White Dwarfs, Neutron Stars & Black Holes Part I : Formation of White Dwarf Star

Stars remain stars as long as the 2 opposing forces, which are “gravity” trying to collapse the star inward & “nuclear fusion” in the star’s core exerting an outward pressure, remain in balance with one another, which as a result, keeps the star stable. In the majority of the stars within galaxies, these 2 opposing forces remain in a relative balance state for billions of years, keeping them stable. But every star runs on nuclear fuel that gets produced at the centre of the star in its core & when this fuel eventually runs out after a few billion years then the inward gravitational push overwhelms it’s counterpart outward pressure from nuclear fusion causing a cataclysmic collapse ultimately resulting in a colossal explosion called a supernova & what remains is sometimes a neutron star or a black hole. Whereas in the case of a small or an average-sized star, there’s no supernova explosion at the end of their lifetime, instead in their final evolutionary stage, after exhausting their nuclear fuel, a small or an average mass star transforms into a white dwarf after shedding off its outer layers into colourful rings of planetary nebula. This formation of a white dwarf, a neutron star or a black hole is again a fascinating process discussed as below __

Nuclear fusion in the core of a star creates outward pressure, which balances the inward gravitational force. This nuclear fusion starts with fusing 4 hydrogen atoms to 1 helium atom & this particular fusion reaction works for billions of years in the lifecycle of a star while the star remains stable in its main sequence phase. Once this hydrogen in the core gets exhausted, then Helium fuses to give Carbon, which marks the start of the horizontal branch phase. Then Carbon core fuses to give Neon & thus progresses up through the periodic table until a core of Iron gets formed. So to summarise, nuclear fusion in a star’s core fuses increasingly higher mass elements until the core element turns into Iron. Once an iron core is formed, fusion ceases as to fuse nuclei heavier than iron, the fusion process would require more energy than the energy that would be released. This is because the binding energy per nucleon starts to decrease for nuclei heavier than iron, as a result of which, having a fusion reaction to create elements heavier than iron would absorb more energy than releasing it.

Before proceeding any further, an important point to remember here is that not all stars will come to this stage of having an iron core before the exhaustion of the nuclear fuel in their core. For instance, our own Sun which is an average mass star, will not see itself having an iron core & will run out of its nuclear fuel long before any iron gets produced in its core. But incase of a high mass/massive star like for instance Sirius, nuclear fusion will work till its core has Iron in it & when this shall happen, as previously stated no more energy will be produced or released which in turn will result in the collapse of the outward thermal pressure, thus allowing gravity acting inward to take over, ultimately leading to a supernova explosion.
Note: if a star is 8 times greater than the mass of the Sun, then it can produce iron in its core.

Now for a small size star like “Proxima Centauri”(Red dwarf star, approximately 4.25 light years away from Earth) or an average size star like our Sun, they remain in hydrostatic equilibrium state, meaning remain stable for in the range of 10 to 100 billions of years before hydrogen in the core runs out & hydrogen fusion stops. Once a star reaches this stage & the star core has helium instead of hydrogen, then as stated above, the inward & outward pressure in the star are no longer in balance & gravity starts to dominate & so the core begins to contract. Now, as the core is getting compressed, the motion of atoms in the core goes more rapid, resulting in the rise of temperature in the core. This temperature rise also results in heating of the region surrounding the inert helium core, eventually reaching a point where hydrogen fusion can start again, but this time not inside the star core but outside of it, in its immediate outer shell. This process is called “Shell Burning” or more precisely, Hydrogen Shell Burning. The energy produced as heat in this process of “Shell Burning” causes the star to expand by pushing the outer layers/shells of the star, since this heat released from shell hydrogen fusion exerts the same outward pressure as nuclear fusion in the hydrogen core in the main sequence phase. As the star expands, so the surface area enlarges & so the surface temperature of this larger surface area star reduces, making it appear cooler & redder. Also, with a larger surface area, the total energy output or luminosity increases, making the star look brighter. With this, the star no longer remains a main-sequence star but has now turned into a Red Giant star. The size of a Red Giant can be in the range of 10 to 100 times the size of its main-sequence star (when it was a stable star). For an average size star like our Sun with a lifetime of approximately 10 billion years & having already lived for about 4.5 billion years, there’s still a long time to cover before the Sun turns itself into a Red Giant & when this shall happen then the enlarged Red Giant Sun would expand beyond the orbit of Mercury, Venus & may be even Earth, thus engulfing them all. But even if Earth somehow survives this Red Giant phase of the Sun, no lifeform on Earth (human life will not exist this far in future) will survive the astonishingly high solar radiation coming from the Red Giant Sun, having lost all its atmosphere & all water evaporated into space.

