cosmic rays from dark matter annihilations

ELSEVIER Nuclear Physics B (Proc. Suppl.) 87 (2000) 366-376

: ~ " - - ' - ' - ' - ' = I

PROCEEDINGS SUPPLEMENTS

www.elsevier.nl/locate/npe

Cosmic Rays from Dark Matter Annihilations P. Salati ~

aLaboratoire Ancil6vien de Physique Th6orique LAPTH Chemin de Bellevue, LAPP B.P. 110, 74941 Annecy-le-Vieux Cedex, France

Time has come to probe for the presence of weakly-interacting massive particles in the Milky Way. These species may contribute a substantial fraction to the mass of our galaxy. They may dominate its gravity and dynamical balance on large scales. Their mutual annihilations would yield several indirect signatures that are potentially detectable on Earth as extra-components to the various cosmic radiations. I will review those indirect signatures and show that the situation has significantly evolved since the last 1997 TAUP Conference. In particular, neutralinos may have followed the collapse of the massive black hole that sits at the galactic center. If so, the resulting dark matter spike would be such a strong gamma-ray and neutrino source that the entire supersymmetric parameter space could be within reach of the near future instruments.

1. A few introductory remarks.

A coherent scheme is emerging in cosmology. The search for remote supernovae SNIa allows for a better determination of the relation between the luminosity distance dL and the red-shift z of the sources. Current observations already constrain the mat ter ~ M and the vacuum ftn energy densi- ties to satisfy

1.3f~M -- ftn --~ -0.4=k 0.2 • (1)

The near-future measurements of the Cosmic Mi- crowave Background (CMB) inhomogeneities will also fix the angular scale of the first acoustic peak. This will soon lead to the determination of the geometry of the universe through its curvature f~K = 1 - ~ M -- ~ A . CMB observations performed so far are compatible with a mean value of ftK = 0. Together with the SNIa result (1), this leads to a vacuum density of ftn ~ 0.7 and to a mat ter density of ~'~M ~ 0.3. This result is in agreement with the measurements of the gas fraction in X-ray clusters which also point toward a value of ~M ~-- 0.35 4- 0.05. If on the one hand mat ter accounts for more than one-third of the closure density, on the other hand, primordial nu- cleosynthesis constrains the baryon density to be ~B ~-- 0.05 4- 0.005. We are therefore lead to the conclusion that a large fraction of the matter in the universe is non-baryonic. This is in agree-

0 9 2 0 - 5 6 3 2 / 0 0 / $ - see front matter © 2000 Elsevier Science B.V. PII S0920-5632(00)00699-X

ment with the scenarios of galaxy formation according to which baryons, at the end of recombi- nation, fall inside the potential wells of a collaps- ing distribution of cold and non-interacting matter. One of the favoured candidates to account for that non-baryonic cold dark mat ter (CDM) is a neutral weakly interacting particle. Such a species is predicted in particular by supersymme- try, a theory that is actively tested at accelera- tors. It is conceivable therefore that most of the dark mat ter in the halo of the Milky Way is made of these so-called neutralinos. Their mutual annihilations would yield several indirect signatures that are potentially detectable on Earth as ad- ditional components to the various cosmic radiations

X + X --~ qq, W + W - , . . . "-4 % P, D, e + ~ u ' s . (2)

Detection of these annihilation products re- lies on several experimental techniques which allow to probe different regions in the (mx , ~r) plane. Searches for antiprotons, antideuterons and positrons are performed by balloon and satellite-borne devices. Because the flux depends on the square of the neutralino density nx, the limit which may be set on the annihilation cross section scales approximately as m× 2. That type of search is mostly sensitive to low neutralino masses. High-energy photons are detected

All rights reserved.

P Salati/Nuclear Physics B (Proc. Suppl.) 87 (2000) 366-376 367

both by air Cerenkov telescopes (ACT) and by satellite-borne instruments. The neutralino annihilation rate, and hence the gamma-ray signal, also scale as m× -2. Because of the background in which that signal is swamped, the corresponding limit on the annihilation cross section approximately scales as the mass m×. This channel com- pares therefore with the direct searches, a tech- nique that is sensitive to the neutralino density n× = PDM/m× and that sets the same kind of limit on ~r. On the contrary, the neutrino channel offers the opportunity to probe for large values of m×. The corresponding limit on the annihilation cross section scales this time as m×-1. The heav- ier the neutralino, the more stringent the bound. This channel is therefore complementary to the other searches.

