The variety of star size

Question

Hello Jayendra, I haven't found anywhere an answer to this question. I find it surprising that stars are so variable in size. I would have thought that as as gas and dust condenses into a protostar that there would be a certain critical mass at which nuclear fusion would begin, after which any further gas would be blown away from the star. Put another way, how can a star get to say 100 solar masses before "igniting" if our own sun ignited at a much smaller mass? I have been told that the nuclear fusion in large stars is different to that in small stars but it would begin in all stars as proton-proton fusion, and presumably at a similar critical mass? Thanks.

Answer

Wow! Paul, your question is most original.

But I think the answer is simple.

The surface layers of a star are THERE, chiefly because the star's gravity is sufficient to pull back the gas. Most prominences are explosive events on the sun, yet the gas loops back due to gravity and magnetism of the sun.

Like wise, in stars with much greater starting mass, even though the fusion starts at the same time as the sun, the accretion does not stop. As the weight of the overlying layers increases, the star begins burning fuel at a faster rate to sustain hydrostatic equilibrium (between gravity and hot expansive forces). In the end by the time the star has gobbled up all the debris in its accretion disk, it is BLUE or even WHITISH! (Not white dwarf).

It all depends on the starting mass of the area or rather volume of space from where the star starts its life, as an EGG (EMBEDDED GASEOUS GLOBULE).

Another reason most people fail to understand is that any gaseous volume that is collapsing under gravity will have its outer layers collapsing faster than its inner layers!

That is because Newton's calculus predicts that gravitational intensity g falls off radially inside the body and as per the inverse square rule outside the body. Perforce, g is at its highest value at the surface. So as the star is collapsing, even after fusion starts, the outermost layers are still in the process of continuing gravitational collapse. The overall massive gravity of the object prevents a blow off of material heated by the reactions within.

This has been observed in spiral galaxies too! The galactic gravitational acceleration g falls off radially within the hub, making the stellar peripheral velocity a linear function of orbital radius, within the hub. And the galactic hub is Huge, extending over 100s of light years!

I often wonder if the globular clusters display the same mechanism. Stellar speeds as a linear function of orbital radius. As though they were like mini galactic hubs themselves!

All red giants are later stages of stellar development and out of the scope of this discussion.

hope that suffices. regards Jayen.

Question

Hello Philip, I find it surprising that stars are so variable in size. I would have thought that as as gas and dust condenses into a protostar that there would be a certain critical mass at which nuclear fusion would begin, after which any further gas would be blown away from the star. Put another way, how can a star get to say 100 solar masses before "igniting" if our own sun ignited at a much smaller mass?

Answer

Hello,

The key answer to your question resides in the *type* of nuclear fusion the star undergoes. For stars of mass less than about 1.5 solar, the proton-proton cycle is the fusion reaction, with the net effect written:

H1 + H1 + H1 + H1 -> He4 + energy

For stars more massive, the C-N-O or carbon -nitrogen -oxygen cycle is key and this doesn't kick in until about 1.3 x 10^7 K, contrasted to the p-p cycle that kicks in much lower and has lower mass thresholds, etc. operative.

You can read much more about the C-N-O cycles and how they apply to the more massive stars here:

http://en.wikipedia.org/wiki/CNO_cycle

Along with the respective energies given off at each reaction step.

Bear in mind too, that though some stars may attain whopping masses, e.g. 100 solar, the price they pay is in a much shorter lifetime. Thus, the more massive star always consumes its nuclear energy stores a lot faster than its much smaller counterparts. It is allotted much higher luminosity (according to the mass-luminosity law) but at a cost in duration.

Think of it as an energy spendthrift, which squanders its energy at a rapid rate, leading to a much earlier death.