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Methodology In this section we introduce the DMFIT tool (sec. 2.1 ) and give details on the GLAST simulations we employed in the present analysis (sec. 2.2 ). |
2.1 The DMFIT Tool DMFIT is a tool that calculates the gamma-ray flux resulting from the pair annihilation of generic WIMPs (i.e. of dark matter particles with specified mass and branching ratios into Standard Model final state annihilation modes). DMFIT is based on the same set of Monte Carlo simulations of hadronizat... |
. The simulations were carried out by the DarkSUSY team using Pythia 6.154 for a set of 18 neutralino masses ranging from 10 up to 5000 GeV, and for 8 “fundamental” Standard Model final states, namely the quark-antiquark pairs [MATH] [MATH] [MATH] , the charged lepton pairs [MATH] and [MATH] , the gauge boson pairs [MA... |
. This channel is not currently available in the latest publicly available DarkSUSY version. For it, we use the analytical approximation to the differential photon multiplicity for [MATH] provided in ref. |
, namely [EQUATION] While the Monte Carlo simulations extend down to a WIMP mass of 10 GeV, DMFIT allows to extrapolate to lower masses. Very light WIMPs have been recently shown to be relevant even in the context of supersymmetry |
, and they can possibly play a role in explaining the puzzling DAMA/LIBRA signal . For channels with heavy particles in the final state, such as [MATH] [MATH] and [MATH] , when the WIMP mass is below the kinematic threshold given by the final state particle mass the current version of DMFIT automatically switches to th... |
DMFIT consists of two data files and one Fortran routine. The code is available from the authors upon request. Conceptually, DMFIT reverse-engineers the use of the DarkSUSY package for the computation of gamma-ray spectra (see Fig. ). In DarkSUSY, the user supplies a given supersymmetric dark matter model, and the pack... |
For the present paper, we interfaced DMFIT with the spectral fitting package XSPEC . XSPEC allows the user to fit for a combination of more than one model at once, freezing or fitting model parameters as desired. By including more than one DMFIT model and imposing that the dark matter masses be the same, one can easily... |
, and to create versions compatible with other spectral fitting packages, including those provided with the GLAST Science Tools 2.2 GLAST Simulation Setup |
To simulate GLAST observations, we employ the GLAST observation simulator tool, gtobssim , part of the GLAST Science Tools package (v9r5p2) |
. All simulations were run for one year for a default scanning mode observation and using the Pass 5 source instrument response functions (P5_v13_0_source). For each source, spectral data files were provided to gtobssim (see sec. for model definitions) to define the source spectrum. For dark matter sources, images defi... |
(v49_600202RB) model provided as part of the GLAST external libraries distribution. In practice, the precise model of the Galactic diffuse emission used has little effect on our results as in all of the cases we consider the background is either dominated by point source emission, or the dark matter source is bright co... |
for a discussion on these Galactic diffuse setups). We comment on this at the end of sec. 5.2 . We did not include the extra-galactic diffuse background, although we did simulate it: in the Galactic center region, the extra-galactic diffuse background is irrelevant. Employing the power-law parametrization resulting fro... |
(which was been shown to likely be an overestimate of the actual extra-galactic gamma-ray flux in ), this component contributes, in an angular region of [MATH] around the center of the Galaxy, only 1-2% of the diffuse Galactic flux and around 50 photon counts above 1 GeV in one year of observation. We discuss this in m... |
Gamma-Ray Sources in the Galactic Center Region 3.1 Astrophysical Sources We include in the present study all gamma-ray sources detected to-date in an angular region of 4 degrees around the Galactic center. We model each source according to either fits to available gamma-ray data, or to spectral models resulting from a... |
3.1.1 3EG J1736-2908 Originally classified as unidentified , after INTEGRAL observations this EGRET source was identified with the X-ray source GRS1734-292 |
, associated with the active Galactic nucleus of a Seyfert 1 galaxy at a redshift of 0.0214 and 1.8 degrees from the Galactic center, having both radio jet and hard X-ray emissions |
. The analysis of ref. indicates that the EGRET source 3EG J1736-2908 exhibits significant time variability; Here, we consider the source median emission |
. 3EG J1736-2908 has no positional counterpart at TeV energies in the HESS survey of the inner Galaxy , which leads to an upper limit on the source above [MATH] GeV. Ref. |
showed that the best fit to 3EG J1736-2908 consists of a broken power law. Here we follow the analysis of ref. , and adopt for 3EG J1736-2908 the following spectrum: |