Dark mat ter may have partially collapsed in domains of larger than average density. A fraction f of the neutralinos may actually be in the form of clumps [1-3] inside which the annihilation rate, and hence the corresponding indirect signals, are increased by a factor of

A clumpy distribution of neutralinos leads therefore to the enhancement C = f x ~ of the various annihilation radiations. (i) In galactic haloes, the clumps should follow the CDM density fluctuations

that are related to the comoving wave vector k through the spectrum [4]

Ak 15 1 = P ( k ) = { lq_~k_t_l~kl .5+Tk2} 2 , (5)

with a = 1.71 x l, fl = 9 x 11.s and 7 = 12 where l = (f/h2) -1. Normalization to as = 0.8 gives A = 2.82 × 106 Mpc 4 when f~ = 1 and h = 0.5. In a restricted wavelength range, it is approximated by a power law

P(k) ~ k ~ (6)

The power spectrum P(k) of density fluctuations behaves as k -3 on small scales, i.e., for structures

typically lighter than Mi " l0 s Mo. As regards a possible clumpy structure of the halo around the Milky Way, the relevant mass range extends from Mi "~ l0 s M® up to Ms "~ 1012 M®. The corresponding spectral index n goes from -2 .6 to -2 .1 . When a numerical value is needed, we will take the effective value of n = -2 .36. Struc- tures smaller than Mi turn out to all have the same density. They contribute identically to the clumpiness factor C. There is no larger structure than the halo itself whose mass Ms reaches 1012 M o in the inner 100 kpc. Because the comoving wave vector k scales as M-1/3, neutralino density fluctuations depend on both the scale M and the redshift z as

~p - - ~ (1 + z) -1 M -("+3)/6 (7) P

The redshift factor (1 -4- z)-1 is typical of the t ~/3 growth of density fluctuations in a flat ma t t e r - dominated universe. Notice that small scale perturbations, for which n = - 3 , all become non- linear at the same time. Their subsequent collapse leads to virialized structures whose densi- ties have been enhanced by a factor of ,-, 180 with respect to the epoch of formation, when ~p/p reached unity. Small scale dark mat ter clumps all have therefore the same density today. The formation redshift of larger structures behaves as

(1 + ZF) c¢ M -(n+3)/6 , (8)

so that today, neutralino clumps with mass above ,-- l0 s M e have a density

p(M) c¢ 180 (1 -t- ZF) 3 c¢ M -(n+3)/2 (9)

The density p(Ms) of the largest possible clump should be comparable to the average dark mat ter density PDM in the galactic halo. If we assume that a fraction f of the latter is exclusively made of small clumps whose mass does not exceed Mi l0 s Me, we find

C = f ~ ' p ( M i ) ' ~ (Ms) (n+3)/2 [. p(Ms) J = f _ _ M i i , (10)

which numerically translates into C = 20 f . For a discussion of the case where the clumps span the mass range from Mi up to Ms, see Ref. [5].

368 P. Salati/Nuclear Physics B (Proc. SuppL) 87 (2000) 366-376

Depending on the fraction f , the enhancement of the indirect signals at stake does not exceed a factor of--~ 20. (ii) Neutralinos may cross the Sun or the Earth. If they interact in their interiors and lose enough energy to get trapped, they eventually concentrate at the cores of those celestial bodies and built up a dense distribution. Tha t is why the center of the Sun and, in a lesser extent the center of the Earth, are bright neutrino sources which will be discussed in section 4. (iii) Neutralinos may also be clumped at the galactic center. If they are distributed so as to built up an isothermal halo, their density profile is given by

p(r) o~ (r 2 + a2) -1 , (11)

with p® --~ 0.3 GeV cm -3 and a ,-~ 1 - 4 kpc. N-body simulations of structure formation show that a central cusp should appear at the centers of galaxies such as the Milky Way. The formation of that cusp drags down some of the cold matter at the core of the system so that the neutralino density profile should be quite peaked in the central region [6-8]. According to [6], the neutralino density diverges as r -1

r - 1

p(r) o¢ (1 + r/a) 2 ' (12)

with p® ~ 0.3 GeV cm -3 and a ,-~ 25 kpc. That central cusp could actually be a bright source of high-energy photons potentially observable by the next generation of ACT's. (iv) Last but not least is the effect of the massive black hole that sits at the center of the Milky Way. Monitoring of the stars in that central region [9] shows evidence for the presence in the inner ~ 0.1 pc of a celestial body whose mass reaches MnH = 2.6 x 106 M o. When collaps- ing, that black hole should have also dragged down some of the neutralinos floating around. Starting from an already cuspy distribution with Pinitial OC r -'y where 7 = 0 - 2, P. Gondolo and J. Silk [10] have shown that if the black hole formation is slow enough as to be adiabatic, neutralinos condense into a central spike whose density profile is given by

Pfinal OCr - ~ ' p (13)

The index %p varies from 1.4 for an initial isothermal distribution to 2.5 in the case of an initial cusp with */ = 2. The effect of that spike on the gamma-ray and neutrino signatures will be discussed in sections 2 and 4. For simplicity, we will assume here that the neutralino central spike amounts to a fraction A of the central black hole so that MDMspike ---- A MBH. Annihilations in that core should not proceed too efficiently under the penalty of erasing the neutralino condensa- tion. Assuming a cosmological density relic of fl×h 2 = 0.1 translates into an annihilation cross section of ,~ 3 x 10 -26 cm 3 s -1. Because the annihilation rate in that central spike cannot exceed the inverse of the age of the galaxy - ,-~ 10 Gyrs - the corresponding density is bounded by

