Either neutralino dark matter or cuspy dark halos

We show that if the neutralino in the minimal supersymmetric standard model is the dark matter in our galaxy, there cannot be a dark matter cusp extending to the galactic center. Conversely, if a dark matter cusp extends to the galactic center, the neutralino cannot be the dark matter in our galaxy. We obtain these results considering the synchrotron emission from neutralino annihilations around the black hole at the galactic center. The composition of dark matter is one of the major issues in cosmology. A popular candidate for non-baryonic cold dark matter is the lightest neutralino appearing in a large class of supersymmetric models [1]. In a wide range of supersymmetric parameter space, relic neutralinos from the Big Bang are in principle abundant enough to account for the dark matter in our galactic halo [2]. A generic prediction of cold dark matter models is that dark matter halos should be have steep central cusps, meaning that their density rises as r to the center. Semi-analytical calculations find a cusp slope γ between ∼ 1 [3] and 2 [4]. Simulations find a slope γ ranging from 0.3 [5] to 1 [6] to 1.5 [7]. It is unclear if dark matter profiles in real galaxies and galaxy clusters have a central cusp or a constant density core. There is mounting evidence that the non-thermal radio source Sgr A at the galactic center is a black hole of mass M ∼ 3× 10 M⊙. This inference is based on the large proper Electronic address: [email protected] 1 motion of nearby stars [8], the spectrum of Sgr A (e.g. [9,10]), and its low proper motion [11]. It is difficult to explain these data without a black hole [12]. The black hole at the galactic center modifies the distribution of dark matter in its surroundings [13], creating a high density dark matter region called the spike – to distinguish it from the above mentioned cusp. Signals from particle dark matter annihilation in the spike may be used to discriminate between a central cusp and a central core. With a central cusp, the annihilation signals from the galactic center increase by many orders of magnitude. With a central core, the annihilation signals do not increase significantly. Stellar winds are observed to pervade the inner parsec of the galaxy [9], and are supposed to feed the central black hole (e.g. [10,14]). These winds carry a magnetic field whose measured intensity is a few milligauss at a distance of ∼ 5pc from the galactic center [15]. The magnetic field intensity can rise to a few kilogauss at the Schwarzschild radius of the black hole in some accretion models for Sgr A [16]. In this letter we examine the radio emission from neutralino dark matter annihilation in the central spike. (Previous studies of radio emission from neutralino annihilation at the galactic center have considered an r cusp but no spike [17].) Radio emission is due to synchrotron radiation from annihilation electrons and positrons in the magnetic field around Sgr A. Comparing the radio emission from the neutralino spike with the measured Sgr A spectrum, we find that neutralino dark matter in the minimal supersymmetric standard model is incompatible with a dark matter cusp extending to the galactic center. There are two ways to interpret our results. If we believe that there is a dark matter cusp extending to the center of our galaxy, we can exclude the neutralino as a dark matter candidate. Conversely, if we believe that dark matter is the lightest neutralino, we can exclude that a dark matter cusp extends to the center of the galaxy. Dark matter candidate. We examine the lightest neutralino in the minimal supersymmetric standard model. This model provides a well-defined calculational framework, but contains at least 106 yet-unmeasured parameters [18]. Most of them control details of the squark and slepton sectors, and are usually disregarded in neutralino dark matter studies 2 (cfr. [1]). So, following Bergström and Gondolo [19], we restrict the number of parameters to 7. Out of the database of points in parameter space built in refs. [2,19,20], we use the 35121 points in which the neutralino is a good cold dark matter candidate [2], in the sense that its relic density satisfies 0.025 < Ωχh 2 < 1. The upper limit comes from the age of the Universe, the lower one from requiring that neutralinos are a major fraction of galactic dark halos. Present understanding of the matter density in the universe (e.g. [21]) suggests a narrower range 0.08 < Ωχh 2 < 0.18, but we conservatively use the broader range. Spike profile. We summarize the results of ref. [13] for the spike profile. We assume the cusp has density profile ρcusp = ρD ( r D )−γ , (1) with ρD = 0.24GeV/c /cm the density at the reference point D = 8.5kpc, the Sun location (this is a conservative value for ρD, see [13]). Then within a central region of radius Rsp = αγD (M/ρDD ) 1/(3−γ) , where αγ is given in ref. [13] and M = (2.6 ± 0.2) × 10 M⊙ is the mass of the central black hole, the dark matter density is modified to ρsp = ρ(r)ρc ρ(r) + ρc . (2) Here ρc = mχ/(σvtbh), where tbh is the age of the black hole (conservatively 10 10 yr), mχ is the mass of the neutralino, and σv is the neutralino–neutralino annihilation cross section times relative velocity (notice that for neutralinos at the galactic center σv is independent of v). Furthermore, ρ(r) = ρR g(r) ( Rsp r )γsp , (3) with g(r) = [1− (8GM)/(rc2)] accounting for dark matter capture into the black hole, γsp = (9− 2γ)/(4− γ), and ρR = ρD (Rsp/D). Annihilation rate. The total number of neutralino annihilations per second in the spike follows from the density profile as Γ = σv m2 ∫ ρsp4πr dr = 4πσvρinR 3 in m2 , (4)