Heavy-neutrino (or neutralino) stars are studied using the general relativistic equations of hydrostatic equilibrium and the relativistic equation of state for degenerate fermionic matter. The Tolman-Oppenheimer-Volkoff equations are then generalized to include a system of degenerate neutrino and neutralino matter that is gravitationally coupled. The properties and implications of such an interacting astrophysical system are discussed in detail. 04.40.Dg, 97.20.Rp, 95.35.+d, 97.60.Jd, 98.35.Jk

Abstract. We report on a calculation of the growth of the mass of supermassive black holes at galactic centers from dark matter and Eddington -limited baryonic accretion. Assuming that dark matter halos are made of fermions and harbor compact degenerate Fermi balls of masses from 10 3 M to 10 6 M , we find that dark matter accretion can boost the mass of seed black holes from about ∼5 M to 10 3−4 M black holes, which then grow by Eddington-limited baryonic accretion to supermassive black holes of 10 6−9 M . We then show that the formation of the recently detected supermassive black hole of 3 × 10 9 M at a redshift of z = 6.41 in the quasar SDSS J114816.64+525150.3 could be understood if the black hole completely consumes the degenerate Fermi ball and then grows by Eddington-limited baryonic accretion. In the context of this model we constrain the dark matter particle masses to be within the range from 12 keV/c 2 to about 450 keV/c 2 . Finally we investigate the black hole growth dependence on the formation time and on the mass of the seed black hole. We find that in order to fit the observed data point of M BH ∼ 3 × 10 9 M and z ∼ 6.41, dark matter accretion cannot start later than about 2 × 10 8 years and the seed BH cannot be greater than about 10 4 M . Our results are in full agreement with the WMAP observations that indicate that the first onset of star formation might have occurred at a redshift of z ∼ 15−20. For other models of dark matter particle masses, corresponding constraints may be derived from the growth of black holes in the center of galaxies.

We report here on a calculation of possible orbits of the fast moving infrared source S1 which has been recently observed by near the Galactic center. It is shown that tracking of the orbit of S1 or any other fast moving star near Sgr A * offers a possibility of distinguishing between the supermassive black hole and extended object scenarios of Sgr A * . In our calculations we assumed that the extended object at the Galactic center is a non-baryonic ball made of degenerate, self-gravitating heavy neutrino matter, as it has been recently proposed by Tsiklauri & Viollier (1998a,b).Subject headings: black hole physics -celestial mechanics, stellar dynamics -dark matterelementary particles -Galaxy: center In spite of the vast and tantalizing work undertaken to resolve the issue of the existence of supermassive black holes (BH) at the centers of galaxies, it seems fair to say that, in this case, the jury is still out (for a current status see e.g. a review paper by Ho 1998). The discovery of quasars in the early 1960's provoked the idea that these extremely powerful emission sources draw their energy from accretion of matter onto compact, supermassive objects of 10 6 to 10 9 solar masses. This has led many to believe that these objects

Aims. We study the distribution of fermionic dark matter at the center of galaxies using NFW, Moore and isothermal density profiles and show that dark matter becomes degenerate for particle masses of a few keV and for distances less than a few parsec from the center of our galaxy. Methods. A compact degenerate core forms after galaxy merging and boosts the growth of supermassive black holes at the center of galaxies. Results. To explain the galactic center black hole of mass of ∼3.5 × 10 6 M and a supermassive black hole of ∼3 × 10 9 M at a redshift of 6.41 in SDSS quasars, we require a degenerate core of mass between 3 × 10 3 M and 3.5 × 10 6 M . This constrains the mass of the dark matter particle between 0.6 keV and 82 keV. The lower limit on the dark matter mass is improved to 7 keV if exact solutions of Poisson's equation are used in the isothermal power law case. We argue that the constrained particle could be the long sought dark matter of the Universe that is interpreted here as a sterile neutrino.

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After a discussion of the properties of degenerate fermion balls, we analyze the orbits of the stars S0-1 and S0-2, which have the smallest projected distances to Sgr A * , in the supermassive black hole as well as in the fermion ball scenarios of the Galactic center. It is shown that both scenarios are consistent with the data, as measured during the last six years by Genzel et al. and Ghez et al. The free parameters of the projected orbit of a star are the unknown components of its velocity v z and distance z to Sgr A * in 1995.4, with the z-axis being in the line of sight. We show, in the case of S0-1 and S0-2, that the z − v z phasespace, which fits the data, is much larger for the fermion ball than for the black hole scenario. Future measurements of the positions or radial velocities of S0-1 and S0-2 could reduce this allowed phase-space and eventually rule out one of the currently acceptable scenarios. This may shed some light into the nature of the supermassive compact dark object, or dark matter in general at the center of our Galaxy.

It has been recently shown (Munyaneza, Tsiklauri and Viollier 1998) that the analysis of the orbits of the fast moving stars close to Sgr A * (Eckart and Genzel 1997) provides a valuable tool to probe the gravitational potential near the Galactic center. As an example, we present here the results on a calculation of possible orbits of the star S0-1 in both, the black hole and degenerate neutrino ball scenarios of the central mass, based on the recent measurements of stellar proper motions at the Galactic center by Ghez et al. 1998. Taking into account the error bars of their analysis, it is shown that within a few years time, the orbit of S0-1 may indeed reveal the nature of the supermassive compact dark object at the Galactic center.

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