Potential of LOFT telescope for the search of dark matter
aa r X i v : . [ a s t r o - ph . C O ] D ec Potential of LOFT telescope for the search of dark matter
A. Neronov , A. Boyarsky , , , D. Iakubovskyi , and O. Ruchayskiy , ISDC Data Centre for Astrophysics, Department of Astronomy,University of Geneva, Ch. d’Ecogia 16, 1290, Versoix, Switzerland Instituut-Lorentz for Theoretical Physics, Universiteit Leiden,Niels Bohrweg 2, Leiden, The Netherlands Ecole Polytechnique F´ed´erale de Lausanne,FSB/ITP/LPPC, BSP 720, CH-1015, Lausanne, Switzerland Bogolyubov Institute of Theoretical Physics,Metrologichna Str. 14-b, 03680, Kyiv , Ukraine National University “Kyiv-Mohyla Academy”,Skovorody Str. 2, 04070, Kyiv, Ukraine CERN Physics Department, Theory Division,CH-1211 Geneva 23, Switzerland(Dated:)
Large Observatory For X-ray Timing (LOFT) is a next generation X-ray telescope selected byEuropean Space Agency as one of the space mission concepts within the “Cosmic Vision” pro-gramme. The Large Area Detector on board of LOFT will be a collimator-type telescope with anunprecedentedly large collecting area of about 10 cm in the energy band between 2 and 100 keV.We demonstrate that LOFT will be a powerful dark matter detector, suitable for the search of theX-ray line emission expected from decays of light dark matter particles in galactic halos. We showthat LOFT will have sensitivity for dark matter line search more than an order of magnitude higherthan that of all existing X-ray telescopes. In this way, LOFT will be able to provide a new insightinto the fundamental problem of the nature of dark matter. I. INTRODUCTION
The nature of dark matter (DM) is one of the mostintriguing questions of modern physics. Mass content ofgalaxies and galaxy clusters, growth of density fluctu-ations through the cosmic history, large scale structureof the Universe – all point towards the existence of newsubstance, the DM, which constitutes some 80% of thetotal mass content of the Universe [1]. If DM is made ofparticles, these particles are not among the known ones.Phenomenologically little is known about properties ofDM particles:– Their overall density is Ω DM h = 0 . ± . anni-hilating and decaying . A lot of attention has been devoted to a class of annihi-lating DM candidates called weakly interacting massiveparticles (WIMPs) (see e.g. [11, 12] for review). Thesehypothetical particles are assumed to interact with or-dinary matter with roughly electroweak strength andhave masses in O (1 − ) GeV to provide the correctDM abundance. Due to their large mass and interactionstrength these particles should be stable and astrophysi-cal signature of their annihilation products is an impor-tant scientific goal of many cosmic missions [10, 13]. Inparticular, γ -rays from DM annihilation are extensivelysearched with γ -ray telescopes [14, 15].There is a large class of DM candidates that inter-act with the ordinary particles super-weakly (i.e. sig-nificantly weaker than neutrinos). These include: ex-tensions of the SM by right-handed neutrinos [16–18],models with extra dimensions and string-motivated mod-els [19], gravitinos [20, 21], axions [22, 23], axinos [24, 25](see e.g. [12, 26, 27] for reviews). These candidates areas possible as WIMPs and from many points of view arevery compelling. The feeble interaction strength of theseDM candidates means that unlike WIMPs: (i) their massis not restricted to the GeV region; and (ii) they can decay into the SM particles. The fermionic DM candi-dates (such as sterile neutrino, gravitino, axino) possesa 2-body radiative decay channel: DM → γ + ν , whilebosonic DM candidates (such as e.g. axion or Majoron)can decay into two photons. These 2-body decays pro-duce photons with energy E γ = M DM c . The cosmo-logically long lifetime makes the intrinsic width of such aline negligible. This provides a clear observational signa-ture of decaying DM candidates: a narrow spectral linein spectra of DM-dominated objects, correlated with DMdensity distribution.Search of the DM decay signal in the keV–MeV massrange was conducted using XMM-Newton [28–34],
Chan-dra [35–40],
Suzaku [41, 42],
Swift [43],