A small or average-sized star, having turned into a Red Giant, still the inert helium core continues to shrink, heating the core while hydrogen fusion in the outer shell also continues. The helium ash (alpha particles) getting produced from shell buring gets constantly rained down in the core below, increasing the density of the core & this continues till electrons of the inert helium core becomes degenerate, meaning the free electrons in the core resist any further compression due to quantum mechanical effects, meaning with the increasing inward push, increasing density & raising temperature the helium atoms loose their electrons, becoming ionized & the free electrons start depositing in the core eventually reaching the point of degeneracy & so the core is then held up by “Electron Degenerate Pressure” ie the pressure that does not depend on temperature, rather exerted by the free electrons. Eventually, the temperature of the core reaches around 100 million Kelvin which is high enough to start it’s 1st Helium fusion (triple-alpha process) in the core of the Red Giant. In the “Triple-alpha process”, 3 ionized Helium-4 nuclei fuse together to give 1 Carbon-12 nucleus with approximately 7.275 MeV of energy being released. This released energy contributes to heating the Red Giant Helium core even more, thus raising the temperature & speeding up the “Triple-alpha process”. But since the Red Giant star core is still degenerate, the increasing heat does not change the pressure, meaning the core doesn’t expand & cool. Due to this, the core temperature rises even more rapidly, increasing the rate of the “Helium Triple-alpha process” in a sudden, explosive runaway approach known as the “Helium Flash”. Energy generated per second in “Helium Flash” is greater than energy generated per second in an entire galaxy. When compared to our Sun, a “Helium Flash” produces approximately 10^11 to 10^13 times the energy output of the Sun per second. This tremendous high energy output from “Helium Flash” is then used to lift the Red Giant star core out of degeneracy, thus allowing the core to again expand & cool. This core expansion is also accompanied by a decrease in the star’s luminosity & a stable helium fusion reaction in the core, meaning the restoration of hydrostatic equilibrium in the core as the star enters a new evolution phase known as the “Horizontal Branch” in the “Hertzsprung-Russell” diagram. In addition, hydrogen fusion in the outer shell surrounding the helium-fusing core also continues. Unlike hydrogen fusion in main-sequence stars, which lasts for many billions of years, helium fusion in Red Giants remains less efficient, with a higher temperature reaction lasting only about 100 million years, which accounts for only about 1% of a star’s entire lifetime (small to average size stars).

One thing to note here is that, hydrogen fusion in a star core requires a temperature of about 10 to 15 million Kelvin while helium fusion starts at a temperature of about 100 million Kelvin, this is because a Helium nuclei has positive charges that are twice that of Hydrogen nuclei & so would require much more energy to overcome the Coulomb Barrier ie “The electrostatic repulsion between 2 or more bodies of similar charge that must be overcomed for nuclear fusion to begin” & the only way this can be made possible is by increasing the temperature of the core.

All stars, regardless of their mass, reach this point of turning into a Red Giant with helium fusion in the core in their lifetime. The journey forward when helium fusion ceases in the core & the elements in the core are mainly Carbon & Oxygen, then the next step in the lifecycle of a star depends solely on the mass of that star. So now, once the core goes out of fuel & helium fusion can no longer take place, then like before, the core will lose its hydrostatic equilibrium & gravity acting inward will take over, contracting the core, which then will raise the core temperature & also heat the outer regions or shells surrounding the core. Eventually, with the increasing heat, multiple layers or shells get formed surrounding the now Carbon-Oxygen core. The immediate shell surrounding the core is the “Helium fusion” shell, where the temperature reaches high enough to restart this Triple-alpha nuclear reaction. Beyond the “Helium fusion” shell, there forms the “Helium core” shell, then the “Hydrogen fusion” shell & finally the extended “Hydrogen envelope” outer layer. Also, evidently, the temperature of these layers lowers while moving from the core to the outermost Hydrogen envelope layer. Energy as heat is given out from the 2 fusion shells, which makes the immediate shells surrounding the fusion shells to expand. Here, the direction of the energy flow always remains outward, ie energy flows from the fusion shells to the outer shells & never inward towards the star core. As the star expands & cools, luminosity increases again & in the HR diagram the star once again moves back to the “Red Giant” branch for the time being. As for the Carbon-Oxygen star core, in case of small or average size stars, meaning stars having a mass lesser than 8 times the mass of the Sun, for them the core never reaches the temperature necessary for the next fusion, meaning the core doesn’t shrink enough to raise the temperature to the level necessary for Carbon-Oxygen core fusion. As a result, no further nuclear fusion & nuclear energy generation in the Carbon-Oxygen core is possible for such stars. Also, these small & average mass stars with Carbon-Oxygen core generate many frequent series of high-speed stellar winds which strip off the outer shells of the star by steadily sweeping away & ejecting the materials in these shells outward into space. This is the “Asymptotic Giant Branch (AGB)” phase of the star where the star as a Red Giant, suffers a significant loss of its mass due to the frequent thermal pulses, aka stellar winds. Eventually, the star sheds all its outer shells or layers by ejecting all of the materials & gas in these outer shells into space, thus creating a planetary nebula. This planetary nebula glows in different colours as UV radiation from the exposed core ionizes this expelled gas & other expelled elements, generating wavelengths of visible light. The exposed star core is nothing but a WHITE DWARF, which is still very hot & compact & the final remnant of the original star. This transition from a Red Giant star to becoming a White Dwarf for a small to intermediate mass star, characterised by shedding the outer layers of the star, creating a planetary nebula, takes about a few 100’s thousand to a few million years. Our star, the Sun will also see the same fate & will eventually turn into a White Dwarf at the end of its stellar evolution lifetime.