Solar masses

Figure 1.6 The lime-scales of the various processes of element synthesis in. stars. The curve gives the central temperature as a function of lime for a star of about one solar mass. TTie curve is schematic. ...

How do these first stars differ from those of today As we have already mentioned, it is mainly because of their different composition. In addition, calculations show that they must have been much heavier (100-1,000 solar masses) and thus much brighter (up to a million times brighter than our sun). 

Table 2.2 The pre-supernova burning stages of a star with 25 solar masses. From Macia et al. (1997)...

The result is a type of onion-like model of the star with an iron-nickel core in the centre. The situation is somewhat different for smaller stars the path branches at the point where carbon burning (12C +12 C) begins. While the heavier stars are not affected by this process, the smaller ones (4-8 solar masses) are completely torn apart by carbon burning. 

These reactions take place in the inner zone of stars heavier than 15 solar masses. Hydrostatic carbon burning is followed by explosive neon burning at temperatures of around 2.5 x 109K. Under these conditions, phosphorus (31P) can be formed, although complex side reactions also occur. In comparison with the formation of... 

Fig. 1. The color-magnitude diagram of NGC 188 from [2] with the location of the detached eclipsing binary V12 [3] overplotted. From radial-velocity measurements we find (assuming an inclination of 90 degrees since we do not yet have photometry of the eclipses) that the masses of the two components are 1.06 and 1.08 solar masses. We estimate that we will be able to reach a precision of 1% in the mass estimate. We are in the process of acquiring eclipse photometry such that the radii and orbital inclination can be determined. Since both components are very close to the cluster turnoff their masses and radii can be directly used to give a very accurate age estimate for the cluster by comparing to isochrones in the (mass, radius) plane and requiring that they both lie on the same isochrone.

Li-depletion is extremely sensitive to mass (and other model parameters - see below). There should be relatively little depletion in solar mass stars compared with lower-mass stars (see Fig. 2). 

Fig. 2. (Left panel) evolutionary tracks using FST in the logTefj vs. log g plane (solid line non gray models with rph = 10 by Montalban et al.,2004) and 2D calibrated MLT (dashed line).(Right panel) Lithium evolution for the solar mass with different assumptions about convection and model atmospheres. The dotted line at bottom represents today s solar lithium abundance. MLT models with AH97 model atmospheres down to Tph = 10 and 100 are shown dotted for cum = 1 and dash-dotted for cpr, = 1.9. The Montalban et al. (2004) MLT models with Heiter et al. (2002) atmospheres down to Tph = 10 (lower) and 100 (upper) are dashed The continuous lines show the non gray FST models for rph = 10 and 100, and, in between, the long dashed model employing the 2D calibrated MLT.

Figure 4.4 Birth Lines for stars descending onto the main sequence, where M0. denotes solar mass...

The 1-solar-mass star is not capable of producing the heavier nuclei and the majority of the elements in the Periodic Table. With sufficient initial mass of H the He core produces 12C, the point at which the star starts to die. The formation of an almost pure He core results in the end of the star s main-sequence lifetime. The core of the star begins to contract, raising the temperature to 108 K until the nuclear reactions involving He start. 

Large-scale production of the heavier nuclei requires a heavier initial mass than that of the Sun. All nuclei up to iron were formed in stars with about 20 solar masses, as summarised in Table 4.2, which shows the important role of heavier stars in the cosmic nuclear synthesis of heavier elements. 

Process Fuel Major products Approximate core temperature (K) Minimum mass in solar masses... 

Stars of mass greater than 1.4 solar masses have thermonuclear reactions that generate heavier elements (see Table 4.3) and ultimately stars of approximately 20 solar masses are capable of generating the most stable nucleus by fusion processes, Fe. The formation of Fe terminates all fusion processes within the star. Heavier elements must be formed in other processes, usually by neutron capture. The ejection of neutrons during a supernova allows neutron capture events to increase the number of neutrons in an atomic nucleus. Two variations on this process result in the production of all elements above Fe. A summary of nucleosynthesis processes is summarised in Table 4.4. Slow neutron capture - the s-process - occurs during the collapse of the Fe core of heavy stars and produces some higher mass elements, however fast or rapid neutron capture - the r-process - occurs during the supernova event and is responsible for the production of the majority of heavy nuclei. 

Low (<1 solar mass) Middle (5-10 solar masses) High (>20 solar masses) Protostar — pre-main sequence — main sequence — red giant — planetary nebula — white dwarf — black dwarf Protostar - main sequence — red giant — planetary nebula or supernova —> white dwarf or neutron star Protostar — main sequence —> supergiant — supernova — neutron star... 

Calculate the diameter of a cloud in the interstellar medium with a density of 102 atoms cur3 if it is to collapse into a star with 1 solar mass. Assume that the cloud is spherical. 

Note Mass, radius and brightness are given in solar units. For example, Sirius A has 2.3 solar masses, is 2.5 times the size of the Sun and is intrinsically 35 times brighter than the Sun. 1 Solar mass = 2 x 1030 kg = 330000 Earth masses 1 solar radius = 700000 km = 110 Earth radii. 

