A realistic assessment of the CTA sensitivity to dark matter annihilation
Hamish Silverwood, Christoph Weniger, Pat Scott, Gianfranco Bertone
PPrepared for submission to JCAP
A realistic assessment of the CTAsensitivity to dark matter annihilation
Hamish Silverwood, a Christoph Weniger, a Pat Scott b andGianfranco Bertone a a GRAPPA, University of AmsterdamScience Park 904, 1098 XH Amsterdam, The Netherlands b Department of Physics, Imperial College London,Blackett Laboratory, Prince Consort Road, London SW7 2AZ, United KingdomE-mail: [email protected], [email protected], [email protected],[email protected]
Abstract.
We estimate the sensitivity of the upcoming CTA gamma-ray observatory to DMannihilation at the Galactic centre, improving on previous analyses in a number of significantways. First, we perform a detailed analyses of all backgrounds, including diffuse astrophysicalemission for the first time in a study of this type. Second, we present a statistical frameworkfor including systematic errors and estimate the consequent degradation in sensitivity. Theseerrors may come from e.g. event reconstruction, Monte Carlo determination of the effectivearea or uncertainty in atmospheric conditions. Third, we show that performing the analysison a set of suitably optimised regions of interest makes it possible to partially compensatefor the degradation in sensitivity caused by systematics and diffuse emission. To probedark matter with the canonical thermal annihilation cross-section, CTA systematics likenon-uniform variations in acceptance over a single field of view must be kept below the0.3% level, unless the dark matter density rises more steeply in the centre of the Galaxy thanpredicted by a typical Navarro-Frenk-White or Einasto profile. For a contracted r − . profile,and systematics at the 1% level, CTA can probe annihilation to b ¯ b at the canonical thermallevel for dark matter masses between 100 GeV and 10 TeV. a r X i v : . [ a s t r o - ph . H E ] S e p ontents Fermi -LAT experiments 2 J factors 95.2 Statistical framework 105.3 Background treatment 12 Current and upcoming gamma-ray experiments are ideally suited to probing the nature ofdark matter (DM), by searching for high-energy photons from annihilation of Weakly Inter-acting Massive Particles (WIMPs; [1–5]). Other so-called indirect
DM detection strategiesinclude searches for neutrinos [6–11] or anti-matter [12–18] produced by DM annihilation.Indirect detection is particularly appealing at the present time, owing to a lack of convinc-ing evidence from DM direct detection [19–24], which seeks to measure energy exchanged incollisions between nuclei and DM in underground experiments, and collider searches lookingfor new particles at the Large Hadron Collider [5, 25–28].Recent data from the Large Area Telescope (LAT) aboard the
Fermi satellite set strin-gent and robust limits on the annihilation cross section of WIMPs as a function of the DMparticle mass, based on a lack of excess gamma-ray emission from dwarf spheroidal galaxies[29].
Fermi data have also led to the discovery of excess emission from the Galactic cen-tre (GC), which has been interpreted in terms of DM annihilation (see e.g. Ref. [30] andreferences therein). Furthermore, the Imaging Air Cherenkov Telescopes (IACTs) HESS,VERITAS and MAGIC search for DM signals in dwarf spheroidal galaxies and the GC [31–33], with the current strongest limits on TeV-scale DM coming from HESS observations ofthe GC [34]. – 1 –ne of the next major steps in high-energy gamma-ray astrophysics will be the construc-tion of the Cherenkov Telescope Array (CTA), which is currently in the design phase [35]and expected to start operations in 2019. Several estimates of the sensitivity of CTA togamma-rays from DM annihilation exist in the literature. All of these agree on the fact thatCTA will improve existing constraints for values of the DM particle mass above O (100) GeV,but substantial differences exist, up to one order of magnitude or more in annihilation crosssection for a given mass, depending on the assumptions made about the telescope arrayconfiguration, analysis setup and observation time [36–38].In this paper we carry out a new estimation of the sensitivity of CTA to DM annihilation,and compare this to the sensitivity of Fermi . We improve on previous analyses in a numberof ways. First, we present a detailed discussion of all backgrounds, including cosmic-rayprotons and electrons, and for the first time in the context of CTA and DM, the effects of thediffuse astrophysical emission. We estimate this from
Fermi -LAT data, suitably extrapolatedabove 500 GeV in order to cover the range of energies relevant for CTA. Second, we study theimpact of systematic errors. There are many sources of systematic uncertainty inherent inCTA measurements: event reconstruction, Monte Carlo determination of the effective area,and uncertainty in atmospheric conditions [35]. A detailed assessment can only realisticallybe performed by the CTA Collaboration itself after the instrument is built; here we insteadpresent a simple but comprehensive statistical framework with which the impacts of thesesystematics on the sensitivity of CTA to DM annihilation can be illustrated and evaluated.Third, we show that performing the analysis over a series of suitably optimised regions ofinterest (RoIs) partially compensates for the degradation in sensitivity due to systematics andbackgrounds. We carry out a multi-RoI ‘morphological’ analysis of the gamma-ray emission,and demonstrate how it improves the CTA sensitivity to DM compared to the so-called ‘Ring’method previously discussed in the literature [36].The paper is organised as follows: in Sec. 2 we describe the CTA and
Fermi -LATexperiments; in Sec. 3 we review the basics of indirect detection with gamma-rays; in Sec. 4we discuss and quantify the cosmic-ray and diffuse gamma-ray background for CTA; in Sec.5 we present our analysis strategy, in particular the implementation of systematic errors andthe RoIs relevant for our analysis; we present our results in Sec. 6 and conclusions in Sec. 7.
