Search for gamma-ray spectral lines with the Fermi Large Area Telescope and dark matter implications

Weakly interacting massive particles (WIMPs) are a theoretical class of particles that are excellent dark matter candidates. WIMP annihilation or decay may produce essentially monochromatic $\gamma$ rays detectable by the Fermi Large Area Telescope (LAT) against the astrophysical $\gamma$-ray emission of the Galaxy. We have searched for spectral lines in the energy range 5–300 GeV using 3.7 years of data, reprocessed with updated instrument calibrations and an improved energy dispersion model compared to the previous Fermi-LAT Collaboration line searches. We searched in five regions selected to optimize sensitivity to different theoretically motivated dark matter density distributions. We did not find any globally significant lines in our a priori search regions and present 95% confidence limits for annihilation cross sections of self-conjugate WIMPs and decay lifetimes. Our most significant fit occurred at 133 GeV in our smallest search region and had a local significance of 3.3 standard deviations, which translates to a global significance of 1.5 standard deviations. We discuss potential systematic effects in this search, and examine the feature at 133 GeV in detail. We find that the use both of reprocessed data and of additional information in the energy dispersion model contributes to the reduction in significance of the linelike feature near 130 GeV relative to significances reported in other works. We also find that the feature is narrower than the LAT energy resolution at the level of 2 to 3 standard deviations, which somewhat disfavors the interpretation of the 133 GeV feature as a real WIMP signal.

Figure 1

Schematic of Limb $\gamma$-ray production by CR interactions in the Earth’s atmosphere, showing the definitions of the zenith angle (${\theta }_{\mathrm{z}}$), the spacecraft rocking angle (${\theta }_{\mathrm{r}}$), and the incidence angle ($\theta$). The dashed line starts at the center of the Earth. Not drawn to scale.

Figure 2

Counts map for the line-search data set binned in $1°\times 1°$ spatial bins in the R180 ROI, and plotted in Galactic coordinates using the Hammer-Aitoff projection. The energy range is 2.6–541 GeV, and the most significant 2FGL sources have been removed using an energy-dependent mask (see text). Also shown are the outlines of the other ROIs (R3, R16, R41, and R90) used in this search.

Figure 3

Energy dispersion model for 100 GeV in all 10 $P_{\mathrm{E}}$ bins. The darker lines show the distributions for the smallest and largest values of $P_{\mathrm{E}}$, while the thinner gray lines show the models for the intermediate $P_{\mathrm{E}}$ bins.

Figure 4

The bias of the energy dispersion for the lowest (highest) $P_{\mathrm{E}}$ bins is indicated by the dashed (solid) line. The shaded regions show the 68% containment for the highest and lowest $P_{\mathrm{E}}$ bins.

Figure 5

$P_{\mathrm{E}}$ distributions for flight and all-sky MC data sets (see text) over (a) the entire energy range (2.6–541 GeV), and (b) the energy range 52–541 GeV.

Figure 6

Derivation of global significance versus local significance given our scan over energy in $0.5{\sigma }_E$ steps and five ROIs: (a) Distribution of the largest $s_{\mathrm{local}}$ values obtained in any ROI at any energy from 1000 MC realizations (points) and the best-fit independent trials curve. (b) The corresponding $s_{\mathrm{local}}$ to $s_{\mathrm{global}}$ transformation.

Figure 7

Local fit significance vs line energy in all five ROIs. Note that $n_{\mathrm{sig}}$ was required to be non-negative. The dashed line at the top of the plot indicates the local significance corresponding to the $2\sigma$ global significance derived with the method described in Sec. 5b.

Figure 8

Local fit significance distribution from our line search. The dashed line shows the expected distribution from the null hypothesis. Note that $n_{\mathrm{sig}}$ was bounded to be positive.

Figure 9

95% C.L. ${\Phi }_{\gamma \gamma }$ in the R16 ROI (black). Yellow (green) bands show the 68% (95%) expected containment derived from 1000 single-power-law (no DM) MC simulations. The dashed lines show the median expected limits from those simulations.

