## 1. IntroductionUltra Compact Objects (UCOs) with radius ( mass of the star) are interesting entities. In principle, trapping of mass-less particles in UCOs potential well is possible or the object can oscillate in its quasinormal modes (Kembhavi & Vishveshwara 1980; Chandrasekhar & Ferrari 1991). Van Paradijs (1979) had pointed out the peculiar behavior of redshift for . Existence of UCO was speculated by Iyer & Vishveshwara (1985), Iyer et al. (1985), and Lattimer et al. (1990). The first calculations, showing the existence of trapped photon or neutrino orbits inside such a UCO were made by Kuchowicz (1965) and de Felice (1969). Recently, Negi & Durgapal (1996) have obtained various types of trajectories of such particles (photons or neutrinos), for different initial conditions, inside a UCO characterized by parabolic density variation. Furthermore, the rotation period and mass of dense matter objects
with are important regarding
sub-millisecond pulsars (smps). Haensel & Zdunik (1989) discussed
the uniform rotation for a static mass of
, and found that nearly all the
existing realistic equations of state (EOSs) fail to provide a
suitable model for smps. They found that in order to have a successful
model for smps, the equation of state (EOS) should correspond to the
matter of maximum stiffness [which corresponds to the condition that
the speed of sound, = speed of light
(= 1 in geometrized units) where
and is the value of Characteristics of the super-dense objects like neutron stars are
based on the calculations of the EOS for the matter at very high
densities. However, the nuclear interactions beyond the density of
g cm In order to obtain an upper limit for the neutron star masses
various theoretical models have been proposed. As the status of EOS of
nuclear matter cannot be established empirically, one can apply
physical constraints to obtain an upper bound of neutron star mass.
Brecher & Caporaso (1976) assumed that the speed of sound in the
nuclear matter equals the speed of light and obtained a value of
as an upper limit of the neutron
star masses by using EOS given by Eq. (1) and a surface density,
g cm Earlier, Rhoades & Ruffini (1974), without going into the
details of the nuclear interactions, assumed that beyond a certain
density g cm Hartle (1978) emphasized that the maximum masses of neutron stars obtained in this manner involve a scale factor, say, , such that, the matching density, , plays a sensitive role to obtain an upper bound on neutron star masses. Usually, is taken to be equal to or greater than one in all the conventional models. For the densities less than , the matter composing the object is assumed to be known and unique. That is, the EOS of the envelope of these stars are chosen so that the `abnormalities' in the sense mentioned above are removed. Friedman & Ipser (1987) calculated the masses of the neutron stars for different values of the matching densities by using EOS's in the envelope given by BPS and NV (Negele & Vautherin 1973), respectively, and concluded that for each case the mass in the envelope is negligible compared to that in the core containing the most stiff material. Furthermore, in all these cases the EOS chosen for the envelope are also uncertain and have little empirical support. Another possibility which leads to an entirely different property
of compact objects is that, in the absence of gravity high density
baryonic matter is bound by purely strong forces. It can be shown that
non-gravitationally bound bulk hadronic matter is consistent with
nuclear physics data (Bahcall et al. 1989) suggesting that bulk
hadronic matter is just as likely to be the correct description of
matter at high densities as the conventional unbound hadronic matter.
In general, the high-density non-gravitationally bound states of
baryons are called "baryon matter" (Bahcall et al. 1990) and the terms
"hadronic matter" or "quark Matter" are used for baryon matter
described by theories of hadrons or quarks. Baryon matter refers to
the saturating, large fermion number limit of these states in theories
of either quarks or hadrons. Bahcall et al. (1990) gave an EOS, based
upon effective field theory, which is consistent with all nuclear
physics data, and low energy interaction data (Lynn et al. 1990), and
they argued that possibly all the neutron stars are Thus, we can summarize the whole scenario of EOS for the super-dense objects as follows: (a) If we consider a hadronic matter we expect the density of the matter to vanish with the vanishing pressure, that is, near the surface of the star we must have an equation of state pertaining to a vanishing density. The model of the super-dense object may have a high density core represented by some stiff EOS surrounded by matter represented by EOS derived from the known nuclear interactions and extrapolated to densities at which these EOS are matched with the stiff EOS in the core. The matter represented by EOS corresponding to hadronic matter is surrounded by empirically known EOS [one or more in sequence] such that we obtain a vanishing small density at the surface of the star where the pressure vanishes. The examples for such models are due to Rhoades & Ruffini
(1974), Hartle (1978), and Friedman & Ipser (1987). Recently,
Kalogera & Baym (1996) considered a model in which the most stiff
core is matched to the WFF (Wiringa et al. 1988) EOS in the envelope,
which is then matched to a crust with the EOS given by BPS.
Glendenning (1992) considered a rotating structure with a core of most
stiff EOS up to a density of
g cm (b) We may choose a baryonic matter surrounding the stiff core or
an entire structure consisting of baryonic matter. In this case we are
free to choose a finite density at the surface of the structure where
the pressure vanishes. The baryonic matter represents a perfect fluid
and can have densities lower than
g cm Thus, to obtain a physically viable, upper mass limit for superdense objects, one may introduce certain constraint on the matching density, , from the observational evidences known at present. The important observational evidences are: (A) The minimum rotation period of the fastest rotating pulsars, PSR 1937 + 214, or PSR 1957 + 20 known to date is 1.558 ms [see, e.g., Müther et al. 1991, and references therein]. Assuming this pulsar as a To avoid the discrepancy in the theoretical results of Hochron et
al. (1993), and the observational data put forward by Dolan (1992),
one may use values of less than
g cm © European Southern Observatory (ESO) 2000 Online publication: December 17, 1999 |