Fermi LAT search for dark matter in gamma-ray lines and the inclusive photon spectrum

Dark matter particle annihilation or decay can produce monochromatic gamma-ray lines and contribute to the diffuse gamma-ray background. Flux upper limits are presented for gamma-ray spectral lines from 7 to 200 GeV and for the diffuse gamma-ray background from 4.8 GeV to 264 GeV obtained from two years of Fermi Large Area Telescope data integrated over most of the sky. We give cross-section upper limits and decay lifetime lower limits for dark matter models that produce gamma-ray lines or contribute to the diffuse spectrum, including models proposed as explanations of the PAMELA and Fermi cosmic-ray data.

Figure 1

The line data set binned in $1.5°\times 1.5°$ spatial bins, plotted in galactic coordinates using a Hammer-Aitoff projection. Photons with energy from 4.8 to 264 GeV are included. The white areas away from the Galactic plane correspond to the locations of 1FGL point sources and have been masked here. The area in white along the Galactic plane is excluded from this ROI.

Figure 2

Counts spectrum from 4.8 to 2604 GeV in 5% bins for photons in the Pass 6 DIFFUSE class (red triangles), the P6_V3 11-month line analysis photon class (green square), and the Pass 6 DATACLEAN class (black circles) for the ROI $|b|>10°$ plus a $20°\times 20°$ square centered at the GC. The dataclean class has the tightest cuts. Additional cuts on the inclination, zenith, LAT rocking angles, and point sources from the LAT 1-year catalog are included.

Figure 3

Energy dispersion for the 100 GeV MC spectral line. The unbinned maximum likelihood best fit for $G(x)$ is shown with its component Gaussian functions. The 68% and 95% containment windows are given by the solid and dashed vertical lines, respectively, and are based on $G(x)$. The ${\chi }^2/\mathrm{dof}$ and $p$-value for the binned data are included in the figure. The fit of $G(x)$ to the MC data is cut off at $|x|>0.2$ (see text).

Figure 4

MC-derived energy resolution (68% energy dispersion fractional containment divided by 2), integrated over the angular acceptance.

Figure 5

Exposure map for 100 GeV in $\mathrm{c}{\mathrm{m}}^2\mathrm{s}$ in Hammer-Aitoff projection, cut for the ROI $|b|>10°$ plus a $20°\times 20°$ square centered at the GC. The map average and square root of the variance is $(5.60\pm 0.61)\times {10}^{10}{\mathrm{cm}}^2\mathrm{s}$. The exposure is calculated over the line data-set energy range at 5% intervals in log-space for use in the flux construction. The average exposure varies by only $\sim 25\%$ over our energy range.

Figure 6

The photon counts spectrum for the inverse ROI ($|b|<10°$ excluding the $20°\times 20°$ square at the GC) (solid squares for left top, open squares for left bottom) and for an albedo photon data set (solid triangles for right top, open triangles for right bottom). The top two plots show photons from the “Pass 6 DATACLEAN” class (see Sec. 2), while the bottom two plots in addition include photons that fail to pass the “PSF cut,” which was designed to improve the LAT PSF. In each subfigure, the top plot (a) shows (with a solid line) a fit of the data to a power-law function $F(E,\gamma )=E^{-\gamma }$ times the appropriate exposure $\epsilon (E)$ (see text); the bottom plot (b) shows the normalized fit residuals and fractional deviation (small triangles) of the data from the fit curve. The top panel shows a prominent bump and dip below about $\sim 13\mathrm{GeV}$, which is mitigated by removing the PSF cut in the bottom panel, indicating that these features are systematic effects. Note that the vertical scale of the residuals is different for the different panels. The errors bars on the entries/bin are $\sqrt{\mathrm{counts}}$, while the errors bars on the residuals are $\pm 1$ sigma to guide the eye.

Figure 7

The inclusive photon counts spectrum (circles) of the expected signal region. The left spectrum includes photons from the Pass 6 DATACLEAN sample, while the right spectra also includes those photons which failed to pass the “PSF cut,” which induces systematic effects below $\sim 13\mathrm{GeV}$, as shown in Fig. 6 with control data sets. A power-law fit (top, line), normalized fit residuals (bottom, circles), and the fractional deviation of the data from the power-law fit (bottom, small triangles) are shown as in Fig. 6. We search for dark matter induced gamma-ray lines above $\sim 13\mathrm{GeV}$ using the left data set, and below $\sim 13\mathrm{GeV}$ using the right data set. For dark matter contributions to the inclusive spectrum, we use the left spectrum (for which the systematics from the PSF cut are not important)—see Sec. 4b.

Figure 8

$E^2\times \Phi$ with power-law fit. The gray band shows the systematic error due to uncertainty in the effective area. The arrow shows the shift due to uncertainty in the absolute energy scale. The intensities and energies shown here are tabulated in Table 1.

Figure 9

Spectral line search energy ranges.

Figure 10

Coverage (a) and power (b) for 5000 MC trials for 7, 20, 50, 100, and 200 GeV spectral lines. The error bars are statistical. The background is simulated by a power-law with index $\Gamma =2.5$. In coverage plots, $f_j$ is not restricted to be greater than zero. Restricting to $f_j>0$ results in over-coverage at low signal fraction.

Figure 11

The complement of the cumulative histogram of $T_j$ for the background only MC (black histogram). The red curve shows the $(1-{\chi }_{cdf}^2)/2$ distribution from Chernoff’s theorem [27], where ${\chi }_{cdf}^2$ is the cumulative chi-squared distribution function.