PDMspike = (2.8 X l0 s M® pc -3) ml00 , (14)

where ml00 = mx/100 GeV. We also infer a typical spike radius of

aspike *'~ 0.13 pc A 1/3 ml"0 Us (15)

2. G a m m a - r a y s f r o m t h e M i l k y W a y a n d b e y o n d .

Neutralino annihilations lead both to a continuous spectrum of high--energy photons as well as to monochromatic gamma-ray lines through the box-mediated direct production

X + X - - ~ ' Y + 7 & "Y+Z ° (16)

The corresponding flux at the Earth may be expressed as

~susy 1 (o'v) N,y / 2 ds (17) - 41r m----~x los pX "

It may be split into an astrophysical piece and a particle physics part. The former term merely amounts to the integral along the line of sight of the dark matter density squared p×2. For a neutralino distribution with total mass M and typical size R, it is approximately given by M 2 R -s . Its bench mark value is -,, 0.1 214o 2 pc -5 in the case of the Milky Way, for R = 100 kpc. The particle physics piece depends on the annihilation cross section (~rv) averaged over the distribution

P. Salati/Nuclear Physics B (Proc. Suppl.) 87 (2000) 366--376 369

function of the neutralino velocities. That distribution function is typical of the system under scrutiny. For the halo of our galaxy, the one- dimensional dispersion velocity is o" = Vc/x/2 "~ 160 km/s whereas for the giant elliptical galaxy M87 at the center of the Virgo cluster, it reaches ,,~ 500 km/s. In relation (17), N~ denotes the total number of continuous or monochromatic photons that are produced in a single annihilation. In the latter case, N~ = 2 for the two-photon reaction while N~ = 1 for the 7 -Z ° channel.

Because the 7-ray signal from annihilating dark matter is faint, the most promising instruments are the atmospheric Cerenkov telescopes. When a high-energy photon impinges on the top of the atmosphere, it generates an electromagnetic shower that spreads over a significant area as it reaches the ground. The initial 7-ray energy is degraded into many optical photons that are potentially detectable by an array of telescopes. Analysis of the shape of that shower allows in principle to reconstruct the direction and the energy of the primary high-energy photon. ACT's get advantage of their large effective detection area. They suffer however from glaucoma as they can only monitor small portions of the sky at the same time. They are perfectly suited for faint and point-like sources such as the ones at stake here, i.e., the central spike at the galactic center or the extra-galactic system M87. Satellite-borne detectors are complementary. They are well suited for large solid angle surveys but their collecting areas are small.

In any case, the detection is made difficult by the presence of various backgrounds in which the signal is swamped. The dominant source arises from the cosmic ray (CR) high-energy electrons that impact on the upper atmosphere and also generate electromagnetic showers. An ACT cannot distinguish between a photon and a CR electron-induced shower. The corresponding flux is given by

(I)¢ = 6.4 × 10 -2 e- G e V - l c m - ~ s - l s r -1 ×

x (E/1 GeV) -33+°'2 (18)

Hadron-induced showers are more extended on the ground than those of the electromagnetic type. Stereoscopy is a powerful tool to discrim-

inate hadrons from electrons and gamma-rays. The CAT experiment, for instance, has already achieved a rejection factor of one misidentified event over a sample of 600 showers generated by CR hadrons whose flux at the Earth is

(I)had ---- 1.8 proton GeV -1 cm-2s -1 sr -1 x

× (E/1 GeV) -275 (19)

For satellite-borne instruments, the only background arises from the 7-ray diffuse emission of interstellar gas that shines under the action of the local CR protons. The corresponding emissivity may be expressed as

In(E) = 2 × 10 -3~ 7 H-1 G e V - l s - 1 sr-1 ×

× ( E / 1 T e V ) - 2 7 3

The hydrogen column density in the direction of the galactic center amounts to NH ~ 1.5 x 1023 H cm -2. The two-photon line seems to be the

-27

~ 1 0 I

fl°:F ~ 10

-31 10

-32 10

-33 10

-34 10

-35 10

E. A ~litz, C. BJq~. P. 84t~3,18i~ attd Fg T ~ , 1 ~

I . . . . . . . I I ~ J i L l I I I I J i l t ] I I I I I ~ l

10 2 10 3 10 4 Neutralino Mass (GeV)

Figure 1. Annihilation rate in the monochromatic channel 2-7 line. Each point corresponds to a specific supersymmetric configuration. The 3-~r detection limit is featured for an optimistic 10 km 2 yr exposure towards M87 together with an energy resolution of A E / E = 0.02 [5].