Figure 10

95% C.L. $⟨\sigma v{⟩}_{\gamma \gamma }$ upper limits for each DM profile considered in the corresponding optimized ROI. Yellow (green) bands show the 68% (95%) expected containment derived from 1000 single-power-law (no DM) MC simulations. The dashed lines show the median expected limits from those simulations. The solid gray line shows the limits derived by Weniger [20] (an independent search for spectral lines from 20–300 GeV) when comparable ROIs and identical DM density profiles were used.

Figure 11

95% C.L. ${\tau }_{\gamma \nu }$ lower limits in R180 for a NFW profile. Yellow (green) bands show the 68% (95%) expected containment derived from 1000 single-power-law (no DM) MC simulations. The dashed lines show the median expected limits from those simulations.

Figure 12

Fits for a line near 130 GeV in R3: (a) at 130 GeV in the P7CLEAN data, using the 1D energy dispersion model (see Sec. 4); (b) at 133 GeV in the P7REP_CLEAN data, again using the 1D model; (c) same as (b), but using the 2D energy dispersion model (see Sec. 4). The solid curve shows the average model weighted using the $P_{\mathrm{E}}$ distribution of the fitted events. Note that these fits were unbinned; the binning here is for visualization purposes, and also that the $x$ axis binning in (a) is offset by 3 GeV relative to (b) and (c).

Figure 13

Fit for a line near 130 GeV in R16: (a) at 130 GeV in the P7CLEAN data, using the 1D energy dispersion model (see Sec. 4); (b) at 133 GeV in the P7REP_CLEAN data, again using the 1D model; (c) same as (b), but using the 2D energy dispersion model (see Sec. 4). The solid curve shows the average model weighted using the $P_{\mathrm{E}}$ distribution of the fitted events. Note that these fits were unbinned; the binning here is for visualization purposes, and also that the $x$ axis binning in (a) is offset by 3 GeV relative to (b) and (c).

Figure 14

Fit for a line-signal signal at 133 GeV in R3 using a 4.4-year P7REP_CLEAN data set and (a) the 1D energy dispersion model; (b) the 2D energy dispersion model. The solid curve shows the average model weighted using the $P_{\mathrm{E}}$ distribution of the fitted events. Note that these fits were unbinned; the binning here is for visualization purposes.

Figure 15

Fit to a $\gamma$-ray line at 133 GeV in the 3.7-year P7REP_CLEAN R3 data using the 2D model, including a scale factor for the width of the energy dispersion. The solid curves show the average model weighted using the $P_{\mathrm{E}}$ distribution of the fitted events. The best-fit width of the energy resolution was $s_{\sigma }={0.32}_{-0.13}^{+0.30}(95\%\mathrm{C}.\mathrm{L}.)$ of that predicted from MC simulations. The dotted line shows the best-fit curve with $s_{\sigma }$ fixed to 1.0. Note that when $s_{\sigma }$ is allowed to vary, the signal model includes two more degrees of freedom than the null hypothesis, so $s_{\mathrm{local}}$ is less than $\sqrt{TS}$. Also, note that these fits were unbinned; the binning here is for visualization purposes.

Figure 16

Fit at the 133 GeV line to the Limb data (P7REP_CLEAN) using the 2D energy dispersion model. The solid curve shows the average model weighted using the $P_{\mathrm{E}}$ distribution of the fitted events. Note that these fits were unbinned; the binning here is for visualization purposes.

Figure 17

Measurement of the P7REP_TRANSIENT-to-P7REP_CLEAN efficiency using the Limb control sample: (a) The distribution of ${\theta }_z$ for all events in the P7REP_TRANSIENT and P7REP_CLEAN Limb samples for $2.6\mathrm{GeV}<E^{\prime }<541\mathrm{GeV}$, including signal and background regions. (b) The P7REP_TRANSIENT-to-P7REP_CLEAN efficiency for Limb data and MC. MC has been weighted to have the same livetime distribution with $\theta$ as the Limb data.