INTEGRAL [44,45] and HEAO-1 [28] cosmic missions, as well as rocket-borne X-ray microcalorimeter [46]. Observations of ex-tragalactic diffuse X-ray background [28, 47]; galaxy clus-ters [29, 36, 37]; Milky Way, Andromeda (M31) and Tri-angle (M33) galaxies [29–32, 44, 45, 47]; dwarf spheroidalsatellites of the Milky Way [30, 34, 38, 40–42, 46] al-lowed to put important constraints on particle physicsparameters, establishing lower bounds on decaying DMlifetime to be at least 8 orders of magnitude longer thanthe age of the Universe [5] (see also [7] for extension forhigher energies). Table I summarizes existing works thatput bounds on decaying DM from observations of indi-vidual objects. In this Table, we do not mention theclaim [48] that the intensity of the Fe XXVI Lyman- γ lineat 8 . exact coincidence between energy of decayphoton and Fe XXVI Lyman- γ , this claim may be testedwith the new missions, discussed in e.g. [50].In what follows we argue that a next-generation X-raymission Large Observatory For x-ray Timing (LOFT) willprovide a crucial improvement in the sensitivity for thesearch of decaying DM in X-rays. LOFT mission is undera study at the European Space Agency (ESA) as one ofthe five medium mission candidates for the launch after2020 in the framework of the “Cosmic Vision” programof ESA. Further details on the LOFT mission could befound at . We alsoshow that LOFT will have a capability to explore al-most the entire parameter space of one of the most of-ten discussed models of decaying DM, the neutrino min-imal extension of the Standard Model of particle physics( ν MSM) [17] if converted into a dedicated DM detectionexperiment (e.g. toward the end of the mission) aimedat ultra-deep exposure of the most favourable (massive,relatively compact) nearby DM halo.
II. STRATEGY OF SEARCHING FORDECAYING DARK MATTER
The number of photons from DM decay is proportionalto the DM column density S DM = R ρ DM ( r ) dr (inte-grated DM distribution along the line of sight) and not tothe R ρ DM ( r ) dr (as in the case of the annihilating DM).As it turns out, this signal is very weakly dependent onthe virial mass of the DM halo and on the assumed darkmatter density profile [30, 54, 55]. Moreover, for objectsthat cover the whole field of view of the telescope, the ex- pected DM decay flux is independent on the distance tothe object. As a result a vast variety of DM-dominatedobjects (nearby galaxies and galaxy clusters) produce acomparable decay signal. Therefore (i) one has a free-dom of choosing the observational targets, avoiding com-plicated astrophysical backgrounds; (ii) if a candidateline is found, its surface brightness profile may be mea-sured, distinguished from known atomic lines and com-pared among several objects with the same expected sig-nal (see e.g. [40]). This allows to distinguish the decayingDM line from astrophysical backgrounds. The case of theastrophysical search for decaying DM has been presentedin the recent White Papers [56, 57].With intrinsic width of the decay line being negligible,its broadening is determined entirely by the virial velocityof DM particles, confined to in a halo: E/ ∆ E ≃ c/v vir .This number ranges from 10 for galaxy clusters to 10 for dwarf spheroidal galaxies. The spectral resolution ofmodern X-ray instruments is insufficient to resolve thisline (with an exception of INTEGRAL’s spectrometerSPI, see [45]). The narrow line is detected on top of acontinuum background. This background has two maincontributions – astrophysical and instrumental. The as-trophysical background is a continuum thermal and non-thermal emission form the source medium: interstel-lar/intraclusted medium of galaxies and galaxy clusters,and from the set of isolated sources, like X-ray bina-ries situated in the source host galaxy or galaxy clusterplus the Cosmic X-ray background (CXB) [58] withinthe instrument’s Field-of-View (FoV). The instrumentalbackground is produced by the charged particles passingthrough the detector and by the electronic noise. Theline signal is centered on the reference line energy E andis smeared over the energy range ∼ (2 − × ∆ E where∆ E is a spectral resolution. The amount of backgroundaccumulated in this energy bin is proportional to the binwidth ∆ E . Thus, improvement of the energy resolutionresults in the decrease of the background and, as a