### Close Friends of Hot Jupiters: The WASP-47 system

Ever since a mechanical failure caused the end of the original Kepler mission in 2013, the Kepler spacecraft has been conducting a survey of new stars, searching for planets across the ecliptic plane in its new K2 mission. The K2 dataset is a goldmine of fascinating science results. One such result is the recent discovery of two new planets in the WASP-47 system.

Until a few months ago, everyone knew that hot Jupiter planets don’t have “friends”, or nearby small planets in close orbits to the host star. These other planets had been searched for extensively, through radial velocity measurements, analysis of the transit times of the hot Jupiters, and even through transits by Kepler during its original mission. All of these searches turned up nothing.

This all changed one day last July, when Hans Martin Schwengeler, a citizen scientist who enjoys poring over Kepler and K2 data searching for new transiting planets by eye, came across the telltale signatures of two extra transiting planets in the hot Jupiter system WASP-47. WASP 47b was, by all indications, a perfectly normal hot Jupiter -- in the discovery paper, Coel Hellier wrote “With an orbital period of 4.16 days, a mass of 1.14 Jupiter masses, and a radius of 1.15 Jupiter radii, WASP-47b is an entirely typical hot Jupiter”. The discovery of additional transiting planets dramatically changed the narrative.

When Hans came across the planets, he posted them to the Planet Hunters forum, where he and other citizen scientists discuss their findings. Andrew Vanderburg came across the post suggesting that a known hot Jupiter had planetary companions. Using his K2 data reduction pipeline, he analyzed the light curve and confirmed Hans’s discovery - there were additional planets in the system, a super-Earth at a 0.8 day period and a Neptune at a 9 day period!
 The WASP-47 transit signals.
Andrew emailed me, and at first I hardly believed that the light curve was real. How could a hot Jupiter have close-in planetary companions? I knew people had been looking for this type of companion for years via both photometry and transit timing variations, but the lack of discoveries indicated that they might not exist. I performed some numerical stability simulations (because it seemed at first like this system could not be dynamically stable!) and sure enough, the N-body simulations showed that the system was likely stable on timescales of 10 million years.

At that point, we formed a team with Hans, Andrew, MIT Professor Saul Rappaport, University of Michigan Professor Fred Adams (my advisor!), and me. Once this team was formed, we devoted ourselves to understanding as much about the systems as we could. Some work by Saul and Andrew confirmed that the planets were all orbiting the same star, Andrew fit the light curve to get the planet properties, and I ran more stability simulations. Soon enough, Fred suggested that I look at what transit timing variations (or TTVs, which happen when transits come late or early because of the gravity of other planets in the system) we would theoretically expect to see from the system - and I found that for the outer two planets, the TTVs should be observable.

I then measured the TTVs from the light curve, and sure enough - there was something there. After some discussion, we realized we could measure the masses of the planets from those TTVs! Though I had never done dynamical fits before, I wrote the code to utilize Kat Deck’s TTVFAST code in a Markov Chain Monte Carlo fit. With some advice from Kat and help from Fred, I eventually got the fits working and we were able to measure or put limits on the masses of each planet.

 Transit timing variations. As the planets gravitationally tug on one another, they arrive "early" and "late" to their expected transit times
In a little less than two weeks, we had put together a paper deriving planet properties from the light curve, mass limits from the TTVs, and showing that you CAN detect companions to hot Jupiters using TTVs!

This result is exciting because it is the very first time a hot Jupiter has been found to have such close-in other planets. Before this discovery, it was unclear if hot Jupiter could have nearby friends, as they might destabilize the friends’ orbits during migration. This discovery opens up new questions about how these systems form - it is possible that there is more than one migration mechanism for hot Jupiters.

The system has become even more exciting, too. Marion Neveu-Van Malle has recently published a paper announcing yet another planet in the system, a Jupiter-mass planet at a 571-day period, which engenders even more questions about how this system formed. Additionally, there has been RV followup resulting in another constraint on the masses (led by Fei Dei, a grad student working with Josh Winn at MIT), Roberto Sanchis-Ojeda of U.C. Berkeley also recently published a paper where he and his coauthors used the Rossiter-Mclaughlin effect to find that the stellar obliquity of WASP-47b is close to 0. All this work has begun to paint a fascinating picture of this system - the first hot Jupiter with hot friends.

Our paper on WASP-47 and its new companions, which was published October 12th, 2015, in ApJ Letters and is available at, was a collaboration between myself (Juliette Becker, a graduate student at the University of Michigan), graduate student Andrew Vanderburg (Harvard CfA), Professor Fred Adams (the University of Michigan), Professor Saul Rappaport (MIT), and Hans Schwengeler (citizen scientist).

### 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…