The stars are not changeless. -
Today we give for expected the fact the stars are evolved: why? Easily, the stars beam because they produce energy, and they disperse it under the form of light, heat and other types of radiation. Within each source of energy the fuel at the end becomes ash, or something of equivalent: also in the stars will happen something of similar. The relative processes occur in immeasurable intervals of time also respect to the entire history of the human civilization. But today this doesn't constitute a problem more.Our actual knowledges (obtained thanks to the observation not more only visual, but extended to all the range of the electromagnetic spectrum) tell us the most part of the stars has a third of the age of the Universe at least, calculated on the average in 15 billions years; but some are certainly more old (the age of the stars in the globular clusters is estimated in 13-14 billions years), and sure there are stars much younger: the formation of thr stars is a phenomenon still actual, that we are able to observe directly. In effects, many of the problems relevant to the stars' birth and the following evolution have been today probably resolved.
Various models explain the possible primer mechanism of the star birth, but the starting condition is always the same: a cloud of gas and dusts contracts under the push of the gravity force: as we say a gravitational collapse.
The H-R diagram. - But before getting
to the heart of the theories on the stellar evolution, it is suitable to introduce a
valued tool, indispensable for the comprehension of the theoretical models drawn from the
data observed: the Diagram of Hertzsprung and Russell.
A large part of the knowledges on the stellar evolution, in effects, depends from statistical relation between brightness and surface temperature; the graphic representation of this connection is the diagram of Hertzsprung-Russell (more commonly named "H-R diagram"). Instead of the temperature, the spectral type or the color of the star are often considered , parameters that depend, besides on other variables, on the temperature.
For the first diagram (Fig.1), developed about seventy years
ago, independently the one from the other by Hertzsprung and Russell, were taken into
account ALL the stars of known absolute visual magnitude and spectral type. It turned out
not all the couples of absolute magnitude/spectral type had the same probability to
happen: the dots of the graph gathered prevalently in some regions,
rather than in others. A lot of the dots arranged along a band that was called "Main sequence"; another fairly conspicuous group went to
dispose in a region to the top right, corresponding to high brightness and color from the
yellow to the red. The stars of this second group have the same spectral type and then the
same surface low temperatures of the faintest stars of the main sequence, but they are
more luminous. If the temperature is the same, it must be equal the quantity of emitted
radiation for area unit. Therefore, spectral type being equal, the brightest stars must be
bigger than the faintest ones. 
Therefore, spectral type being
equal, the brightest stars must be bigger than the faintest ones. So the feeblest main
sequence stars were called "red dwarfs", while those of the disconnected
group, in the upper part, were named "red giants".
Additionally, there were few stars brighter than the giants, that were named "supergiants",
and faint stars like the red dwarfs, but generally white, that were called "white
dwarfs" (in the bottom left). The region is approximately thickened around a
straight line lightly inclined as to the axis of the abscissas, while the supergiants one
is almost parallel.
The early diagram shows, as you can see, a non-linear pattern: the spectral type, in fact, is a discontinuous variable; for this reason we often use in its place the INDICE DI COLORE, that is a linear function of the spectral type (Fig. 2).
This diagram (developed with ALL the stars whose spectrums and distances were known at that time) seems to suggest that in the universe the giant stars are more numerous than the dwarf stars. But the giants are evidently observable to distances immensely greater than the dwarfs. If we draw a graph pertinent to the stars not more 10 Parsec away (Fig. 3), we'll see the giants result quite absent, the red dwarfs predominate, and the white dwarfs fairly appear.
It is important to point out that, while the region of the dwarfs extends from the spectral types O and B up to the M types uninterruptedly, the region of the giants presents a discontinuity, ("Gap of Hertzsprung") where the stars are very rare, among the A5 and G0 types.
We return, now, to the gravitational collapse that is the beginning of the stellar evolution.
