Dark matter search

The first evidence for dark matter comes from the observation by the Swiss as-tronomer F. Zwicky [17] in 1933 of the rotation curves of velocity versus radial distance for stars and gas in spiral galaxies. This gave indirect proof for the existence of missing mass in the form of non-luminous matter. In fact, using simple newtonian gravity, con-sider a star of mass m at distance r from the galactic centre, with velocity v. Then from the equality between gravitational and centrifugal forces we obtain

mv²

r = mM(r)G

r² (1.32)

where M(<r) is the mass inside radius r:

M(<r) =

∝r³ if m is inside the nucleus of the galaxy

M_tot if m is outside the nucleus of the galaxy (1.33) with M_tot the total mass of the galaxy. So in the first case we have v ∝ r and in the second we expect v ∝ r^−1/2. Therefore the velocity should increase at small r and decrease at large r. But for many spiral galaxies, the rotation curves are almost flat at large r, as shown in Fig. 1.34. Possible explanation are a spherical halo of Dark Matter or a modification of gravity at small accelerations [19] (such theories are called MOND, MOdified Newtonian Dynamics).

1) galaxy rotation curves

Begeman et al., MNRAS 249 (1991)

The Evidence for DM

v

(r) =

r G

M (r) r m v

(r)

r = G

mM (r) r

‘centrifugal’ ‘centripetal’

with

M (r) = 4⇡

Z

⇢(r) r

dr

v

(r) ∼ const ⇒ ρ

(r) ∼ 1 r

particles distributes like 1/r²

Figure 1.13: Fit to the rotation curve of galaxy NGC 6503. The rotation curves of the single components are also shown: the dashed curves are for the visible components, the dotted curve for the gas and the dash-dotted curve for the dark halo. Picture taken from [18].

1.5.1 Evidence of Dark Matter at galactic and galaxy cluster scales Recently results based on the same principle were reported in [20] (some examples in Fig. 1.14), using as reference scale Ropt: the radius containing 83% of the total luminous

CHAPTER 1. COSMIC RAYS IN THE UNIVERSE

matter in a particular galaxy. Additionally, a direct evidence of Dark Matter (DM) was

Figure 1.14: Best fit to the velocity of spiral galaxies as a function of the rotation curve. The fit includes two components: the dotted line represents the galactic disk contribution and the dashed line the dark matter halo contribution. The galaxies shown are arranged by magnitude.

Picture taken from [20].

obtained with the image of the famous Bullet Cluster [21]: two colliding galaxies that showed the presence of collisionless DM (see Fig. 1.15 ).

Figure 1.15: Optical (left) and X-ray (right) image of the merging cluster 1E0657-558. The white bar indicates a 200 Mpc scale. The green contours are related to the gravitational lensing measurements that allowed in the X-ray picture to disentangle the interacting baryonic plasma (red and yellow) matter from the collisionless DM (blue). Picture taken from [21].

28

1.5.2 Search of Dark Matter with cosmic rays

The particle that we know exists and with properties to allow it to be the dark matter candidate is the neutrino, since it interacts very little with ordinary matter. But a light neutrino could contribute only in part to the matter density and an additional form of dark matter is required. WIMP particles (Weakly Interacting Massive Particles), not explained by the Standard Model (SM) of particle physics, are expected to explain the presence of this matter. Particle physicists regard supersymmetry as the most viable extension of the SM. The Lightest Supersymmetric Particle (LSP) or neutralino, is stable and is a good cold dark matter in the form of a WIMP candidate. However the LSP is not the only option for particle dark matter. Other proposed particles are the axion (an ultra-light particle), the sterile neutrino and the Kaluza-Klein particle. Their mass varies from theµeV to the TeV scale [22].

We consider that dark matter particles undergo the following reaction in the galaxy:

DM + DM→SM + SM. (1.34)

SM could be any kind of Standard Model particle. Antiprotons, for example, can be produced only by spallation in the ISM and measuring its flux can help in understanding if there are other sources. A summary plot with the various measured cosmic-ray fluxes multiplied by R^2.7, where R is the rigidity¹, is shown in Fig. 1.16. The presence of

Figure 1.16: Fluxes of the elementary cosmic rays multiplied by R^2.7. The different colors in the axis refer to the particular species. Picture taken from [23].

DM is probed by studying the positron fraction, defined as the ratio of the number of positrons divided by the total number of electrons and positrons e⁺/(e⁺+ e⁻), and

1The rigidity for a particle of charge Ze and momentum p is defined as R = _Ze^pc, where c is the speed of light.

CHAPTER 1. COSMIC RAYS IN THE UNIVERSE

the electron plus positron flux (all-electron). Taking into account only the spallation production of positrons, one expects that the positron fraction decreases as function of energy. Contrary to the expectations, several experiments measured an increase (see Fig. 1.17). We show also the all-electron flux measured by DAMPE in Fig. 1.18 compared to previous results. The excess in the positron fraction and in the all-electron flux can be

29. Cosmic rays 5

Energy (GeV)

1 10 10²

))-(eF)++(eF)/(+(eFPositron Fraction

0 0.05 0.1 0.15 0.2 0.25

HEAT AMS-02 PAMELA

Figure 29.3: The positron fraction (ratio of the flux of e⁺ to the total flux of e⁺ and e⁻) [26,24,30]. The heavy black line is a model of pure secondary production [28] and the three thin lines show three representative attempts to model the positron excess with different phenomena: green: dark matter decay [29]; blue:

propagation physics [32]; red: production in pulsars [40]. The ratio below 10 GeV is dependent on the polarity of the solar magnetic field.

and polarity of the solar cycle [37] in the opposite sense to that of the positron fraction.

There is at this time no evidence for a significant primary component of antiprotons. No antihelium or antideuteron has been found in the cosmic radiation. The best measured upper limit on the ratio antihelium/helium is currently approximately 1×10⁻⁷ [38]

The upper limit on the flux of antideuterons around 1 GeV/nucleon is approximately 2×10⁻⁴(m²s sr GeV/nucleon)⁻¹[39].

29.2. Cosmic rays in the atmosphere

Figure 29.4 shows the vertical fluxes of the major cosmic-ray components in the atmosphere in the energy region where the particles are most numerous (except for electrons, which are most numerous near their critical energy, which is about 81 MeV in air). Except for protons and electrons near the top of the atmosphere, all particles are produced in interactions of the primary‡cosmic rays in the air. Muons and neutrinos are products of the decay chain of charged mesons, while electrons and photons originate in decays of neutral mesons.

‡ When discussing cosmic rays in the atmosphere, ‘primary’ is used to denote the original particle and ‘secondary’ to denote the particles produced in interactions.

June 5, 2018 19:57

Figure 1.17: Comparison of the positron fraction measured by several experiments [24–26]. The black line represents the expectation of pure secondary production [27]. Picture taken from [11].

explained with the existence of Dark Matter [33], the secondary production of positrons as products of interaction of cosmic rays with the ISM [34], or with the production of high energy electrons and positrons from electrons accelerated in the magnetosphere of pulsars [36]. Recently, observations from the HAWC telescope suggest that pulsars can explain this excess [35]. Until now there is not a unique explanation for the excess, so more data is needed to give a clearer picture.