Neutron stars observations

This represents an upper limit for the dimensions of the nucleus. Compared with the estimates for the size of the atom, obtained from kinetic theory calculations on gases, which are typically 4x10 9 m. we can see that the nucleus is very small indeed compared to the atom as a whole - a radius ratio of 10-5, or a volume ratio of 10 15, which supports Rutherford s observation that most of an atom consists of empty space. We can also conclude that the density of the nucleus must be extremely high - 1015 times that encountered in ordinary matter, consistent with density estimates in astronomical objects called pulsars or neutron stars. 

Abstract After some historical remarks we discuss different criteria of dynamical stability of stars and the properties of the critical states where the loss of dynamical stability leads to a collapse with formation of a neutron star or a black hole. At the end some observational and theoretical problems related to quark stars are discussed. 

The discovery of the quark structure of matter led to the suggestion of possible existence of quark stars, which are even more compact than neutron stars. In the presence of indefiniteness concerning the quark structure of matter it is not possible now to make definite statements about the existence or nonexistence of stable quark stars, observational and theoretical investigations on this topic are still in progress. 

In this review I first make a historical excursus into the problem, mentioning the results of the key works. Several criteria of stability are discussed, with the main focus on the static criteria, and the energetic method, which permits to obtain conclusions about the stability (sometimes approximate) in a most simple way. Critical states of compact stars at the boundary of the dynamic stability are considered, at which the star is becoming unstable in the process of energy losses, and a collapse begins leading to formation of a neutron star or a black hole. Physical processes leading to a loss of stability are discussed. At the end some observations and theoretical problems connected with quark stars are considered. 

Figure 3. The observable and proper masses of neutron star models with non-ideal matter, from Cameron (1959).

There are no firm observational contradictions to the conventional model of the hadronic neutron star. 

Abstract From the earliest measurements of the masses of binary pulsars, observations of neutron stars have placed interesting constraints on the properties of high-density matter. The last few years have seen a number of observational developments that could place strong new restrictions on the equilibrium state of cold matter at supranuclear densities. We review these astronomical constraints and their context, and speculate on future prospects. 

However, it is impossible to isolate the matter in the core of a neutron star for detailed study. It is thus necessary to identify observable aspects of neutron stars that can be, in some sense, mapped to the equation of state of high-density material. In this review we discuss various constraints on the equation of state from astronomical observations. We focus on observations of accreting binary systems. 

We start by listing a few of the structural aspects of neutron stars that are affected by high-density microphysics and can be observed astronomically. We assume that the neutron star is in dynamical equilibrium. In this list, by mass we mean the gravitational mass, rather than the sum of the rest masses of the individual particles. 

The mass function, which is a pure combination of observables, is a lower limit to the possible mass of star 2 if the orbit is other than edge-on (that is, if % < 90°) or the observed star has mi > 0, then m2 > / Thus, observation of one star constrains the mass of the other star. Note, incidentally, that in a neutron star binary system with a high-mass companion (mi m2), / is low... 

If one of the stars in the binary is not a neutron star, then the tests become less precise. Suppose that one observes the optical light from the companion to a neutron star. In addition to the spectral information that allows measurement of P and i i, one also has photometric information (e.g., the total optical flux from the companion). The companion is distorted into a pear shape by the gravity of the neutron star, with the point towards the neutron star. Therefore, from the side there is more projected area and hence greater flux than from either end. If the orbit is edge-on (i = 90°) then the flux varies maximally if the orbit is face-on (i = 0°) then there is no variation. Therefore, by modeling the system one can estimate the inclination from the flux variations. This is called the method of ellipsoidal light curves (Avni Bahcall 1975). 

A more model-dependent way to constrain neutron star structure has to do with measurements of orbital frequencies in the accretion disk near the neutron star. Suppose that the frequency of some observed phenomenon could be identified with an orbital frequency vor >, and that this phenomenon lasted many cycles. The orbital radius f 0rb is clearly greater than the stellar radius R. In... 

In just the last year, several observations have allowed new constraints on neutron star structure (1) a mass of M > 1.6 M (at >95% confidence) has been measured for a neutron star (Nice et al. 2003) (2) the first surface redshift, 2 = 0.35, has been detected from a neutron star (Cottam et al. 2002), and (3) the first non-sinusoidal light curve has been measured from an accreting millisecond neutron star (Strohmayer et al 2003). These observations, along with many previously available data, hold out good hope for strong constraints on high-density matter in the next few years. 

In section I we consider the dynamics of rotation of a two-component neutron star and obtain the relaxation solutions for spin-down rate of the star. In section II we compare our solutions for the relaxation process with the observation data from the Vela pulsar. 

Alpar, A. (2003), Accretion models for young neutron stars , in Pulsars, AXPs and SGRs observed with BeppoSAX and other observatories . Edited by G. Cusumano, E. Massaro, T. Mineo. p. 197 [astro-ph/0306179]. 

Burgay, M. et al. (2003), An increased estimate of the merger rate of double neutron stars from observations of a highly relativistic system , Nature 426 531-533. 

Halpern, J.R, Gotthelf, E.V., Mirabal, N., Camilo, F. (2002), The next Geminga deep multiwavelength observations of a neutron star identified with 3EG J1835+5918 , ApJ 573, L41. 

Kaminker A.D., Yakovlev, D.G., Gnedin, O.Y. (2002), Three types of cooling superfluid neutron stars theory and observations , A A 383, 1076. 

Tsuruta, S., Teter, M.A., Takatsuka, T., Tatsumi, T., Tamagaki, R. (2002), Confronting neutron star cooling theories with new observations , ApJ 571, L143. 

The value of the maximum mass of neutron stars obtained according to our analysis appears rather robust with respect to the uncertainties of the nuclear and the quark matter EOS. Therefore, the experimental observation of a very heavy (M > 1.6M ) neutron star, as claimed recently by some groups [41] (M ss 2.2 M ), if confirmed, would suggest that either serious problems are present for the current theoretical modelling of the high-density phase of nuclear matter, or that the assumptions about the phase transition between hadron and quark phase are substantially wrong. In both cases, one can expect a well defined hint on the high density nuclear matter EOS. 

The value of the compactification radius, Rc In the present approach this radius was a free parameter. For demonstration we chose the radius Rc = 0.33 10 13 cm, when the strange A baryon could behave as the first excitation of a neutron. Such an extradimensional object can mimics a compact star with neutrons in the mantle and A s in the core. With smaller Rc the exotic component appears at larger densities - we may run into the unstable region of the hybrid star and the extra dimension remains undetectable. However, with larger Rc the mass gap becomes smaller and the transition happens at familiar neutron star densities. In this way, reliable observations could lead to an upper bound on Rc. 

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