The gravitational collapse and the protostars. - In 1947, Bok and Reilly examined some dark and cold nebulae with the characteristic globular appearance; the study of the more massive of these objects ( "Globules of Bok") allowed to observe they are all in a phase of gravitational collapse. The masses able to originate a gravitational breakup are too big to believe that only a star can born; almost certainly is activated a mechanism always starts off the formation of a large number of stars. Now rises the problem how the cloud can split, once initiated a more or less homogeneous collapse; the more satisfying model, confirmed by recent (1995) observations of the HST, refer to the so-called phenomenon of the "Photoevaporation".
The phase of the gravitational collapse can last (according to the masses into play) hundred of thousands or millions years; is it impossible, therefore, to observe the stellar evolution for beings limited in the time as we are? Not at all: on the contrary, our Milky Way (and today, thanks to HST, nearly the whole universe) offer us a lot of phenomena whose observations, opportunely studied and explained, we can use to extrapolate all the phases of the protostars' birth (we call protostar an "embryo" of star whose source of energy is still originated from the gravity force, not yet from the thermonuclear reactions).
From the protostar to the star. - The protostar's phase is fairly agitated, alternating periods of calm to others of extremely violent activity; the normal life of a star, instead, is characterized of a relative stability. The astrophysicists begin to call star a celestial object at the time the thermonuclear reactions start inside it and the body enters in balance, that is it doesn't fall more on itself neither dilates, scattering in the space. Let's see how it happens.
In the protostar temperature and pressure increase with an equilibrium thanks to which part of the radiation fades away in the space, removing and dispersing the shell of gas and dusts surrounding the protostar; but this loss of energy allows however a subsequent gravitational contraction that, in its turn, causes other energy, and then other heat, that contributes to warm again the core. Despite the loss of radiation, then, the temperature of the protostar continues to raise until, if the mass is big enough, achieves the necessary values to the ignition of the thermonuclear fusion.
The thermonuclear fusion generates the transformation of hydrogen in helium, with a mass loss of the 0,7% about, changing into energy according to the well known Einstein formula. Thanks to this production of energy, the gravitational contraction is stopped: the true star is born, characterized, as regards to the preceding phase, from a relative stability. This stability lasts until all the inner hydrogen hasn't been converted in helium: that is for millions years for the more massive stars, or for billions, as for the stars of comparable mass like the Sun or smaller. The life of a star is as briefer as bigger is its mass: in fact, as more massive is the star, as more energy it must produce to contrast the immense gravitational pressure. Moreover, in relation to the masses into play, the thermonuclear reactions can happen in two separate manners: through the "proton-proton" cycle for the stars of comparable mass like the Sun, or through the "carbon-nitrogen" cycle for densier stars. The way of producing energy is different in the two cases, and diverse is the resulting stellar evolution. To realize these various evolutionary ways, the aid of the H-R diagram is essential.
Diagrams of the clusters and stellar evolution. - Today is proved the location of a star on the diagram H-R depends on three indicators: mass, chemical constitution and age. This results readly comprehensible if we look at the star clusters' diagrams.
These are families of stars, whose members were born roughly in the same age and by the
same material. Then, of the three mentioned parameters, the initial chemical composition
and the age are invariable. The position on the H-R diagram so depends only by the
parameter mass.
Moreover, the diagram is valid even if the distances are not known, and therefore the
absolute magnitude of the stars: belonging to the same cluster, in fact, we are able to
reasonably consider them all set to the same distance, and so the shape of the diagram
function of the apparent magnitude and the spectral types will be in every case valid.
Now we consider the stars of a young cluster like Orion (Fig. 4),
where the stars are still in the making. They (all born from the same material) have more
or less the same initial chemical composition besides a roughly equal age: therefore, if
they were generated all with the same mass, reaching the equilibrium after the phase of
protostar they should have all equal temperature and brightness, and so they should fall,
in the H-R diagram, all on the same dot. As this doesn't happen, it is evident that
temperature and brightness, that is the position on the diagram, are determined above all
by the mass.
Moreover: are evident, going to right, many dots scattered like a fan, for the most part
not belonging to the main sequence. Those dots represent stars that don't have still
achieved the equilibrium: the protostars. We know in fact the stars, more they are heavy,
more they early arrive to the main sequence. Therefore the straggling points, to the
right, coincide to the protostars with minor mass that, using much more time in order to
arrive to the main sequence, don't have reached it yet and are still in the gravitational
contraction phase.