370 R Salati/Nuclear Physics B (Proc. Suppl.) 87 (2000) 366-376

most promising reaction to look for, provided the instrument has a good energy resolution. The resulting monochromatic photons have an energy E~ = m×. Relation (17) translates into [11]

I)susy = 3.8 x 10 -11 photon cm -2 s -1 sr -1 x .y

x (ev)29 m~-o 2 J(u) , (21)

where (av)29 is the annihilation cross section for the two-photon line process expressed in units of 10 -29 cm s s -1 while mlo = mx/ lO GeV. The line of sight integral J is expressed as a function of its bench mark value. The latter is given by the product r®p~ where a galactocentric distance of r® = 8.5 kpc has been assumed together with a halo density of p® = 0.3 GeV cm -3, typical of the solar neighborhood. If a NFW halo profile - relation (12) - is assumed for the neutralinos clumped at the galactic center, the line of sight integral becomes {J> ,-, 103 (1°/0) when averaged over an angle 0 from the center. The next generation of ACT's will typically have an effective collecting area of 0.1 km 2, an angular resolution of 0.1 °, a threshold of 50 GeV as well as an energy resolution of + 15 %. If the observation of the putative neutralino clump sitting at the galactic center is performed during 0.1 yr - two or three months equivalent - the collected statistics of the 3,-ray line annihilation photons amounts to

photons <~rv>29 m l 2 ( O ) , (22) Y =l.3× 10 5

to be compared to a background of CR electrons of

Are = 2.9 x l0 s electrons mi-0 ~'s -i-g . (23)

That electron background is uniformly distributed on the sky. It exhibits fluctuations of amplitude ~ which have a smaller chance of being interpreted as a signal when the significance S = N~/v/ ' f f~ is large. Requiring a 3-~r detection, this method is sensitive down to

2 (O'V>7.- / > 5 X 10 -29 cm a s -1 ml00 °'s5 (24)

By comparison, a 1 m 2 satellite-borne telescope with an energy resolution of 1 % would reach a similar sensitivity with

2 ((rv)-¢~ > 2 x 10 -28 cm a s -1 rnl001"is , (25)

should it monitor for two entire years a region of the sky within 1 ° from the galactic center. The small number of collected events is nevertheless a problem. Whatever the method - ACT or satellite - only the upper fringe of the supersymmetric configurations in the ((o'v>~,~ , mx) plane can be probed. The situation is quite different if we

~ i !a) . . . . . . . . . . . M87 1041 ,~ (b) m, = 1 TeV

Eo = 100 OeV

l~ 102 / k . . . . . . . . . . . . . . ,

Z 10

, (e) " ' . . . . . . ~

10 -2 _ ~ , , , I - - , L , , , , , , I - - ~

1 10@ (orcrnin)

Figure 2. The radial profiles of the neutral ino- induced signal (solid curves) and of the various backgrounds (dotted and dashed lines) are plotted as a function of the angular distance to the source centers. A fiducial model with m× = 1 TeV and (erV>cont.N~/ -- 10 -25 cm 3 s -1 is taken while a threshold of 100 GeV is assumed. The backgrounds are respectively labeled as (a): elec- tronic; (b): hadronic; (c): extragalactic; (d): M87 and (e): Milky Way gamma-ray diffuse emissions [5].

now assume the existence of a central neutralino spike. A precollapse NFW halo profile would be associated in that case to a present core radius of -,, 0.01 pc together with a total neutralino mass amouting to a fraction ), ,,0 10 -3 of the central massive black hole. An ACT would reach a 3-or

t?. Salati/Nuclear Physics B (Proc. Suppl.) 87 (2000) 366-376 371

detection limit of

2 (~rv);.~ >_ 3 x 10 -34 cm3s -1 ml00 -015 , (26)

for a detection cone encompassing a region within 0.1 ° from the galactic center. An impressive set of supersymmetric configurations becomes ex- plorable - see Fig. 1. Should Gondolo and Silk's analysis turn out to be correct, the galactic center would be a remarkable hot spot on the 7-ray sky.

Annihilation photons make it also possible to investigate the presence of neutralinos in extra- galactic systems. The most promising site is the giant elliptical galaxy M87 at the center of the Virgo cluster, some 15 Mpc away. That galaxy is known to contain large amounts of dark matter. Its line of sight integral of ,-, 10 M® 2 pc -5 is two orders of magnitude larger than for the isothermal halo around our Milky Way. Furthermore, M87 extends on ,-, 30 arcmin and appears as a point-l ike source, well-suited for an ACT observation. Finally, if a fraction f of the neutralinos that pervade M87 is in the form of clumps, the annihilation signals are enhanced by a factor of C ,~ 13 f to 40 f , depending on whether the clumps are smaller or bigger than Mi "~ l0 s M® [5]. In addition to the other backgrounds already discussed above, an extra-galactic component should also be considered as well as the diffuse emission arising from the in situ spallations of cosmic rays with the gas inside M87 i t se l f - see Fig. 2. Depending on the fraction f , the continuum 7-ray signal from M87 is detectable by the next generation of ACT's for a part of the supersymmetric configurations outlined in the upper- left panel of Fig. 3. Because low-energy photons are predominantly produced in neutralino annihilations, the lower the detection threshold, the better the sensitivity. Finally, even with the annihilation rate enhanced by a factor of 40, the gamma ray lines are out of reach, at least with the present and near future instruments.

