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### Ringing stars that are this big

 An illustration of the surface and interior of a giant star. Credit: Paul Beck
Last year I wrote about how some of the results of my PhD thesis were being questioned in the literature. I remarked at the time that, "No scientist enjoys having their results challenged," but since then I've realized that it's actually not that bad. In fact, it's a sign you're doing the right things scientifically. If you aren't doing important work, then no one is going to take much notice, and when people do take notice and ask good questions, it provides an opportunity to do more science! (Well, provided one takes a growth mindset.) So I decided to take the opportunity and last year I began branching out.

As I explained previously, the scientific issue at hand is really quite simple: Either my "retired A stars" really are the evolved counterparts of A-type stars like Vega and Sirius, with masses greater than 1.5 times the mass of the Sun, or they're really not much heavier than the Sun. The test is also straight forward: go out and measure the masses of some of my stars, and compare the direct measurements to the predictions of the models I was using. The difficult part is putting all of this into practice.

One way of directly measuring a star's mass is to see how it rings. Wait, let me step back for a second. The stars that I study have convective outer layers, in which hot gas rises, cools and falls back down toward the star's interior. Kinda like in a bowl of miso soup:

Video credityouareahippo

These rising bubbles of gas bump against the stellar surface and cause it to ring. (The motion of these gas bubbles is what gives rise to stellar "flicker," the phenomenon discovered and studied by Fabienne Bastien) Even though the bubbles do their bumping randomly, the star will vibrate, or ring, at its natural frequencies (see my previous post on resonances). A good analogy once relayed to me by Peter Goldriech is to imagine throwing pebbles at a bell. There will be lots of random strikes, but the bell will still ring at its natural tone. If you know the shape and composition of the bell and you measure its resonant frequencies, in principle you could back out how massive the bell is. The same is true for stars!

One of my target stars, romantically named HD185351, happens to reside in the field of view of the NASA Kepler Mission, and I teamed up with Daniel Huber to apply for director's discretionary time to observe it. I'm glad we asked when we did, because the Kepler space telescope broke down soon thereafter. Fortunately, we received our observations and were able to do our analysis, known as "asteroseismology." Dan, myself and others used a similar technique to measure the mass and spin-orbit alignment of the Kepler-56 planetary system, and Dan (and his collaborators) have used asteroseismology to measure the masses of hundreds of Kepler target stars.

While I said that one can measure the mass from asteroseismology, one really only measures the stellar density and the surface gravity of the star. The density scales as

$\rho \sim \frac{M}{R^3}$

and the gravity scales as

$g \sim \frac{M}{R^2}$

Two equations, two unknowns, and some algebra yields the mass, $M$. However, we went one step further and directly measured the radius of HD185351 using the CHARA array with another technique called "interferometry." The details of this sort of measurement probably deserve their own blog post, but basically we combined a bunch of little telescopes atop Mt. Wilson and used them as a big, single telescope to measure how big the star appears on the sky. When combined with the known distance to the star, we can get the physical size of the star, or its radius $R$.

 Measuring "angular diameters" like we did for HD185351. Image credit UNL Astronomy.
 The CHARA Array at Mt. Wilson, which is useful for measuring very small angles.
We put all of these measurements together and found that HD185351 is, indeed, larger than 1.5 Solar masses, making it a bona fide retired A star (our paper has been accepted to ApJ and our preprint is on the arXiv). Things are a bit complicated because we actually get two different mass measurements. This disagreement has inspired us to make more measurements of this type with the K2 Mission, and additional interferometric observations are underway. But our two mass measurements of HD185351 bracket our model prediction (2.0 and 1.6 Solar compared to the model-based estimate of 1.87 Solar), and both estimates are greater than 1.5 Solar. Further, Jamie Lloyd was kind enough to provide his own model prediction before we completed our analysis. His best estimate of this star's mass was 1.2 Solar, which is inconsistent with all of our estimates.

However, this is just one measurement and there's plenty more work to be done. But the key is that when two astronomers engage in a theory-based debate, the best thing to do is to go get some data. That's what my group be doing in the months to come, and we'll publish our measurements as we make 'em. Stay tuned as we work to solve the Case of the Retired A Stars!

### 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 started by downloading a stock photo of J.J. from NBA.com, which I then loaded into OpenOffice Draw:

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…