[EQUATION] The integrated flux above 0.1 GeV for this spectral model is [MATH] photons per cm per s. The integrated flux above 200 GeV is [MATH] , thus fully compatible with HESS limits |
. The location of the source is assumed to be coincident with the location of GRS1734-292 3.1.2 3EG J1744-3011, HESS J1745-303 Source counterparts for the extended unidentified very high energy gamma-ray source HESS J1745-303, 1.4 degrees from the Galactic center, were recently examined in ref. |
. Among possible matches, ref. discusses a supernova-remnant/molecular cloud association and a high spin-down-flux pulsar. The unidentified EGRET source 3EG J1744-3011 |
is also a plausible association from an energetic standpoint , while the positional coincidence with the HESS source is not conclusive |
. However, the position of HESS J1745-303 is well within the 95% uncertainty level region for 3EG J1744-3011. The third EGRET catalog quotes for 3EG J1744-3011 an integrated photon flux of [MATH] and a best-fit value for the spectral index in the 0.1 to 10 GeV range of [MATH] . The HESS data |
indicate for HESS J1745-303 a spectral index [MATH] (significantly softer than what was originally reported in ), and an integral flux between 1 and 10 TeV of [MATH] . Here, we assume that (a) HESS J1745-303 is a point-like source, (b) 3EG J1744-3011 is the same source (hence has the same position) as HESS J1745-303, a... |
[EQUATION] We determined the location of the power-law break, [MATH] GeV, by requiring a match to the integrated photon fluxes individually quoted for 3EG J1744-3011 |
and for HESS J1745-303 . We show the EGRET bow-tie, the HESS data and the spectrum outlined above in the left panel of Fig. . As discussed in ref. |
, the gamma-ray flux from hadronic sources is generically proportional to [MATH] , where [MATH] is the proton index at the source and [MATH] is the index of the diffusion coefficient |
. This allows for spectra that are quite soft in the TeV regime, and with different slopes in other energy bands . This argument motivates the broken power-law spectrum assumed here (and shown in the left panel of Fig. ), although a more complex setup is not excluded (see e.g. the discussion in |
). Using the spectral model outlined above, we obtain a total flux above 0.1 GeV of [MATH] 3.1.3 HESS J1747-281 [G 0.9+0.1] Very high energy gamma-rays were detected in 2004 by the HESS instrument from the composite supernova remnant G 0.9+0.1, approximately 1 degree from the Galactic center |
, and reported in ref. . The source is one of the weakest TeV sources ever detected, and is not associated with any counterpart in the EGRET catalogs |
. The location of the source is consistent within the statistical errors with the position of the pulsar wind nebula in G 0.9+0.1 |
. Ref. estimates an integrated flux above 200 GeV of [MATH] , assuming a photon index [MATH] . The broadband emission from G 0.9+0.1 was fitted in ref. |
with a one-zone inverse Compton model featuring a parent population of accelerated electrons with a broken power-law spectrum (spectral index 0.6 below 25 GeV and of 2.9 above 25 GeV), and assuming a uniform magnetic field strength [MATH] G within the pulsar wind nebula. The dominant radiation field off of which the ac... |
. Here, we assume the same setup, and show the spectral energy distribution ( [MATH] ) we obtain in the right panel of Fig. , together with the HESS data. The spectral model we adopt gives an integrated flux above 0.1 GeV of [MATH] and of [MATH] above 200 GeV, and is consistent with the EGRET non-detection of this sour... |
3.1.4 3EG J1746-2851 and HESS J1745-290 [Sgr A EGRET observed a pronounced source excess at the Galactic center position , subsequently designated in the second (third) EGRET catalog by 2EG (3EG) J1746-2852 |
. The source location in the energy range above 500 MeV indicated perfect compatibility with the Galactic center . A subsequent re-analysis |
used the point spread function as determined by the pre-flight EGRET calibration for 6 energy bins above 1 GeV, and found that the location of 3EG J1746-2851 is off-set from the Galactic center at a high confidence level. Ref. |
indicates that the best fit source position is at [MATH] and [MATH] . Subtracting the diffuse emission and allowing for a total source-excess extent up to [MATH] , ref. |
attributes to 3EG J1746-2851 a flux excess of [MATH] above 0.1 GeV. The photon spectrum quoted in is well represented by a broken power law with a break energy of 1.9 GeV. The best fit broken power-law spectrum from the EGRET data is |
[EQUATION] Ref. showed that the spectrum reported in can also be well fitted by a scenario where, in addition to the diffuse Galactic gamma-ray background, 3EG J1746-2851 is fueled by WIMP pair annihilation in the Galactic center. This interpretation prefers rather light WIMPs ( [MATH] GeV) and large pair annihilation ... |
