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Stellar evolution in brief

Dans le document The DART-Europe E-theses Portal (Page 25-28)

2.2 An overview about compact objects

2.2.1 Stellar evolution in brief

Theproto-stars form in relatively dense molecular clouds composed of dust and cold hydrogen [33]. The cloud contracts and stretches depending on external conditions of the interstellar medium (stellar wind, nearby su-pernova, radiation pressure) so that density fluctuations appear that fragment the cloud. The fragmentation consists of a local gravitational collapse that overcomes the thermal pressure of the medium. The process is called theJeans instability. In the case where the typical mass of the local over-density reaches a critical mass known as theJeans mass, it undergoes a gravitational collapse (ie. a gravitational potential energy loss) during which time the temperature of the core increases. At this stage, the proto-star only emits light whose source is the star gravitational potential energy and is qualified as aT Tauri star [34] provided its mass is below 3 M. As more and more matter is accreted on the center of mass, the core density keeps on increasing. In parallel, the temperature continues to increase until it eventually reaches the hydrogen fusion temperature ignition (typically T ∼107K). If so, the newly formed star becomes a main sequence star. In this configuration the star is in a hydrostatic equilibrium: the gravitational potential energy that tend to attract matter is balanced by the internal energy released through nuclear fusion reactions in the core. In the case where the initial mass of the cloud is insufficient to trigger nuclear reactions (typically below 0.08 M), the proto-star continues radiating its potential energy and evolves into abrown dwarf 4 [35]. On the contrary, if the mass is large (typically above 80M) the star luminosity exceeds theEddington luminosity 5.

4Eventually nuclear burning of the deuterium contained in the core may begin and rapidly stop

5TheEddington luminosityis a threshold luminosity a star must possess so as to stay in hydrostatic equilibrium. Beyond this limit the radiation pressure becomes more important than gravity and gaz is ejected from the star.

A very useful tool to visualize the evolution and distribution of stellar populations is theHertzsprung-Russel (HR) diagram [36]. It is a figure showing the luminosity of a star as a function of its surface temperature. With a very good approximation, stars can be regarded as a black body (ie. a body whose emitted spectrum only depends on its temperature) even if this underlying assumption is not always justified at all stages of stellar evolution. Populations are displayed which correspond to several evolutionary stages: Main sequence (MS) stars, dwarfs, giant branch, supergiant, etc.. All are not accessible to every star as the destiny of a star is guided by its initial mass. Indeed more massive stars will ”burn” their nuclear fuel faster. As an example, a 6 M star will spend 108yrs on the MS whereas a Sun-like star will spend 1010yrs.

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Figure 2.3: Color-magnitude diagram with various star populations. The color or spectral type is a classification of stars as a function of their emission spectrum and of their surface temperature while the magnitude quantifies its brightness.The main sequence forms a long stripe on which a star will spend 90 % of its life. Depending on its initial mass it will go through distinct evolution stages.

As an example, the Sun is a yellow dwarf lying on the MS. Its planned evolution for the 4.5 billion years to come is to transform into a red giant before slowly cooling down and form a white dwarf. Some other representations display constant radius lines which have some importance to explain a star brightness: the larger surface a star offers to the interstellar medium the brighter it appears for an observer. Radius also conditions the temperature:

more surface means more efficient energy transfers with the interstellar medium.

Following sections describe the known stellar evolution scenarios for low and high-mass stars. These two populations are animated by distinct physics which lead to the formation of different star remnants.

Low-mass stars

The population of low-mass stars (0.8< M <8M) is characterised by a specific nuclear reaction on-going in its core: the proton-proton chain reaction (PP cycle) [37]. During the reaction, the hydrogen lying in the core is transmuted into helium. The reaction also produces two atoms of hydrogen that may be re-injected at the beginning of the resulting cycle for the PPI sub-cycle. The PP cycle is the dominant one and occurs within a star sitting on the MS. the livetime of a star on the MS is approximately 1010(M/M)−2.5 yrs. At some point hydrogen is depleted in the core and the Proton-proton (PP) cycle progressively stops. The produced amount of helium during the PP cycle is inert for the core temperature is not sufficient to ignite its combustion.

The hydrostatic equilibrium is no longer ensured and gravity tends to overcome the star internal energy. As a consequence the star contracts. So far an onion layers structure has formed with helium at the core and a surrounding residual layer of hydrogen. Nuclear reactions have stopped and convection motion of gases now dominates, allowing for the remaining hydrogen to burn at the periphery. The cooling of the star is associated to the expansion of the most superficial regions (its radius can exceed 103R). The growth of the star increases the surface it offers to the cold interstellar medium: the star temperature decreases (turns red) whereas the luminosity increases. On the HR diagram this stage correspond to the now called red giant leaving the MS and moving to thehorizontal branch. Collapsing matter heats up the core of the newly formedred giant and triggers the helium burning. The main reaction mechanism is the triple-alpha reaction (3α reaction) through which three helium atoms fuse to produce a single carbon atom. Two cases should be discriminated depending on the progenitor mass:

• 0.8< M < 2M The inert helium core produced by burning hydrogen layers enriches the star core and progressively increases the core pressure. As the mass of the He core grows, it contracts until it is supported by degenerate electron pressure. A fundamental property of degenerate matter is that the pressure is no longer temperature dependent. The core continues to contract until it reaches 108 K. At this temperature, triple-αreactions begin in the core. As the rate of energy production for the triple-α process goes as T40, this induces a violent, runaway He-burning.

