You’ve probably heard of the strangest denizens of the Universe — objects like neutron stars and black holes (subjects of forthcoming articles!), for which a deep understanding of how they work requires quite a bit of pre-requisite physics and mathematics involving general relativity and/or the current understanding of the Standard Model of nuclear forces.
White dwarfs, though maybe being more unheralded in the popular press, are fantastical objects in their own right, much more common than black holes and neutron stars (there’s one right in our galactic backyard!), and understandable at a basic level with first- or second-year physics. To begin with, let’s see how we can tell that these objects are made up of a kind of matter that is not found anywhere on Earth and what some of their basic properties are.
First Observational Clues
It’s not at all obvious to most people, but many of the stars you can see with the naked eye are actually multiple star systems. In fact, here’s a list of the 10 brightest stars as seen from the Earth, excluding the Sun (duh) and whether they’re actually members of a multiple-star system:
✅ Sirius — binary system with a white dwarf companion.
Canopus — nope, it’s solo.
✅ Alpha Centauri — triple star system.
Arcturus — nope, single.
Vega — nope, single. Maybe we could introduce Vega to Arcturus…
✅ Capella — a quadruple system (double-binary)!
✅ Rigel — another (at least) quadruple system.
✅ Procyon — like Sirius, also has a white dwarf little buddy.
✅ Achernar — binary system.
Betelgeuse — nope, single.
✅ Hadar — triple star system!
Ok, so I threw in a whole extra star — I mean, it’s a free article, so the value here is off the charts.
So when you observe Sirius, if you’re careful to reduce the glare, what would you see? This!
Now, one thing that’s essential to learning about these systems is their distance away from us. That’s actually not too hard to calculate — following the ideas in this article (Distances to Stars), we can observe the parallax shift of Sirius over 6 months, pull out a calculator, and yadda-yadda-yadda (trigonometry!) we’ve got it. It turns out that Sirius is actually one of the closest stars to us (which, to a large extent, explains why it’s the brightest-looking star), only about 2.6 parsecs away (8.6 light-years). Once we know that, here’s what we do: we measure the brightness of Sirius and then calibrate it to what the brightness would be if it were 10 parsecs away. We can do the same thing with the Sun’s brightness, and what we find out is that Sirius is about 25 times more luminous than the Sun — calibrating the brightness at some uniform distance means that you’re just looking at the true “wattage” of these stars. Using the same technique, Sirius B only emits about 5.6% of the Sun’s energy each second.
Next step: run the starlight through a spectrometer! From the observed peak wavelength (roughly the color of the star) we can calculate its temperature. Then the pro-level move is to look at a pair of diagnostic spectral lines that are very sensitive to temperature (a future article also!). The result is that we can nail down the surface temperature of Sirius (and its companion) pretty easily: Sirius is about 10,000 K and the little companion is about 25,000 K — so hot that it essentially glows a bluish shade of white. Hence the “white” part of “white dwarf”.
Mind-boggling Calculations
So much of the beauty of astrophysics is what we can find out when we combine observational data with physics. It’s pretty easy to get the luminosity and temperature from observations, but it turns out that if you want to know the size of the stars, simple observations won’t help you. Pretty much all stars are just resolved to points of light in even powerful telescopes, so their diameters/radii have to be calculated. And it’s pretty easy! The relationship is
where the dotted-circle represents quantities in solar units. So then the size of Sirius A is (the Sun’s temperature is about 5800 K)
And, amazingly, for Sirius B, it’s
Only 1% the size of the Sun! That’s why we call it a “dwarf” star. There’s another everyday object that’s about 1% the size of the Sun — the Earth! So that little companion is roughly Earth-sized. Here’s what they’d look like in scale with each other (their separation is not to scale!)
Ok, there are 4 main physical quantities we usually want to know about stellar systems: Luminosity (check), Radius (check), Temperature (check), and Mass. We know 3 of them — how will we calculate the masses? That’s a bit tougher, especially for single stars. But for stars in a binary system we can nail it down fairly easily, especially if we’re able to track the system for a while and determine the orbits. Here’s what we see for this pair:
The interesting thing here is that, just considering their sizes, you’d think that A is so much more massive than B that A would remain pretty stationary during an orbit. It’s not technically true that one object always orbits the other; they both actually orbit the center of mass of the system. Now, if A is way more massive than B, then the center of mass is basically just at A’s position so it doesn’t wiggle much. That’s actually how B was discovered in the first place — astronomers in the 1800s noticed that Sirius A wobbled quite a bit and so inferred the presence of B. But look — A and B are always on opposite sides of the CM (at the origin), so you can see that the distance from the CM of the system to A is always about half the distance to B at the same time. So as long as we know the average separation between them (20 AU) and the period of the orbit (50 years), both things that are easy to observe, we use Newton’s version of Kepler’s 3rd Law to calculate the mass!
This is the total mass of both stars together. How can we separate them out? By looking at that ratio of the individual orbits! If B orbits twice as far away from the CM as A, it must be half the mass, exactly like balancing a see-saw. So that tells us that, finally, the mass of Sirius A is about 2.1 solar masses, and the mass of Sirius B is about 1.1 solar masses.
A New, Bizarre Kind of Matter
But, my goodness, can an object that tiny (the size of the Earth) pack as much mass as the Sun? How dense is that?? Density is mass divided by volume, so we can compute it:
WHAT??? That’s 100,000 times as dense as lead! There is simply no substance on Earth that comes anywhere near this. 1 cubic centimeter of this stuff (a grape!) would weigh about 1500 kg, or about as much as a car. And remember, the remarkable thing is that we’ve calculated all this using observations of the system and some basic physics. Trying to imagine that objects the size of the Earth made up of such exotic matter actually exist is what really drew me in to astrophysics in the first place.
What is the stuff that these white dwarfs are made of? What else can we know about them? It turns out, quite a bit. You’ll have to wait on the edge of your seat for White Dwarfs, Part 2!!
On Deck:
The next article I’m working on addresses a bit of philosophy and the power of using science and reason as a lever for understanding, and how we can perform really simple experiments to determine things that seem unknowable.
If you’re a student/teacher and want to see lots of worked examples that I like to include in my classes when I teach the “standard” University Physics 1 and 2 courses, feel free to browse the (growing) collection of 150+ videos at
And if something is especially cool and you’re inclined to leave a “tip” I’m not above coffee or pizza:
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A big heart for cranking things all the way up to eleven with HADAR.