3. T h e a n t i m a t t e r s i g n a t u r e : ~), e + & I).

The mutual annihilations of the neutralinos potentially concealed in the galactic halo could also produce an excess of ant imatter particles such

-23

~ 10

"-'AO Z ~1o

A

§ lO 10

10

lO

10

10

10 10 2 10 3 10 4

Neutralino Mass (GeV)

Figure 3. Annihilation rates in the continuum channels. The threshold has been set equal to Eta = 50 GeV. Considering M87 as the source, the 3-or detection limits for exposures of 0.01 km 2 yr are also presented. The region below the heavy solid lines will not be accessible, even with the next generation of Cerenkov telescopes. The lower solid line shows the region of accessibility if the annihilation rate is enhanced by a factor of 40 due to clumpiness [5].

as antiprotons, positrons and even antideuterons. Cosmic ray fluxes are about to be measured with unprecedented precision both by balloon borne detectors [12] and by space instruments [13]. The various ongoing experiments are also hunting for traces of antimatter. The search for antinuclei has actually profound cosmological implications. The discovery of a single antihelium or anticarbon would be a smoking gun for the presence of an- t imatter islands nearby. Alternatively, an excess of antiprotons at low energy - below ~, 1 GeV - has also been advocated as a potential signal for the putative supersymmetric dark matter.

As regards the antiproton cosmic radiation, the problem arises once again from the existence of a background. High-energy cosmic rays, mostly

372 P. Salati/Nuclear Physics B (Proc. Suppl.) 87 (2000) 366-376

protons, do produce antiprotons when they interact on the interstellar material

p(CR) + H(ISM) --+ /~ + X. (27)

Those secondary antiprotons propagate throughout the galaxy in just the same way as any other species. The erratic structure of the galactic magnetic fields results into the diffusive transport of the cosmic rays, both in the disk itself as well as in the ,,, 3 kpc thick layers above and be- neath it. Particles typically spend -~ 5 Myr in the disk where they cross a column density of ,,, 10 g cm -2 with which they interact or annihilate. During the remaining 90% of the time, they are confined in the magnetic fields that have spread out of the disk. If they survive to their diffusion throughout the Milky Way, they eventually escape into intergalactic space. Because the secondary antiprotons are not produced at rest, the low-energy part of their spectrum is expected to be depleted. A ,-, 10-20 GeV proton has actually little chance to produce an antiproton at rest by impinging on an hydrogen atom of the interstellar medium. Previous calculations of the seconday ~ flux at the Earth showed that the spectrum reaches a maximum for T~ ,-~ 2 GeV and significantly decreases below that peak. For just the same kinematic reasons, the mutual annihilation of neutralinos should favour on the contrary the production of low-energy primary antiprotons. The supersymmetric antiproton spectrum is actually flat. There is quite an excite- ment to extract from the observations a possible

exotic component which would signal the presence of supersymmetric dark matter in the galaxy. Unfortunately, it has been recently realized [14- 16] that a few processes add up together to flatten out, at low energy, the spectrum of the conventional secondary antiprotons from which a potential primary component becomes hard to sepa- rate. The dominant energy loss mechanism is the inelastic but non-annihilating interactions of antiprotons with the interstellar protons. The latter are excited towards resonant states and hence absorb part of the antiproton energy. Ionisation losses marginally contribute. The low-energy tail of the ~ spectrum is therefore replenished by the more abundant populations from higher energies.

P D ona to . N, F o r n e n g o , P. S a l a t i (19~81 I O s ~ r . . . . 7 ~ - ~ . . . . . F . . . . - r - ~

D AMs/IssA

x ~x x xx~ x

1 0 - a

* ~ x g a u g i n o

1 0 " 4 i ° . m i x e d

o h i g g s i n o L

1 0 ~ 5 [ I I I I ~ l , ~ I I I I i I J , r ~ I' L I I I ~ I I I

0 1 O0 200 300

m x (CeV)

Figure 4. The supersymmetric ]3 flux has been integrated over the range of IS energies extending from 0.1 up to 3 GeV/n. The resulting yield NI7 ) of antideuterons [17] which AMS on board ISS can collect is plotted as a function of the neutralino mass m x . Modulation has been considered at solar maximum.

That effect is further strengthened by solar modulation which also shifts the energy spectrum towards lower energies. As a result of these effects, the secondary ~'s are much more abundant at low energy than previously thought. Disentangling an exotic supersymmetric contribution from the conventional component of spallation antiprotons may turn out to be a very difficult task. The antiproton signal of supersymmetric dark matter is therefore in jeopardy.

Antideuterons, i.e., the nuclei of antideu- terium, are a priori free from such problems [17]. They form when an antiproton and an antineu- tron merge together during a spallation reaction or when a neutralino pair annihilates. Both antinucleons must be at rest with respect to each other in order for fusion to take place successfully. A spallation reaction creates very few slow antiprotons. The production of low-energy secondary antideuterons is further suppressed as both antin-

R Salati/Nuclear Physics B (Proc. Suppl.) 87 (2000) 366-376 373

ucleons must be at rest. The energy loss mecha- nisms are also much less efficient. With a bind- ing energy of B ,-~ 2.2 MeV, the antideuteron is a fragile nucleus. Any interaction, such as an inelastic but non-annihilating scattering, that would lead in principle to the I ) ene rgy loss is also associated to an energy transfer that de- stroys the antideuteron. On the other hand, su-

l0 a ,

10 z

l0 t

0.1 I

0 10- '

