Science Sunday: The Stars – Part III: Low-Mass Shinys

This one’s about the red-boxed stars

On the last Science Sunday, I discussed all the basic stellar populations, putting up little descriptions of each part of the HR diagram. For the next few posts, I want to go in more depth regarding each portion of the diagram, starting with the Main Sequence. As always, Wikipedia will be a major source of information. Aside from that, I’ll also *gasp* be using actual notes from my actual Stellar Interiors class that I actually took (and somehow passed) this past spring. Actually! So there might be some actual truth to this post! Don’t count on it though.

Without further ado, let’s get into it.

The Main Sequence (hereon referred to as MS) spans a mass range from about 0.08 solar masses up to (and beyond?) let’s say 100 solar masses. For reference, 1 solar mass is basically the mass of our Sun. Because MS stars span such a large dynamic range, I’m going to chop even this post into two “smaller” ones. As you might infer from the title, this post will cover low-mass MS stars. This means that we’ll be discussing stars whose initial masses don’t exceed 6 solar masses. Why this particular cutoff in the mass range? Well, something super duper extra special happens to stars above this range when they die. But those are details for another Sunday.

So, low mass MS stars. The basics were covered last time, but I’ll copy those here and move from there.

The Main Sequence: Where stars of all types reside after their initial birth. Stars on the Main Sequence will be fusing hydrogen into helium (by way of either the p-p chain or the CNO cycle) in their cores, much like our own Sun. Roughly about 10% of a star’s initial mass will be involved in fusion over its lifetime as a Main Sequence star, with 0.7% of that mass being converted into energy. […skipping over a lot of it…] If we divide the total energy production of the Sun in its lifetime (1.26 x 10^44 J) by this rate (1.26 x 10^34 J/year), we get out that the Sun should last about 10^10 years, or 10 billion years.

As was stated, MS stars are defined by hydrogen fusion in their cores producing the light that allows them to be seen. For many of these low-mass MS stars (mass < 2 solar masses), the overwhelming majority of hydrogen fusion takes place via the proton-proton chain (hereafter the pp chain). The pp chain works something like this…

Two lone protons are chilling around in the core of a star. Their companion electrons, that would make them neutral atoms, have long since been stripped off. It’s really hot (~10 million Kelvin) and really dense (screw you and your numbers). As such, even though they’re naturally opposed to being around one another, they’re able to overcome their mutual repulsion and FUSE into a single, bare, deuterium nucleus. In doing so, they spit out some antimatter (the antielectron), and a neutrino (which ends up escaping from the star very quickly). This first step takes a dumb long time (~1 billion years), and produces about 0.42 MeV of energy. The escaped antielectron will undoubtedly meet up with a normal electron and form a joint suicide pact, going on to release 1.02 MeV of energy. The total produced in this step is ~1.44 MeV of energy, which corresponds to just about 2.3 x 10^(-13) Joules, or the amount of energy coming off of a 40-watt lightbulb in 5.75 femtoseconds.

Link for Helium-3 formation

Almost immediately (1 second) after that deuterium nucleus is formed, another proton that isn’t looking where it’s going just slams face (face?) first into it, creating a helium-3 nucleus, as well as producing about 5.5 MeV of energy. You can see a schematic of this in the link above. The yellow ball popping out is light in the form of gamma radiation.

This final stage differs a wee bit depending on just how hot it is in the star’s core, but I don’t really care. I’m going to give the simplified version here. Over the next million years, two helium-3 nuclei have a hell of a time smacking together to make helium-4, producing another 12.9 MeV of energy and two chaos-wreaking protons. Altogether, this whole process produces about 27 MeV of energy. That’s just about 4.3 x 10^(-12) Joules of energy.