Fermi -LAT experiments
Gamma rays in the GeV to TeV regime initiate electromagnetic cascades in the atmosphere,which start at an altitude of 10–20 km and generate a focused cone of Cherenkov light thattypically covers several hundred meters on the ground. Air Cherenkov telescopes detectgamma rays by observing this dim Cherenkov light with optical telescopes. The overall lightyield, the shape and the orientation of the air shower gives information about the energyand arrival direction of the gamma ray. Because observations can only be performed during(nearly) moonless nights, the observation time per year is limited to approximately 1000hours.Current active Imaging Air Cherenkov Telescopes (IACTs) are HESS II (Namibia; [39]),VERITAS (Arizona; [40]), and MAGIC (La Palma ). Although all three instruments have anactive program to search for DM signals in various regions of the sky (see e.g. Refs. [31–33]), http://magic.mpp.mpg.de/ – 2 –nly HESS can observe the GC high above the horizon ( θ z ∼ ◦ , compared to θ z (cid:38) ◦ forVERITAS and MAGIC). As a shorter transmission length through the atmosphere allowsfor a lower threshold energy, HESS is ideally situated to search for DM signals from theGC. Non-detection of a DM signal by HESS provides the strongest current limits on the DMself-annihilation cross section, for DM masses around the TeV scale [34].CTA will consist of several tens of telescopes of at least 3 different types, with sizesbetween about 5 and 24 meters, covering an area of several square kilometres. The sensitivitywill be a factor ten better than current instruments, the field of view (FoV) will be up to 10 ◦ in diameter, and the energy threshold O (10 GeV).CTA is envisaged as a two-part observatory, with southern and northern sites. CTASouth is the most relevant for DM searches towards the Galactic centre. The location ofthe southern array has not yet been settled, but the main candidates are now the KhomasHighlands in Namibia and Cerro Paranal in Chile. The final design is also not yet fixed.Apart from construction and maintenance questions, relevant remaining design choices arethe relative emphasis on higher or lower energies, the angular and energy resolution, and theFoV. A first detailed Monte Carlo (MC) analysis was presented in Ref. [41], where 11 differentconfigurations for the southern array were discussed. Depending on the array configurationand gamma-ray energy, the point source sensitivity varies within a factor of five, and canbe further improved by about a factor of two with alternative analysis methods [41].In this paper we will concentrate on the proposed configuration known as ‘Array I’ [41], which is a balanced configuration with three large ( ∼
24 m aperture), 18 medium ( ∼
12 m) and56 small telescopes ( ∼ (cid:46) at its threshold energy of 20 GeV, which thenincreases quickly with energy to about 4 × m at 1 TeV and 3 × m at 10 TeV. Theangular resolution in terms of the 68% containment radius is about r (cid:39) . ◦ at threshold,and drops to below 0 . ◦ at energies above 1 TeV. The energy resolution is relatively largeat threshold, with σ ( E ) /E (cid:39) This is based on the adoption of a standard Hillas-based analysis. This is a classical analysis method,based on zeroth (amplitude), first (position) and second (width and orientation) momenta of the images [42]. In particular, we adopt the version based on the Hillas-parameter analysis of the MPIK group. Thechoice of analysis method can impact the projected sensitivity; e.g. the Paris-MVA method produces aneffective area that is at energies around 1 TeV about ∼ ∼ . – 3 – − ‘ [deg] − − G a l a c t i c L a t i t ud e b [ d e g ] ONOFF − − ‘ [deg] − − G a l a c t i c L a t i t ud e b [ d e g ] Figure 1 . The different RoIs that we consider in this paper. The red star indicates the GC, whilethe blue star indicates the centre of the FoV.
Left:
RoIs used in the Ring method of Ref. [36] as‘signal’ and ’background’ regions; we refer to these as simply ‘ON’ and ‘OFF’ regions, respectively.A diagram detailing the construction of the annulus and the ON-OFF RoIs is given in Ref. [36], andthe exact dimensions we use are given in Subsection 5.1.
Right:
Separation of the ON and OFF RoIsinto 28 sub-RoIs, which we use in our morphological analysis.
In fact, in the case of searches for DM particles with GeV to TeV masses, these systematicswill turn out to be one of the limiting factors. Detailed instrumental uncertainties (e.g. thecovariance matrix of reconstruction efficiencies in different regions of the FoV) will probablyonly become available once the instrument starts to operate, so in this paper we resort to afew well-motivated benchmark scenarios.The traditional observing strategy employed by IACTs in searching for DM annihilation(e.g. Ref. [34]) involves defining two regions on the sky expected to have approximately thesame regular astrophysical emission, but different amounts of DM annihilation. The regionwith the larger expected annihilation is dubbed the ‘ON’ region, the other is called the ‘OFF’region, and the analysis is performed using a test statistic defined as the difference in photoncounts from the two regions. This is referred to as an ‘ON-OFF’ analysis, and obviouslyobtains the most power when the ON and OFF RoIs are chosen to differ as much as possiblein their predicted annihilation rates.The RoIs chosen for ON-OFF analyses may lie in the same or very different FoVs.Different FoVs allow a greater contrast in DM signal between ON and OFF regions, but havethe potential to introduce differential systematics across the two FoVs. The ‘Ring method’[36] is an ON-OFF analysis technique optimised for DM searches towards the GC with IACTs,which fits the ON and OFF regions into a single FoV, producing an approximately constantacceptance across the entire analysis region. Although both regions are expected to containDM and background contributions, in the Ring method the ON and OFF regions are typicallyreferred to as the ‘signal’ and ‘background’ regions. For simplicity, here we just call themON and OFF.A simple way to model the results of an ON-OFF analysis is to construct a Skellam likeli-hood [38, 43, 44], which is based on the expected difference between two Poisson counts (i.e. inthe ON and OFF regions). However, once the assumption that astrophysical backgrounds areidentical in the ON and OFF regions becomes questionable, a more straightforward method– 4 –s simply to carry out a regular binned likelihood analysis. In this case, one predicts thephoton counts in each RoI using detailed background and signal models, and compares themdirectly to the absolute number of photons observed in each RoI. This is the strategy thatwe investigate here for CTA, using both the original Ring method RoIs and a finer spatialbinning. We show these two sets of RoIs in Fig. 1, and discuss their optimisation in Sec. 5.We still refer to the two-RoI analysis as the ‘Ring method’ even though we carry out a fulllikelihood analysis rather than an ON-OFF analysis. We refer to the multi-RoI analysis asa ‘morphological analysis’, as it uses the expected spatial distribution of the DM signal toimprove limits.