Stellar evolution has consequences in the development of luminosity and colours of stellar populations, as well as chemical enrichment. Boissier and Prantzos (1999) have produced a more-or-less classical model of the evolution of the Milky Way, making a detailed study of this aspect, known as chemo-photometric evolution , using an IMF similar to the Kroupa-Scalo function in Chapter 7 this detail is significant because the Salpeter(O.l) function often used has a smaller contribution from stars of around solar mass which dominate the light at late times. The chemical evolution results are combined with metallicity-dependent stellar isochrones, synthetic stellar spectra by Lejeune et al. (1997) and a detailed treatment of extinction by dust. Some of their results are shown in Fig. 8.39. 

In the early thirties of the last century Baade and Zwicky conjectured in their studies of supernova explosions that supemovae represent a transition from ordinary stars to compact objects, whose size is an order of magnitude smaller than the size of a white dwarf. At that time it was already known that the atomic nucleus consists of neutrons and it was clear that the density of the remnant objects must be of the same order as the nuclear density. Baade and Zwicky predicted that a supernova explosions will result in objects composed of closely packed neutrons (neutron stars). Prior to the beginning of the second World War (1939) a number of theoretical works by Landau, Oppenheimer, Volkoff and Snider showed, that indeed objects could exist with sizes about 10 km and masses about a solar mass. The density in these objects is about the nuclear saturation density and they basically consist of neutrons with a small amount of protons and electrons. The studies of neutron stars were subsequently stopped most likely due to the engagement of the nuclear scientists in the development of the nuclear bomb both in the West and the East. 

Another important result obtained by Armenian physicists during the 1960s, is the observation that the mass of superdense objects is limited and is about several solar masses. This conclusion made in the beginning of the 1960s, actually proved the statement that the stars with masses above several solar masses turn into black holes at the end of their evolution. These works have stimulated intensive studies of black holes which are continued until now. 

Figure 6. Central density as a function of stellar core mass (in solar mass units) for the critical states, from Bisnovatyi-Kogan (2002).

The short lifetimes of high-mass stars means that HMXBs are not thought to be long-lived, typically only a few million years. As a result, even at an Eddington accretion rate of M = 1018 g s 1, only a few hundredths of a solar mass is transferred to the neutron star. Therefore, the mass of a neutron star in an HMXB is expected to be close to its birth mass. In contrast, LMXBs can last for tens of millions of years and in principle accrete tenths of a solar mass. 

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... 

Abstract We discuss the high-density nuclear equation of state within the Brueckner-Hartree-Fock approach. Particular attention is paid to the effects of nucleonic three-body forces, the presence of hyperons, and the joining with an eventual quark matter phase. The resulting properties of neutron stars, in particular the mass-radius relation, are determined. It turns out that stars heavier than 1.3 solar masses contain necessarily quark matter. 

Figure 5. The neutron star gravitational mass (in units of solar mass Mq ) is displayed vs. the radius (left panel) and the normalized central baryon density pc (po = 0.17 fm-3) (rightpanel).

The consequences for the structure of the neutron stars are illustrated in Fig. 9, where we display the resulting neutron star mass-radius curves, comparing now results obtained with different nucleonic TBF, in analogy to Fig. 5. One notes that while in Fig. 5 the different TBF still yield quite different maximum masses, the presence of hyperons equalizes the results, leading now to a maximum mass of less than 1.3 solar masses for all the nuclear TBF. 

Figure 11. The gravitational mass (in units of the solar mass M ) versus the normalized central energy density (eo = 156 MeV fm-3) (left panel) and versus the equatorial radius (right panel). The thin lines represent static equilibrium configurations, whereas the thick fines display configurations rotating at their respective Kepler frequencies. Several different stellar matter compositions are considered (see text for details).

Table 1. The critical mass and energy released in the conversion process of an HS into a QS for several values of the Bag constant and the surface tension. Column labeled MQs,max denotes the maximum gravitational mass of the final QS sequence. The value of the critical gravitational mass of the initial HS is reported on column labeled Mcr whereas those of the mass of the final QS and the energy released in the stellar conversion process are shown on columns labeled Mfi and Econv respectively. BH denotes those cases in which the baryonic mass of the critical mass configuration is larger than the maximum baryonic mass of the QS sequence (M r > MQS>max). In these cases the stellar conversion process leads to the formation of a black hole. Units of B and a are MeV/fm3 and MeV/fm2 respectively. All masses are given in solar mass units and the energy released is given in units of 10B1 erg. The hadronic phase is described with the GM1 model, ms and as are always taken equal to 150 MeV and 0 respectively. The GM1 model predicts a maximum mass for the pure HS of 1.807 M .

Figure 12. Cooling of hybrid star configurations of Fig. 9 with color superconducting quark matter core in 2SC+X phase. Different lines correspond to hybrid star masses in units of the solar mass.

Figure 13. Quark star configurations for different antineutrino chemical potentials r = 0, 100, 150 MeV. The total mass M in solar masses (MsUn = M in the text) is shown as a function of the radius R (left panel) and of the central number density nq in units of the nuclear saturation density no (right panel). Asterisks denote two different sets of configurations (A,B,f) and (A ,B ,f ) with a fixed total baryon number of the set.

In summary, the extinct radioactivities which have a limited time of existence in the solar system, constrain the time interval between the late stages of stellar nucleosynthesis and the formation of the solar system. Some production may also occur within the solar system during active periods of the young Sun. There have been numerous studies about how this matter was added into the solar system as a late spike of about 10 solar masses of freshly stellar processed material or from constant production in the galaxy (Wasserburg et al. 1996 Goswami and Vanhala 2000 Russell et al. 2001). These models are refined constantly with the input of new data and will probably continue to evolve in the future. 

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