Science Sunday: The Stars – Part II: All Types of Shiny Things

Oh snap! It’s that time again!

On the first Science Sunday, I discussed the Sun. After that, I talked about charged particles and light. The goal there was to talk about light and charged particles in order to build up the machinery for this and later blog posts, where I hope to talk about all of the wonderful things that they do in the Universe. Very specifically, I wanted to introduce the concept of different types of light occurring at different wavelengths, so that I had a reference for when I talk about it here. I’ll probably be referencing it often, so be sure to keep an eye out for links like this that use it as a reference.

In great contrast to the first post, today I’m going to talk about the Sun not being special at all. Instead I’ll cover most of the known types of stars that reside in our Milky Way, including the Sun as one amongst billions. Today we talk about stellar populations.

As with before, I’ll steal from Wikipedia liberally. Onward!

So if we’re going to be talking about stellar populations in bulk, then it would probably be responsible of me to start with the Hertzprung-Russell Diagram. This diagram is a convenient little ditty that was devised separately by scientists Ejnar Hertzsprung and Henry Norris Russell in order to see the relationships between the temperatures and luminosities (read: brightnesses) of stars. It’s also known as a color-magnitude diagram, as color corresponds to the temperature of a given star, and magnitude corresponds to the inherent brightness of that star. It’s pretty clearly shown above.

Before continuing any further, let me explain the relevant pieces of this diagram, which itself contains a wealth of information. First, the axes. The vertical Y-axis is the magnitude axis, where objects with smaller magnitudes correspond to higher brightnesses. If this is confusing to you, don’t worry, as you’re most surely not alone. Blame for the Magnitude System falls squarely on the shoulders of Hipparchus (the guy who created it), Norman Robert Pogson (for formalizing it), and the human eye (for perceiving brightness logarithmically). The horizontal axis is the color axis, where the color for a given star corresponds to the numerical difference between its B and V-band magnitudes.

Hey, whoa Nick, what in the hell are you talking about when you refer to the B and V-bands?!

Hmm… well, let’s back it up a little bit more and talk briefly about filters and the electromagnetic (EM) spectrum. For more on the latter, see the previous Science Sunday post.

Light doesn’t just come in one flavor to fit every palette. There’s a whole selection of varieties of light called the EM spectrum, where these different varieties are separated by how long their individual wavelengths are. These wavelengths range from light waves longer than your physical height (meters), on down to waves shorter than the physical “size” of a single electron (femtometers), and beyond in both directions. When we want to isolate a specific section of this massive range, we use some material to block out everything else, with that material being called a filter. A filter for, as an example, visible light works in much the same way that a security checkpoint does at the airport, letting in the legitimate passengers (the visible light), and (hopefully) screening out bombs and terrorists (an overdramatic characterization of light outside the visible wavelengths).

If we want to then break up visible light into colors that we (more or less) recognize as familiar, we use narrower filters. One particular set of filters does this (well really, every set of optical filters does this), and assigns to different wavelength ranges the letters U, B, V, R, and I (near-Ultraviolet, Blue, Yellow-Green, Red, near Infrared respectively). Note that V, which stands essentially for “visible”, encompasses “yellow-green” because our eyes are most sensitive to yellow-green light as opposed to everything else. With all that said, when I refer to B and V-bands, I’m referring to the wavelength ranges falling within the B and V filters.

Right. So, something appears “bluer” if it’s brighter in the blue filter than it is in the yellow-green filter. This will make its B-V color negative, where more-negative means more-blue (mathematically, if it’s brighter in B than in V, then the object’s B magnitude will be smaller than the object’s V magnitude. When you subtract the two, you’ll get a negative number. Like 1 – 2 = -1). On the contrary, if it is instead brighter in the yellow-green than it is in the blue, then we say that the object is “redder”, and it will have a positive B-V color. That’s because its peak brightness occurs at longer wavelengths, with the longest of the visible wavelengths being in the red. It’s all relative, much like temperature. We’d say that a 90-degree day is “cooler” than a 110-degree day, even though 90 degrees is nowhere near being actually “cold” by our standards.