. We show the EGRET data as the red solid contours in Fig. . The somewhat conservative error bars also include the uncertainty in the energy determination according to the binning employed in |
Gamma-ray emission above 100 GeV from the direction of the Galactic center was recently reported by several ground-based gamma-ray observatories, including CANGAROO |
, VERITAS , HESS and MAGIC . Here, we will focus on the high-statistics 2003 and 2004 HESS data from the point-like source HESS J1745-290, compatible with the gravitational center of the Galaxy. No unique identification of HESS J1745-290 has been possible so far, but at least three different astrophysical objects have ... |
); Second, the location of HESS J1745-290 is compatible with the supernova remnant Sgr A East, featuring bright shell-like radio emission surrounding Sgr A itself |
; Third, a candidate pulsar wind nebula, G359.95-0.04, was recently discovered [MATH] away from Sgr A in a deep Chandra survey of the Galactic center region |
. In addition, the possibility of associating HESS J1745-290 with WIMP dark matter annihilation was addressed in . The latter interpretation would require large WIMP masses and pair annihilation cross sections, which, although theoretically possible, appear to be rather unnatural from a theoretical particle physics sta... |
. Fig. shows in green the HESS data from the 2003 observations and in blue those from the 2004 observations In the present study we consider three different scenarios to model the gamma-ray sources 3EG J1746-2851 and HESS J1745-290: |
Scenario 1 . The two gamma-ray sources are two different individual sources, with 3EG J1746-2851 offset from the Galactic center as in |
. A two-source model was for instance proposed in ref. , where HESS J1745-290 is associated to Sgr A , while 3EG J1746-2851 is mostly fueled by the supernova remnant Sgr A East. Extrapolating Eq. ( ) up to energies probed by HESS, however, vastly over-predicts the flux of very high energy gamma-rays actually measured. ... |
, including the possibility that the EGRET source is associated to a young pulsar with gamma-ray properties similar to Vela, but with a larger gamma-ray power |
. To model the EGRET source, we modify here the 3EG J1746-2851 spectrum from multiplying the spectrum in ( ) by an exponential cut-off factor [MATH] . As in |
, we choose the cutoff scale [MATH] GeV, which could indeed be plausible in the young pulsar scenario . The model is shown by the black solid line in Fig. labeled “Scenario 1”. The integrated photon flux above 0.1 GeV for this source is [MATH] |
As far as the HESS J1745-290 source is concerned, we adopt here the black hole plerion model of ref. . In this scenario, a sub-relativistic outflow of particles from an inner, inefficiently radiating magnetized corona, i.e. the advection-dominated accretion flow, powers a black-hole plerion where both the X-ray and TeV... |
, the broadband emission of several hadronic models, extrapolated in the energy range relevant for GLAST, would be comparable to what we use here. In particular, we implemented models based on both photo-meson processes and on proton-proton collisions, as described in |
, and find that the impact on the ability of GLAST to reconstruct dark matter particle properties using these models instead of the black hole plerion setup is negligible. To appreciate this point, we compare the integrated photon flux above 0.1 GeV for the three mentioned models. We obtain a flux of [MATH] for the bla... |
Scenario 2 . We assume for this scenario that 3EG J1746-2851 and HESS J1745-290 actually correspond to the same source, and are thus positionally coincident with the Galactic center. We refer to the spectrum resulting from the curvature radiation-inverse Compton model described in |
. In this scenario, electron acceleration is produced by the ordered rotation-induced electric fields near Sgr A . Electron radiative losses consist of both curvature radiation and inverse Compton scattering. While the inverse Compton scattering on IR photons of the highest energy electrons produces an emission peaking... |
, possibly reproducing the gamma-ray emission detected by EGRET. The details of the GeV peak depend on the configuration of the magnetic field in the acceleration zone, which in turn could spoil the assumption of isotropic electron emission assumed in Fig. 6 of |
, where the GeV emission actually exceeds the EGRET data. We therefore assumed that the broadband emission for this model is compatible with the data in |
by assuming a suppressed curvature radiation emission in the GeV range. We show the resulting spectral energy distribution with the dashed line in Fig. , labeled “Scenario 2”. The integrated gamma-ray flux above 0.1 GeV for this scenario is [MATH] |
Scenario 3 . As pointed out above, 3EG J1746-2851 might be associated with dark matter annihilation. We assume for this scenario that this is indeed the case, and define below a supersymmetric dark matter setup (DM model C) that provides a good fit to the EGRET data, while at the same time being consistent with the oth... |