“Um…what gives? I thought this process produced a star’s light. It takes over a billion years and doesn’t make enough energy to power my TV!” Well maybe you should hush and think for a second. There’s more than just 6 damn protons in a star’s core right? Right! And all the light that’s produced at the surface has to come from these reactions in the core right? Right! So let’s be smart about this. If we measure the brightness of a given star, let’s say our Sun for instance (~4 x 10^33 watts or Joules per second), we can extrapolate back to find out just how many times this is happening in the Sun’s core every second. 4 x 10^33 Joules produced every second, and each process produces ~4 x 10^(-12) Joules. That means that every second, this process is happening roughly 1 x 10^45 times in the Sun! Yeah. There’s a lot of protons in stellar cores.

More massive stars still use the pp chain, but also get a significant contribution from the Carbon-Nitrogen-Oxygen cycle. Look on wikipedia for that. I’m lazy, and there’s more to talk about than different methods of fusion.

Let’s keep looking into the interiors of these stars, and consider how all of this energy gets out. Now, stars are all about energy transport. You’ve got to get all of that energy that’s generated in the core out to the surface of the star somehow. Typically, energy gets out from the core by scattering the light produced by fusion outward from particle to particle over ~10 million years (the figure changes depending on what type of star we’re talking about). That scattering is demonstrated by the white path of photons in the picture above.

However, with most stars, energy transport by outward scattering of radiation isn’t the most efficient method of transport throughout the entirety of the star. And nature is nothing but efficient. Always (he says as he remembers his appendix…). Soooo…the star will instead turn to convection in order to transport energy outward. HOW DOES THIS WOOOOOOORK!? Consider a pot of boiling water.

Convection of the Agua

You put a pot of water on the stove and it’s cold. You turn the stove on and the pot gets heated from below. Now as we all know, hot water rises and cool water sinks. So, hot bubbles created by the heating from below rise to the top of the water, reach the surface, release their heat (energy) to the air above, cool off, and sink back to the bottom where they’re heated again. And thus the cycle continues. This is what happens in stars, except instead of water it’s hot plasma rising and falling back into the star.

Now, convection in low mass stars is interesting, as the location of the convective layer changes based on the mass of the star. For stars with masses less than that of the Sun, the convective layer starts at the surface, and extends downward from there into the star as the mass of your star decreases. Going upward from 1 solar mass, the convective layer starts at the core and grows outward with increasing mass. This is illustrated in the graphic that I copied out of my notebook below.

Ok so this is like the first science-ish plot to appear on this blog, so pay attention to it. m/M is the mass fraction of the star, and M/Mo is the actual mass of the star in solar masses. The shaded area is where convection occurs in the star, as a function of mass fraction and the overall mass of the star.

Why the division at 1 solar mass (oh geez oh geez the Sun is super duper extra special!)? Well, for stars of less than one solar mass, their exteriors are really cool (temperature-wise). In addition, the temperature of the star doesn’t drops off very steeply as you move from the core of the star to the surface of it. As such, radiative energy transfer becomes very inefficient. Convection on the other hand is more efficient (due to EQUATIONS that I’m too lazy show here), and thus the energy from the interior of the star gets transported outward via convection.

With stars that are greater than 1 solar mass, the conditions are a bit different. In these circumstances, the star’s interior is really really hot. It’s so hot that the temperature toward the core of the star doesn’t decrease very sharply as you move outward in the star. As such, the core transports energy outward via convective bubbles, until the temperature of the star starts to decrease sharply again with distance from the star’s center. The hotter a star is in its interior, the farther out this convective layer extends.

Alright. That’s enough for now. This was a huge information dump. Until next time!

Here are some non-wikipedia, non-class notes references that I may have stolen from for this post:

Disclaimer disclaimer, this is scientific musing at best. This is not to be taken as a definitive source of information. If anything, maybe just a primer. But seriously though, learn this for yourself. Don’t rely on me. At least, not until I get a doctorate and am qualified to teach this type of stuff. Blah blah stolen from wikipedia, blah blah order of magnitude calculations. Feel free to ask questions!