Baryonic matter

In the late seventies, the history of the early Universe was described with the help of the hot Big-Bang scenario the universe originated from an initial singularity and had then expanded, being filled by radiation and subsequently by non relativistic matter (baryon and Dark Matter). 

Three most popular DM candidates could contribute to the explanation of the above wealth of observations. Historically, faint stars/planetary objects constituted of baryonic matter were invoked first, with masses smaller than 0.1 solar mass (this is the mass limit minimally needed for nuclear burning and the subsequent electromagnetic radiation). The search for massive compact halo objects (MACHOs) was initiated in the early 1990s based on the so-called microlensing effect — a temporary variation of the brightness of a star when a MACHO crosses the line of sight between the star and the observer. This effect is sensitive to all kind of dark matter, baryonic or nonbaryonic. The very conservative combined conclusion from these observations and some theoretical considerations is that at most 20% of the galactic halo can be made up of stellar remnants (Alcock et al. 2000). 

The other kind of dark matter must be non-baryonic (NDM) and is thought to consist of some kind of particles envisaged in extensions of the Standard Model ... 

A small degree of matter-antimatter asymmetry, with a baryon number B (ratio of net number of baryons Nb — N-g in a co-moving volume to the entropy S) in the range 10-11 to 10-8. 

Fig. 4.1. Schematic thermal history of the Universe showing some of the major episodes envisaged in the standard model. GUTs is short for grand unification theories and MWB is short for (the last scattering of) the microwave background radiation. The Universe is dominated by radiation and relativistic particles up to a time a little before that of MWB and by matter (including non-baryonic matter) thereafter, with dark energy eventually taking over.

The existence of dark matter (either baryonic or non-baryonic) is inferred from its gravitational effects on galactic rotation curves, the velocity dispersions and hydrostatic equilibrium of hot (X-ray) gas in clusters and groups of galaxies, gravitational lensing and departures from the smooth Hubble flow described by Eq. (4.1). This dark matter resides at least partly in the halos of galaxies such as our... 

D. Lynden-Bell and G. Gilmore (eds.), Baryonic Dark Matter, Kluwer, Dordrecht, 1990, and in Sarkar (1996). 

In the standard case there are four variables to be calculated the total system mass M (not counting non-baryonic dark matter), the mass of gas g, the mass existing in the form of stars (including compact remnants) s and the abundance Z of the element(s) of interest, assuming certain initial conditions and laws governing the SFR and flows of material into and out of the system. 

Fig. 11.15. Conditions for gas loss from a galaxy, as a function of gas mass Mg and the ratio < > of dark matter to baryons (stars + gas), assuming an energy input of 1038 erg s-1 and maximum dissipation from cloud-cloud collisions. PSS denotes the relation between < > and Mg deduced from observation by Persic, Salucci and Stel (1996). After Ferrara and Tolstoy (2000).

The distribution of elements in the cosmos is the result of many processes, and it provides a powerful tool to study the Big Bang, the density of baryonic matter, nucleosynthesis and the formation and evolution of stars and galaxies. This textbook, by a pioneer of the field, provides a lucid and wide-ranging introduction to the interdisciplinary subject of galactic chemical evolution for advanced undergraduates and graduate students. It is also an authoritative overview for researchers and professional scientists. 

Abstract The equation of state (EOS) of nuclear matter at finite temperature and density with various proton fractions is considered, in particular the region of medium excitation energy given by the temperature range T < 30 MeV and the baryon density range ps < 1014 2 g/cm3. In this region, in addition to the mean-field effects the formation of few-body correlations, in particular light bound clusters up to the alpha-particle (1 < A < 4) has been taken into account. The calculation is based on the relativistic mean field theory with the parameter set TM1. We show results for different values for the asymmetry parameter, and (3 equilibrium is considered as a special case. 

Results for the composition of nuclear matter at temperature T = 10 MeV with proton fraction V/"1, = 0.2 are shown in Fig. 1, for symmetric matter Yp0t = 0.5 in Fig. 2. The model of an ideal mixture of free nucleons and clusters applies to the low density limit. At higher baryon density, medium effects are relevant to calculate the composition shown in Figs. 1, 2, which are described in the following sections. 

Figure 1. Composition of nuclear matter with proton fraction 0.2 as function of the baryon density, T = 10 MeV.

