### Updates from the Exolab: Characterizing a Brown Dwarf Found with Kepler

This is a guest post from my graduate student, Ben Montet. In it, he describes his work studying a brown dwarf in the Kepler field, which is documented in a recently submitted paper available on astro-ph at http://arxiv.org/abs/1411.4047.

Ben is a fourth-year graduate student in the Exolab studying M dwarfs and their companions. He is also interested in using dynamical effects in multiple-planet systems to better understand both the planets in these systems and their host stars. He has previously written for Astrobites and FiveThirtyEight. You can find him on Twitter @benmontet.
The longtime follower of this blog has no doubt read a considerable amount about exoplanets. But in my opinion readers have been underserved when it comes to their more massive cousins, the brown dwarfs. Brown dwarfs have masses to low to ignite hydrogen fusion in their cores, yet too massive to be planets (they are capable of fusing deuterium, unlike less massive gas giant planets). However, the truth is, brown dwarfs and planets aren’t that different! We discovered the first bona fide brown dwarf in 1995, the same year the first exoplanet was found orbiting a sunlike star. Today, we know of a few thousand of each.

We think there are many---perhaps billions---of free-floating planets in the Milky Way, drifting through the galaxy far away from the gravitational influence of any one star. For brown dwarfs, we know this to be true! Nearly all brown dwarfs we’ve observed are singletons, wandering through space all alone.  While this is fine for them, it makes our lives as astronomers harder. We can measure the distance to these systems (through their parallax), their luminosities, and their spectra, but that’s the only information we get.

We would like to tie these observables into physical parameters like mass, radius, and chemical composition (metallicity). Just like we can for exoplanets, we can measure these best when we find a brown dwarf transiting a bright star. Enter the Kepler telescope. In 2011, just before I joined the Exolab, John and team published a paper about LHS 6343 C, a brown dwarf in the Kepler field transiting one member of a wide binary system consisting of two M dwarfs.  They analyzed six weeks of data from Kepler, adaptive optics imaging from Palomar, and a handful of radial velocity observations from Keck to measure the mass and radius of the brown dwarf.

Now that the primary Kepler mission is over, we have the chance to do a lot more. In this paper, we analyze all the Kepler data: nearly 100 eclipses! We also have more than 30 radial velocity observations to measure the mass ratio between the brown dwarf and its host star (shown below). With these data, we can measure the mass ratio and radius ratio to half a percent each. At this point, the conventional strategy is to characterize the star as well as possible. With near-IR spectroscopy from TripleSpec at Palomar and Robo-AO visible-light adaptive optics imaging, we measure a mass and radius of the host star such that we can measure the mass and radius of the brown dwarf to about 2%. This is the best anyone has ever done for a cool, old brown dwarf!

 (left) Kepler data showing the light curve, with the best-fitting transit model as a thin black line. (right) RV data over one orbit of LHS 6343 C, with the best-fitting orbital model as a thin, red line. In both cases, the residuals to the best-fitting model are shown at the bottom.

But what if we didn’t have to rely on stellar models at all? From the transit light curve, one can measure both the stellar density and the size of the transiting companion’s orbit. With these two alone, the mass ratio between the star and the companion can be calculated. Adding in the RVs, which measure the mass ratio slightly differently, one can not just measure the relative masses, but the absolute mass of each object! Then, using the stellar density again, the radius of each object can be measured.

Because we can measure the light curve shape so well, we use this technique to measure a model-independent mass and radius of the brown dwarf to a precision of about 3%. What’s really interesting is that this method predicts the stellar masses to be a little bit larger than what the models we use predict. The discrepancy isn’t big enough to make any strong claims that the models are wrong, but it is just approaching the edge of statistical significance. This is one of several results that have recently come out or will come out in the next few months suggesting that M dwarfs may be a little bigger than this particular set of models predict.

 Secondary eclipse of LHS 6343 C behind its host M dwarf. In black is the raw Kepler data; in red we bin the data to reduce random noise. The best-fitting eclipse model is shown in blue, with the uncertainties shown as dashed lines.
Now that we have the mass and radius, the next step is to measure the luminosity of the brown dwarf to compare to theoretical evolutionary models. To do this, we want to observe the secondary eclipse, when the brown dwarf passes behind its host star. We observe this event in the Kepler bandpass, where the brown dwarf is 0.0025% as bright as the M dwarf it orbits (shown right). We also plan to observe the eclipses in the infrared with the Spitzer telescope, where the brown dwarf should be as much as 100 times brighter relative to the M dwarf! With these observations, we should be able to determine if the brown dwarf has thick clouds in its atmosphere or not, how variable the atmosphere of the brown dwarf is in time, and if the stellar evolutionary models of brown dwarfs, never tested before in this parameter space, are accurate. Stay tuned!

### On the Height of J.J. Barea

Dallas Mavericks point guard J.J. Barea standing between two very tall people (from: Picassa user photoasisphoto).

Congrats to the Dallas Mavericks, who beat the Miami Heat tonight in game six to win the NBA championship.

Okay, with that out of the way, just how tall is the busy-footed Maverick point guard J.J. Barea? He's listed as 6-foot on NBA.com, but no one, not even the sports casters, believes that he can possibly be that tall. He looks like a super-fast Hobbit out there. But could that just be relative scaling, with him standing next to a bunch of extremely tall people? People on Yahoo! Answers think so---I know because I've been Google searching "J.J. Barea Height" for the past 15 minutes.

So I decided to find a photo and settle the issue once and for all.

I then used the basketball as my metric. Wikipedia states that an NBA basketball is 29.5 inches in circumfe…

### Finding Blissful Clarity by Tuning Out

It's been a minute since I've posted here. My last post was back in April, so it has actually been something like 193,000 minutes, but I like how the kids say "it's been a minute," so I'll stick with that.
As I've said before, I use this space to work out the truths in my life. Writing is a valuable way of taking the non-linear jumble of thoughts in my head and linearizing them by putting them down on the page. In short, writing helps me figure things out. However, logical thinking is not the only way of knowing the world. Another way is to recognize, listen to, and trust one's emotions. Yes, emotions are important for figuring things out.
Back in April, when I last posted here, my emotions were largely characterized by fear, sadness, anger, frustration, confusion and despair. I say largely, because this is what I was feeling on large scales; the world outside of my immediate influence. On smaller scales, where my wife, children and friends reside, I…

### The Force is strong with this one...

Last night we were reviewing multiplication tables with Owen. The family fired off doublets of numbers and Owen confidently multiplied away. In the middle of the review Owen stopped and said, "I noticed something. 2 times 2 is 4. If you subtract 1 it's 3. That's equal to taking 2 and adding 1, and then taking 2 and subtracting 1, and multiplying. So 1 times 3 is 2 times 2 minus 1."

I have to admit, that I didn't quite get it at first. I asked him to repeat with another number and he did with six: "6 times 6 is 36. 36 minus 1 is 35. That's the same as 6-1 times 6+1, which is 35."

Ummmmm....wait. Huh? Lemme see...oh. OH! WOW! Owen figured out

x^2 - 1 = (x - 1) (x +1)

So $6 \times 8 = 7 \times 7 - 1 = (7-1) (7+1) = 48$. That's actually pretty handy!

You can see it in the image above. Look at the elements perpendicular to the diagonal. There's 48 bracketing 49, 35 bracketing 36, etc... After a bit more thought we…