We summarize the positions and integrated gamma-ray fluxes (above 0.1, 1 and 5 GeV) for all the sources considered in the present study in Tab. |
3.2 Dark Matter Models Our choice of the particle dark matter models for the present study was motivated by the following four guidelines: |
1. we wish to span a reasonable range of masses and final state branching ratios; 2. we choose theoretically well motivated particle physics frameworks that can be easily reproduced with publicly available computational tools; |
3. we require a neutralino thermal relic abundance in accord with the cosmological cold dark matter density 4. we require models be consistent with gauge coupling unification as well as with collider searches and other particle physics constraints. |
Our models A and B are defined, in the context of the constrained minimal supersymmetric Standard Model (CMSSM), by the Grand Unification scale values of the universal scalar soft-breaking mass [MATH] , gaugino mass [MATH] , trilinear scalar coupling [MATH] , by the ratio of the two Higgs doublets vacuum expectation va... |
As described above, we picked model C augmenting the four requirements above by the request that the gamma-ray spectrum give a reasonable fit to the spectrum of the unidentified source 3EG J1746-2851 close to the Galactic center. In turn, this implies a low neutralino mass, [MATH] GeV, as shown e.g. in |
. Such low neutralino masses are not easily found in the context of the CMSSM, while they can naturally arise in models with a light Higgs spectrum, see e.g. |
. We thus resorted to defining DM model C by specifying weak-scale values for the relevant supersymmetric parameters (see Tab. ). Notice that DM model C is very close to the benchmark scenario [MATH] -max of ref. |
, but the input parameters were massaged in order to achieve the desired neutralino relic abundance and to suppress the branching ratio [MATH] through cancellations between the squark and charged Higgs mediated contributions. |
We give snapshots of the particle spectra of models A, B and C in Tab. . In the table we list the masses, in GeV, of the lightest CP even Higgs ( [MATH] ), of the gluino ( [MATH] ), the lightest stop ( [MATH] ) and stau ( [MATH] ), the lightest first generation squark ( [MATH] ), the lightest chargino ( [MATH] ), and t... |
. As a side comment, we notice that all the models we employ feature rather light particle masses. We expect all of these models to give detectable signatures at the Large Hadron Collider (see e.g. the estimates of ref. |
and ). We collect in Tab. astrophysically relevant properties of the models under consideration here. In particular, we specify the lightest neutralino mass ( [MATH] ) in GeV, the neutralino relic abundance ( [MATH] ), the thermally averaged pair annihilation cross section times velocity, computed at [MATH] [MATH] ) in... |
Different mechanisms drive the neutralino relic abundance in the three models we consider here. In particular, model A lies in the so-called stau co-annihilation region |
, where the quasi-degeneracy of the lightest neutralino and stau entails a suppression of the otherwise excessive neutralino relic abundance via efficient stau-neutralino and stau-stau annihilation processes. DM model B lies in the focus point region |
, where the [MATH] parameter is driven to a relatively small value by a large GUT-scale input universal scalar soft-breaking mass. A large higgsino fraction and co-annihilation processes with the next-to-lightest higgsino-like neutralinos and chargino dictate a sizable effective annihilation rate, with a dominant gauge... |
. DM model C features a light neutralino that mainly pair-annihilates through light Higgs exchange. It can be thought of as a “bulk region” type model |
Since the scope of the present analysis is to assess the potential of GLAST to pinpoint particle dark matter properties, we purposely choose here a somewhat optimistic dark matter density profile towards the Galactic center. The reference setup is an adiabatically contracted version of the Navarro et al. profile outlin... |
. This model is implemented in DarkSUSY as profile “ adiabsm ” and is close to the widely used Moore profile . Our reference model features in fact an inner slope scaling with the galacto-centric radius approximately as [MATH] . Our choice is physically well motivated by the scenario of adiabatic contraction of dark ma... |
. For the sake of comparing with previous studies, in addition to our reference profile we also consider a Navarro, Frenk and White (NFW) profile |
for DM model B, with scaling radius [MATH] kpc and scaling density [MATH] . Other dark matter density profiles are also consistent with available data on the distribution of matter in the Galaxy |