Anyway, we organize stars in this way (magnitude vs. color) because stars tend to fall along pretty distinct tracks when we do. What do I mean by that? Well, check these labels out here in relation to where each subtype falls on the HR diagram (labeled HR diagram below this section; rest assured that each of these will have its own lengthy, long-winded blog post in the future):

  • 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. The length of this lifetime can be (roughly) derived by calculating the amount of mass that’s converted into energy and dividing it by the energy output by the star per year. For the Sun, we have its *rough* initial mass of 2 x 10^30 kg. 10% of that is 2 x 10^29 kg, and 0.7% of THAT is 1.4 x 10^27 kg. If you convert mass into energy using that famous equation of Einstein’s: E = mc^2, you find that over the Sun’s main sequence lifetime, it’ll produce 1.26 x 10^44 Joules of energy. For reference, the average energy consumption per year in the United States is 335.9 million BTUs per person, which works out to about 3.54 x 10^11 Joules per person. Since the US has roughly 314 million people, this rounds out to an annual energy consumption rate of about 1 x 10^20 Joules (or roughly a hundred billion billion Joules) per year. If the Sun only produced as much energy as the United States consumed per year, it’d last for roughly 10^24 years, or 1 million billion billion years. However the Sun produces about 4 x 10^26 Joules per second (4 million times the amount of energy we consume in a year). This means about 1.26 x 10^34 Joules per year!. 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.
  • The Subgiants: Stars become subgiants when a) they are less than ~8 times as massive as our own Sun, and b) they have already run out of hydrogen fuel in their cores or are at the tail end of their hydrogen fusion. The difference in b) is determined by how massive the star is initially. In fact, what you’ll find out is that everything regarding a star’s evolution is determined by its initial mass and composition, but I digress. If a star’s mass is above, say, a few solar masses, then its core will be depleted of hydrogen (filled now with inert helium) and contract. This contraction will increase the temperature and density of the hydrogen gas around the helium core, and initiate hydrogen fusion in a thin shell around that core. If instead a star has less than a few solar masses, it will forego an abrupt shutting-off of core fusion in lieu of a more gradual slow-down of core fusion, with some slower contraction of the core. Overall, stars are in this phase before they jump into the Red Giant Branch.
  • The Red Giants: As the name implies, these stars are red and physically gigantic in size. Not exactly rocket science right there. Stars become red giants when they evolve out of the subgiant phase. They’re earnestly fusing hydrogen in a thin shell around their inert helium cores, and fusing it at a higher temperature than they were in their Main Sequence phase. Because the efficiency of hydrogen fusion is strongly dependent on temperature (~T^4, though not nearly as strongly dependent as helium fusion is!), the hydrogen-fusing shell outputs more energy than the hydrogen core used to. This excess of energy pumps up the star’s luminosity by a factor of >1,000! This extra bit of luminosity makes the star really bloated and extends the hydrogen envelope of the star as well. Because of the extended atmosphere, you have more light going over more surface area and over longer distances. Due to many scatterings with atoms in the envelope over this distance, as well as something magnificent called convection, the emergent light is less-energetic than the light that emerges from the surface of Main Sequence stars. Thus, the star appears cooler, and redder. Red star + big star = Red Giant!
  • The Horizontal Branch: As the hydrogen shell in a red giant star continues to fuse, the helium products of that fusion get dumped onto the core of the star, which then contracts and heats up. When the core temperature reaches 10^8 K (100 MILLION!), the helium core will ignite almost all at once, in what’s known as the helium flash. During this time, the hydrogen-fusing shell is still in existence on top of the helium-fusing core. However, when the core ignites, it will expand and thus greatly expand the hydrogen shell sitting above it, diminishing the fusing efficiency of that shell. This decrease in luminosity will cause the size of the star to plummet (but not down to Main Sequence sizes). As the star evolves through the Horizontal Branch, it will essentially maintain the same luminosity while growing progressively hotter (for reasons which I forget and are in my Stellar Interiors notes in my office). This is the reason why it’s called the horizontal branch; stars on this branch all have the same luminosity (again, essentially), but vary widely in temperature.
