Neutron stars cooling

The commonly accepted pulsar model is a neutron star of about one solar mass and a radius of the order of ten kilometers. A neutron star consists of a crust, which is about 1 km thick, and a high-density core. In the crust free neutrons and electrons coexist with a lattice of nuclei. The star s core consists mainly of neutrons and a few percents of protons and electrons. The central part of the core may contain some exotic states of matter, such as quark matter or a pion condensate. Inner parts of a neutron star cool up to temperatures 108iT in a few days after the star is formed. These temperatures are less than the critical temperatures Tc for the superfluid phase transitions of neutrons and protons. Thus, the neutrons in the star s crust and the core from a superfluid, while the protons in the core form a superconductor. The rotation of a neutron superfluid is achieved by means of an array of quantized vortices, each carrying a quantum of vorticity... 

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

Here we will discuss two scenarios for the proto-neutron star cooling which we denote by A and B, where A stands for cooling of a star configuration with SC whereas B is a scenario without SC. The initial states for both scenarios are chosen to have the same mass Mi(A) = A(l>) for a given initial temperature of T = 60 MeV. The final states at T = 0, however, have different masses Mf(A) / Mf(B) while the total baryon number is conserved in the cooling evolution. The resulting mass differences are AM (A) = 0.06 M , A M(B) = 0.09 M and AM (A) = 0.05 Me, A M(B) = 0.07 M for the Gaussian and Lorentzian models, respectively. 

In this report the results of old calculations (Mayle 1985 Woosley, Wilson, Mayle 1986 Mayle, Wilson, Schramm 1987) of collapse driven explosions and new calculations of the Kelvin-Helmholtz proto-neutron star cooling will be compared with the neutrino observations of supernova 1987a. The calculations are performed by a modern version of the computer model of Bowers and Wilson 1982. (See Mayle 1985 for more recent improvements). 

There are a number of other interesting limits to be drawn on neutrino properties by somewhat more sophisticated use of the supernova dynamics. Putting another neutrino-antineutrino pair [30], i.e., another two species, into any calculation of the neutron star cooling would probably accelerate this process unacceptably. Further, one can place an upper limit [5] of 45 eV on the mass of any species mixing with the electron neutrino, else no supernova mechanism would succeed, delayed or prompt. 

Neutron stars are thought to form in supernova explosions. The outer layers of the star crystallize as the newborn neutron star cools by neutrino emission. Estimates, based on the expected breaking strain of the crystal lattice, suggest that anisotropic stresses, which build up as the pulsar loses rotational energy, could lead to e < 10 the exact value depends on the breaking strain of the neutron... 

However, one must be careful because in an LMXB the optical emission from the accretion disk (whether in the outer, cool regions or as reprocessed X-ray emission) can outshine the companion by a large factor. This makes spectral lines difficult to measure and also complicates the ellipsoidal light curve technique. The ideal systems to study are therefore transient systems, which undergo periods of active mass transfer (often for a few weeks to a few months) before lapsing into quiescence, where there is little to no mass transfer. During quiescence, the companion is still distorted by the gravity of the neutron star, hence the flux variations still occur, but without any contamination by the accretion disk. There is a relatively new approach similar to this that... 

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

Romani, R.W. (1987), Model atmospheres for cooling neutron stars , ApJ 313, 71. 

The following stage is core collapse caused by electron capture or photodisintegration of iron. According to the traditional view, collapse leads to formation of a neutron star which cools by neutrino emission and decompression of matter when it reaches nuclear density (10 g cm ). The rebound that follows generates a shock wave which is capable of reigniting a good few nuclear reactions as it moves back out across the stellar envelope. 

Fig. 5.4. Schematic evolution of the internal structure of a star with 25 times the mass of the Sun. The figure shows the various combustion phases (shaded) and their main products. Between two combustion phases, the stellar core contracts and the central temperature rises. Combustion phases grow ever shorter. Before the explosion, the star has assumed a shell-like structure. The centre is occupied by iron and the outer layer by hydrogen, whilst intermediate elements are located between them. CoUapse followed by rebound from the core generates a shock wave that reignites nuclear reactions in the depths and propels the layers it traverses out into space. The collapsed core cools by neutrino emission to become a neutron star or even a black hole. Most of the gravitational energy liberated by implosion of the core (some 10 erg) is released in about 10 seconds in the form of neutrinos. (Courtesy of Marcel Amould, Universite Libre, Brussels.)...

We have made three new calculations following the cooling of proto-neutron stars until the luminosity fell below an observable level. In the first model a soft equation of state (EOS) was used (gravitational critical mass 1.50 MQ). The proto-neutron star was selected by taking a post bounce calculation of the core of a 25 M0 star and removing all the mass but for the inner 1.64 M0. The second model was made with a stiffer EOS using the same core as the first model. The third model was made by... 

If we plot the Kamiokande and IHB data together as in Figure 3, we see that for the first two seconds a fairly high luminosity is followed for 10 seconds by a much lower luminosity. We infer from this fact that there may have been a 2 second period of accretion, followed by the explosion and subsequent Kelvin-Helmholtz cooling of the proto-neutron star. 

Perhaps the most novel aspect of SNl987a is the detection [6,7] of neutrinos from the production and cooling of a compact remnant. One hopes this is only the beginning of a new field of astronomy. The analysis I present here [5], parallel to the analysis of many other authors [23-28], finds remnant binding energy 2.0 0.5 X 1053 ergs and remnant mass 1.2 to 1.7 Mq consistent with what one expects for neutron star generation. An upper limit of 10-15 eV may also be inferred for the electron neutrino mass. 

The supernova 1987A in the Large Magellanic Cloud has provided a new opportunity to study the evolution of a young neutron star right after its birth. A proto-neutron star first cools down by emitting neutrinos that diffuse out of the interior within a minutes. After the neutron star becomes transparent to neutrinos, the neutron star core with > 1014 g cm-3 cools predominantly by Urea neutrino emission. However, the surface layers remain hot because it takes at least 100 years before the cooling waves from the central core reach the surface layers (Nomoto and Tsuruta 1981, 1986, 1987). 

Figure 1 shows the cooling behavior of neutron stars during the first one year after the explosion. The total luminosity of the surface photon radiation Lph (left) and the surface temperature Ts (right), both to be observed at infinity, are plotted as a function of time, for three nuclear models PS (stiff), FP (intermediate), and BPS (soft). The temperature scale refers to the FP model. 

Figure 1 Observed photon luminosity vs. time during a year after the supernova explosion predicted from standard cooling theory of neutron stars. Shown are three representative nuclear models PS (dashed), FP (solid), and BPS (dot-dashed). The detection limit from Ginga is shown as a horizontal line.

The behavior of hehum at low temperatures is quite different from that of all other materials. When cooled under atmospheric pressure, helium liquefies at 4.2 K, but it never solidifies, no matter how cold it is made. This behavior is inejqrlicable in terms of classical physics where, at a sufficiently low temperature, even the very weak interatomic forces that exist between helium atoms should be sufficient to draw the material together into a crystalline solid. Furthermore, the liquid in question has maity extraordinary properties. In particular, it undergoes a transition at 2 K to a state of superfluidity, such that it has zero viscosity and can flow without dissipation of energy, even through channels of vanishingly small dimensions. This frictionless flow of the liquid is closely analogous to the frictionless flow of the electrons in a superconductor. On Earth, superfluidity and superconductivity are exclusively low-temperature phenomena, but it is inferred that they probably also arise in the proton and neutron fluids within neutron stars. 

---