! O-S

10-4

10-6 10 ~

r. mmto, N. Pcnmp. ~ a u ( t i n )

...... D AMS/ISSA ~ ........ ~ ........ ~ ....... ~ ........ ~ .... .'I~! i!i ~_i_ ............ 1 ']

• ~*" !~/.! • . ':"~ ;::ii

'.!"i

iliii • ...... , ....... ~ ....... , ....... , ........ i .... ';;.! ........ i ...... ,I

l0 -~ 10"4 10 "~ 10 ..4 10 ~ 10-* 0.1 1 @~ (T~ = 0.24 GeV) (m-~ s -1 sr -1 CeV-')

Figure 5. In this scatter plot, the antideuteron yield NI3 of Fig. 4 is featured against the supersymmetric ~ flux [17]. The antideuteron signal is estimated at solar maximum. This corresponds to the AMS mission on board the space station. The ~ flux is derived on the contrary at solar min- imum, in the same conditions as the BESS 95 + 97 flights whose combined measurements are in- dicated by the vertical shaded band for a ~ energy of 0.24 GeV. The correlation between the antiproton and antideuteron signals is strong.

persymmetric D's are mostly manufactured at rest. In neutralino annihilations, antinucleons are predominantly produced with low energies. This feature is further enhanced by their subsequent fusion into antideuterons, hence a fairly flat spectrum as shown by F. Donato at this conference. Below a few GeV/n, secondary an-

tideuterons are suppressed with respect to their supersymmetric partners. Tha t low-energy sup- pression is orders of magnitude more effective for antideuterons than for antiprotons. This makes cosmic-ray antideuterons an alternate probe for supersymmetric dark matter. Fluxes are nevertheless quite small. A dozen only of secondary D's should be collected above an interstellar energy of ,,- 3 GeV/n on board the future space station borne AMS detector. Less than one secondary event is expected below that value where the bulk of the primary 13's is concentrated. The corresponding yield Nl3 is plotted as a function of the neutralino mass m x in Fig. 4. A decent amount of supersymmetric configurations can be probed. In Fig. 5, the sensitivity limits of the BESS 95 + 97 ~ and of the future 13 searches are compared.

Neutralino annihilations should also produce an extra flux of positrons. Those particles lose energy via synchroton emission and the inverse Compton scattering on both the CMB and diffuse starlight. As shown by E. Baltz and J. Edsj5 [18], primary fluxes are generally too small to be visible when an isothermal halo model and canonical propagation parameters are assumed. They are typically an order of magnitude or more smaller than the Heat [19] measurements. Furthemore, the excess at 6-50 GeV in the Heat data has not been confirmed by the recent measurements that are now in agreement with a pure secondary ori- gin of the positron radiation [20].

4. T h e h u n t f o r n e u t r i n o s : t r a v e l a t t h e c e n t e r o f t h e E a r t h .

Neutralinos may be captured by celestial bodies as they cross them and lose energy by scattering on a nucleus therein. The capture rate is the sum of a pure geometrical

Fgeo 9.6 x 1026s -1 0.3 v3OO m~-o 1 M p× .× ~ E,

(28)

and gravitational term

rg~v ~ 6.1 x 102~s -1 px°3 (~3oo~-1x J ra~o 1 x

374 P Salati/Nuclear Physics B (Proc. Suppl.) 87 (2000) 366-376

( M ) ~ Re × W (29)

where pO.3 ._ m×/0.3 GeV cm -3 and V 3°° is "X

the neutralino velocity expressed in units of 300 km/s. The sum of the product (a~v)2 6 {X~l/A~ over the various nuclear species with averaged mass fraction ( X i / a n d atomic number Ai is de- noted by ~. Neutralinos concentrate at the centers of the Sun and of the Earth where dense distributions built up. Those are strong neutrino sources through the mutual annihilations taking place there. A steady regime is soon reached where annihilations and captures balance each other. In particular, free-escaping muon- neutrinos are emitted. A few of them get trans- muted into muons as they interact in the ground below some terrestrial detector. This results into a flux of up-going muons that may be observed through the Cerenkov light which the particles radiate as they pass through water or ice.

The idea to instrument with optical modules a large domain in the polar cap or in the ocean is strongly pushed forward. Those so-called neutrino telescopes are actually mostly sensitive for large neutralino masses, a domain out of the reach of the above-mentionned investigations. The neutralino annihilation rate Fa in the solar core is just given by the trapping rate Ft. The subsequent neutrino flux Cv varies therefore as

o" ~ o( r ~ = r c o¢ ~ . (30)

m X

The neutrino energy Ev scales typically as m×. The conversion of these neutrinos into muons proceeds through weak charged current exchange whose cross section varies like G~ mp E~, ~x mx. The flux of up-going muons does not depend much therefore on the neutralino mass since both factors of m× cancel each other. Finally, muons lose through ionization on the order of 0.26 GeV for each meter of ice or water which they cross. The effective size of the conversion region in- creases with neutrino energy. The up-going muon signal crudely scales as m×. The larger the neutralino mass, the better the limit on the interaction cross section of those particles. A word of caution : the latter generally decreases with rn x

and neutrino absorption inside the Sun tends to degrade the muon signal at high energy.

