Fermi-LAT measurement of the diffuse gamma-ray emission and constraints on the Galactic Dark Matter signal
We study diffuse gamma-ray emission at intermediate Galactic latitudes measured by the Fermi Large Area Telescope with the aim of searching for a signal from dark matter annihilation or decay. In the absence of a robust dark matter signal, we set conservative dark matter limits requiring that the dark matter signal does not exceed the observed diffuse gamma-ray emission. A second set of more stringent limits is derived based on modeling the foreground astrophysical diffuse emission. Uncertainties in the height of the diffusive cosmic-ray halo, the distribution of the cosmic-ray sources in the Galaxy, the cosmic-ray electron index of the injection spectrum and the column density of the interstellar gas are taken into account using a profile likelihood formalism, while the parameters governing the cosmic-ray propagation have been derived from fits to local cosmic-ray data. The resulting limits impact the range of particle masses over which dark matter thermal production in the early Universe is possible, and challenge the interpretation of the PAMELA/Fermi-LAT cosmic ray anomalies as annihilation of dark matter.
00 \journalnameNuclear Physics B Proceedings Supplement \runauth \jidnuphbp \jnltitlelogoNuclear Physics B Proceedings Supplement
The Milky Way halo has long been considered a good target for searches of indirect signatures of dark matter (DM). WIMP DM candidates are expected to produce gamma rays, electrons and protons in their annihilation and decays and such emission originating in our Galaxy would appear as a diffuse signal. At the same time, the majority of the Galactic diffuse emission is produced through radiative losses of cosmic-ray (CR) electrons and nucleons in the interstellar medium. Modeling of this emission presents one of the major challenges when looking for subdominant signals from dark matter.
In this analysis we test the diffuse LAT data for a contribution from the DM signal by performing a fit of the spectral and spatial distributions of the expected photons at intermediate Galactic latitudes. In doing so, we take into account the most up-to-date modeling of the established astrophysical signal, adapting it to the problem in question (1). Our aim is to constrain the DM properties and treat the parameters of the astrophysical diffuse gamma-ray background as nuisance parameters. Besides this approach, we will also quote conservative upper limits using the data only (i.e. without performing any modeling of the astrophysical background).
We follow (2) in using the GALPROP code v54 (3), to calculate the propagation and distribution of CRs in the Galaxy and the whole sky diffuse emission. In (2) various standard parameters of the CR propagation were studied in a fit to CR data and it was shown that they represent well the gamma-ray sky, although various residuals (at a level (2)), both at small and large scales, remain. In our work, we use the results of the fits to the CR data from (2) but we allow for more freedom in certain parameters governing the CR distribution and known astrophysical diffuse emission and constrain these parameters by fitting the models to the LAT gamma-ray data. Despite the large freedom we leave in the models we see residuals in our ROI at the level and at significance. These residuals can be ascribed to various limitations of the models: imperfections in the modeling of gas and ISRF components, simplified assumptions in the propagation set-up, unresolved point sources, and large scale structures like Loop I (4) or the Galactic Bubbles (5). Since residuals do not seem obviously related to DM, we focus in the following on setting limits on the possible DM signal, rather than searching for a DM signal.
2 DM maps
We parametrize the smooth DM density with a NFW spatial profile (6)
and a cored (isothermal-sphere) profile (7):
For the local density of DM we take the value of GeV cm (8), and the scale radius of 20 kpc (for NFW) and 2.8 kpc (isothermal profile). We also set the distance of the solar system from the center of the Galaxy to the value 8.5 kpc. For the annihilation/decay spectra we consider three channels with distinctly different signatures: annihilation/decay into the channel, into , and into . In the first case gamma rays are produced through hadronization of annihilation products and subsequent pion decay. The resulting spectra are similar for all channels in which DM produces heavy quarks and gauge bosons and this channel is therefore representative for a large set of particle physics models. The choice of leptonic channels provided by the second and third scenarios, is motivated by the dark matter interpretation (9) of the PAMELA positron fraction (10) and the Fermi LAT electrons plus positrons (11) measurements. In this case, gamma rays are dominantly produced through radiative processes of electrons, as well as through the Final State Radiation (FSR). We produce the DM maps with a version of GALPROP slightly modified to implement custom DM profiles and injection spectra (which are calculated by using the PPPC4DMID tool described in (12)).
3 Approach to set DM limits
We use 24 months of LAT data in the energy range between 1 and 100 GeV (but, we use energies up to 400 GeV when deriving DM limits with no assumption on the astrophysical background). We use only events classified as gamma rays in the P7CLEAN event selection and the corresponding
P7CLEAN_V6 instrument response functions (IRFs)
3.1 DM limits with no assumption on the astrophysical background
To set these type of limits we first convolve a given DM model with the Fermi IRFs to obtain the counts expected from DM annihilation. The expected counts are then compared with the observed counts in our ROI and the upper limit is set to the minimum DM normalization which gives counts in excess of the observed ones in at least one bin, i.e. we set upper limits given by the requirement , where is the expected number of counts from DM in the bin and the actual observed number of counts.