Still: in accordance with the theory the considered stars, having the same origin,
should arrange in a line and not, like it occurs, in a band. In effects, in the band of
the main sequence there are also stars show for several reasons small changes in
relatively long times. However the theoretical conditions exist surely in the time when
the nuclear reactions begin. The stars situated in this phase are exactly disposed in a
line, named "line of zero age", that runs along the bottom side of the
main sequence.
So, the study of the H-R diagrams is more simple because the members of every star cluster
constitute an homogeneous group for age and starting chemical composition. If the
homogeneity could concern the masses too, it would be logical expect H-R diagrams all with
the same appearance. Why doesn't this happen? In the answer to this question there is the
key for the comprehension of the stellar evolution (Fig. 5).
A first general wiew (Fig. 6) tells us the majority of the
stars are in the main sequence. It means that the longest period of the life of a star
takes place on there.
Comparing the diagrams of a young open cluster and a very old globular one (Fig. 7), we notice in the first graph the upper portion of the
main sequence (blue stars) is populated, while it entirely lacks in the globular cluster's
diagram, where instead is richly represented the family of the red giants.
Sandage, in 1957, developed a composite diagram, making a coincidence with the zero age lines of 10 clusters (Fig. 8); this diagram showed some very important facts.
This diagram confirms what we had first noticed comparing the diagrams of some individuals clusters. We summarize the results:
Here is the key to understand the stellar evolution: in 1942 Schonberg and Chandrasekhar had found the hydrogen combustion is as quicker as brighter and more massive is the star; and when a certain percent of hydrogen is converted in helium the star leaves the main sequence. At that moment the star becomes brighter and less blue; and afterwards, through a phase where it is not in equilibrium, it grows into a red giant.
This theory explains:
These results allow to start interpreting the clusters' H-R diagrams.
At the beginning, all the stars are on the main sequence, except those with small mass, in
the low right, that have not reached it yet.
With the passing of time, the the more massive stars of the cluster drift away to become red giants. Since the brightest stars evolve more rapidly, we have few chances to observe such a star during the relatively brief interval of its existence when it passes from the main sequence to the region of the red giants. This explains how there isn't almost any star in the gap of Hertzsprung. As the evolution is slower at lower brightness, the gap grows thin little by little the age of the cluster increases. In the oldest clusters the gap is totally absent.
From the position the stars migrate from the main sequence to the region of the red giants, therefore it is possible to calculate the age of the cluster. What does it happens after a star passed across the stage of the giant? We can deduce this one from the diagrams of the oldest known clusters, as M67 and the globular clusters. In these cases a new branch appears, not present in any of the youngest clusters: the RR Lyrae variables (Fig. 9). So, the luminous blue stars once populated the upper part of the main sequence of an old cluster are before grown into red supergiants. Later on, when the helium is become their more important source of energy, they have moved to the left, in the region of the RR Lyrae. Finally, after a sequence of events not completely understood yet, the stars arrive at the final stage, becoming, according to their mass, white dwarfs, neutron stars or, perhaps, black holes.
The graphs of the globular clusters are very similar to the very old open cluster M67 one (Fig. 10). However, although their main sequences terminate to the same point, suggesting about the same age for the one and for the others, the giants of M67 achieve only a brightness even to 100 times the Sun, while those of the globular clusters obtain a luminosity equal to 10.000 times the solar one. The theory proves this diversity is due to a difference in the chemical composition, that causes a difference in the opacity of the stellar matter: M67 has a more elevated metals percentage.
The observation generally shows the age is associated with the chemical composition: the youngest stars are more rich in heavy elements in comparison with the oldest ones. From here the idea the stars in their inside have produced in the course of their existence elements more heavy than the hydrogen, during the following bursts and the loss of matter that must accompany the ending phase of their life, before they are reduced to the last phase of white dwarfs or pulsar, they would get rich the interstellar matter of heavy elements, and from this interstellar matter, abounding in these elements, stars of a successive generation would be formed. The fact that M67 has a age comparable to the globular clusters one, and they are poor of heavy elements, but has a chemical composition similar to the other youngest galactic clusters one, it suggests the enrichment of massive elements has occurred more quickly on the galactic plane than in the halo.