conse-quence, improvement of the sensitivity of the instrumentfor the line detection.The significance of the line signal from a diffuse sourceincreases with the collection area of the detector. It isproportional to the product of the effective area, A eff onthe solid angle subtended by the FoV (for those DM halosthat have angular size larger than the FoV) that is tothe “grasp” A eff Ω fov of the instrument [46]. Comparisonof potential of different instruments for the detection ofDM decay line could be conveniently presented in termsof “energy resolution vs. grasp” diagram [46], as shownin Fig. 1.In this figure, the inclined lines show the “equal sen-sitivity” sets of instrumental characteristics. Indeed,the signal-to-noise ratio for the DM decay line sensitiv-ity improves as R ∝ p A eft Ω fov / ∆ E , so that the lines“grasp” ∝ “energy resolution” correspond to instrumentswhich provide the same signal-to-noise ratio if they op-erate in the same energy band. One could define R as a“figure of merit” for the weak line search, see e.g. [59]. Ref. Object Instrument Cleaned exp, ks[28] Diffuse X-ray background HEAO-1,
XMM-Newton
XMM-Newton
20, 40[30] Large Magellanic Cloud
XMM-Newton
Chandra /ACIS-S3 Not specified[31] M31 (central 5 ′ ) XMM-Newton
Chandra /ACIS-S3 67[32] Milky Way halo, Ursa Minor dSph
XMM-Newton
Chandra /ACIS 1500[37] Galaxy cluster 1E 0657-56 (“Bullet”)
Chandra /ACIS-I 450[46] Milky Way halo X-ray microcalorimeter 0.1[44] Milky Way halo INTEGRAL/SPI 5500[33] M31 (central 5 − ′ ) XMM-Newton /EPIC 130[45] Milky Way halo INTEGRAL/SPI 12200[41] Ursa Minor
Suzaku /XIS 70[38] Draco dSph
Chandra /ACIS-S 32[39] Willman 1
Chandra /ACIS-I 100[40] M31, Fornax, Sculptor
XMM-Newton /EPIC ,
Chandra /ACIS 400, 50, 162[51] Willman 1
Chandra /ACIS-I 100[43] Segue 1
Swift /XRT 5[52] M33
XMM-Newton /EPIC 20-30[53] M31 (12 − ′ off-center) Chandra /ACIS-I 53[34] Willman 1
XMM-Newton
Suzaku /XIS 200, 200TABLE I: Summary of existing X-ray observations of different objects performed by different groups.Parameter Requirement GoalEnergy range 2–30 keV 1–40 keV2–80 keV [60, 61] 1–80 keV [61]Eff. area 12.0 m (2–10 keV) 15 m (2–10 keV)1.3 m (@30 keV) 2.5 m (@30 keV)∆E <
260 eV <
180 eV(FWHM, @6 keV)FoV (FWHM) <
60 arcmin <
30 arcminTABLE II: Scientific requirements for the LOFT LAD in-strument (from [60, 61]). The energy range of LOFT LADdetector can be extended beyond 30 keV (the nominal range)to the energies up to 80 keV (see [61] for the latter number).At those higher energies the LAD collimator becomes moreand more transparent to X-rays [60].
We have arbitrarily fixed R = 1 for the parameter choicecorresponding to the averaged over the energy band char-acteristics of the EPIC camera of the XMM-Newton tele-scope [46].The comparison shown in Fig. 1 adopts an assump-tion that the level of background in different instrumentsis comparable. This is true if the background on top ofwhich the DM signal is searched is the CXB. However, ifthe background is of instrumental nature, the compari-son of different instruments has to include an additionalparameter, which is the level of background. We includethis parameter in our considerations below.
III. LOFT CHARACTERISTICS RELEVANTFOR DM DETECTION
The main instrument on board of LOFT will be theLarge Area Detector (LAD). LAD will be an X-ray tele-scope with effective collection area A eft ≃
10 m (seeFig. 3) sensitive in the 2-80 keV energy range [60]. LADwill be composed of the Silicon Drift Detectors (SDD)with energy resolution below 300 eV. The SDDs willbe covered by microchannel plate collimators provid-ing the Field of View of 1 ◦ in the energy range below ≃
30 keV and becoming increasingly transparent to X-rays at higher energies up to 80 keV [60, 61].The energy resolution, of LAD is determined by thecharacteristics of the silicon detectors and of the detec-tor electronics [60]. Using the response functions of theLOFT satellite[78], we simulated narrow line at differ-ent energies and then approximated the obtained spec-trum by the Gaussian profile (see left panel of the Fig. 2).The obtained best-fit value of Gaussian dispersion is thenused to calculate FWHM. The results are shown in theright in Fig. 2. They can be approximated as a linearfunction of energy:FWHM( E ) = 0 .