Figure 18

Fits for a 133 GeV line in inverse ROIs (P7REP_CLEAN) using the 2D energy dispersion model: (a) A, (b) B, (c) C, and (d) D. See text for definitions of regions A, B, and C; region D is $|b|<10°$, $90°<l<110°$. The solid curves show the average model weighted using the $P_{\mathrm{E}}$ distribution of the fitted events. Note that these fits were unbinned; the binning here is for visualization purposes.

Figure 19

Two measures of the calorimeter-tracker event direction agreement for events with $125\mathrm{GeV}<{\mathrm{E}}^{\prime }<145\mathrm{GeV}$: (a) The distance of closest approach (DOCA) between the extrapolation of the tracker direction and the centroid of the calorimeter energy deposition. (b) The angle between the tracker direction and the primary axis of the energy deposition in the calorimeter. In both curves, the MC has been weighted to have the same livetime distribution with $\theta$ as the all-sky data, and the small ($<0.005$) error bars on the all-sky sample have been suppressed for visual clarity.

Figure 20

Fit at the 133 GeV line in R16 (P7REP_CLEAN) using the 2D energy dispersion model (a) for events with $\theta <50°$, and (b) for events with $\theta >50°$. The solid curves show the average model weighted using the $P_{\mathrm{E}}$ distribution of the fitted events. Note that these fits were unbinned; the binning here is for visualization purposes.

Figure 21

Fit at the 133 GeV line in the Limb (P7REP_CLEAN) using the 2D energy dispersion model (a) for events with $\theta <50°$, and (b) for events with $\theta >50°$. The solid curves show the average model weighted using the $P_{\mathrm{E}}$ distribution of the fitted events. Note that these fits were unbinned; the binning here is for visualization purposes.

Figure 22

Evaluation of the optimal values of $\Delta l$ and $R_{\mathrm{GC}}$. The plots show $S/N$ as a function of (a) $\Delta l$ and (b) $R_{\mathrm{GC}}$ normalized to the maximum for different DM density profiles (see legend) for DM annihilations (solid lines) and decays (dashed lines). For (a), $\Delta b$ has been fixed to 5°, and $R_{\mathrm{GC}}$ has been fixed to the optimal value for the associated DM density profile (see text). The vertical dashed line shows the fixed value of $\Delta l$ that was chosen for all optimized ROIs. (We do not show the case for DM annihilation with a contracted NFW profile, for which the optimal ROI is smaller than our Galactic plane mask.) For (b), $\Delta b$ and $\Delta l$ have been fixed to 5° and 6°, respectively.

Figure 23

Effect of variations in observing profiles on the energy dispersion model: (a) Observing profiles, $t_{\mathrm{obs}}(\theta ;\widehat{p})$, for several directions with the same right ascension as the Galactic center, but different declinations ($\pm 30°$, $\pm 60°$, and $\pm 90°$). (b) The corresponding energy dispersion models for $E=100\mathrm{GeV}$.

Figure 24

CR background contamination estimation: (a) The fraction of events in the P7REP_SOURCE sample also present in the P7REP_CLEAN sample as a function of energy for all the ROIs. (b) The counts spectrum of events in the P7REP_SOURCE sample but not the P7REP_CLEAN sample for the R180 ROI. The dashed line in (a) is the ratio $\mathrm{A}\mathrm{c}{\mathrm{c}}_{\mathrm{SOURCE}}(E^{\prime })/\mathrm{A}\mathrm{c}{\mathrm{c}}_{\mathrm{CLEAN}}(E^{\prime })$.

Figure 25

Distribution of signed significances for ROIs along the Galactic plane for all $E_{\gamma }<56\mathrm{GeV}$: (a) for $2°\times 2°$ ROIs, and (b) mean $s_{\mathrm{local}}$ versus $E_{\gamma }$; the large gray error bars show the rms of the distribution at a given energy, and the small black error bars show the error on the mean. Note that these results were made using only a set of nonoverlapping ROIs.