Chandrasekhar limit

Evolution from the main sequence the Schbnberg-Chandrasekhar limit... 

Fig. 5.7. Evolutionary tracks for Z = 0.02 (near solar metallicity) stars with different masses in the HR diagram. (Luminosities are in solar units.) Points labelled 1 define the ZAMS and points labelled 2 the terminal main sequence (TAMS), the point where central hydrogen is exhausted. The Schonberg-Chandrasekhar limit may be reached either before or after this (for M > 1.4 Af0). Points marked 3 show the onset of shell hydrogen-burning. Few stars are found in the Hertzsprung gap between point 4 and point 5 , where the surface convection zone has grown deep enough to bring nuclear processed material to the surface in the first dredge-up. Adapted from Iben (1967).

A further effect during evolution up the AGB is mass loss through stellar winds, at an increasing rate as the star increases in luminosity and radius and becomes unstable to pulsations which drive a super-wind in the case of intermediate-mass stars. For stars with an initial mass below some limit, which may be of order 6 M , the wind evaporates the hydrogen-rich envelope before the CO core has reached the Chandrasekhar limiting mass (see Section 5.4.3), the increase in luminosity ceases and the star contracts at constant luminosity, eventually becoming a white dwarf (Figs. 5.15, 5.19). A computed relation between initial stellar mass and the final white-dwarf mass is shown in Fig. 5.21. 

When the core of a massive star exceeds the Chandrasekhar limit, it collapses and energy is absorbed by photo-disintegration of 4He through the reaction... 

Astronomers use a variety of methods to determine the distance to objects in the universe. One of the most effective is the standard candle provided by Type la supemovae. These supemovae originate in a binary star system when a white dwarf star accretes matter from its companion. When the white dwarf reaches the Chandrasekhar limit of 1.4 solar masses, a thermonuclear runaway occurs that completely disrupts the star in a cataclysmic explosion that makes the supernova as bright as an entire galaxy. Because Type la supemovae occur in stars with similar masses and because the nuclear burning affects the entire star, they all have essentially the same intrinsic brightness and their apparent brightness observed from Earth can be used to derive the distance to the supernova. 

A star whose initial mass is between 1 and about 5M0 (an intermediate mass star) is thought to evolve into a white dwarf of typically 0.6 to 1MQ (Weidemann Koester 1983). As a result, main sequence stars can lose more than 50% of their initial mass. Since the Chandrasekhar limit for the maximum mass of a white dwarf is near IAMQ, if this mass loss did not occur, there would be many more supernova and many fewer white dwarfs in the Milky Way than are observed. 

In the end of thermonuclear evolution, the core of a massive star can lose mechanical stability for various reasons. In the stellar mass range 8M < M < 20M a partially degenerate core with mass close to the Chandrasekhar limit Mcore Men and high density (p 109 — 1010 g/cm3) appears. Under these physical conditions, the chemical potential of degenerate electrons becomes so high that neutronisation reactions e + (A, Z) (A, Z — 1) + ve... 

The helium shell burning instability has two consequences. As Fig. 18 implies, not only the nuclear luminosity (JM enucdM) becomes large at the peak of the instability, but also the surface luminosity. Quickly, values exceeding the white dwarf s Eddington luminosity are achieved. This will lead to radiation driven mass loss from the white dwarf (cf. Kato Hachisu 1999), which questions whether it can ever reach the Chandrasekhar limit. 

As we have seen above, it is not easy for a white dwarf to accrete in such a way that it can grow to the Chandrasekhar limit. However, there is one more problem which has not been mentioned yet the angular momentum problem. Most white dwarfs accrete via an accretion disk. Therefore, the specific angular momentum of the accreted matter may... 

The Schonberg-Chandrasekhar limit [30] represents a limit above which an isothermal non-degenerate core can support the remainder of the star. Its value is ss 0.1 — 0.15M and is valid for stars with total mass between 2 and 6 Mq. Less massive stars develop an electron-degenerate core and more massive stars ignite helium before this value is reached. 

A scenario referred to as a sub-Chandrasekhar-mass supernova envisions a C-O WD capped with a helium layer accreted by a companion, and which explodes as the result of a hydrodynamical burning before having reached the Chandrasekhar limit. This type of explosions may exhibit properties which do not match easily the observed properties of typical SNIa events. It cannot be excluded, however, that they are responsible for some special types of events, depending in particular on the He accretion rate and on the CO-sub-Chandrasekhar WD (SCWD) initial mass (e.g. [85]). Unidimensional simulations of He cataclysmics characterized by suitably selected values of these quantities reach the conclusion that the accreted He-rich layer can detonate. Most commonly, this explosion is predicted to be accompanied with the C-detonation of the CO-SC WD. In some specific cases, however, this explosive burning might not develop, so that a remnant would be left following the He detonation. Multidimensional calculations cast doubt on the nature, and even occurrence, of the C-detonation in CO-SC WD (e.g. [86]). 

Another important thing to note about software standards is that they must always grow. Shrinkage is considered unthinkable. Most ISO language standards grow substantially in size at each standards cycle until they collapse into obscurity rather like stars which exceed the Chandrasekhar limit and collapse into a white dwarf. For example the ISO C standard increased from 190 pages in ISO C 9899 1990 to around 400 pages in ISO C 9899 1999. This is a natmal implication... 

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