### Research Summary: Searching for binaries in calibration spectra

Today's blog post is by Juliette Becker, a first-year astrophysics graduate student at the University of Michigan working with Prof. Fred Adams on exoplanet dynamics, among other topics. While her work is mostly focused on theoretical astrophysics at the moment, Juliette has extensive experience as an observational astrophysicist from her time as an undergraduate at Caltech (see e.g. Muirhead, Becker et al. 2014). At Caltech, Juliette was also the captain of the track and cross-country teams, setting school records in the 3000 steeple chase, as well as the 6k and 10k distance events. In today's post, she describes her latest paper, which summarizes the work she started with me as an undergrad and saw through to completion, with her paper accepted to ApJS last week. Like reaching the finish line in a 10K event, publishing cutting-edge research requires pacing, endurance and patience!

When I was a sophomore at Caltech, I took the introductory astronomy class, Ay20, with Professor John Johnson. His enthusiasm and approachability inspired me to ask if I could work on a research project with him during the following summer as part of the Summer Undergraduate Research Fellowship (John was a SURF researcher in 1999!). Not only did he say yes, but he also told me about a really exciting prospect. There were years of calibration spectra for the California Planet Survey sitting unused on disk. The targets are rapidly rotating, extremely hot ($T_{\rm eff} > 9000$~K) B-type stars, which were used as nearly featureless "blackbodies" in the sky to illuminate the spectrometer optics the same way as a program star.

These calibration spectra had been used to calibrate the radial velocity spectra of smaller target stars, but since the calibrators were rotating so rapidly, there was not much immediate use for them beyond this humble, utilitarian purpose. If someone could extract radial velocity information from these spectra, they could potentially do a search for binary (stellar) companions around these massive rotating stars, as the radial velocity of a star with a companion changes over time as the companion "tugs" its host star around. My first task was to do an order-of-magnitude calculation of the precision attainable from a star spinning at 200 km/s. I found that thanks to the high signal-to-noise in these spectra, we could expect a radial velocity precision of greater than 1 km/s, which is more than enough to detect binary companions all the way down to red dwarfs! (This calculation is in the Appendix of my paper).

The difficulty in extracting these radial velocities arises from the fact that massive, rapidly rotating stars have very few spectral lines, each of which are nearly as broad as the spectrometer's orders (wavelength regions recorded by the spectrograph). While normal CPS targets have thousands of spectral features, a calibrator might have only 10-15 spectral lines. The attached figure taken from our paper for an example of what the comparison looks like for a single spectral order.

To extract the radial velocity data from spectra of rapidly rotating stars, we cannot use traditional methods of fitting the Doppler shift in small chunks of a spectrum and deriving the true radial velocity from a distribution of these shifts. To make maximal use of the few spectral features we have, we fit the entire spectrum – all pixels and orders – simultaneously. This allows the orders without any spectral features to serve as ‘anchor’ orders, setting the continuum level of the fit even as the wide spectral features could otherwise result in an artificially low continuum level.

Our method is described in our paper (details below!), which has been accepted to ApJS and is posted on the arXiv today. As a bonus, not only do we present our functional method for extracting radial velocities from echelle spectra of rapidly rotating stars, but we give absolute radial velocities and rotational velocities ($V\sin{i}$) for each star in our sample (more than 200 stars in all, some of which did not have prior literature measurements).

Here's the preprint of our paper. Enjoy!

Extracting Radial Velocities of A- and B-type Stars from Echelle Spectrograph Calibration Spectra
Juliette C. Becker, John Asher Johnson, Andrew Vanderburg, Timothy D. Morton

### 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…