The LAT aboard the
Fermi satellite is a pair-conversion detector, with a large FoV and anenergy range from 30 MeV to above 300 GeV. Since its launch in 2008 the dominant observa-tion strategy has been a full-sky survey providing roughly equal exposure in all directions ofthe sky. The
Fermi -LAT is a formidable tool in the search for signals of DM annihilation. Itcurrently provides the strongest constraints on the DM self-annihilation cross section, basedon a combined observation of 15 dwarf spheroidal galaxies [29].The
Fermi -LAT provides an accurate measurement of the Galactic diffuse emission(GDE) up to energies of about 100 GeV. Above 100 GeV the number of detected photonsbecomes very small, due to the LAT’s comparatively small effective area ( ∼ ). Thisis about the energy where the acceptance of IACTs starts to become sizable. Close to theGalactic disc and the GC, LAT measurements are actually dominated by GDE. This diffuseemission will be a critical foreground for any DM search, and—depending on the details ofthe search strategy—might mimic a DM signal.Compared to IACTs, the LAT is an extremely clean gamma-ray telescope. Its plasticscintillator anti-coincidence detector, together with cuts on different event reconstructionquality estimators, allows proton and electron contamination in the gamma-ray sample tobe suppressed to a level well below the very dim extragalactic gamma-ray background. Themain uncertainties in the measured fluxes, especially at the high energies we are interestedin, are hence of a statistical nature. The systematic uncertainty of the effective area is at thelevel of 10% [45], so we will neglect it throughout. Assuming that the annihilation cross-section of DM does not depend on the relative velocitybetween particles, the calculation of the gamma-ray flux from DM annihilation can be dividedinto two parts.The first part accounts for the DM distribution, and is commonly known as the ‘ J -factor’. This is an integral of the DM density squared along the lines of sight (l.o.s.) withina cone ∆Ω that covers a certain RoI: J (∆Ω) = (cid:90) ∆Ω dΩ (cid:90) l.o.s d l ρ DM ( r ) . (3.1)The DM density profiles seen in N -body simulations of Milky-Way type galaxies are best fitby the Einasto profile [46] ρ DM ( r ) ∝ exp (cid:18) − α (cid:20)(cid:18) rr s (cid:19) α − (cid:21)(cid:19) , (3.2)– 5 –hich we assume for our calculation of the J -factors for the GC. We normalise to a local DMdensity of ρ DM ( r (cid:12) ) = 0 . − , choosing α = 0 . r s = 20 kpc, and r (cid:12) = 8 . ρ DM ( r ) ∝ r γ ( r s + r ) − γ , (3.3)where γ = 1 . r s = 20 kpc thescale radius. We normalised this profile in the same way as the Einasto profile (Eq. 3.2).The second part of the flux calculation covers the actual particle model for DM. Togetherwith the J -factor, it yields the differential flux of DM signal photons,dΦd E = (cid:104) σv (cid:105) π m d N γ d E J (∆Ω) . (3.4)Here (cid:104) σv (cid:105) is the velocity-averaged DM self-annihilation cross section, in the limit of zerorelative velocity. The DM mass is given by m DM , and d N γ / d E is the annihilation spectrum,i.e. the average number of photons produced per annihilation per energy interval, whichdepends on the particular annihilation channel. For the gamma-ray yields, we will take theresults from Ref. [48].To calculate the expected number of signal events in a given observing time T obs , betweenenergies E and E , we weight Eq. (3.4) by the energy-dependent effective area A eff andintegrate over the energy range in question, µ DM = T obs (cid:90) E E d E dΦd E A eff ( E ) . (3.5)Note that for simplicity, throughout this paper we neglect the effects of the finite angularand energy resolution of CTA, as well as variations of the effective area within the FoV. Asdiscussed above, the 68% containment radius of the point spread function (PSF) is around θ (cid:39) . ◦ at the lowest energies that we consider, and significantly better at high energies.This is significantly smaller than the RoIs that we adopt ( cf. Fig. 1). The energy resolutionat 20 GeV is however quite large ( σ ( E ) /E (cid:39) b ¯ b spectrum with a log-normal distribution with a width of σ (ln E ) / ln E = 50%increases the peak signal flux relative to an assumed E − background by a factor of about 1.5;for σ (ln E ) / ln E = 20% this drops to a factor of 1.1. This is mostly due to event migrationfrom smaller to higher energies. Neglecting the finite energy resolution of CTA will henceaffect our projected limits at most by a few tens of percent. The dominant backgrounds for DM searches at the GC are the GDE and, in case of IACTs,the flux of cosmic rays that pass the photon cuts. Here we discuss the characteristics of thesecomponents, and describe how they enter our analysis. For an analysis including the effects of energy resolution see Ref. [38]. – 6 – .1 Cosmic-ray background
CR electrons constitute an essentially irreducible background for gamma-ray observationswith IACTs, because the electromagnetic cascades that they induce are practically indistin-guishable from those caused by gamma rays. A possible way to discriminate between thetwo is to use the detection of Cherenkov light from the primary particle as a veto. Thisis however beyond the reach of current and next-generation instruments [35]. Due to theirrelatively soft spectrum, CR electrons are especially relevant at low energies, were they areresponsible for most of the measured flux of particles that are either gamma rays or electrons.We parameterise the electron flux per unit energy and solid angle asd φ d E dΩ = 1 . × − (cid:18) E TeV (cid:19) − Γ (GeV cm s sr) − , (4.1)with Γ = 3 . E < . E > (cid:15) p ∼ − to 10 − for current instruments. The electrons produced in electromagneticcascades from neutral pion decay are the dominant contributors to the detectable Cherenkovlight. This means that if a cosmic-ray proton with a given energy is mistakenly reconstructedas a gamma-ray, the gamma-ray is usually reconstructed to have roughly a third as muchenergy as the actual incoming proton.Here we adopt the proton flux per unit energy and angle [51]d φ d E dΩ = 8 . × − (cid:18) E TeV (cid:19) − . (GeV cm s sr) − , (4.2)which we shift to lower energies by a factor of 3 to account for the reduced Cherenkovlight emitted by hadronic showers [52]. We note that in principle heavier CR species arerelevant, especially He, but these can be effectively accounted for by increasing the protoncut efficiency factor (cid:15) p .Throughout the present analysis, we will adopt a proton cut efficiency of (cid:15) p = 10 − fordefiniteness. We note, however, that assuming that the proton rejection factor is constantacross all energies is a simplification. At lower energies shower shape cuts are less effectiveat discriminating CR protons from gamma-rays. Thus our CR proton background is un-derestimated at low energy, yielding a slight over-estimation of sensitivity at low energies.However, even with this approximation we are still able to reproduce the background ratesshown in Ref. [41] for Array I to within a factor of two, for energies of up to 10 TeV. We notethat when switching off protons entirely (which corresponds to (cid:15) p = 0) the background ratesremain practically unchanged at energies below 2 TeV, as in our setup they are dominatedby electrons. We also checked that with our assumptions we can reproduce the point source– 7 – Gamma-ray energy E [GeV]10 − − − − − − − D i ff e r e n t i a li n t e n s i t y E d φ / d E [ G e V c m − s − s r − ] → ExtrapolationGC, χχ → ¯ bb h σv i = 3 × − cm s − m χ = 1 TeV BG ( e − + hadr.)hadr. ( (cid:15) p = 10 − ) e − diff. γ -rays (ON)diff. γ -rays (OFF)DM spectrum (ON)DM spectrum (OFF) Figure 2 . Background fluxes relevant for our analysis. Isotropic CR backgrounds are shown in black:protons with an assumed cut efficiency of (cid:15) p = 10 − (black dotted), electrons (black dashed), andtotal isotropic CR backgrounds (black solid). Galactic diffuse emission (GDE) is shown in red, andan example spectrum of DM annihilating to gamma-rays via b ¯ b is shown in green. We give the DMand GDE curves for the ON and OFF regions defined in the Ring Method, as described in Section 3.Beyond 500 GeV, we extrapolate the GDE spectrum using a simple power law. sensitivity for Array I to within a factor of two below 100 GeV, and within a few tens ofpercent above.While the flux of CRs is isotropic across the sky, their acceptance by CTA is not. Thecharacterization of this variation in CR acceptance rates is a non-trivial task, and methods todeal with non-isotropic acceptance rates are discussed in [53]. For this analysis we make thesimplification of assuming an isotropic CR acceptance, though we note that our statisticalframework can accommodate anisotropic uncertainties in the combined CR and gamma-rayacceptance, as discussed in Subsection 5.2.As formal gamma-ray and CR electron efficiencies we adopt (cid:15) γ = (cid:15) e = 1, and note thatthese values (along with (cid:15) p ) are defined with respect to the effective area of Array I fromRef. [41].In Fig. 2, we show the contributions from CR electrons and protons assuming (cid:15) p = 10 − ,and their sum. Note that in the highest energy range that we consider in this work, 6.7 to10 TeV, 100 hr of CTA observations lead to approximately 7 . × or 1 . × CR backgroundevents in the OFF and ON regions, respectively. For comparison we also show the gamma-rayflux from a reference DM annihilation signal, based on a thermal annihilation cross sectionand a DM mass of 1 TeV, within the ON and OFF regions employed in our version of theRing method ( cf.