Moreover, the examination of the globular clusters diagrams gives prominence to other remarkable peculiarities: apart from the total absence of blue giants and the whole first branch of the main sequence, it can be noticed the Gap of Hertzsprung is now populated, and there are situated the variables of the RR Lyrae type. According to Baade, the two types of graphs would characterize two distinct stellar populations, one typical of the galactic halo, named "Population II", the other of the galaxy arms, and this is called "Population I".
Stellar models. - We go back now to the initial phase of the thermonuclear reactions primer, trying briefly to describe the various evolutionary ways the life of the star could follow. We know two possible cycles of the hydrogen fusion: the proton-proton cycle and carbon-nitrogen one. The presence of the one or the other depends on the mass. With masses also little higher than the Sun, the temperature achieves, thanks to the dreadful gravitational pressure, values among 16 and 30 milions of degrees, sufficient to prime the carbon-nitrogen cycle. Here the hydrogen burns as much more quickly as more high is the temperature, and thus as greater is the mass of the star, as smaller is the nucleus that produces most part of the energy. This is the reason, because of the excessive density of this nucleus (density that makes it opaque to the radiation) why not all the energy created in it is able to come out. The most external layers of the nucleus, on the contrary, succeed to eject large amount of energy by irradiation, across the huge shell, formed by gas much less dense as regards to those that form the nucleus, and just for this gas it is transparent, unlike the nucleus, to the electromagnetic radiation.
If the star has equal or minor mass of the Sun, the inner temperature doesn't never arrive to the 16 milions of degrees necessary to prime the carbon-nitrogen cycle, and instead the proton-proton cycle starts, less influenced by the temperature. In this case, the area destined to the production is much bigger and less dense than in the stars of greater mass, and the same energy leaves it much more easily, by irradiation. Since, according to the previous model, the external layers are much denser and less hot, in this event, they result opaque to the radiation, so the dispersion of energy, through them, occurs by convection.
When the core of the star has transformed all its hydrogen in helium, the thermonuclear fusion stops, and the production of energy ceases; the upper shell then, not more sustained by the energy produced in the inside, returns to collapse, and, so doing, creates new energy, this time of gravitational origin; part of this energy tends to run away to the outside, but the residual one develops heat in the hydrogen layer not even burnt that has remained around the nucleus of helium, and the temperature raises up to ignite again the thermonuclear reactions. So the energy produces in a shell surrounding the nucleus of helium; this energy is inclined to expand the upper layers, and spreading they get cold, and the star swells to sizes unthinkable in comparison with the ones it had in precedence: it has been transformed in a red giant, with a small nucleus of extremely dense helium, around which a thin shell of hydrogen burns, and an extremely rarefied but immense envelope, relatively cold if compared to the superficial temperature the star had before expanding.
All the stars of mass exceeding the 0,2 of the solar one become red giants, but ot all of them in the same way; and not they all in the same manner, above all, end once gone beyond also this phase. In the nucleus of all red giants, in fact, the hydrogen has been transformed in helium. This one, in its turn, could transform, through other processes of thermonuclear fusion, in carbon and oxygen, elements provided with a greater atomic weight. But the thermonuclear reactions capable of this new transmutation require, in order to start, temperatures about 100 millions of degrees. They could be achieved by means of the gravitational contraction: all depends on the mass.
As regards the stars with masses among 0,2 and 0,5 of the solar one, the ontraction doesn't succeed to raise the temperature up to the fatal 100 millions of degrees. The star becomes a red giant, but once burned out the shell of hydrogen surrounding the nucleus of helium, the thermonuclear reactions are extinguished for ever, and the star collapses in an extremely dense configuration named white dwarf.