Figure 12

Signal significance for the line, inverse ROI, and albedo data sets with and without the PSF cut. A trial factor is not applied to the signal significance. All data sets show an excess at 7 GeV and a deficit at 10 GeV. In the line data set and inverse ROI data sets, the 7 and 10 GeV features have magnitude of significance $\ge 3\sigma$. Removing the PSF cut decreases the magnitude of their significance, particularly in the line dataset and inverse ROI.

Figure 13

Line data-set spectral line fitting results, excluding the PSF cut, for 7 GeV. Removing the PSF cut from the line data set reduces the signal significance from $2.9\sigma$ to $1.2\sigma$, indicating that the feature is caused by a systematic effect. (a) Composite unbinned maximum likelihood fit (signal and background components in blue dashed, combined signal+background in solid red). Signal pdf shown in inset (blue dashed line). (b) Normalized residuals for the composite fit. (c) Standard error ($1\sigma$) CL error ellipse. (d) Profile of the log-likelihood (LL) for the signal fraction, which is maximized with respect to the spectral index at each point. Note that there are two blue lines in the top left figure, one for the background, which is largely indistinguishable from the red line, and one for a small simulated signal, which is barely distinguishable from the x-axis in this plot, but also shown in the inset.

Figure 14

95% CL flux upper limit (integrated over the entire ROI) for photons from spectral lines. The bin-to-bin correlations are due to the overlap of the energy ranges, which is shown in Fig. 9. There is a systematic uncertainty on these upper limits of 23% for $E\le 130\mathrm{GeV}$ and 30% for $E>130\mathrm{GeV}$ (see text).

Figure 15

Top row: Dark matter annihilation 95% CL cross-section upper limits into $\gamma \gamma$ (left) and $Z\gamma$ (right) for the NFW, Einasto, and isothermal profiles for the region $|b|>10°$ plus a $20°\times 20°$ square at the GC. $\gamma Z$ limits below $E_{\gamma }<30\mathrm{GeV}$ are not shown; see text for explanation. Bottom row: Dark matter decay 95% CL lifetime lower limits into $\gamma \nu$ for the NFW profile and same ROI. Systematic effects from the photon line flux upper limits are not included.

Figure 16

Measured intensity (black) and largest allowed intensity (various colors) for WIMP annihilation to $W^{+}{W}^{-}$ for WIMP masses 86, 139, 224, 360, 578, 923, 1495, 2405, 3867, 6219, and 10000 GeV, for the region $|b|>10°$ plus a $20°\times 20°$ square at the GC.

Figure 17

Cross-section upper limits for dark matter annihilation to $b$-quarks or gluons from the diffuse gamma-ray background spectrum for the region $|b|>10°$ plus a $20°\times 20°$ at the GC, assuming the NFW, Einasto, or isothermal dark matter halo profiles. No photons from astrophysical background sources have been included, making these limits very conservative. The horizontal dashed line is the cross section for a thermally produced WIMP ($3\times {10}^{-26}{\mathrm{cm}}^3{\mathrm{s}}^{-1}$).

Figure 18

As in Fig. 17, but for dark matter annihilation to $W$-bosons or $e^{+}{e}^{-}$. The annihilation to $e^{+}{e}^{-}$ only includes prompt photons from final states radiation and none from high-energy leptons inverse Compton scattering off starlight or cosmic microwave background photons The green and red shaded regions can explain the PAMELA and Fermi CR data, respectively. They are taken from [59], but we have rescaled their regions by $(3/4{)}^2$ to a local density of ${\rho }_{\odot }=0.4\mathrm{GeV}{\mathrm{cm}}^{-3}$ from $0.3\mathrm{GeV}{\mathrm{cm}}^{-3}$ used in [59].

Figure 19

As in Figs. 17 and 18, but for dark matter annihilation to ${\mu }^{+}{\mu }^{-}$ or ${\tau }^{+}{\tau }^{-}$.

Figure 20

As in Figs. 17 and 18, but for dark matter annihilation to $\varphi \varphi$, where $\varphi$ is a new low-mass force mediator with mass 0.1 GeV (1 GeV), and decays to $e^{+}{e}^{-}$ (${\mu }^{+}{\mu }^{-}$) in the figures on the left (right).

Figure 21

Lifetime lower limits for dark matter decay to $b$-quarks, gluons, $W$-bosons, or $e^{+}{e}^{-}$ from the diffuse gamma-ray background spectrum for the region $|b|>10°$ plus a $20°\times 20°$ at the GC, assuming the NFW dark matter halo profile (Einasto and isothermal give very similar constraints). No photons from astrophysical background sources have been included, making these limits very conservative.

Figure 22

As in Fig. 21 but now for dark matter decay to ${\mu }^{+}{\mu }^{-}$, ${\tau }^{+}{\tau }^{-}$, or $\varphi \varphi$, where $\varphi$ is a new low-mass force mediator with mass 0.1 GeV (1 GeV), and decays to $e^{+}{e}^{-}$ (${\mu }^{+}{\mu }^{-}$) in the figure on the left bottom (right bottom). The green and red shaded regions can explain the PAMELA and Fermi CR data, respectively. They are taken from [59], but we have rescaled their regions by $4/3$ to a local density of ${\rho }_{\odot }=0.4\mathrm{GeV}{\mathrm{cm}}^{-3}$ from $0.3\mathrm{GeV}{\mathrm{cm}}^{-3}$ used in [59].