  • The Asymptotic Giants: As the star moves through helium fusion on the horizontal branch, it will of course drop the product of helium fusion deeper into its core. In this case, the product is carbon. So, carbon builds up in the core, and the helium core grows outward on top of the new carbon core. Much like how the helium core was inert on the Red Giant branch, here the carbon core will be inert as it’s not hot enough to ignite. Outside of the carbon core, you’ll have your helium shell fusing (more on this in a sec), and on top of THAT you have the hydrogen shell still plugging away. When it’s in this double-shell burning phase, it’s officially on the Asymptotic Giant branch. This is the phase of utmost interest to me, because it’s a very dynamic phase of stellar evolution. For one, the star is so bright and so extended that it’s actually losing a fair amount of its envelope via stellar winds and stellar pulsation. This mass loss rate is sometimes as high as 10^(-4) solar masses per year (sometimes even higher!). For reference, a solar mass is 2 x 10^33 grams, so 10^(-4) of that would STILL be like 2 x 10^29 grams every year. EVERY YEAR! That’s bananas! (B-A-N-A-N-A-S!) For reference, the Earth is roughly 6 x 10^27 grams in mass. This means that every year, these stars blow off more than 50 Earth’s worth of mass, just because they’re crazy like that. The second dynamic bit is the fact that once the star is in this phase, it never quite reaches an equilibrium point again where it maintains some stable shape. Its hydrogen outer shell dominates the energy output and increases the temperature and mass of the inner helium shell. When enough matter and temperature have built up in the inner helium shell, it goes through a mini helium flash which we call a thermal pulse, and the star increases in brightness and size for a brief amount of time. During this pulse outward, the hydrogen shell expands and effectively shuts off, until the helium shell dies down and contracts again. After the contraction the hydrogen shell begins fusing again and the cycle restarts. The time lag between successive pulses is on the order of 1,000 years (“on the order of” is astronomer-speak for “somewhere between one half of this number and 5 times this number”). There’s another, short-term pulsation mechanism called the K-mechanism, but I’ll leave that for another time.
  • The White Dwarfs: The Asymptotic Giant branch represents the last phase of stellar evolution where you can still call the object a star. After this point, the star will have puffed off its envelope through stellar winds and pulsations, leaving behind the white-hot carbon/oxygen core in the center of a brightly-shining planetary nebula. This core is what we call the white dwarf. This object is as hot as some of the hottest starts (recall, it came from the hot interior of an Asymptotic Giant) and has a mass comparable to our own Sun’s. However its size is about that of the Earth’s. As you might imagine, this combination makes it a very dense object. Simply based off of the information that I’ve given you here, you can derive just how dense this is (well, approximately anyway). Let’s say that our white dwarf has a mass M of about 1 solar mass (2 x 10^33 grams), and a radius R equal to the Earth’s radius (about 6.4 x 10^3 km, so 6.4 x 10^8 cm). First, we calculate the volume: V = (4/3) π R^3 = (4/3) π (6.4 x 10^8 cm)^3 = 1.1 x 10^27 cm^3. Average density is defined as M/V, so the density of this white dwarf will be (2 x 10^33 g)/(1.1 x 10^27 cm^3) = 1.83 x 10^6 grams per cubic centimeter! That is FREAKING absurd! A cubic centimeter would be like the size of your pinky, halfway above the top knuckle. In that small volume, a white dwarf would pack in 1.83 x 10^6 grams (or 1.83 x 10^3 kg, or 1.83 MEGAGRAMS!) of matter! That’s nearly a third of the Earth’s mass on tip of your finger. Crazy. There’s other crazy stuff with white dwarfs, but I’ll get to that another time.

They’re all grouped in these tracks on the HR diagram, all in relation to their temperatures (color) and brightnesses (magnitude).

An HR diagram depicting all the above-mentioned populations and more, with the source stellar cluster next to it. For reference, this is M15, a globular cluster.

Ok so this post is going to be longer than I had originally anticipated, so I’m going to do the rest in later installments. This should be enough now to get your astronomy juices flowing again though. Note that there are hundreds of subtypes of stars, and I’ll try to get to those in the future. Until next time!

*Because I’m really just that lazy, all of my facts and figures either come from my faulty memory or from somewhere on the internets. Conversions and calculations were done almost entirely on my iPhone, and may be a little (or a lot) off due to rounding and general laziness. This is certainly not an ultimately-reliable source for facts and figures, just an astronomer rambling about stuff that gets him excited. Enjoy for your own pleasure, but cite at your own peril! In fact, seriously, don’t cite at all. If you’re citing this as a source, you need some serious serious help.