Y. Ascasibar
Astrophysikalisches Institut Potsdam
An der Sternwarte 16, Potsdam 14482 (Germany) yago@aip.de
Summary.
According to the current paradigm, about 80 per cent of the cosmic matter is composed of cold dark matter particles, whose gravitational influence plays a fundamental role in galaxy formation and evolution. It is the object of this talk to discuss additional effects, due to annihilation or decay of such particles, that could yield detectable signatures. In particular, for particle masses between 1 MeV and 4
GeV, heat from dark matter annihilation may considerably suppress star formation, at different epochs and on different scales, from dwarf galaxies to galaxy clusters.
By definition, dark matter is not supposed to interact with the electromagnetic field, i.e. it does not emit, absorb, nor reflect light. Its presence, first suggested in order to explain the mass of the Coma cluster [1], can only be infered from its gravitational influence. Nowadays, the contribution of dark matter particles to the total energy density can be measured with unprecedented accuracy [2], and the processes of gravitational collapse and structure formation have been thoroughly studied. Yet, apart from the fact that it must be cold (i.e. nonrelativistic), the details of the dark matter physics are nevertheless one of the most fundamental unsolved problems in Astrophysics and Cosmology.
From a particle Physics perspective, many competing theories predict the existence of new stable particles, some of which could, in principle, account for all the cosmic dark matter. The working definition of dark matter stated above is definitely not valid within this context. Depending on the details of underlying model, dark matter particles are indeed expected to interact amongst themselves, and even (albeit with a very small probability) with ordinary baryonic matter and photons (see e.g. [3, 4] for recent reviews).
In particular, Light Dark Matter (LDM) particles [5, 6], with masses m dm of the order of a few MeV, can produce large amounts of relatively low-energy photons, electrons, and positrons through different annihilation (or decay, e.g. [7, 8]) channels. The emissivity, for the case of decaying particles, is proportional to the dark matter density, ρ dm
, while it is proportional to ρ 2 dm for

2 Y. Ascasibar the annihilation products. In fact, the relevant quantity is the number density of dark matter particles, n dm
= ρ dm
/m dm
, and thus, for a given mass density
(which can be inferred from different observations, or computed by means of cosmological N-body simulations), LDM particles are expected to yield a signal much larger than that arising from heavier candidates.
On particle scales, the LDM model predicts [9, 10, 11, 12] small deviations in the ratio between neutral and charged currents (the so-called NuTeV anomaly), as well as on the anomalous magnetic moment of electrons and muons (which would explain the slight discrepancy between the value of the fine structure constant measured from the quantum Hall effect and the theoretical estimate based on QED). On astrophysical and cosmological scales, the electrons, positrons and gamma rays arising from LDM decay or annihilation are expected to have an even more noticeable effect. In particular, we discuss the 511 keV line due to the annihilation of positrons at rest and the gamma-ray continuum emission from the galactic centre. Finally, we also briefly explore the possibility that LDM annihilations could inject a significant amount of energy to the surrounding baryonic gas.
When two dark matter particles decay or annihilate, their energy goes into the primary products. In the case of LDM, these can only be gamma-ray photons in the ∼ MeV range and electron–positron pairs. The latter would also radiate most of their initial kinetic energy in the gamma-ray continuum, eventually annihilating (almost at rest) with the electrons of the interstellar medium, giving rise to an emission line at 511 keV.
2.1 511 keV Line
Astrophysical positron sources (e.g. supernovae, or the central black hole) could in principle produce enough positrons to match the measured intensity of the 511 keV annihilation line observed at the galactic centre. However, it is extremely difficult to understand how they could result in the spherically symmetric and extended (
INTEGRAL satellite [13].
∼ 9 ◦ FWHM) morphology observed by the
LDM provides an admittedly exotic explanation of the phenomenon, but it naturally reproduces the observed intensity and morphology of the emission, assuming reasonable values for both the dark matter and the Milky Way parameters. A thorough comparison with INTEGRAL/SPI data [12] shows that LDM particles should be bosonic and self-annihilating, and the required cross-section implies the existence of both bosonic and fermionic mediators as long as m dm
< 100 MeV.
Concerning the Milky Way itself, if most of the galactic positrons did indeed arise from dark matter annihilations, the intensity of the 511 keV line