The meson fields op, too and po are found by solving a set of equations self-consistently as shown in [11], Also expressions for the energy density, pressure and the entropy density can be found there. The empirical values of the binding energy of nuclear matter and nuclear matter density are reproduced using the above mentioned parameterization. The nuclear matter EOS can be found expressing the chemical potentials as functions of temperature, baryon density... 

We conclude that not only the a-particle but also the other fight clusters contribute significantly to the composition. Furthermore they also contribute to the baryon chemical potential and this way the modification of the phase instability region with respect to the temperature, baryon density and asymmetry can be obtained. As an example, for symmetric matter the baryon chemical potential as a function of density for T = 10 MeV is shown in Fig.3... 

In order to study the effects of different TBF on neutron star structure, we have to calculate the composition and the EOS of cold, catalyzed matter. We require that the neutron star contains charge neutral matter consisting of neutrons, protons, and leptons (e, p ) in beta equilibrium. Using the various TBF discussed above, we compute the proton fraction and the EOS for charge neutral and beta-stable matter in the following standard way [23, 24] The Brueckner calculation yields the energy density of lepton/baryon matter as a function of the different partial densities,... 

Figure 6. The single-particle potentials of nucleons n, p and hyperons , A in baryonic matter of fixed nucleonic density pN = 0.4 fm-3, proton density pp/pN = 0.2, and varying density pz/pN = 0.0, 0.2, 0.5. The vertical lines represent the corresponding Fermi momenta of n, p, and . For the nucleonic curves, the thick lines represent the complete single-particle potentials Un, whereas the thin lines show the values excluding the contribution, i.e., U + uffi.

The results obtained with a purely baryonic EOS call for an estimate of the effects due to the hypothetical presence of quark matter in the interior of the neutron star. Unfortunately, the current theoretical description of quark matter is burdened with large uncertainties, seriously limiting the predictive power of any theoretical approach at high baryonic density. For the time being we can therefore only resort to phenomenological models for the quark matter EOS and try to constrain them as well as possible by the few experimental information on high density baryonic matter. 

For the description of a pure quark phase inside the neutron star, as for neutrino-free baryonic matter, the equilibrium equations for the chemical potentials,... 

However, a more realistic model for the phase transition between baryonic and quark phase inside the star is the Glendenning construction [16], which determines the range of baryon density where both phases coexist. The essential point of this procedure is that both the hadron and the quark phase are allowed to be separately charged, still preserving the total charge neutrality. This implies that neutron star matter can be treated as a two-component system, and therefore can be parametrized by two chemical potentials like electron and baryon chemical potentials [if. and iin. The pressure is the same in the two phases to ensure mechanical stability, while the chemical potentials of the different species are related to each other satisfying chemical and beta stability. The Gibbs condition for mechanical and chemical equilibrium at zero temperature between both phases reads... 

Concerning the quark matter EOS, we found that a density dependent bag parameter B p) is necessary in order to be compatible with the CERN-SPS findings on the phase transition from hadronic to quark matter. Joining the corresponding EOS with the baryonic one, maximum masses of about 1.6 M are reached, in line with other recent calculations of neutron star properties employing various phenomenological RMF nuclear EOS together with either effective mass bag model [39] or Nambu-Jona-Lasinio model [40] EOS for quark matter. 

Table 2. Composition of electrically and color neutral mixed phases, corresponding quark number chemical potentials and average baryon number densities pB = n/3 in unities of nuclear matter saturation density po = 0.17/fm3. The various components are defined in Tab. 1.

The pressure of the main three phases of two-flavor quark matter as a function of the baryon and electrical chemical potentials is shown in Figure 7 at r/ = 0.75. In this figure, we also show the pressure of the neutral normal quark and gapless 2SC phases (two dark solid lines). The surface of the g2SC phase extends only over a finite range of the values of //,. It merges with the pressure surfaces of the normal quark phase (on the left) and with the ordinary 2SC phase (on the right). 

Under the assumptions that the effect of Coulomb forces and the surface tension is small, the mixed phase of normal and 2SC quark matter is the most favorable neutral phase of matter in the model at hand with r/ = 0.75. This should be clear from observing the pressure surfaces in Figs. 7 and 8. For a given value of the baryon chemical potential /i = fin/3, the mixed phase is more favorable than the gapless 2SC phase, while the gapless 2SC phase is more favorable than the neutral normal quark phase. 

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