### A Data-Driven Solution to the Stellar "Mass Mess"

Guest post by Dr. Luan Ghezzi. Luan was a postdoctoral researcher in the Harvard Exolab from 2013-2015, funded by CAPES under the Brazilian federal program Science Without Borders. This past summer he returned home to Rio de Janeiro, Brazil to continue his research into the physical properties of stars as measured from high-resolution spectroscopy. In addition to doing research at the Harvard CfA, he was also a research advisor in the 2015 Banneker Institute.

The detection of the first extrasolar planet around a solar-type star intrigued astronomers all around the world. The newly discovered system had a planet with almost half the mass of Jupiter orbiting its star at approximately 12% the average distance between Mercury and the Sun, a configuration that is radically different from the one we observe in our own Solar System. In the following twenty years, almost 2000 other extrasolar planets were discovered and confirmed, and nearly 4000 candidates await further confirmation/validation. However, these impressive numbers don’t mean that we know everything about the planetary systems out there. New exciting results dazzle us every day, like the hot friends of Hot Jupiters or the disintegrating planet around the cosmic death star.

Devising a model that accounts for the formation and evolution of all the discovered systems so far is one of the biggest challenges in Astronomy nowadays. One key ingredient involves a little bit of cosmic "genetics." When a child is conceived, genetics is able to tell us the probabilities that the individual will have certain characteristics (for example, the color of the eyes) based on the parents’ characteristics. It seems so far that the same holds for the parent stars of extrasolar planets.

We now know that a star with a higher abundance of metals (which means, for astronomers, every element heavier than H and He) has higher probability of hosting a giant planet (with a mass similar to that of Jupiter). The repeated confirmation of this link by independent research groups was a big step because it established that the formation of a specific class of planet is tied to one of the properties that mainly determine the evolution and fate of stars: the chemical composition. But how about the other key parameter for stellar evolution: the mass?

 The key plot from Johnson et al. 2010 showing that the likelihood of a star hosting a Jupiter-mass planet appears to increase with stellar mass.
Building up on earlier contributions, John Johnson and collaborators published a paper in 2010 to further explore the role of stellar mass in the formation of giant planets. The analysis of a sample of roughly a thousand stars from the California Planet Survey revealed that the probability of hosting giant planets increases linearly with stellar mass, going from 3% for M dwarfs to 8.5% for FGK dwarfs and finally to 14% for the retired A stars. This was a striking result since there was now stronger evidence that both of the fundamental properties that mainly govern the lives of stars also affected the formation of planets around them.

However, as often happens in science, additional analyses have muddied the waters a bit. Recently there have suggestions that the masses of the retired A stars could have been overestimated, thus creating an artificial correlation with the probability of hosting giant planets. Despite some back and forth in the literature in the following years, the controversy has remained open due to a lack of empirical results (theory can only take us so far after all). I like to think of this situation as the stellar mass mess

 It doesn't do this in Rio de Janeiro!
Upon my arrival at the CfA in January 2014, during a typical really cold New England winter (seriously, it gets really cold!), John and I decided that tackling this mass mess was a good start for my post-doc there. By that time, John and collaborators were finishing a paper in which they use model-independent measurements to confirm that HD 185351 is indeed a typical retired A star (blog post here). In a perfect world, we would just simply extend this analysis to the other 243 retired A stars. But in reality, this would be demand too much time on too many telescopes, so we needed an alternative for my two-year postdoc.

The solution was to gather data from the largest database that was not fully explored: the literature! We conducted an extensive search for benchmark evolved stars which had masses determined independently from stellar evolution models. After reading about a couple of hundred papers, we were able to compile of list of 59 benchmark stars: 26 members of binary systems (in the Milky Way as well as Small and Large Magellanic Clouds) with dynamical masses and 33 isolated stars with asteroseismology-based masses. We then determined model-dependent masses for this same sample using very heterogeneous input parameters collected from the literature, the PARAM code kindly provided by Leo Girardi and PARSEC grid of evolutionary tracks.

The comparison between model-independent (y axis) and model-dependent (x axis) is shown in the figure below. We can see a very good agreement for a relatively large mass interval (~0.7 - 4.5 solar masses), even though heterogeneous data was used to derive the results. The percentage difference between the two sets of masses (in the sense Evolutionary Tracks - Reference) is -1.30 +/- 2.42% and no trends were observed in the residuals relative to the input parameters. Similar good agreements were observed in the comparisons for the radii (-4.81 +/- 1.32%) and surface gravities (0.71 +/- 0.51%). We have also found a good consistency between independently determined ages for members of the same binary systems.
 I learned that this is what Americans refer to as a "money plot." It shows that model-based masses for evolved stars match the true masses measured by empirical methods. The masses of our evolved "benchmark" stars are not overestimated by the models!
Put together, our results show that the determination of evolutionary parameters using the PARSEC models and the PARAM code is capable of providing reliable masses, radii, surface gravities and ages. In particular, the masses do not seem to be significantly affected by systematic errors that would end up overestimating them. This conclusion is really important because it corroborates many studies involving topics that range from extrasolar planets to Galactic evolution. If you are interested in more details, check out our ApJ Paper, Ghezzi & Johnson (2015).
 The stars in Ghezzi & Johnson (2015) occupy the so-called giant branch of the H-R diagram, illustrated above. Specifically, our "benchmark" stars are in stages 8-10, mostly with R > 10 R☉. It's impossible for our masses to be correct according to the models while incorrect at and near stage 8, where the Johnson et al. "retired A stars" are.

One concern might be that we studied stars that are more evolved than those in the study of Johnson et al. However, since stars follow a single evolutionary sequence that varies smoothly in time and has no discontinuities, it is impossible for the model grids to be correct in the more evolved part of the giant branch while simultaneously being erroneous by as much as 50% a bit further down. (That is, unless we're willing to throw out everything we know about stellar evolution! Ed.)

Although our most recent study was a big step to solve the mass mess, much work remains to be done. That’s why myself, John and our collaborators are coordinating multiple efforts to improve the precision of observed parameters, providing better input to the stellar evolution models. For instance, John and I are revisiting the retired A star sample with new analyzes. Spoiler Alert! Preliminary results do confirm that the correlation between occurrence of giant planets and stellar mass holds. Stay tuned for these new exciting results!

### 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…