A. NICOLAIDIS 1981

x

Figure 2. The galactic rotational velocity, due to a spherical

neutrino halo, as a function of the rescaled distance x.

Upper curve corresponds to Mv = Mc, lower to Mv = Mc. For

a Mc = 1011 Mʘ, real distance is obtained by multiplying the

dimensionless x by 36 Kpc.

curve corresponds to 11

10

c

M, 10 c

M

, lower

curve corresponds to 11

10

c

M, c

M

) and

there is agreement with the trends of the experimental

data.

We may reach our findings by making appeal to an

even simpler model [15,16]. A gravitational potential

well of the size of the galactic halo is filled up with neu-

trinos, which are treated like a Fermi-Dirac gas at zero

temperature. The total number of neutrinos is related to

the Fermi momentum, itself determined by the minimum

kinetic energy required for the neutrino to escape from

the galaxy. It is found then that the radius of the galaxy is

23

3Rq

53 2

10 cm

CDM0.5 eVm

, in full agreement with our results. In another

study, the analysis of the neutrino clustering by employ-

ing techniques of statistical mechanics favors again a

neutrino mass of few eV [17].

Is it possible to detect the cosmological relic neutrinos?

The gravitational clustering effect we studied here, en-

hances the local densities, however the average neutrino

energy is very small and the corresponding weak cross-

section (of the order of ) renders detection by

conventional means highly unlikely [18].

The few eV mass scale for the sterile neutrino, that our

study suggests, fits nicely with the findings of the reactor

and short-based neutrino oscillation experiments [3]. On

the other hand the cosmological verdict for a few eV-

mass sterile neutrino is rather unclear. The standard

framework provides the constraint

.

A modified though cosmology, with additional

radiation, can accommodate a few eV neutrino [19]. In

another direction, there is strong evidence for the exis-

tence of a 17 keV massive neutrino [20,21]. The coexis-

tence of distinct mass scales for the neutrinos, sub-eV,

eV and keV, indicates the complexity of neutrino physics.

Clearly we need further experimental information and

novel theoretical insights to decode the hidden dynamics.

In summary we presented a simplified model for the

gravitational clustering of massive neutrinos in the gal-

axies. There is no adjustable parameter in our analysis

and despite its simplicity the overall features of galactic

dynamics are reproduced.

Acknowledgements

I would like to thank Nicos Vlachos for helping me to

use the program MATHEMATICA in the numerical work.

This research was supported in part by the Templeton

Foundation and the EU program “Human Capital and

Mobility”.

REFERENCES

[1] A. Romanino, “Neutrino Physics,” CERN Yellow Report

CERN-2012-001, pp. 153-182.

[2] A. Strumia and F. Vissani, “Neutrino Masses and Mix-

ings and…,” arXiv:hep-ph/0606054.

[3] C. Giunti, “Phenomenology of Sterile Neutrinos,” arXiv:

1110.3914 [hep-ph].

[4] N. Mavromatos, “Neutrinos and the Universe,” Invited

Paper to NUFACT11, arXiv:1110.3729 [hep-ph].

[5] C. Tao, “Astrophysical Constraints on Dark Matter,” arXiv:

1110.0298.

[6] H. de Vega and N. Sanchez, “Highlights and Conclusions

of the Chalonge Workshop 2011,” arXiv:1109.3187 [as-

tro-ph.CO].

[7] A. Dolgov, “Cosmological Implications of Neutrinos,”

Surveys High Energy Physics, Vol. 17, No. 1-4, 2002, pp.

91-114. doi:10.1080/0124421021000054202

[8] M. Zombeck, “Handbook of Space, Astronomy and As-

trophysics,” Cambridge University Press, Cambridge, 1990.

[9] S. Chandrasekhar, “Stellar Structure,” University of Chi-

cago Press, Chicago, 1939.

[10] L. Landau and E. Lifshitz, “Statistical Physics,” Addison-

Wesley Publishing Co., Boston, 1969.

[11] J. Huntley and W. Saslaw, “The Distribution of Stars in

Galactic Nuclei: Loaded Polytropes,” Astrophysical Jour-

nal, Vol. 199, 1975, pp. 328-335. doi:10.1086/153695

[12] R. Viollier, F. Leimgruber and D. Trautmann, “Halos of

Heavy Neutrinos around Baryonic Stars,” Physics Letters

B, Vol. 297, No. 1-2, 1992, pp. 132-137.

doi:10.1016/0370-2693(92)91081-J

[13] R. Viollier, D. Trautmann and G. Tupper, “Supermassive

Neutrino Stars and Galactic Nuclei,” Physics Letters, Vol.

306, No. 1-2, 1993, pp. 79-85.

CDM[14] V. Rubin, W. Kent Ford Jr. and N. Thonnard, “Extended

Rotation Curves of High-Luminosity Spiral Galaxies. IV-

Systematic Dynamical Properties, SA through SC,” As-

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