3.2 DM limits with modeling of astrophysical background
In this analysis we model the diffuse emission as a combination of a dark matter and a parameterized conventional astrophysical signal and we derive the limits on the DM contribution using the profile likelihood method. More precisely, for each DM channel and mass the model which describes the LAT data best is the one which maximizes the likelihood function defined as a product running over all spatial and spectral bins ,
where is the Poisson distribution for observing events in bin given an expectation value that depends on the parameter set (, ). is the intensity of the DM component, represents the set of parameters which enter the astrophysical diffuse emission model as linear pre-factors to the individual model components (cf. equation 4 below), while denotes the set of parameters which enter in a non-linear way. We sample non-linear parameters of the astrophysical background on a grid (for computational efficiency).
The linear part of the fit is performed with the GaRDiAn code in the following way. The CR source distribution (CRSDs) is a critical parameter for DM searches and we define a parametric CRSD as sum of step functions in Galactocentric radius , and treat the normalization of each step as a free parameter in the fit to gamma rays
The sum over is the sum over all step-like CRSD functions, the sum over corresponds to the sum over all Galactocentric annuli (details of the procedure of a placement of the gas in Galactocentric annuli and their boundaries are given in (2)). denotes the gamma-ray emission from atomic and ionized interstellar gas
while the one from molecular hydrogen
The outlined procedure is then repeated for each set of values of the non-linear propagation and injection parameters to obtain the full set of profile likelihood curves. We scan over the three parameters: electron injection index, the height of the diffusive halo and the gas to dust ratio which parametrizes different gas column densities (see Table 1). In this way we end up with a set of profiles of likelihood , one for each combination of the non-linear parameters. The envelope of these curves then approximates the final profile likelihood curve, , where all the parameters, linear and non-linear have been included in the profile. Limits are calculated from the profile likelihood function by finding the values for which is and , for and 5 C.L. limits, respectively.
An important point to note is that, for each DM model, the global minimum we found lies within the 3(5) regions of many different models, providing a check against a bias in our procedure. This point is illustrated in Figure 1, where the profile likelihoods for the three nonlinear parameters, , and d2HI, are shown. To ease reading of the figure the profiling is actually performed with further grouping DM models with different DM masses, but keeping the different DM channels, DM profiles and the annihilation/decay cases separately. The curve for the fit without DM is also shown for comparison. Each resulting curve has been further rescaled to a common minimum, since we are interested in showing that several models are within around the minimum for each DM fit. The profile, for example, indicates that all models with from 1.9 to 2.4 are within around the minimum illustrating that the sampling around each of the minima for the six DM models is dense. Similarly, the d2HI profile indicates that all models with d2HI in the range (0.120 - 0.160) mag cm are within from the minima for each of the six DM models. Finally the profile indicates that basically all the considered values of are close to the absolute minima. This last result is not surprising since, within our low-latitude ROI, we have little sensitivity to different and basically all of them fit equally well. There is some tendency to favor higher values of when DM is not included in the fit, while with DM the trend is inverted. Although the feature is not extremely significant it is potentially very interesting.
Upper limits on the velocity averaged annihilation cross section into various channels are shown in Fig. 2, for isothermal
profile of the DM halo
Overall, rather than being due to residual astrophysical model uncertainties, the remaining major uncertainties in the DM constraints from the Halo region come from the modeling of the DM signal itself. The main uncertainty is in the normalization of the DM profile, which is fixed through the local value of the DM density. We use the recent determination GeV cm from (8), which has, however, a large uncertainty, with values in the range 0.2-0.7 GeV cm still viable. A large uncertainty in is particular important for annihilation constraints since they scale like , while for constraints on decaying DM the scaling is only linear. A less important role is played by the uncertainties in the DM profile, since in our region of interest different profiles predict similar DM densities. A better determination of the local DM density, as well as of the parameters determining the global structure of the DM Halo, is therefore of the utmost importance for reducing the uncertainties related to DM constraints from DM halo, but it is beyond the scope of this paper and is the subject of dedicated studies.
|Non linear Parameters||Symbol||Grid values|
|index of the injection CRE spectrum||1.800, 1.925, 2.050, 2.175, 2.300, 2.425, 2.550, 2.675|
|half height of the diffusive halo
||2, 4, 6, 8, 10, 15 kpc|
|dust to HI ratio||d2HI||(0.0120, 0.0130, 0.0140, 0.0150, 0.0160, 0.0170) mag cm|
|Linear Parameters||Symbol||Range of variation|
|eCRSD and pCRSD coefficients||,||0,+|
|local Hto CO factor||0-30 cm (K km s)|
|IGB normalization in various energy bins||free|
- CRSDs are traditionally modeled from the direct observation of tracers of SNR and can be observationally biased.
- It should be noted that in our case, where we mask along the plane, the expression actually simplifies considerably since only the local ring factor enters the sum, since all the other rings do not extend further than 5 degrees from the plane.
- Limits obtained using the NFW profile are only slightly better.
- The parameters , , , , , are varied together with as indicated in Table LABEL:pdiffusion.
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