), along with a ICS spectrum produced by GALPROP utilizing a cosmic-ray lepton injection model as described in the text. The normalizations of the prompt and ICS components have been adjusted to give the best fit to the data.

Figure 13

Spectrum obtained by a GCE template with $\gamma =1.0$ in our default ROI for the IG, performed for the 17 different diffuse models. We explicitly show the spectrum extracted for the p6v11, p7v6 and p8v6 models, while we use 14 of the diffuse models taken from [9] to form the median and the 16% and 84% percentiles as confidence limits. We show the full energy range (left) as well as the high-energy region (right). See text for details.

Figure 14

The bin-by-bin preferred NFW inner slope $\gamma$ (left) and axis ratio (right), repeating the default IG analysis using the GALPROP-based model A, rather than p6v11. For the inner slope, the globally preferred value of 1.13 is close to our default value of 1.14. Further we see that at high energies the fit again prefers a flatter profile. In terms of the axis ratio, as for our default analysis we see a general preference for a stretch perpendicular to the plane, with a greater stretch being preferred in the high-energy regime.

Figure 15

As for Fig. 14 but showing results cumulative in energy.

Figure 16

Preferred value for $\gamma$ and the axis ratio for a GC analysis that utilizes the diffuse emission model A [9] as opposed to the Fermi-LAT based p7v6 diffuse emission model. In this case we also add a model for the Fermi bubbles taken from [54]. We find features that are generically consistent with our default model near the spectral peak of the GCE ($\approx 1–3\mathrm{GeV}$), but which prefer a steeply peaked profile stretched perpendicular to the Galactic plane at low $\gamma$-ray energies. This may be due to a clear oversubtraction of the plane by model A near the GC, which was not intended to fit the $\gamma$-ray data very close to the Galactic plane.

Figure 17

Same as Fig. 16 plotted as a function of the minimum analysis energy, rather than individually in each energy bin. In this case, we see that the global results are dominated by the emission near the peak of the GCE intensity ($\sim 1–3\mathrm{GeV}$). We then find results that are globally qualitatively similar to those of our default analysis, preferring $\gamma =1.13$ and an axis ratio of 1.32.

Figure 18

Spectrum for our default IG analysis (left) and an identical analysis with an extra template in the form of the model F ICS contribution (right). This addition is motivated by the observation in [9] that the p6v11 diffuse model gets the ICS modeling wrong at high energies. Given the large coefficient obtained by the ICS template this appears to be true, but this issue appears to leave the basic features of the GCE unchanged. In both figures the coefficients of the diffuse components are rescaled to facilitate the comparison between templates. See text for details.

Figure 19

Spatial morphology of our default template for the Fermi bubbles and two alternatives, within our region of interest for the IG analysis. The cream region corresponds to the interior of the bubbles, and the blue region to the exterior. The templates are taken from [54] (“default bubbles”), [79] (“alternate bubbles”), and [78] (“Fermi paper bubbles”).

Figure 20

The spectrum of the GCE template in the default case (green points), when the Fermi bubbles template is omitted entirely (red points), and when the default Fermi bubbles template is replaced by an alternative prescription (dark and light blue points).

Figure 21

Same as Fig. 16 for a model where the default bubbles template is replaced by the alternative bubbles template shown in Fig. 19. We find almost no difference between these models in terms of the parameters of the GCE fit, indicating that the bubbles template and the GCE template are not in any way degenerate, and that the bubbles only contribute marginally to the $\gamma$-ray data within the GC ROI. The best fit $\gamma$ in this case is $\gamma =1.12$, and the best fitting axis ratio is 1.44.

Figure 22

Preferred value for $\gamma$ and the axis ratio for a GC analysis that utilizes the 2FGL PS catalog, instead of the 3FGL catalog used in our default analysis. This provides an easier comparison to previous works, such as [8]. We note that, unlike our default analysis, which utilized $\gamma =1.00$ for the ellipticity analysis, owing to the more peaked profile preferred in the 2FGL analysis, we calculate the ellipticity assuming a value $\gamma =1.20$. The globally best fitting value of $\gamma$ for our 2FGL analysis is $\gamma =1.14$.

Figure 23

The spectrum extracted in the IG analysis by a $\gamma =1.1$ GCE template for four different data sets: Pass 7 all source (P7 source), Pass 8 all source (P8 source), Pass 7 ultraclean Q2 front-converting (P7 UC Q2F), and Pass 8 UCV BestPSF (P8 UCV BestPSF). All other options are set to the IG defaults. We see the difference between Pass 7 and 8 is far less important than the differences between varying event selections within Pass $7/8$.

Figure 24

Plotted are the mean and one standard deviation on the best fit $\gamma$ value for the GCE template determined using 16 (17) diffuse models for Pass 7 (Pass 8) data. This is done using our default IG analysis for the same four data sets described in Fig. 23, where UCV4 is shorthand for UCV BestPSF.