As shown in Ref. [21], the limit of ,,~ 2 - 4 × 103 muons km -2 yr -1 (E~ > 1 GeV) set by the Baksan detector [22] just grazes the top of the set of supersymmetric configurations in the (¢~ , rex) plane. The few configurations which are excluded by Baksan are also excluded by the direct searches. Because the capture rate in the Earth is dominated by scalar interactions, the correlation between the up-going muon flux from the Earth core and the spin-independent cross section es~ is strong. Such a correlation does not exist in the case of the neutrinos originating from the Sun where the neutralino capture also depends on ax- ial interactions. The main source of background arises from the showers produced by cosmic rays impinging on the top of the atmosphere. In order to reject the downward-going muons, several optical modules need to be hit during a single event, the time patern allowing then to reconstruct the trajectory. The next generation of neutrino telescopes will be more sparsely instrumented. Muon ionization implies therefore a larger threshold of ,,~ 25 GeV to be compared to the present value of ~ 1 GeV. There is an irreducible background arising from the cosmic ray induced shower neutrinos produced on the other side of the Earth. With a 10 km 2 yr detector, supersymmetric configurations will be probed at the 3 -e level over a range of up-going muon fluxes extending from ,,, 10 to 104 particles km -2 yr -1.

Following a previous suggestion by A. Gould, a new population of neutralino dark mat ter has been recently found - at least theoretically - in the solar system [23]. Some neutralinos are gravi- tationally trapped by scattering on the outer layers of the Sun and evolve on grazing and quite eccentric orbits. Precession of the perihelion oc- curs as a result of the non-Coulomb nature of the gravitational potential which the particles expe- rience as they venture below the solar surface. Perturbations due to planets, mostly Jupiter, can make the orbits a little less eccentric so that the particles no longer intersect the Sun. Protected against a new and fatal scattering, a new population of neutralinos builts up, with very elongated orbits. It can persist in the solar system for more

P Salati/Nuclear Physics B (Proc. Suppl.) 87 (2000) 366-376 375

than a Gyr. This new population intersects the Earth orbit. This leads to an enhancement by at most a factor of ~ 2 in the rates for direct detection. Because those solar system neutralinos have a lower velocity than their halo partners, they are more efficiently trapped in the Earth core - see Eq. (29). The capture rate and the up-going muon flux sensitively depend on that velocity distribution. For some supersymmetric configurations with m× = 60 - 100 GeV, the muon signal can exceed by two orders of magnitude that predicted for halo neutralinos alone. The net effect [24] of that new population is to shift upwards by at most an order of magnitude the constellation of supersymmetric configurations in the (¢u , m×) plane. They are now configurations exceeding the Baksan limit. Those are nevertheless already excluded by the direct detection bound on (rsi.

If the halo profile is cuspy, the collapse of the massive black hole that sits at the galactic center generates the formation of a highly dense neutralino spike. To illustrate how strong a neutrino source such a clump could be, let us crudely es- t imate the corresponding up-going muon flux at the Earth. To commence, the neutralino annihilation rate inside the central spike is just set by the inverse of the age of the system, hence a value of ,-~ 3 x 10 - i s s -1. The total number of annihilations taking place therein amounts to

N~ ,~ 9 × 1043s -1 )~ m-1100, (31)

where A and rnl00 have been defined at the end of section 1. Let us assume in addition that neutralinos mostly annihilate into weak gauge bosons. The latter subsequently decay into muon neutrinos

X + X --+ W - + W + -+ I ~+ u u + . . . (32)

with a branching ratio Bu ~ 0.1. We infer a muon-neutr ino flux at the Earth of

B~, N,, ~u-- 47rr----~O -- (10-3vs-lcm -2) Aml-01o • (33)

Two-body decay implies a typical neutrino energy of Ev "~ E w /2 ,,~ m x / 2 . The converted muon follows the impinging neutrino direction and keeps typically half of its energy so that

E~, ,,, m×/4. The muon attenuation length because of ionization is

R u --~ (100m) rex00. (34)

We crudely approximate the conversion cross section by

a u ~ , = 10 -3scm 2 ~ • (35)

The neutrino to muon conversion rate is given by the product

PH20 R• o'v-+/~ "~ 3 × 10 - 9 m/00 . (36)

This leads to a muon signal

N , ~ (9.5 x 105km-2yr -1) A ml00, (37)

to be compared to an atmospheric up-going muon background of --~ 5 particles km -~ yr -1 above a threshold of 25 GeV. The neutrino signal from the galactic center spike should be clearly visible by the next generation of neutrino telescopes. A detailed analysis may be found in Ref. [10] as well as in P. Gondolo's contribution to this meeting. As Gondolo and Silk conclude, haloes with inner cusps may have spikes so bright that the absence of a neutrino signal already places upper limits on some supersymmetric configurations, depending on the inner halo slope 7.

