Erik Petigura (Berkeley) and collaborators found a turnover in the planet-radius distribution at small radii in this high-impact paper. They found this (more-or-less) by weighting their data samples with inverse selection probabilities. These kind of reweighted-data estimators are often unbiased but always high variance: They put the largest weights on the most marginal data. Fortunately, in the beautiful new world of exoplanets, sharing is the norm, and Petigura generously shared all of his data with Tim Morton (Princeton), Foreman-Mackey, and me. Awesome!

Today Foreman-Mackey and I pair-coded a forward model of the Petigura *et al* planet sample, using parameterized distribution functions, the completeness calculated by the original team, and a model for transit probability. With assumptions of independent planets (okay assumption), stationary distributions as a function of host star properties (bad assumption), negligible uncertainties (bad assumption) and separable period–radius distribution (bad assumption), it is possible to write down a fully justified likelihood function and turn the inference crank. That is, there are no real methodological freedoms. That's cool! We built and turned that crank today, also employing an iPython notebook (my first time). We got some preliminary results, which require some work to check. The thing I am excited about is that our assumptions are essentially the same as those of Petigura *et al* but our method is both simple and (conditionally) optimal.

So, what's the answer?

ReplyDeleteWe will show you as soon as we show it to Erik, who has first right to object to any stupidity.

ReplyDeleteMaybe it is high impact, but the turnover in radius distribution was found in our paper (fig .9) well before that paper was posted:

ReplyDeletehttp://arxiv.org/abs/1212.4853

Hi Subo-- I don't see much of a turnover in your Figure 9; and actually part of what we're seeing is that there doesn't actually seem to be evidence for the turnover that Erik sees in the radius function, when we do the full inference, and especially accounting for errors in R.

ReplyDeleteHi Tim,

ReplyDeleteFirst of all, we are plotting in log scale, Erik is in linear scale. Be careful when you compare the plots.

There are a few trends from our Fig 9.:

1) For planets with R < ~3 R_Earth, dN/dlogR is consistent with being flat for P > 10 days.

2) For planets with R >~3 R_Earth and R <~ 10 R_Earth with 10days ~3 R_Earth, and P > 50 days, the dN/dlogR slope is relatively shallow as a function of R.

Erik's paper on radius distribution was on 5 days<P<50 days. I think there is a break in the slopes of radius distribution (whether you call it a turnover or not) at ~3 R_Earth for planets with P < 50days. Do you agree?

[Sorry, some sentence was incorrectly typed in the above message. Here is the revised version -- it would be great if David could remove the previous version of my comment.]

DeleteHi Tim,

First of all, we are plotting in log scale, Erik's y-axis is in linear scale. Be careful when you compare the plots.

There are a few trends from our Fig 9.:

1) For planets with R < ~3 R_Earth, dN/dlogR is consistent with being flat for P > 10 days (red and green).

2) For planets with R >~3 R_Earth and R <~ 10 R_Earth with 10 days < P < 50 days, dN/dlogR decreases as R increases (red). There is a break in dN/dlogR distribution at ~3 R_Earth for P < 50 days.

3) For P > 50 days and P < 250 days with 3 R_Earth < R < 10 R_Earth, dN/dlogR slope is relatively shallow as a function of R (green).

Erik's paper on radius distribution was on 5 days < P < 50 days (http://arxiv.org/pdf/1304.0460v1.pdf). I think there is a break in the slopes of radius distribution (whether you call it a turnover or not) at ~3 R_Earth for planets with P < 50days from the results of our paper. Do you agree?

BTW, I was referring to the following paper by Erik, which he made a claim about radius distribution:

ReplyDeletehttp://arxiv.org/pdf/1304.0460v1.pdf

David's blog post links to another paper in his blog, in which little statement has been made on radius distribution in the main text.