213 keV + 4 . × − E keV . (1)Our analysis considers two possible LOFTconfigurations[79]: “Requirements” and “Goal”.Parameters of each configuration are summarised inTable II. FIG. 1: Sensitivity of X-ray telescopes for the dark matterdecay line detection in terms of the “energy resolution vs.grasp” diagram (c.f. [46]). Two red solid curves correspond tothe LAD detector in two different observation modes: obser-vations of localized sources of the angular extent i & ◦ rangeand observations of the large angular scale diffuse emissionfrom the Milky Way with the steradian-sized FoV of LAD athigher energies. Dashed line shows the grasp of the WFM de-tector of LOFT. Inclined grey lines with marks in 1-100 rangeshow improvement of the sensitivity for the line search due tothe increase of effective area / FoV and improvement of en-ergy resolution. Level “1” corresponds to average parametersof the XMM-Newton
EPIC camera. Notice that points on thecurves for LOFT and INTEGRAL/SPI correspond to differ-ent energies, from 1 to 100 keV and from 20 keV to 7 MeV,respectively.
IV. SENSITIVITY FOR THE DM LINEDETECTIONA. Signal from extended sources in the field ofview of collimator
We begin with an estimate of the sensitivity of theLAD detector for weak diffuse lines in the energy rangebelow 30 keV where the collimator limits the FoV to 1 ◦ .To this end we take the background spectrum shown inFig. 4, and compute the number of background photonsin the bin with the size equal to FWHM over the time T exp chosen to be 100 ksec (a typical timescale of a singleobservation). We then estimate the 3 σ upper limits onthe line flux in each narrow energy, based on the statis-tical error on the background counts: F line, σ ( E ) < p × N bkg ( E ) A eff ( E ) T (2)
100 1000 10000 100000 1e+06 1e+07 3 3.1 3.2 3.3 3.4 3.5 3.6 3.7 3.8 3.9 C oun t s Energy, keVFakeit gaussianBest-fit 200 220 240 260 280 300 320 340 360 5 10 15 20 25 30 E ne r g y r e s o l u t i on ( F W H M ) , e V Energy, keVLAD RequirementsLAD Requirements, best-fit
FIG. 2:
Left : an example of simulated line at 3.5 keV, to-gether with its best-fit gaussian model used to calculateFWHM.
Right:
LAD energy resolution for “Requirements”payload as function of energy and its best fit (1) calculatedfrom our simulations. E ff e c t i v e a r ea , m Energy, keVLAD, RequirementsXMM-Newton, MOS1+MOS2
FIG. 3: Characteristics of the LAD Effective areas for LADinstrument in the “Requirements” payload. For comparisonthe effective area of combined EPIC MOS1 + MOS2 camerasof
XMM-Newton is shown in black.
FIG. 4: Background of LAD instrument (compared to theCXB, lower curve). The instrumental component has beenobtained using
LAD Requirements v6.3.bkg background filefrom ISDC LAD response and background page [62].
Flux, ph/(cm s) Energy, keVLAD Requirements, simulationsLAD Requirements, estimateLAD Goal, simulationsLAD Goal, estimateXMM-Newton, M31 upper bound
FIG. 5: The 3 σ upper bound on the flux in the line froma diffuse source detectable by LAD detector. Thick lines:results based on simulations and subsequent detection of aline. Dashed line: 3 σ estimates, based on the statistical 3 σ upper bound of the instrumental background, see Eq. (2). 3 σ upper bound on DM flux from XMM-Newton observations ofM31 central part [33] (blue) is shown for comparison. (an additional √ XMM-Newton exposure of the same du-ration. This demonstrates that in spite of somewhathigher background level of the LAD detector (contraryto
XMM-Newton it includes the CXB scatterd by thecollimator walls), the upper limit on the line flux withinthe FoV is better. The obvious reason for this is much larger effective area of the detector. Further improve-ment of sensitivity of LAD, compared to
XMM-Netwon (not reflected by the figure) is that LAD collects largerDM line signal in a similar exposure. This is due to thelarger FoV.