For masses among 0,5 and 3 times the solar one, the helium formed owing to the thermonuclear burning falls to the core below, increasing its mass with interesting consequences. When the helium burning in the core will be ran out, the end is the same of the preceding event: a white dwarf.
In stars with mass exceeding 3 times the solar one, the inner part attains the necessary temperature to burn the helium before the core degenerates, so in this area the thermonuclear reactions gradually produce the energy able to sustain the upper shells of the star, that remains in balance, and they transform the helium in carbon and oxygen in a non violent way. When the helium is finished in the whole new nucleus, except a thin external shell, the inner thermonuclear reactions stop, the layer of unburned helium contracts increasing the own temperature up to ignite like before had happened for the hydrogen. At this point inside the red giant there are two shells in which the nuclear fuel burns: one more external, with the hydrogen changing into helium, and one more internal, with the helium transforming itself in carbon. In the inside of them, there is a nucleus of carbon and oxygen and, on the grounds of the mass, several cases can occur: if the mass is inferior to 4-5 solar masses, the nucleus doesn't achieve ever the necessary temperature to ignite new thermonuclear reactions. For more greater masses, but under 9 solar masses, a rapid and violent ignition of the carbon and the oxygen triggers in the core, maybe enough to destroy the star in an enormous burst. Finally, if the star achieves 9 solar masses, the ignition temperature takes place inside the core before the gas forming it degenerates, and in this event happens a non violent production, in state of equilibrium, of elements like neon, sodium, magnesium, silicon and sulphur more heavy little by little. At temperatures some more higher these elements too are forced by complicated thermonuclear transmutations to melt in iron in brief time. And at this point we stay, because from the iron to more heavy elements the nuclear fusion could be obtained only supplying energy.
Then, once reached this phase, whatever is the mass of the star, also though it has formed a nucleus of iron, this is unable to burn producing new energy, such as hold up the weight of the following layers. Also for these stars then the moment of the end has come. And the end of these stars is a fast and extremely catastrophic event. But the subject has already been dealt, when we have mentioned about the supernovae.
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1
. - It shows that the first diagram (Fig. 1) doesn't have a linear course, as the spectral type is a discontinuous variable, having some discreet values only. For this reason, today, the type setting the color index (B-V) in abscissa is more used, that (Fig. 2) in practice is a function almost linear of the spectral type. The index of color (B-V) signifyes the difference between the magnitudo in the Blue (photographic magnitude) and the magnitudo in the Yellow (visual magnitude).2
. - Below the 0.2 of the solar mass the gravitational pressure is not sufficient to lead the protostar to the necessary temperature to the ignition of the thermonuclear mechanism: it is the case of the "brown dwarfs", real abortions of stars.3
. - A white dwarf is called a celestial object where the matter, no more sustained by the production of nuclear energy, falls down on itself achieving abnormal density as regards to the reproducible physical standards on the Earth. The state of the matter in this density is no more comparable to any of the three states we know by straigh experience: it is no more either gaseous, or liquid, or solid, it is said that it is the "degenerate" state, and it has special characteristics, on which is not the case here to pause, only to specify that, because the degenerated matter doesn't emit bright energy, whatever is the temperature, the adjective "white" is referred only to the shell of matter not degenerated surrounding the star, shell that, achieving extremely elevated temperatures, it is so bright to make observable, at the distance of some light years, the companion of Sirio, despite the brightness of Sirio itself, and despite its sizes don't exceed the planet of terrestrial type ones.4
. - At these pressures, in fact, the nucleum of helium is degenerate, and one of the characteristics of the degenerated matter is that it don't enlarge when running hot. So temperature and pressure continue to rise without causing expansion, and then always more highly, up to reach the 100 millions degrees necessary to ignite the fusion of the helium, but, the matter being degenerate, continues to elevate the temperature in a catastrophic way, such as to develop in few instants as energy as the stars of a galaxy all together normally produce it. All this energy breaks out in a catastrophic burst succeeding in a new expansion of the same nucleus that has caused it, and then in a decrease of the density, up to the point it is no more degenerate, and the remaining helium continues at this point to burn in a balanced way, like the hydrogen in the case of a normal star.