Astrophysical Effects of (Light) Dark Matter 3
Fig. 1.
Constraints on the inner logarithmic slope of the density profile, γ ≡
£ d log ρ d log r
¤ r
→
0
. The maximum likelihood ratio is plotted as a function of γ . Roughly speaking, a given value of γ is ∼ e −
∆
MLR
( γ ) times less likely to explain the data than γ min
= 1 .
03 [12].
would also provide an extremely accurate map of the dark matter density profile, particularly in the always controversial innermost regions. More precisely, the inner logarithmic slope of the density profile can be tightly constrained,
γ = 1 .
03 ± 0 .
04 (Figure 1), in encouraging agreement with the results of cosmological N-body numerical experiments (e.g. [14]).
It must be said, though, that such a tiny error budget does not include the (obviously much larger) systematic error arising from several simplifying assumptions, such as spherical symmetry or local annihilation. A more accurate computation would require the choice of a particular dark matter model, the distribution of the baryonic gas in the Galaxy and its chemical composition, the intensity and spectrum of the background radiation density and the magnitude and orientation of the magnetic field. Once they are properly accounted for, the 511 keV line would provide an unvaluable diagnostic tool to constrain the properties of the dark matter particles, as well as the shape of the Milky Way (and maybe other) dark matter haloes.
2.2 Continuum
A significant fraction of the initial energy of the positrons will be radiated away at different wavelengths, most notably gamma rays. The main emission mechanisms are the final state radiation (also known as internal bremsstrahlung)
[15, 16], inverse Compton scattering of background photons, and in-flight positron annihilation [17]. All these processes give rise to a gamma-ray continuum that must be compared with existent data in order to test the viability of the LDM scenario.

4 Y. Ascasibar
Fig. 2.
Gamma ray flux expected for m dm
= 30 (leftmost curves) and 100 MeV
(rightmost curves) LDM particles (solid and dashed lines correspond to galactic longitudes | l | < 30 ◦ and | l | < and EGRET (diamonds) data.
5 ◦ , respectively), compared to COMPTEL (circles)
A comparison of the expected final state radiation with observational gamma-ray data [18] from COMPTEL/EGRET satellites is shown in Figure 2. Apart from the aforementioned uncertainties in our crude modeling of positron propagation, as well as on the exact internal bremsstrahlung emission (see the discussion in [16]), the details of the comparison play also an important role on the final constraint one obtains for the dark matter mass
[12, 19]. Comparing with the whole area observed by the satellites (solid lines) or making the approximation that all the gamma-ray emission comes from the innermost 5 degrees (dashed lines) results in significantly different upper limits for m dm
. Moreover, it is also of critical importance to make an accurate
(and self-consistent) estimate of the contribution from astrophysical sources in order to obtain a reliable constraint.
The most interesting, however, is not the energy that reaches us as gamma rays, but the uncertain amount (see e.g. [20]) that is actually absorbed by the surrounding baryonic gas, which is thus heated and ionized. On the scale of individual objects, annihilating LDM would effectively act as a “cosmic heater” at the centre of every dark matter halo, providing an energy source that is completely independent from (and perhaps larger than) feedback from star formation [21].
Figure 3 shows that the heating rate expected from annihilating dark matter (dashed lines) is usually much lower than the cooling rate (solid lines) given

Astrophysical Effects of (Light) Dark Matter 5
Fig. 3.
Heat injection by annihilating dark matter (dashed lines), assuming that all energy is absorbed by the gas, compared to the local cooling rate (solid lines) in a dwarf galaxy, the Milky Way, and a galaxy cluster. The insets shows the cooling function used, taken from [22].
by the cooling function of a primordial gas (plotted in the inset). Energy injection is only relevant near the centre ( ∼ 6 pc, 160 pc, and 5 kpc for a dwarf galaxy, the Milky Way and a galaxy cluster, respectively).
Although these regions are relatively small, it is there where most of the star formation is expected to take place. Even more importantly, ionization by Coulomb collisions or inverse Compton-scattered CMB photons would dramatically change the cooling curve of the gas, which would reduce the cooling rate by several orders of magnitude in dwarf galaxies. The net effect on galaxy formation and evolution is difficult to quantify, but simple energetic arguments
[21] suggest that annihilating LDM particles might play a crucial role in the cosmic star formation history.
Perhaps the most important lesson that I have learned from this exercise is that, contrary to what the name suggests, dark matter may not only (at least, indirectly) interact with “normal” matter, but even shine at gammaray (and potentially other) frequencies. The amount of interaction might only be of (remarkable) philosophical or academic interest for heavy dark matter candidates; for LDM, it supposes a substantial change to our current paradigm of how galaxies are supposed to form their stars.
Most surprisingly, such a radical prediction of the model is not enough to rule it out immediately. Quite the opposite, a heat source at the centre of every dark matter halo that prevented star formation in the innermost

6 Y. Ascasibar regions of galaxies would be more than welcome from an astrophysical point of view. A more elaborate prediction of the consequences of LDM annihilation may turn out to find the long-sought solution to several unsolved problems in
Cosmology... or the ultimate piece of evidence that falsifies the LDM scenario.
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