This process is called the helium flash [38]. The sudden heating releases enough thermal energy to overcome the Fermi energy level and matter in the core is no longer degenerate. The outer layers are opaque and this violent process is not visible for a distant observer. In other words the star luminosity is constant and moves on the horizontal branch toward high temperatures. In this way the red giant star finally acquires a new thermal source and regains it hydrostatic equilibrium. Once again when the helium core is depleted the star contracts and triggers the fuse of heavier elements provided its mass is sufficient.

The repetition of the process tends to make the onion structure more and more complex as the star moves to theAsymptotic giant branch (AGB)6(this phase last one million years for a solar mass star).

• M >2MThose stars are dominated by the carbon-nitrogen-oxygen cycle (CNO cycle) during the MS phase (even if the PP cycle still occurs). This case is simpler than the previous one since the thermal expansion regulates the core temperature. As a result temperature smoothly increases until reaching the limit temperature for helium burning.

Both ways result in a AGB star with an inert core composed of carbon and oxygen, an helium layer surrounding the core and another superficial layer hosting the burning of hydrogen residues. As the star tries to regain hydrostatic equilibrium, there are successive stages of shell burning. Over time, the shell burning becomes unstable causing stronger and stronger thermal pulses inside the star. Eventually, the instabilities become so large that the outer layers of the star are ejected (stellar winds). After 105years, the ionized gas envelope forms aplanetary nebulaeand leaves a hot core which will slowly cool down and lose energy. This object is supported by the pressure from a degenerate gas of electrons and forms awhite dwarf [39]. Their small radius (∼0.01R) give them a low luminosity and are hence found in the bottom-left part of the HR diagram (see Fig 2.3).

High-mass stars

For the population of high-mass stars (M >8M), the initial stages of the evolution are the same as in the low-mass case: once the core is hydrogen exhausted, the star collapses and its envelop expands. However more massive stars go further in the process as they are able to reach theblue supergiant stageonce they began fusing their carbon in the core. As the cycle of burning, depletions, contraction, expansion goes on, the temperature limit necessary to light on further nuclear reactions increases. This results in the acceleration of the burning rate of each element: helium, carbon, oxygen, nitrogen, neon, magnesium, ... Typically the burning of oxygen

6Only stars that are heavy enough to trigger the fusion of elements heavier than helium can reach this stage of stellar evolution.

lasts∼1 year whereas the burning of silicon lasts about 1 day [40]. Also each phase releases less and less energy as shown on Fig (2.4). Once a star starts to produce inert iron in its core the fusion cycle breaks. Indeed the fusion of iron is an endothermic reaction (i.e. energy needs to be put into the system for further reactions to occur), and is thermodynamically disfavoured.

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Figure 2.4: Binding energy per nucleon curve. The dotted line shows the upper limit number of nucleonsA= 56 (iron) to allow for the fusion nuclear reactions to release some energy. For higher values of A the reaction is disfavoured and compromises the coherent structure of the star.

At this point the nuclear fuel is exhausted in the core and the blue supergiant collapses. Unlike low-mass stars, the star is not massive enough to support the relativistic matter collapse. When the compacted mass exceeds a particular mass named the Chandrasekhar limit of about 1.4M, electron degeneracy is no longer efficient to counter the incoming matter. The density of the core sharply increases and soon a neutronisation occurs that produces neutrons and neutrinos through the inverse beta decay (e+p→n+ν) and electron capture (AZX+eAZ−1Y +νe) reactions. Electron degeneracy in the core indeed disfavours the creation of electrons as all Fermi levels are already occupied.

A contraction occurs and continues until the electrons in the atoms are pulled inside the nucleus. This re-duction in particle number causes the core to contract until it is stopped by neutron degeneracy pressure.

Ultra-relativistic matter bounces onto the core and create shock waves that propagate outwards. This phe-nomenon is known as a type II supernova [41]. At such high densities neutrinos are trapped in the collapsing core (Rcore∼50km). Mechanism driving the next steps are not well known. It is believed the nuclear equation of state plays an important role as it stiffens towards high densities above 1014g/cm3. This leads to the forma-tion of a shock sonic wave propagating from the core to the outer medium. It is also suggested the explosion is revived by a post-bounce neutrino burst provoked by the initially trapped neutrinos on the core. It is made possible by the decreased neutrino opacity by the shock wave. But other revival mechanisms are investigated such as the magneto-rotational mechanism [42] and acoustic mechanism [43].

After the gigantic explosion occurred, the central core of the massive star is surrounded by a metal enriched environment. The core continues to collapse until either a new pressure contribution prevents any further collapse or the core mass is simply too important. The latter case lead to the formation of a stellar-mass black hole. Both ways head to the formation of compact objects which will be studied hereafter.

Dans le document The DART-Europe E-theses Portal (Page 25-28)