, including cored profiles . For the latter, supersymmetric dark matter models would generically give a negligible gamma-ray flux, and an analysis similar to what we present here would be impossible. Notice that we neglect here the effect of dark matter clumpiness, that generically contributes to enhance the gamma-ray ... |
The gamma-ray signal from dark matter annihilation can be cast, in the notation of , as [EQUATION] where [EQUATION] is the line-of-sight dark matter density squared in the [MATH] direction averaged within the solid angle [MATH] , and where [MATH] is the relative differential photon yield for Standard model final state ... |
In order to fit the EGRET data on 3EG J1746-2851 with our DM model C, we needed to rescale the integrated line-of-sight dark matter density squared for that model by a factor 2.3. This means that for DM model C, the profile we use is assumed to be slightly less peaked in the innermost region (a slope intermediate betwe... |
We quote in Tab. the integrated gamma-ray fluxes, in different angular regions and above different gamma-ray energy thresholds, for the three DM models and for model B for the case of the NFW profile. We also give the fluxes from the [MATH] and [MATH] final state modes. Notice that the scaling of fluxes with angle for ... |
We show the spectral energy distribution ( [MATH] ) for the gamma-ray emission resulting from neutralino pair annihilation for models A, B and C in Fig. . In the figure, we do not include the monochromatic line emissions. |
DMFIT: Modeling Simulated Dark Matter Sources In this section, we examine fits to the simulated GLAST spectra from dark matter only, prior to considering the full complications of the Galactic center. This analysis is broadly applicable to any relatively isolated gamma-ray source which may have a dark matter origin (lo... |
. For instance, the brightest clump considered in ref. features, for 5 years, the same order of magnitude of photon counts as we consider here. Alternatively, the signal we employ can be thought to refer to a less luminous clump, but with a WIMP model with a larger pair-annihilation rate. |
4.1 Example: 3EG J1746-2851 Here we address the question of the origin of 3EG J1746-2851 by simulating GLAST observations for both the DM model C and for the broken power-law models (plus exponential cut-off) assumed for the EGRET spectrum of this source (Scenario 1, see Eq. ( ) and ref. |
). As pointed out in ref. , the class of astrophysical sources that could be most easily confused with a dark matter annihilation signal are in fact gamma-ray pulsars, whose spectra can be modeled with a power-law plus exponential cut-off ( [MATH] |
. Notice that our spectral model corresponds here, at large energies, to [MATH] [MATH] GeV and [MATH] The simulated spectra we use here are extracted within a radius of one degree and contain [MATH] 11,000 and [MATH] 15,000 photons detected at energies above 1 GeV, respectively. Fitting the dark matter spectrum ( [MATH... |
Here we have assumed the true dominant final state, [MATH] , in our dark matter fits. However, employing instead a [MATH] final state or a [MATH] final state (with [MATH] constrained to be greater than [MATH] GeV) gives unacceptable fits to both the DM model C and Scenario 1 spectra, so these final states are effective... |
As remarked in ref. , a spectrum with a hard power law plus an exponential cutoff, as expected for a gamma-ray pulsar , is potentially problematic to distinguish from a dark matter annihilation spectrum, depending on the source brightness. We find that we can tell the two shapes apart, in the case of DM model C (as wel... |
. As also pointed out in ref. , other handles beyond a spectral analysis nonetheless exist to discriminate between an astrophysical source such as a gamma-ray pulsar and a dark matter signal. These include for instance source variability (see for instance Ref. |
and , where blind searches for a pulsed component in the high energy data were suggested), spatial extent, location and multi-wavelength counterparts |
From the example discussed in this section, we see that in one year GLAST will easily determine the spectral shape of 3EG J1746-2851 and, if it is the result of dark matter annihilation, determine the dark matter particle mass with high precision. Given knowledge of the dark matter density profile, we can also recover ... |
4.2 Extracting Particle Properties The simulated one year GLAST spectra for DM models A and B have [MATH] and [MATH] counts in the energy range [MATH] GeV and within a radius of 1 degree, respectively. The fact that the dark matter particle mass is significantly higher for these models than for model C and the relative... |
mean that we can easily limit the energy range to [MATH] GeV without losing significant photon statistics (see Fig. ). Using a higher energy cut is also advantageous when considering the affect of background sources (see sec. 5.1 ). |
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