Question

Describe how a star’s luminosity and surface temperature change as it ages.

Answer 1

The life of a star is an ever going battle against gravity.
first as the gas gets denser with gravity bringing it closer.
As it contracts, it loses potential energy, of which half is used to heat up the star(internal energy) and the other half is radiated away(contributing to Luminosity).

As the star contracts, the increasing temperature and pressure in the core, ultimately triggers the hydrogen fusion reaction producing helium. The resultant pressure from the radiation stops gravity from taking over at this point. and the fusion goes on happily for many millions of years.

while the gods while away their time, watching over the humanity, eons pass, and the hydrogen in the core starts to dwindle. radiation pressure lessens and gravity gets a chance again. The star starts contracting again, thus releasing more energy. This increases its luminosity even more. Also, in the outer shells, because of the energy released from contraction, temperature rises and hydrogen burning can trigger. This keeps the star in the hydrogen burning phase for another few million years.

once gravity takes over, the star begins its journey inwards yet again, this time only stopping when conditions for fusion of ever heavier elements are achieved as He then B, then C,N,O ….up to Iron. Note that every next heavier nuclear reaction takes place at an ever increasing temperature. but during this time, every time the inner shells or the core contract, the outer core also expands (and thus cool)taking the star towards a red giant phase. Also note that both radius and luminosity increase greatly during these phases.

what happens during these contractions also defines the fate of the star which ultimately depends on its mass.
If its lesser than about 10 solar masses, because of density differences between the various shells that had formed(hydrogen burning shell, helium burning shell etc), an instability results which causes a lot of mass loss from the star. This ends up as a shell around the core which we know as a planetary nebula. The C-N-O core that is left is stabilised by the pressure of degenerate nucleons and keeps radiating its internal energy and lasts the age of the universe.

If its heavier than 10 solar masses, the C-N-O core contracts and heats up sufficiently to trigger the next set of heavy nuclei reactions. After every nuclear burning is exhausted, there follows gravitational contraction, further heating up and so on.

Finally iron nuclei are left in the core. These nuclei do not release energy during fusion but consume it. hence no more fusion occurs at this point. The gravity heaves once more and the iron nuclear are rendered into protons and neutrons which in the intense pressure fuse to form neutrons. These neutrons when come closer generate massive shock waves that travel throughout the star outwards, expelling the mass of the star in the form of a supernova explosion, which incidentally would be the brightest and most luminous event in the whole galaxy.

The neutron rich core that is left again is on the mercy of gravity. If its mass is less than 2 solar masses, it stabilises there with gravity balanced against the degenerate neutron pressure. Thus forms the neutron star.

However for heavier neutron cores, gravity has something else in mind. the degenerate neutron pressure cannot stop the contraction and the entire core collapses into nothingness. The ultimate victory of gravity. A black hole.

Answer 2

This might be a small question, but big explanation would be needed to understand it. I will try to explain at my best, without going into the complexities.

The luminosity of a star can be given as
Luminosity = Flux per unit area x Surface Area of the star \[Luminosity = \sigma T ^{4} * 4\pi R^{2}\] Thus the change in luminosity of a star with time is mainly due to the change in R (we can say, the change in the surface area of the star) and Temperature.

Here I can explain how surface area and temperature varies with the aging and I am choosing a massive star as the specimen here. When T and R varies, the luminosity varies by the fourth power of T and by the squared value of R and similar effects if the value decreases.

A star in its main sequence stage will have a specific mass and this indicates the rate of aging of the star. The greater the mass, the shorter the life it spends on the main sequence. A star is also made up of number of layers right from the core to the surface (means different gradients)

When a star finished using its fuel, I mean the mass of the core (10% of the stars entire mass is generally considered as its core) and only the core can undergo nuclear fusion at the main sequence stage, though the efficiency of the fusion depends upon the fusion mechanism (ex. p-p or triple alpha), the hydrostatic equilibrium of the star breaks. It means the photon pressure from the core can no longer balances the gravity. The helium left over in the core is inert and the fusion could not take place in this helium zone.

"Thus the surface of the star starts falling back towards the core resulting in a small decrease in its radius(L decreases), meanwhile due to the falling mass, the density of the star increases slightly which further increases the temperature inside(L increases). When the sufficient temperature for fusion (>10^7 for hydrogen fusion) is reached (this happens only if the star's mass is sufficient to provide the pressure and density to reach the temperature needed) in the immediate next layer to the core, that layer starts fusing hydrogen and pushes the surface over it, outwards (away from the core) thereby increasing the surface area (L increases)."

When this layer completes hydrogen fusion (no more hydrogen is left to fuse in that layer), the same process mentioned above (within the double quotes"..") repeats, thus increasing the pressure, density and temperature. This phase is the variable phase mentioned as instability strip in the HR diagram. Thus when a sufficient temperature is reached for the core to fuse helium (the product of hydrogen fusion), the red giant star balances the hydrostatic equilibrium. The fusion of helium in the core begins with Helium flash, a sudden increase in luminosity.

The same cycle of change in amount of fuel (fuse-able material), temperature, density and pressure takes place producing new elements like Carbon, Nitrogen, Oxygen, Silicon, etc.. until the core is left with iron. Till the production of iron all the fusion reactions are exothermic, gives energy, but the fusion of iron is endothermic, needs a lot of energy to fuse iron. This amount of required energy is really huge even in stellar dimensions.

But it can be achieved, when the entire mass of the star (when the hydrostatic equilibrium fails completely and gravity alone dominates the scene) falls onto the core. All theses, breaking of the equilibrium and falling back onto the core, happens within a fraction of a second, releasing a large amount of energy and thereby fusing even iron and even heavier elements. Thus the heaviest elements known are formed through this event called the Supernova Type II. Here, the temperature increases tremendously thus increasing the luminosity (approx. equal to the luminosity of a galaxy). Until this the luminosity is concerned with the ENTIRE range of the electromagnetic spectrum and it ends here.

The remnant of this event depends on the initial mass again (depending upon the the amount of energy provided to break the degeneracy pressure), thus the remnant may be a white dwarf (the bare core made of degenerate matter and all the shells are scattered around it forming a planetary nebula in many cases) or a neutron star (the bare core made of degenerate neutrons which gives high energy pulses) or a black hole.

In the case of a white dwarf, the luminosity is only because of the temperature since the radius becomes constant. In the case of neutron star, since a new axis called the magnetic axis has formed because of the outermost envelope of charged particles, the emission will not be continuous as before but are pulses arising from the end of the magnetic axis. Depending upon the inclination of this axis with respect to us, we may or may not observe them. In the case of black whole, the energy provided by the mass of the star was sufficient to break even the neutron degenaracy and the emission could not be obtained in the visible region of the electromagnetic spectrum.

Answer 3

well put @mruna_cp

Answer 4

thank u @zaphodplaysitsafe