Section 3). The CR foreground is stronger than the DM signal by 2–3orders of magnitude. Fig. 2 also shows a reference GDE gamma-ray background spectrum,– 8 –hich we discuss next.
In 2006 HESS discovered diffuse gamma-ray emission from the GC at energies of 0.2–20 TeV[54]. The emission was found to be correlated with molecular clouds in the central 200 pc ofthe Milky Way, and is confined to Galactic latitudes | b | < . ◦ and longitudes | (cid:96) | < . ◦ . Thespectrum suggests a hadronic origin. The absence of evidence for diffuse emission outsidethis window strongly influenced the choice of search regions for DM signals in previousanalyses [34, 36].Below 100 GeV, the GDE has been measured extremely well by the Fermi -LAT [55].At these energies, it is expected to be dominated by π decay from proton-proton interactionand bremsstrahlung. Diffuse gamma rays below 100 GeV are an important background insearches for TeV-scale DM, particularly with CTA, which will have an energy threshold oftens of GeV.To estimate the amount of GDE in different sky regions, and to study its impact onDM searches at the GC, we adopt the P7V6 GDE model by the LAT team. This modelextends up to 500 GeV, above which we use a simple power-law extrapolation. The P7V6GDE model was fit using data between 50 MeV and 50 GeV, and structures with extensionsof less than 2 ◦ were filtered out. As much of our analysis is done outside the bounds of theoriginal data used to build the GDE model, e.g. at energies up to 1 TeV, and within 2 ◦ of theGC, the effects of GDE on our analysis should be considered as approximate only. Howeverwe do not expect large changes in our results when using more realistic GDE models: evenfactor two changes in the background fluxes would affect our limits only at the ∼ Fermi -LAT diffuseanalysis for future work.In Fig. 2, we show the contribution that we inferred from this particular GDE modelin the ON and OFF regions. For 100 hr of CTA observations, at energies of 6.7–10 TeV thiscorresponds to about 1 . × and 4 . × events respectively in the OFF and ON regions.This is a factor of ten higher than the reference DM signal at its peak value, and larger inthe ON than in the OFF region. For these reasons, the GDE is a very important backgroundthat should not be neglected in DM searches at the GC. J factors For our version of the Ring method, we begin with the standard annulus of Ref. [36], withan inner radius r and outer radius r . The centre of this annulus is offset from the GC( b = (cid:96) = 0 ◦ ) by some Galactic latitude b . We then consider a circular region centred on theGC, with some radius ∆ cut . The area in which the annulus and this circular region intersectis what we refer to as the ‘ON’ region. The ‘OFF’ region consists of the remaining partof the annulus, outside the central disc. We adopt the parameters optimised for Array Ein Ref. [36]: b = 1 . ◦ , r = 0 . ◦ , r = 2 . ◦ and ∆ cut = 1 . ◦ . Further, we exclude theGalactic disc within | b | ≤ . ◦ from both the ON and OFF regions, as per Ref. [36]. Theresulting two RoIs can be seen in the left panel of Fig. 1. The corresponding solid angles and This is not relevant to our discussion except at very high DM masses, close to 10 TeV. See http://fermi.gsfc.nasa.gov/ssc/data/access/lat/BackgroundModels.html for details on the BG model. – 9 – factors are ∆Ω ON = 1 . × − sr, ∆Ω OFF = 5 . × − sr, J ON = 7 . × GeV cm − and J OFF = 1 . × GeV cm − .For our morphological analysis, we take the area covered by these two RoIs, and divideit into 1 ◦ × ◦ squares. We horizontally merge the various leftover regions resulting from thisdissection into adjacent regions, yielding a total of 28 RoIs. These spatial bins are shown inthe right panel of Fig. 1.For comparison, we also consider DM annihilation in the Draco dwarf spheroidal galaxy,which, to a good approximation, is a point source to both CTA and Fermi at low energies (inthe upper parts of their respective energy ranges, both would observe Draco as a somewhatextended source). For this analysis, we use the J -factor and solid angle from Table 1 of Ref.[29]: ∆Ω Draco = 2 . × − sr, J Draco = 6 . × GeV cm − . We use a binned Poisson likelihood function for comparing a DM model µ to (mock) data n L ( µ | n ) = (cid:89) i,j µ ijn ij n ij ! exp( − µ ij ) . (5.1)Here the predictions of model µ are the number of events µ ij in the i th energy bin andthe j th RoI, which are compared to the corresponding observed counts n ij . We use 15logarithmically-spaced energy bins, extending from 25 GeV to 10 TeV. Depending on theanalysis (Ring or morphological), we use either two (Ring) or 28 (morphological) spatial bins(i.e. RoIs).Each model prediction is composed of 3 parts: a gamma-ray signal resulting from DMannihilation (Eq. 3.5), an isotropic cosmic-ray background, and the GDE. In our statisticalanalysis each of these components can be rescaled via a parameter: (cid:104) σv (cid:105) for the DM gamma-ray signal, and linear rescaling factors R CR and R GDE for the isotropic cosmic-ray backgroundand the GDE respectively, µ ij = µ ij DM + µ ij CR R CR ,i + µ ij GDE R GDE ,i . (5.2)Given that CR flux is isotropic to a good approximation and that we adopt the simplifyingassumption that acceptance are isotropic, the µ CR ij s are trivially related by µ CR ij /µ CR ik =Ω j / Ω k , where Ω j denotes the angular size of the j th RoI. Note that we do not vary therelative normalisations of the CR electron and proton spectra, only their sum. We also donot allow the GDE to be rescaled independently in each RoI, as this would simply allow theGDE to adjust to the data in its entirety in every bin, effectively non-parametrically.Systematic uncertainties in the signal rates can be accounted for by multiplying thepredicted signals µ ij by scaling parameters α ij and β i , then profiling the likelihood over theirvalues. We assume Gaussian nuisance likelihoods for all α and β , with respective variances σ α and σ β independent of i and j . Strictly, the distributions should be log-normal so thatthey go smoothly to zero as α and β go to zero, but for small σ this makes practically nodifference; typical values of σ that we will consider in the following section are ≤ .