B. Signal from the Milky Way halo visible for a“bare detector”
At energies above 20 −
40 keV, the collimator of theLAD will be not able to stop photons falling at large inci-dence angle, so that LAD increasingly becomes a “nakeddetector” sampling photons from large, steradian scaleFoV. Such a design is optimal for the search of diffuseemission from the Milky Way halo [46, 57]. The DM sig-nal is accumulated in all the pointings of the telescope,no matter where the pointing is directed. This allows toachieve extremely long exposures in a multi-year opera-tion of the telescope. It is not possible to estimate whatwill be the effective field of view of the LAD detector atthese energies. As an estimate we take Ω fov , high = 1 sr.We remind that the sensitivity estimate, R , scales as R ∝ p Ω fov , high / ∼ −
40 keV where the instrument works as awide FoV detector. The main difference with the calcu-lations of the previous section is that the central part ofthe Milky Way is a bright X-ray source. The emissionfrom this source is the sum of emission from high massand low mass X-ray binaries and cataclysmic variables.Measurement of the collective emission from the MilkyWay sources within a steradian scale FoV by SPI [63]provides a reference value for the level of sky backgroundon top of which the DM line signal from the Milky Wayshould be detected F MW ≃ − (cid:18) E
100 keV (cid:19) − . phcm s keV . (3)The limits calculated for the background level (3) anda year-long exposure time are shown in Fig. 6. For com-parison, the same figure shows the upper limit on the lineflux within a steradian FoV of SPI found by [45]. Onecould see that, in accordance with the expectations, thelimits which would be derived from the LAD data aretighter than those from the SPI. FIG. 6: Flux limits on DM decay line with large FoV (“bare”)LAD detector expected from a year-long observation of diffuseemission within Ω ≃ C. Limits on the decaying DM lifetime
To convert the limits on the line flux into the limits onthe lifetime of the decaying DM, τ dm , we note that fluxin line (in photons per cm per sec) is given by F line = (cid:18) τ dm m dm (cid:19) (cid:18) M fov πD L (cid:19) (4)where the first term is determined by the basic propertiesof DM particles, while the second one is the characteristicof the object being observed.For nearby objects that cover the whole FoV of theinstrument one can express M fov πD L ≃ S dm Ω fov π (5)where S dm is the average DM column density in a givendirection. This quantity changes very little among ob-jects of different masses and sizes [30, 54, 55] and its typi-cal values are 10 ÷ . M ⊙ / pc . Using this fact and takinginto account that for 2-body decays the mass of DM is re-lated to the energy of emitted photon via E γ = M dm c ,we convert the upper bound on the flux limit into the FIG. 7: Bounds on lifetime of decaying dark matter (for de-cays DM → γ + ν or DM → γ + γ ) (grey shading) and expectedimprovement from the LOFT LAD detector. Red solid lineshows possible LOFT bound assuming 1 Ms exposure withthe average dark matter column density S = 300 M ⊙ / pc . lower limit on decaying DM lifetime: τ dm = S dm Ω fov πE γ F line ≈ . × sec (cid:18) S dm M ⊙ / pc (cid:19) (cid:18) Ω fov (cid:19)(cid:18)
10 keV E γ (cid:19) (cid:18) − ph / sec / cm F line (cid:19) (6)From Fig. 5 one sees that the upper limits on theline flux is expected to be at the level of 10 − − − ph / cm / sec. Substituting these values into (4) onefinds the sensitivity of the LAD detector at the level τ dm ∼ sec – at least an order of magnitude bet-ter than existing bounds at these energies. This limitis shown in Fig. 7 as a function of energy. To estimatethe sensitivity in the ”naked detector” mode, we assumethat the FoV of the detector grows as a powerlaw in the20-40 keV energy range. Detailed simulations are neededto get a more precise estimate of the opening of the FoVwith increasing energy. V. IMPLICATIONS FOR STERILE NEUTRINODM MODELS
