My Current Projects

How do we know that our understanding of low mass stellar theory is right? What does it mean to actually understand how a star works? To answer these questions stellar theorists construct sophisticated models that predict what the observable properties of a star should be based on a few fundamental stellar parameters such as mass and chemical composition. If these fundamental parameters are known for a given star and then observations of the same star match the predictions of a theoretical model we can say that such model is successful in explaining how the star works.

So, more specifically, what are these fundamental parameters that should be used as input to a model and what observable quantities should our model predict? Mass is by far the most fundamental attribute of a star, with its chemical composition playing a secondary role. It is often said that if a star is a stew then its mass is its main ingredient, with chemical composition being the spices that give a subtle taste to it and make it interesting. A star's spectrum is the observable we are after. The spectrum is a decomposition of the starlight into a color continuum, much like a rainbow decomposes sunlight by spreading out its colors. Because different wavelengths of light carry information about different physical processes in a star's atmosphere the spectrum can tell us a lot of information about what is going on at the surface of the star, including information about its chemical composition, temperature, and surface gravity. The figure at the top of this column shows four typical spectra for red dwarfs, observed by the Hubble Space Telescope for this project.

So how do we know that the models are right? In this project my collaborators and I observed 10 stars with precisely known masses and tested whether or not the models could replicate the observed spectrum for the known masses. Because stars with known masses must be binary stars where both stars are very close to each other the light form both stars in the binary system is blurred together if observed through Earth's atmosphere. So we used the Hubble Space Telescope to get a better view where we could separate the light from each star. The figure above shows four spectra fro

So what are the results? It turns out the leading models (Baraffe et al. 2015) do a pretty good job! They could be more specific in their predictions though, especially when it comes to chemical composition, but I am told that Isabel Baraffe's group is working on it as is Aaron Dotter's MESA group.

For more on this project check out this presentation from the Cool Stars 19 conference.

The figure above is a modified version of a Hurtzsprung-Russell Diagram, or HR diagram for short, for stars and brown dwarfs lying close to the stellar-substellar boundary. The HR diagram is the basic tool of stellar astronomy because a star's position in the diagram can tell us most of what there is to know about a star. I like to think about is as the periodic table of stars, with the important distinction that whereas the periodic table is made up of a given number of chemical elements the HR diagram is a continuum. In this modified version I plotted luminosity, a star's total light output in all colors, in the horizontal axis and stellar radius in the vertical axis, both in solar units. For historical reasons the luminosity axis is inverted with brighter stars towards the left and is logarithmic.

Do you see a gap and then a jump in radius after spectral type L2? That gap indicates the end of the stellar main sequence, with the smallest and least massive possible stars having a radius of about 8.6 percent that of our Sun. Our knowledge of substellar evolution tells us that brown dwarfs shining in the luminosity range indicated in this diagram should be young, and young objects have larger radii. That is why we interpret the jump in radius as a transition from stars to brown dwarfs. I first published this result in 2014, in a paper titled "The Hydrogen Burning Limit".

That paper was influential, but limited in its scope. It studied only 63 objects and those objects were pre-selected to cover a range of colors and temperatures. What we really need is a volume-limited sample where we study all objects in a given volume. That is the only way of knowing that our sample is representative of the overall stellar population. We can then study population properties. For instance, we should expect more stars than brown dwarfs in this luminosity range because stars have a very long lifetime whereas brown dwarfs spend only a small fraction of their lives in this luminosity range. The diagram above is not yet volume-limited, but it already hints at an accumulation of stars at the bottom of the main sequence, at spectral types L0 to L1. When this diagram is complete in the sense that it includes all objects in a given volume of space it will give us much stronger evidence about the end of the stellar main sequence.

As I mentioned before, mass is by far the most fundamental parameter of a star or brown dwarf. If we wish to obtain a thorough understanding of how stars work in their interiors, why their atmospheres radiate at a certain effective temperature, and how they evolve in time we must study stars with precisely measured masses. The need for these measurements is particularly dire in the case of very low mass stars and brown dwarfs, for which several aspects of stellar theory are still not settled. Unfortunately stars with directly measured masses are few and far in between because masses are extremely difficult or even impossible to measure in most cases. We therefore must make the most of the star masses we have and be on the lookout for newly discovered stellar systems that are good candidates for mass measurements.

The only way of measuring a star's mass is by measuring the gravitational attraction between two components of a binary star system, and doing so requires mapping out the binary's orbit. The figure above shows the orbits of the Epsilon Indi BC system, which I recently published. The system consists of two brown dwarfs (the B and C component) that orbit each other around their common center of mass, which in turn orbits the much more distant A component, a star much like our Sun. The red and blue orbits are the orbits of the B and C components around the center of mass, at the origin of the coordinate system. These brown dwarfs are so close to each other that we do not normally see them as separate dots in the sky. We see their combined light, which wobbles in a barely measurable way as the stars orbit their common center of mass. The black orbit is the orbit of the combined center of light, for which we measure this minute wobble. This wobble motion is combined with motion from two other sources: the relative motion of the star and our Sun around the center of the Galaxy (the proper motion), and an apparent motion caused by Earth's orbit around the Sun (the parallax motion, from which we derive the distance to the star). Decomposing this 10 variable motion is a fairly evolved mathematical problem. The equations cannot be solved algebraically and the solution must rely on statistical and numerical methods. I spent the better part of an year developing a computer program to solve them.

Now that I already developed the mathematical machinery to solve the orbital problem and achieved good results with Epsilon Indi BC my collaborators and I want to apply the method to other binary systems for which we can derive masses. My collaborators and I have been tracking the orbital wobbles of at least 20 other interesting objects and several members of our RECONS team will now use my computer codes to obtain masses.

The poster below shows some of our candidate systems and goes into some detail about how we measure their orbits. Click and zoom to see full size.