on the Sizes of Stars

Stars are easy to understand.  The definition of a star is pretty clear: Stars are self-gravitating masses of gas* that sustain nuclear fusion in their cores.  Even if we don’t exactly follow it (astronomers often consider white dwarfs**, neutron stars, and pre-main-sequence stars as “stars” even though by the above definition they’re not) the definition is clear and easy to follow.

Applying it isn’t.

What we know about the different types of star is almost entirely based on their surfaces. We can compute physical model the innards of stars (informed by asteroseismology, which determines the inner layers of the Sun in much the same way seismology teaches us about the internal structure of the Earth) and see what happens, and at some point, the star is small enough that its core temperature never gets high enough to sustain fusion. That object is a brown dwarf.
Now, you would think that, because it’s a fundamentally different kind of object (fusion=yes versus fusion=no), a brown dwarf ought to be easy to spot. Unfortunately, this is not the case – there’s a continuous range of surface temperatures stretching from tens of thousands of degrees to below room temperature.  The surface doesn’t really care what the innards are doing.  So, astronomers have spent the last fifty years debating where the actual dividing line falls.  It would be great if it fell at the transition between spectral types M and L, say, between M9 and L0 (disappearance of titanium oxide, appearance of vanadium oxide and clouds) but estimates of the smallest star have ranged anywhere from M7 to L7.

A friend of mine from graduate school, Sergio Dieterich, thinks he’s finally found it.

One of the interesting things about stars and starlike objects is that there’s a range of masses where the size is fixed.  Brown dwarfs, again, have no fusion energy source, so what’s predicted to be supporting them is electron degeneracy pressure, buoyed up by whatever heat energy they have left over from their collapse.

What you’d really like to find are two ancient objects orbiting each other with measurable masses that are almost the same, where one (the star, which is being held up by nuclear fusion) is much brighter and hotter than the other one (the brown dwarf that’s been cooling off for billions of years).  We may yet find such a system, but waiting for that perfect star system to fall into our lap doesn’t seem like a productive use of time particularly when there are other ways.

For instance: the interesting thing about electron degeneracy pressure is that the more mass you add to something, the SMALLER it becomes, so the very smallest object should be the most massive brown dwarf or the least massive star. (Effectively, everything between Jupiter and an M7 star is almost the same radius, so… it’s entirely possible to have a planet that’s larger in radius than the star it orbits.)

Armed with this idea, Serge attempted to measure the radii of a large number of objects that could have been stars or brown dwarfs.  With photometry over a large range of colors, he reconstructed how much energy was coming out of the object and what its effective temperature is.  Thus, using the equation L=4 pi R^2 sigma T^4 (where T is the temperature and L is the total energy coming out of the object), he could compute the radius (R) of the object.

The smallest object Serge could find was 2MASS J0513-1403, which had a spectral type of L2.5.  With some uncertainties because not very many objects were studied (they’re dim, and it takes a lot of time to collect that data) it’s clear that the boundary is somewhere between L1 and L4.  That means, interestingly enough, that there ARE some stars that have clouds.  It’s kind of cool to think about.

You can read more about it here.

* Well, plasma, but they started out as gas.

** Even though they don’t have “star” in their name, various classes of them have it: ZZ Ceti stars, for example.  Also: No, it shouldn’t be ‘dwarves’, it’s ‘dwarfs’ because this is astronomy and we make up our own words.

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