03, wellwithin the range where this is a good approximation. With these scaling parameters, thelikelihood function becomes L ( µ , α , β | n ) = (cid:89) i √ πσ β e − (1 − βi )22 σ β (cid:89) j ( µ ij α ij β i ) n ij √ πσ α · n ij ! e − µ ij α ij β i e − (1 − αij )22 σ α . (5.3)– 10 –his formulation accounts for systematic uncertainty on any factor that enters linearly inthe calculation of the total signal, such as effective area. The parameters α ij , which varyacross both energy bins and RoIs, account for e.g. uncertainties related to non-uniformitiesin the acceptance of CTA within a FoV. We will refer to all uncertainties described by α ij as differential acceptance uncertainties . Reasonable values for σ α are of the order of a fewpercent [56, 57]. The parameters β i , on the other hand, describes systematic uncertaintiesfor a given energy that apply equally over the whole FoV.Here we are most interested in the cross-RoI systematics, as systematics that applyequally across the whole FoV will essentially just degrade an entire nσ confidence-level sen-sitivity curve by an offset of less than nσ β (although the rescaling could differ with energy,if σ β were permitted to vary with energy). We therefore investigate the impacts of allow-ing each α ij to vary independently, and simply set β i = 1 for all i . The impacts of e.g. anenergy-dependent systematic uncertainty on the Fermi or CTA effective areas could be easilyaccounted for by also profiling over each β i .Perhaps the largest source of uncertainties is the modelling of the CR acceptance. Whilein this analysis we assume an isotropic CR acceptance, this is a simplification, as noted above.This anisotropic acceptance could be incorporated in our analysis framework, but a detaileddiscussion is beyond the scope of this work.Taking the likelihood function Eq. (5.3), we perform a maximum likelihood analysisacross α ij , (cid:104) σv (cid:105) , R CR , and in certain cases, R GDE . We can determine the maximum likelihoodvalue of α ij simply by solving d L ( µ ij , α ij , β i | n ij )d α ij = 0 , (5.4)and demanding that α ij be positive. This gives α ij = 12 (cid:18) − σ α µ ij β i + (cid:113) σ α n ij − σ α µ ij β i + σ α µ ij β i (cid:19) . (5.5)In our morphological analysis we divide the FoV into bins of 1 ◦ squared, as laid outin Subsection 5.1 above. The systematic acceptance uncertainty in each bin is described byindependent normal distributions in the likelihood function, which implies that the correlationscale of these uncertainties is of the order of ∼ ◦ . Since the uncertainties are treated asstatistically independent in the individual bins, they tend to average out. In fact, decreasingthe solid angle of the bins by a factor of four would be roughly equivalent to reducingthe differential acceptance uncertainty by a factor of two. Hence, when we quote theseuncertainties for our morphological analysis, it is important to keep in mind that they referto ∼ ◦ correlation scales, which we adopt here as reference value. A full exploration of theeffect of different correlation scales would require more detailed knowledge of the detectorperformance, and is beyond the scope of this analysis.The mock data n that we use for deriving sensitivities in the following section assumea fixed isotropic cosmic-ray background component with R CR ,i = 1 in all bins, and nocontribution from DM annihilation. Depending on the analysis, we either include no GDE( R GDE ,i = 0 for all i ) in the mock data, or a fixed GDE with R GDE ,i = 1. The mock data setsthat we employ are not Poisson realisations of a model with these assumptions, but rathersimply the expectation number of events given these assumptions; this has been referred toas the “Asimov data set” [58]. – 11 –e calculate 95% confidence level (CL) upper limits by increasing the signal flux (orannihilation cross-section) from its best-fit value, whilst profiling over the remaining parame-ters, until − L changes by 2.71. In the case of the differential point-source sensitivity thatwe discuss in the next section, for a 95% CL upper limit we also require at least one energybin to contain at least 3.09 events [59]. In this calculation, we determine background ratesover the 80% containment region of the PSF, following e.g. Ref. [41]. Note that we neglectinstrumental systematics when evalulating Fermi -LAT sensitivities (setting α ij = β i = 1). In both our Ring and morphological analyses, we allow the isotropic cosmic-ray backgroundrescaling factor R CR ,i to vary between 0.5 and 1.5 in our fits. We then profile the likelihoodover this parameter in each energy bin.Including the GDE in our analysis is more complicated, as in principle, the data-drivenGDE model derived by Fermi could already contain some contribution from DM annihilation.Therefore, to gauge the impact of the diffuse emission upon current analysis methods, for ouranalysis with the Ring method we inject the GDE into our mock dataset n , with R GDE ,i = 1in all bins. We then carry out a full analysis with a model µ where the GDE normalisationis left free to vary, i.e. R GDE ,i is left free in the fits, but we require it to be non-negative. Theidea in this exercise is to leave the analysis method as much as possible unaltered relative toprevious analyses, but to make the mock data fed into the method more realistic. Leavingthe GDE free to vary in each energy bin produces the most conservative constraints andavoids assumptions on the GDE energy spectrum. The results of this analysis are given inSec. 6.2.Our morphological analysis allows a more refined inclusion of GDE. Using more thantwo RoIs allows us to better exploit the shape differences between the GDE, which is con-centrated along the Galactic plane, and the DM annihilation signal, which is sphericallydistributed around the GC. For this analysis we again include the GDE in the mock datawith R GDE = 1 in all bins, and allow the individual R GDE ,i values to vary in each energy bin.To implement this analysis we use lookup tables: for each DM mass, and each energy binand RoI, we consider a range of DM cross-sections. For each cross-section value, we calculatethe maximum likelihood point when profiling numerically over R BG and R GDE , and analyti-cally over all α ij using Eq. (5.5). Storing these values then gives us a partial likelihood as afunction of cross-section in that bin, for each DM mass. For a given DM mass, we can thencombine the partial likelihoods in different bins to determine cross-section limits at arbitraryconfidence levels. The results of this analysis are given in Sec. 6.3 and 6.4. To keep the discussion as independent from specific DM scenarios as possible, in this sectionwe will often quote the differential sensitivity , which is the sensitivity to a signal in an isolatedenergy bin. This measure is commonly used in the gamma-ray community (see e.g. Ref. [56]).Here we consider energy bins with a width of (cid:39) .
