### Kepler meets Einstein when a stellar skeleton bends space-time

Gravity-Bending Find Leads to Kepler Meeting Einstein

This is a press release by my postdoc, Dr. Phil Muirhead. Last summer he compiled a list of all of the planet candidates around the M dwarfs (red dwarfs) targeted by the NASA Kepler mission. One of our summer students, Andrew Vanderburg, noticed that the light curve of one of the candidate transiting Jupiters looked very strange. If a hot Jupiter transits a star, it should take about 20 minutes for the planet to move across the limb of the star, causing the light to go from the full, out-of-transit level, to the minium level during a full transit (eclipse). Here's what the light curve of Kepler Object of Interest number 256 looks like (KOI-256):

 The light curve of KOI-256, along with the all-star cast of Muirhead et al. (2013)

Where the light level first decreases is called "ingress," and for KOI-256 the ingress time is about a minute, instead of 20 minutes. Weird! After pondering this a bit, Andrew and Phil realized that the ingress time implies an Earth-sized object. But why does an Earth-sized object block 2.6% of the light?

The next clue came when another undergraduate researcher, Juliette Becker, stepped in. She applied for time on the TripleSpec spectrometer on the 200-inch telescope at Palomar. The Caltech Optical Observatories director, Shri Kulkarni, allows undergrads to apply for 2 hour blocks of time during the summer for a research project of their own. Juliette won two hours of time with her proposal, and she started measuring the Doppler shift of the star. What she found was surprising: The star is getting yanked around by something that is (mostly) unseen, yet it is actually more massive than the star. Here are Juliette's radial velocities, which she measured from her spectroscopic observations (gotta love Caltech undergrads!):

Hot Jupiters tug on their stars and cause them to move by hundreds of meters per second but this star is getting yanked around by hundreds of kilometers per second! But remember, the ingress time implies that the object is the size of the Earth. The size of a small planet, but the mass of a star? Well, that's a pretty good description of a white dwarf. When stars like our Sun die, they leave behind "skeletons" in the form of tiny, super-hot yet faint white dwarf stars, which then cool down over time.

KOI-256 is orbited by a white dwarf on a 1.38-day orbit. When the white dwarf goes behind the red-dwarf star, the star blocks the white dwarf's light, causing a 2.6% dip in the total light from the system. When the white dwarf passes in front of the red dwarf, there is a tiny decrement of light:

The dip was evident when Caltech postdoc Avi Shporer and Phil looked carefully a half-period away from the main eclipses. However, the transit (passage of WD in front of RD) was 2x shallower than expected. The dashed line above shows the depth expected when an Earth-sized object blocks light from a red dwarf. The solid line shows the actual transit depth. Why the shallow transit?

The answer is provided by Einstein's theory of general relativity. Massive objects can warp space time, causing light that is traveling through that space to be bent. The white dwarf around KOI-256 bends light rays that would normally miss our telescopes into our path, causing the system to appear brighter, thereby filling in the transit dip. Here's a really cool movie showing the effect of the WD warping space-time:

This effect is known as gravitational lensing, and it has been observed for stars near the Sun during a total solar eclipse, for stars lensing other stars in the Galaxy, and for galaxies. KOI-256 is the first time a transiting white dwarf has been observed to lens light from the star it orbits. Kepler meets Einstein!

### 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…