5. C o n c l u s i o n s .

Quite a few developments have arisen since the last TAUP Conference at Gran Sasso.

The antiproton signal of neutralinos is fading away as it may be swamped in a secondary flux whose spectrum is flatter than previously estimated. If on the one hand, disentangling a supersymmetric primary component is harder, on the other hand, the limit which may be set on the models becomes also more stringent. In any case, a detailed calculation of the secondary antiproton spectrum is more than ever needed. Such an analysis should also incorporate for the sake of coherence the light nuclei abundances in cosmic rays in order to constrain the parameters of the propagation model. Antideuterons could provide a priori an alternate probe - even if the fluxes at stake are very small.

376 P. Salati/Nuclear Physics B (Proc. Suppl.) 87 (2000) 366-376

A refined treatment of the neutralino capture in the Sun has lead to the discovery of a com- pletely new population of neutralinos bound to elongated orbits inside the solar system. This new dark matter distribution in our vicinity implies an increase by a factor of ~ 10 of the corresponding up-going muon fluxes originating from the Earth core.

N-body simulations point toward the presence of a dense dark matter cusp at the galactic center. The collapse of the central massive black hole could have condensed even further the neutralinos into a highly dense spike which would be a strong neutrino and 7-ray source. Future neutrino telescopes and ACT's could well be able to probe entirely the various configurations of the standard supersymmetric model for galactic dark matter.

Finally, searching for a "/-ray signal from extra- galactic dark matter may be within reach of the next generation of ACT's, provided that the neutralinos are clumped. This would allow us to check the cosmological principle as regards the nature of dark matter. Following Giordano Bruno, we should actually expect the solution to the dark matter puzzle to apply to any system in the universe.

To conclude this contribution, I should say that time has come for optimism and that the solution to the missing mass problem is more than ever within reach of the near future instruments.

Acknowledgemen t s : P. S. would like to thank the organizers of TAUP 99 for the warm and re- laxing atmosphere of the Conference.

REFERENCES

1. L. BergstrSm, J. Edsj5 and P. Ullio, Phys. Rev. D 58, 083507 (1998).

2. L. BergstrSm, J. EdsjS, P. Gondolo and P. Ullio, Phys. Rev. D 59, 043506 (1999).

3. P Ullio, astro-ph/9904086. 4. M. Davis, G. Efstathiou, C.S. Frenk, and

S.D.M. White, Astrophys. J. 292,371 (1985). 5. E.A. Baltz, C. Briot, P. Salati, R. Tall-

let and J. Silk, preprint lapth-763/99 and astro-ph/9909112, to be published in Phys-

icM Review D. 6. J.F. Navarro, C.S. Frenk and S.D.M. White,

Astrophys. J. 462, 563 (1996). 7. A.V. Kravtsov, A.A. Klypin and A.M.

Khokhlov, Astrophys. J. Suppl. 111, 73 (1997).

8. Moore et al., Astrophys. J. Letters 499, L 5 (1998).

9. A.M. Ghez, B.L. Klein, M. Morris and E.E. Becklin, Astrophys. J. 509, 678 (1998).

10. P. Gondolo and J. Silk, Phys. Rev. Lett. 83, 1719 (1999).

11. L. Bergstrom, P. Ullio and J. Buckley, As~ tropart. Phys. 9, 137 (1998).

12. H. Matsunaga, Ph.D. thesis, University of Tokyo, 1997.

13. S. Ahlen et al., Nucl. Instrum. Meth. A350, 351 (1994).

14. A. Bottino, F. Donato, N. Fornengo and P. Salati, Phys. Rev. D 58, 123503 (1998).

15. L. BergstrSm, J. Edsj5 and P. Ullio, astro-ph/9902012 (1999).

16. J.W. Bieber et al., Phys. Rev. Lett. 83, 674 (1999).

17. F. Donato, N. Fornengo and P. Salati, preprint lapth-722/99 and FTUV/99-9 and astro-ph/9904481, submitted to Physical Rev iew D.

18. E.A. Baltz and J. EdsjS, Phys. Rev. D 59, 023511 (1999).

19. S.W. Barwick et al. (Heat Collaboration), As- trophys. J. Letters 482, L 191 (1997/.

20. M. Boezio et al. (Caprice Collaboration/, Proceedings of the 26th ICRC, contribution OG.l.l.16 (1999), Salt Lake City, USA.

21. L. BergstrSm, J. Edsj5 and P. Gondolo, Phys. Rev. D 58, 103519 (1998).

22. M.M. Boliev et al. (Baksan Collaboration), Nucl. Phys. B (Proc. Suppl.) 48, 83 (1996), TAUP 95, Toledo, Spain, 17-21 September 1996, ed. A. Morales.

23. T. Damour and L.M. Krauss, Phys. Rev. Lett. 81, 5726 (1998)& Phys. Rev. D 59, 063509 (1999).

24. L. BergstrSm, T. Damour, J. EdsjS, L.M. Krauss and P. Ullio, Journal of High Energy Physics 010, 9908 (1999).

cosmic rays from dark matter annihilations

Documents