17 dex (approximately six bins per decade),and quote sensitivities in terms of projected one-sided 95% CL upper limits.We will start with a discussion of the point source sensitivity, which is relevant for DMsearches in dwarf spheroidal galaxies. The remaining part of this section will then discuss DMsearches at the GC. Finally, we will present projected upper limits on the DM annihilationcross-section for various annihilation channels and DM profiles.– 12 – Gamma-ray energy E [GeV]10 − − − − − − − − D i ff e r e n t i a l s e n s i t i v i t y E d φ / d E [ G e V c m − s − ] Draco, χχ → ¯ bb h σv i = 3 × − cm s − m χ = 1 TeV CTA 100hFermi 10yr Fermi LAT PSCCTA PSC CTA extended src. ( θ = 0 . ◦ )CTA extended src. ( θ = 0 . ◦ )Draco χχ → ¯ bb spectrumwith J -factor uncertainty Figure 3 . Differential sensitivity of
Fermi -LAT (blue) and CTA (green) point source observations, interms of 95% CL upper limits. The
Fermi -LAT differential sensitivity assumes an observation time of10 years, with energy bins of ∆ log E = 0 .
165 size between E = 5 . E = 0 .
173 size between E = 25 GeV and10 TeV. Sensitivities for extended sources of different sizes are also shown for CTA (green dashedand dot-dashed). The DM annihilation spectrum from the Draco dwarf galaxy uses a J -factor of6 . +3 . − . × GeV cm − from Table 1 of [29], with the band covering the uncertainty range. Some of the most powerful targets for indirect DM searches with gamma rays are dwarfspheroidal galaxies. In order to compare the potential of CTA with the abilities of currentinstruments like
Fermi -LAT, it is instructive to consider their differential point source sen-sitivity. In Fig. 3, we show the differential sensitivity of CTA, assuming an observation timeof 100 hours, compared to the one of
Fermi -LAT after ten years of observation (assuming20% of the time is spend on the source). Due to its much larger effective area, CTA willoutperform
Fermi -LAT at energies above about 100 GeV, where
Fermi becomes limited byphoton statistics.For comparison, we show the signal flux expected from the dwarf spheroidal galaxyDraco, in the case of a DM particle with m χ = 1 TeV mass, annihilating into b ¯ b final stateswith an annihilation cross section of (cid:104) σv (cid:105) = 3 × − cm s − . Draco is one of the mostpromising targets, and the envelope shows the uncertainty in the projected signal flux, whichis primarily related to its overall mass (taken from Ref. [29]).Dwarf spheroidal galaxies have half-light radii of a few times 0 . ◦ (see e.g. Ref. [60]),and at high energies will appear as extended sources for CTA. For comparison, we show theimpact on the expected sensitivity in Fig. 3. We derive these sensitivity curves by assuming– 13 –hat a dwarf is observed by CTA to have an angular extent given by the sum in quadratureof the 68% PSF containment radius and the intrinsic angular extent indicated in the figures.This effect will degrade the sensitivity by a factor of a few at TeV energies. As can be seen inFig. 3, for a gamma-ray spectrum from hadronic processes like annihilation into b ¯ b , CTA willoutperform Fermi for DM masses above about 1 TeV. However, the sensitivity of CTA willstill fall about two orders of magnitude short of testing the canonical thermal cross-section.In order to understand how the limits scale with observing time, it is helpful to realisethat in this transition regime the limiting factor for CTA is the enormous background ofCR electrons (and to a lesser degree unrejected protons and light nuclei; see Fig. 2). TheseCR electrons can easily swamp weak sources even if the number of events that are detectedfrom the source is much larger than in case of
Fermi -LAT. Indeed, apart from the differencein the effective area, the main difference between space-based and ground-based gamma-raytelescopes is their respective abilities to reject backgrounds. This is relatively simply realisedby an anti-coincidence detector in the case of
Fermi , but extremely challenging in the caseof Cherenkov Telescopes like CTA. This means that even a larger observing time with CTAwould not significantly affect the point-source sensitivity at the low energies relevant for TeVDM searches. In contrast, much longer observation times with space-based and practicallybackground-free instruments like
Fermi could (at least in principle) improve on existing limitsby orders of magnitude.
The most intense signal from DM annihilation is expected to come from the GC. The large CRbackground will in that case be of lesser relevance than for observations of dwarf spheroidalgalaxies, making the GC a particularly promising target for CTA. Previous analyses foundthat CTA will improve existing limits (with the strongest ones coming currently from HESS)by an order of magnitude or so [36–38]. However, all existing analyses have neglected theimpact of the GDE, which is strongest in the direction of the Galactic center. We willdemonstrate here that this in fact has a significant impact on DM searches with CTA.In Fig. 4, we show the differential sensitivity for a DM signal in the GC that we obtainwhen using our version of the Ring method ([36], cf.
Fig. 1), under various assumptionsabout the GDE and instrumental systematics. When creating mock data for our baselineanalysis, we include individual estimates for the GDE in the different RoIs. The Ring methodis only sensitive to integrated fluxes measured in the ON and OFF regions. In our likelihoodfit to the mock data the normalisations of the DM and the GDE components are thereforedegenerate, as these two components in general contribute a larger flux to the ON than theOFF region – whereas variations in the average intensity in both regions can be absorbedby slight changes in the CR background normalisation. An increased DM contribution canbe compensated for by a smaller GDE contribution, and vice versa. This degeneracy breakswhen the GDE contribution drops to zero, at which point the − L increases with increasingDM annihilation cross-section, which then leads to a conservative upper limit on the DM flux.The curves that we show in Fig. 4 where the GDE has not been included are basedon neglecting GDE in the the mock data and the subsequent analysis (setting R GDE = 0everywhere). We see here that in the case of the Ring method, neglecting the GDE artificiallyimproves the projected sensitivity by a factor of up to about 3. Furthermore, neglectinginstrumental systematics (as in Ref. [37]) increases the sensitivity again by another factorof a few. For comparison, we again show the flux expected from a DM particle with 1 TeVmass, annihilating into b ¯ b at the canonical thermal rate.– 14 – Gamma-ray energy E [GeV]10 − − − − − D i ff e r e n t i a l s e n s i t i v i t y E d φ / d E [ G e V c m − s − ] ON Region, χχ → ¯ bb h σv i = 3 × − cm s − m χ = 1 TeVFermi LAT, Ring methodFermi LAT, Ring method,neglecting GDE CTA, Ring methodCTA, Ring method,neglecting GDECTA, Ring method,neglecting GDE, 0% syst.ON Region χχ → ¯ bb spectrum Figure 4 . Differential sensitivity of
Fermi -LAT (blue) and CTA (green) for GC observations, usingthe Ring method as defined in Section 3. The two upper solid lines show our baseline estimate for thesensitivity, with galactic diffuse emission and a differential acceptance uncertainties of 1% included.For comparison, the dashed green line shows the differential sensitivity for CTA neglecting the GDE,but still including systematics of 1%; the dash-dotted lines in blue and green show the differentialsensitivity for
Fermi -LAT and CTA respectively, neglecting GDE and instrumental systematics. Ob-servation times and energy binning are the same as in Fig. 3. The purple line shows the gamma-rayspectrum from the ON region assuming a DM mass of 1 TeV and an annihilation cross section of (cid:104) σv (cid:105) = 3 × − cm s − to b ¯ b , using the Einasto profile from Eq. (3.2). Since the GDE component is varying independently in each energy bin, our statisticalframework is insensitive to spectral information that could help to discriminate between theGDE and the DM signal. Including this information could potentially increase the sensitivityof the Ring method, but would require precise assumptions on the poorly known spectrumof the GDE. By including spectral information, the authors of Ref. [32] were able to improvethe limits derived from observations of Segue 1 by MAGIC by a factor of between 1.9 and 3.3,compared to a standard analysis using only spatial information. Applying similar analysistechniques to CTA could yield in the best case a comparable improvement in sensitivity.However, the uncertainty in the GDE spectra has to be carefully addressed in that case,which we leave to future work.