Figure 25

Same as Fig. 11 for an analysis of the Galactic Center ROI that uses only the 25% of P8R2_Source class events with the best angular reconstruction (PSF3). Compared to an analysis utilizing the full data set, the low-energy analysis prefers a center that is closer to Sgr A*, though we still do note a statistically significant offset. The three white dots denote the positions of nearby 3FGL point sources (from left to right 3FGL J1746.3-2851c, 3FGL J1745.6-2859c, 3FGL J1745.3-2903c).

Figure 26

Here we show the IG analysis spectra obtained by three different GCE templates with $\gamma =1.2$, in green that associated with a full template, in blue the results for the north and south regions of the template (where $|b|>|l|$) and in red the east and west contribution (where $|l|>|b|$). We show this using the p6v11 diffuse model (top) and p7v6 model (bottom) for four different regions: $|b|,|l|<15°$ (left), $|b|,|l|<20°$ (second from left), $|b|,|l|<40°$ (second from right), and the full sky (right). All ROIs mask the plane at 1°. See text for details.

Figure 27

Here we show the impact of changing the size of the PS mask on the spectrum extracted for the best fit GCE template in the IG analysis. In green we show the default mask, which varies with energy according to the PSF of Fermi, in blue use a mask size fixed at the highest energy considered, and in red the lowest energy. We show this for all source data on the left and UCV BestPSF data on the right, from which it is clearly a much bigger issue in source data. Note that in both cases for the largest mask, in red, where the high-energy points go to zero correspond to a failure of the fit to converge given the very low statistics.

Figure 28

On the left we show the spectrum and normalization of the GCE in the IG analysis for the best fit profile slope of $\gamma =1.14$, compared to the GC analysis for an identical best-fitting profile slope. We note that the GCE in the GC ROI contributes a smaller normalization than in the IG ROI, a result which hints at a potential steepening of the inner-profile slope as a function of radius. On the right, the GCE spectrum for the default IG and GC analyses is shown with both using the model A diffuse emission model. Here we use the best-fit profile values from the default analyses, $\gamma =1.14$ for the IG and 1.05 for the GC. Here we see that when using the same diffuse emission models the GCE templates can produce similar fluxes at 5° from the GC, but note this is not true for all diffuse models. See text for details.

Figure 29

Here we show two variations on the results shown in the left-hand panel of Fig. 3. On the left we show the default results in red, but in green show what happens if we fix the lower index [$n_2$ in Eq. (2)] to be 1.5 for the GCE PS template and 1.4 for the disk PS template. The simulated data 90% confidence interval (blue) shown also assume a fixed value of $n_2$ both in the production of the simulated data and the analyses. On the right, we again show the default analysis in red, but this time the simulated data is generated assuming a smoothed spectrum for the GCE shown inset, rather than the spectrum extracted for the Poissonian GCE template shown in black. The smoothed spectrum is determined by fitting the data to a power law with an exponential cutoff. See text for details.

Figure 30

Best fit source-count functions derived from a fit over 2–50 GeV for a GCE PS (solid curve) and disk PS (dashed curve). The various colors correspond to five variations on the modeling: default analysis with p6v11 (red), use of a thick disk (orange), move to p7v6 (purple), model F (khaki), and default analysis but fixing the lower index [$n_2$ in Eq. (2)] of the GCE and disk PS to be 1.5 and 1.4 respectively (green). For the default analysis only we show the 68% confidence limits also, to give some indication of the statistical uncertainty. In black dots we show a histogram of the observed flux from 3FGL sources in that energy range , with 68% Poissonian error bars simply coming from counting statistics.

Figure 31

Here we show the spectrum associated with all templates at high energies in the IG analysis. We show this for p6v11 (left) and model F (right) diffuse models. Note in both the coefficients of the diffuse components have been rescaled to make the comparison between templates more straightforward. See text for details.

Figure 32

Here we show the analogue of the right-hand side of Fig. 4, but for the first two high-energy bins separately. The second energy bin, shown on the right, is the focus of Appendix pp6. It is clear that in this bin oversubtraction is more pronounced than in the lowest energy bin. The residuals for the two higher energy bins not shown are much closer to the left-hand plot than the right.

Figure 33

Preferred $\gamma$ for the default analysis for two different energy binnings: the binning employed in the main text for statistical analyses (left) and equal log spaced bins (right).

Figure 34

Cumulative version of Figs. 6 and 7, for the IG (left) and GC (right).

Figure 35

Cumulative version of Figs. 8 and 10, for the IG (left) and GC (right).

Figure 36

The effect of convolving the extracted spectrum for the GCE with the energy dispersion of Fermi. Green dots show the original spectrum, orange dots the spectrum after convolution with the energy dispersion function (note that this is not an estimate of the “true” spectrum), and orange crosses the spectrum after convolution if the original spectrum is truncated above 10 GeV.