Sterile neutrino is a decaying DM candidate that hadrecently attracted a lot of attention (see e.g. [50, 64–66]for review). Sterile neutrino is a right-chiral counterpartof the ordinary (left-chiral) neutrinos ν e , ν µ , ν τ . Addingthese particles to the SM Lagrangian makes neutrinosmassive and provides a simple and elegant explanationof the observed neutrino flavor oscillations and of thesmallness of neutrino masses (the so-called “type I see-saw model”) [67–70]. These particles are neutral withrespect to all Standard Model interactions (weak, strongand electromagnetic) (see e.g. [50, 71] for details). Theyinteract with the matter only via mixing with ordinaryneutrinos and in this way effectively participate in weakreactions [50] with strongly suppressed rate (as comparedto the ordinary neutrinos). Production of such particlesin the primordial plasma [16, 72–75] and their decaysare controlled by the same parameter – sterile neutrinomixing angle sin (2 θ ) ≪ τ dm = 1024 π αG F sin (2 θ ) m dm ≈ . × sec (cid:20) − sin (2 θ ) (cid:21) (cid:20) m dm (cid:21) . (7)To be a DM candidate, the interaction strength of ster-ile neutrinos should be too feeble to make any sizablecontribution to active neutrino masses [76].The ν MSM model provides an explanation to threeknown ”beyond Standard Model” of particle physics phe-nomena: dark matter, baryon asymmetry of the Uni-verse and neutrino masses, adding three sterile neutrinosto the Standard Model particle content [17, 77]. Thelightest of the three sterile neutrinos served as the DM.The combination of X-ray bounds, of primordial abun-dance results in both upper and lower bounds on the massand mixing angle of DM sterile neutrino in the ν MSM.The range of allowed masses of sterile neutrino DM is1 −
50 keV [45, 50, 64].The estimates of the bound on the DM sterile neu-trino mixing angle expected from LOFT observations areshown in Fig. 8. Interestingly, the“Requirements” con-figuration of LOFT is expected to provide the best con-straints. This is mostly due to the fact that the “Goal”configuration is optimized for point sources and thereforeLAD FoV is reduced from ∼ ◦ to ∼ . ◦ . This reduces4 times the expected signal from DM decays (providedthe DM column density is constant across the FoV) whilethe background level reduced only slightly.One could see that LOFT will be able to explore signif-icant fraction of the available range of the mixing angles θ within ν MSM. Already one 1 Ms long exposure of a dSphgalaxy like Ursa Minor will improve the existing boundson θ by two orders of magnitude. Moreover, taking intoaccount importance of the DM nature problem, and theunique characteristics of LOFT, which make it an excel-lent DM detector, one could imaging a scenario in whichthe LAD instrument might be operated as a dedicatedDM detector (e.g. toward the end of the mission), accu-mulating a total year scale exposure of a nearby DM halo.This would allow a further boost of sensitivity of the de-tector by a an order of magnitude. In this case LOFT will FIG. 8: Grey shading: Bounds on sterile neutrino parameters.Blue hatching shows the allowed parameter space of ν MSMmodel. Orange shading shows the sensitivity limit of LOFTfor 1 Ms exposure. provide an almost full test of the ν MSM and either dis-cover the sterile neutrinos or possibly leave only a narrowwindow of mass 1 keV < m wdm < α bound suffers from some uncertainties [64], unexplored.To probe the mass range below 4 keV, one might use theLAD data in the energy range below 2 keV. It is clearthat the quality of the data in this range is significantlydegraded. However, taking into account the unique pos-sibility to explore the full allowed parameter space of aviable DM model (to find the DM or rule out the model)might serve as a good motivation for the challenging taskof data analysis in this energy range. VI. CONCLUSIONS
We have shown that LOFT will be a powerful detectorof light decaying DM. From Figs. 7, 8 it is clear thatLOFT will be one-two orders of magnitude imore sensi-tive for the detection of DM line in the DM mass range4-200 keV than all ongoing and past missions. This willprovide a qualitatively new insight into the nature of theDM particles within various ΛWDM scenarios, includingthe most popular one with sterile neutrino DM. Signif-icant improvement is also expected at the highest ener-gies above 30 keV, where the LAD instrument becomesa “naked detector” with the steradian-scale FoV. Such aconfiguration proves to be optimal for search of diffuseall-sky signal from DM decaying in the Milky Way halo(c.f. [46, 57]).The energy range of LOFT is crucially important fortesting the reference ν MSM model. This is clear fromFig. 8. If operated as a dedicated DM search experiment, LOFT will be able to probe almost all parameter spaceof ν MSM. [1] P. Ade et al. 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