It is instructive to see the results that one would obtain by applying the Ring method to
Fermi -LAT instead of CTA data. As shown in Fig. 4, the resulting sensitivity curve simplycontinues the curve from CTA to lower energies. This can be readily understood, as in bothcases the actual limits are driven by the same GDE. We can see that the GDE is the factor– 15 – Gamma-ray energy E [GeV]10 − − − − − D i ff e r e n t i a l flu x E d φ / d E [ G e V c m − s − ] χχ → ¯ bb h σv i = 3 × − cm s − m χ = 1 TeVCTA Ring methodCTA Morph. analysis CTA Morph. neglecting GDE,0% systCTA Morph. analysis, 3% syst.CTA Morph. analysis, 0.3% syst.ON Region χχ → ¯ bb spectrum Figure 5 . Same as Fig. 4, but comparing our previous Ring analysis (green) with our morphologicalanalysis (red), again assuming 100 hr of observation. The solid lines show our baseline estimate forthe sensitivity of the two analysis methods, with galactic diffuse emission included and differentialacceptance uncertainties of 1%. The dotted orange line shows the same morphological analysis as ourbaseline estimate but neglecting the GDE and assuming 0% systematics. Also shown are sensitivitiesproduced using the morphological analysis including GDE but using systematics of 3% (dashed) and0.3% (dash-dotted) instead. holding back the Ring analysis. This motivates us to consider a procedure capable of takinginto account morphological differences between the GDE and DM signal, which is what wediscuss next. Here we take an important first step towards an improved DM search strategy for CTAby proposing a morphological analysis of the gamma rays from the GC. We will estimatethe most optimistic limits that one can obtain on DM annihilation in the presence of theknown GDE, assuming that the morphology of the GDE is perfectly understood. To thisend, we define the 28 subregions distributed as shown in the right panel of Fig. 1. They areall part of the original RoI from the Ring method. This has the advantage that the requiredobservation strategy and results are directly comparable.Fig. 5 shows that with our morphological analysis, the projected differential sensitivityis better by a factor of three than what can be obtained with the Ring method. Note that thelimiting factor in our results, at least for sub-TeV energies, is now not the GDE but differentialacceptance uncertainties, namely relative systematic uncertainties in the photon acceptancein different regions of the same
FoV. For this uncertainty, we assume 1% throughout, which is Considering the energy spectrum of the signal as we do here of course also improves CTA limits [38]; allour analyses are carried out including this information. Once a signal is detected however, if gamma-ray linesor virtual internal Bremsstrahlung seem relevant, a primarily spectral analysis would be preferable [61, 62]. – 16 – rather realistic value. This might however vary by a factor of a few up or down, dependingon the experimental details ( cf.
Sec. 5.2). Indeed, varying the systematic uncertainty in areasonable range has a significant impact on the actual projected constraints. Note thatsystematics of 0.3% give results extremely close to that of 0% systematics. Also shown forcomparison in Fig. 5 is our morphological analysis assuming 0% systematics and neglectingthe GDE, i.e. α i = 1 for all i , and R GDE ,i = 0 for all i in both mock data and model. We now present our results in terms of limits on DM annihilation, in the common (cid:104) σv (cid:105) -vs-mass plane, assuming DM annihilation into different final states with a branching ratio of100%. First we provide some context by summarising the most relevant previous work, andlater compare these to our own results.In Fig. 6, we show existing experimental limits from the Fermi -LAT satellite [29] andHESS [34], on DM annihilation into b ¯ b . In this figure, all limits from the GC are rescaled toour baseline Einasto DM profile. Projected limits correspond to 100 hr observation time forCTA. The Fermi -LAT limits reach the thermal cross section for DM masses below about 10GeV. The HESS limits are strongest close to 1 TeV, where they reach 3 × cm s − .Also shown are the projected limits for CTA from Refs. [36–38]. The analysis given inRef. [37] assumes an observation time of 500 hr, and we have rescaled their limits to accountfor our baseline DM profile and observation time of 100 hr. In fact, even after this rescaling,the projected limits from Ref. [37] remain the most optimistic; they apparently do not accountfor systematic uncertainties or the effects of the GDE, and make use of an extended arraywith 61 mid-sized telescopes. This extended array is assumed to contain 36 extra mid-sizedtelescopes, as an additional, rather speculative, US contribution on top of the baseline array.The limits presented in Ref. [36] include no GDE and no spectral analysis. They werebuilt upon a profile derived from the Aquarius simulation, and therefore include an effectivesubstructure boost compared to a regular NFW profile. We have removed this boost in orderto allow direct comparison with our results, and those of others. The inclusion of substructureincreases the J -factor and thus also the signal, which results in a stronger limit. As we useidentical regions of interest to those of [36], we can estimate the substructure boost factorby comparing ON region J -factors: [36] give their result as J ON,Aq. = 4 . × GeV cm − ,while our smooth Einasto profile (Sec. 3) gives J ON, Ein. = 7 . × GeV cm − . This yieldsa boost factor of 6.31; we hence multiply the limits of Ref. [36] by this factor for presentationin Fig. 6.The limits presented in Ref. [38] are derived in a similar fashion to the Ring methodones in the present analysis, including spectral analysis, but neglect contributions from theGDE, systematics and proton CRs.Our projected CTA upper limits on the annihilation cross-section using our versionof the Ring method are shown in Fig. 6 by the thick green line. In contrast to Ref. [36],we include the expected GDE as discussed above ( cf. Fig. 5). As a consequence, we findsomewhat weaker limits at intermediate masses than in this previous work. From Fig. 4 onecan see that neglecting GDE in the Ring method (in the mock data) falsely improves the Although we introduced the morphological analysis method primarily to improve limits in the presenceof the GDE, we also compared its performance to that of the Ring method in the case of no GDE and 0%systematics. In this case the morphological analysis produces limits that are marginally better than those ofthe Ring method. This is expected, as the smaller RoIs still provide an additional constraint on the spatialdistribution of the signal. – 17 – DM particle mass m χ [GeV]10 − − − − − − S e l f - a nn i h il a t i o n c r o ss - s ec t i o n h σ v i [ c m s − ] χχ → b ¯ b , 100 hours CTA Ring methodCTA Morph. analysisCTA Morph. analysis (3% syst.)CTA Morph. analysis (0.3% syst.) HESS GCFermi-LAT dSphDoro et al. et al. et al.
Figure 6 . Upper limits on the DM annihilation cross section using the previous Ring method (green)and our morphological analysis (red), assuming 100 hr of observation of the GC. The thick solidgreen and red lines are our baseline estimates of the limits attainable using the two analysis meth-ods, assuming differential acceptance uncertainties of 1% and including GDE. The red dashed anddot-dashed lines show the limits produced in the morphological analysis assuming 3% and 0.3% sys-tematics, respectively. Also shown are current limits on the DM annihilation cross section (thin solidlines;
Fermi -LAT dwarf analysis in blue [29], HESS GC observations in pink [34]), as well as variousprojected CTA limits, both official (thin dotted lines; Doro et al. et al. et al. sensitivity by a factor of ∼ −
3, which agrees with the factor ∼ ∼ . Fermi -LAT happens (by chance?) to be very similarin the rather complicated ON and OFF regions chosen by HESS.Most importantly, moving from the Ring method to our morphological analysis yields asensitivity improvement by up to an order of magnitude . We show in Fig. 6 that morphologicalanalysis improves the projected limits by up to a factor of ten for high DM masses comparedto the Ring method. This is mostly due to the fact that the large number of subregionsallows an efficient discrimination between the morphology of the GDE and a putative DMsignal. Note that the projected limits again depend critically on instrumental systematics,and as indicated by the band in Fig. 6. This is due to the large number of measured eventsin the RoIs. For our baseline DM profile, we find that the thermal annihilation cross sectioncan be only reached if instrumental systematics (namely differential acceptance uncertaintiesas discussed above) are under control at the sub-percent level. At the same time, increasingthe time over which the GC is observed by CTA will have a negligible effect on the projectedlimits.Finally, we discuss how the projected limits depend on the adopted annihilation channelor DM halo profile. These results are shown in Fig. 7. Besides our baseline scenario, where weassumed an Einasto profile and annihilation into b ¯ b final states, we show limits for annihilationto τ + τ − , W + W − , µ + µ − , and t ¯ t with an Einasto profile, and to b ¯ b with an alternative densityprofile. We find that in the case of annihilation via the τ + τ − channel, CTA would be able toprobe annihilation cross-sections well beyond the thermal value even for a standard Einastoprofile. In the case of a contracted NFW profile with a inner slope of γ = 1 .
3, as describedin Sec. 3, the J -factor increases by a factor of 2.9 (summed over all RoIs). If this profileis indeed realised in nature, it would bode well for future observations with CTA, as CTAcould probe well beyond the canonical thermal cross section for a large range of DM particlemasses between 100 GeV and 10 TeV. In this paper we have performed a new estimate of the CTA sensitivity to DM annihilation.Here we summarise our main conclusions: • We showed that the effect of Galactic diffuse emission substantially degrades the sensi-tivity of CTA when using a traditional two region analysis as previous official studieshave done.
We have assessed the impacts of all backgrounds, including protons andelectrons in cosmic-rays hitting the atmosphere and, for the first time in this type of This is not directly apparent from Fig. 5, where the difference is merely a factor of three. The reason isthat a DM signal would appear in several energy bins simultaneously, which strengthens the limits in the casewhere the GDE is correctly modelled. Note that fluctuations of the limits, which are most visible in the cases of µ + µ − and W + W − final stateswith strong final state radiation, come from variations in the adopted effective area. – 19 – DM particle mass m χ [GeV]10 − − − − − − S e l f - a nn i h il a t i o n c r o ss - s ec t i o n h σ v i [ c m s − ] χχ → b ¯ b , Einasto χχ → b ¯ b , Contracted NFW χχ → τ + τ − , Einasto χχ → W + W − , Einasto χχ → µ + µ − , Einasto χχ → t ¯ t , Einasto Figure 7 . Comparison of (cid:104) σv (cid:105) limits from CTA observations of the GC, assuming different annihi-lation channels and DM halo profiles. Einasto lines assume the main halo profile described in Sec. 3.The contracted NFW profile with an inner slope of γ = 1 . analysis, diffuse astrophysical emission. The impact of including the galactic diffuseemission can be observed in particular in Fig. 4, where the CTA differential sensitiv-ity is found to be substantially degraded (solid line) with respect to the case wherethe GDE is neglected in the analysis (dashed green line). Although we only adoptedone particular GDE scenario (which is an extrapolation of Fermi LAT observations tohigher energies), we do not expect these conclusions to change when adopting otherrealistic GDE models. • Including systematic errors substantially degrades the CTA sensitivity.
In this paperwe introduced a statistical framework that allowed us to account for the impact ofdifferential acceptance uncertainties within a FoV on DM limits from CTA. This impactcan be seen in Fig. 5, where the sensitivity of CTA to DM annihilation is shown forthree different values of the magnitude of these systematics: 3% (dashed), 1% (solid)and 0.3% (dash-dotted). • A morphological analysis substantially improves the sensitivity of CTA.
Our morpho-logical analysis allows a proper exploitation of the shape differences between the GDE,which is concentrated along the Galactic plane, and the DM annihilation signal, which isspherically distributed around the GC. The constraints derived under this approach aremore stringent by a factor of a few compared to those obtained with the Ring analysis.This is best seen by comparing the red (morphological) and green (non-morphological)curves in Figs. 5 and 6. – 20 –
Prospects for detecting WIMPs with CTA.
Our most realistic estimate of the upperlimits on the DM annihilation cross section possible with 100 hr of GC observation byCTA are shown as a red solid line in Fig. 6. These correspond to a morphologicalanalysis assuming annihilation to b ¯ b , systematics of 1%, and include diffuse emission.In order to reach canonical thermal cross section, shown as a horizontal line, systematicerrors should be reduced to less than 0.3%. If the DM profile is steeper than NFWor Einasto, the sensitivity curve drops below the thermal cross-section for a broadrange of masses, as we show in Fig. 7. Here, for the same annihilation channel anda contracted profile rising as r − . , CTA is found to be able to probe WIMPs with athermal cross-section between 100 GeV and 10 TeV. Acknowledgements.
We thank Arnim Balzer, David Berge, Jan Conrad, Christian Farnier,Mathias Pierre and Jennifer Siegal-Gaskins for useful discussions. PS acknowledges supportfrom the UK Science & Technology Facilities Council, and GB from European ResearchCouncil through the ERC Starting Grant
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