Finding Exoplanets around Bright Stars

Benjamin Pope

NASA Sagan Fellow, NYU

Dunlap Seminar

Slides available at
benjaminpope.github.io/talks/toronto/toronto

Transiting Planets

Exoplanet-style transit light curve of Venus from James Gilbert on Vimeo.

Large searches for exoplanets like the Kepler mission have shown planets to be common in our Galaxy - now we want to learn about their atmospheres and compositions.

The best options are those around bright stars, like 55 Cancri e - subject of 367 papers in the last decade!

My Sagan Fellowship project is to search for planets transiting naked-eye stars (V mag < 6.5) in order to find ideal targets for characterization with the upcoming James Webb Space Telescope.

Asteroseismology

Stars ring like bells, with acoustic and buoyancy oscillations.

l=2, m=2 oscillation

Their frequencies tell us about stellar interior structure.

Power spectrum of the Sun's 5-minute oscillations

Helioseismic Power Spectrum

Kepler Photometry

The Kepler Space Telescope, launched in 2009, looks for planets by the transit method, and also does asteroseismology.
After the failure of a reaction wheel in 2012, it is now operating as the 'K2 Mission', with very unstable pointing (hence the shaking in the videos you'll see).
To get the photometry, you can just sum the pixel values in a window containing the whole PSF...

but the pixels have different gains ("inter- and intra-pixel sensitivity variation")...

and the pixel window doesn't necessarily track the whole PSF perfectly ("aperture losses").

For sufficiently bright stars, though, light fills the CCD wells with electrons that spill up and down the column, ruining the photometry as they leave the aperture.
Kepler saturates on stars brighter than ~ 11th mag (log scale: 5 mag = factor of 100) - but we want to look at stars 10k times brighter.

Halo Photometry

What if we just look at unsaturated pixels?
Flux \(f_i \) at cadence i is a sum over j pixels \(p_{ij}\) with weights \(w_j\):

\[ f_i \equiv \sum\limits_i w_j p_{ij} \]
In the OWL method (Hogg & Foreman-Mackey), you choose weights to minimize variance of the final light curve - but this has limited success.
To find the appropriate weights, we instead minimize the Total Variation

\[\begin{align} TV \equiv \dfrac{\sum_i |f_i - f_{i-1}|} {\sum_i f_i } \end{align} \]

This is the L1 norm on the derivative of the time series.

This has analytic derivatives you can compute with autograd - easy to optimize.

Note that these light curves are basically a sum of sine waves - anything but sparse in the derivative!

But they're sparse in the Fourier domain... perhaps this is relevant?

Pleiades

Πλειάδες, the Seven Sisters

Alcyone, Atlas (dad), Electra, Maia, Merope, Taygeta, Pleione (mum)

Combined Figure

Atlas lightcurve: raw (top) and halo (bottom)

White, Pope et al., 2017

Combined FigureCombined Figure

Lightcurves of All Seven Bright Pleiades

White, Pope et al., 2017

I am currently searching all bright stars in K2 for transiting planets - none so far, but plenty of asteroseismology!

Aldebaran

α Tauri

الدبران ,the follower

... follows the Pleiades!

Hatzes & Cochran, 1993 claimed an early detection of a \(628.96 \pm 0.90\) d RV planet around Aldebaran - finally confirmed in Hatzes et al., 2015!
All Data
A Gaussian Process reanalysis of this data by Will Farr detects p-mode acoustic oscillations at 2.2 μHz - can we confirm this with K2?
GP PSD

Yes! We get the same frequency with K2!

Aldebaran K2 Light Curve
Without this asteroseismology, we have

\[M = 1.27^{+0.24}_{-0.20} \, \mathrm{M_{\odot}}\] and age \(4.9^{+3.6}_{-2.0} \, \rm Gyr \)
With this new constraint, we have

\[M = 1.16^{+0.07}_{-0.07} \, \mathrm{M_{\odot}}\] and age \(6.4^{+1.4}_{-1.1} \, \rm Gyr \)

Using MESA models, we find that on the main sequence Aldebaran b had a semi-major axis of \(1.50 \pm 0.03 \) AU and Aldebaran had a luminosity \(2.0 \pm 0.7 \, L_\odot \)...

so Aldebaran b had an insolation comparable to Earth when its star was on the main sequence.

The Future

The method generalizes well to simulated data for the upcoming TESS mission. We have many K2 halo datasets and are working our way through them - between these missions we should cover the whole sky.
We still don't have an explanation for the unreasonable effectiveness of the L1 norm in this algorithm - help us understand!
All our code is open source at github.com/hvidy/halophot - play with it!
We have a solution looking for problems - we want to extend this to TESS, JWST, and even ground-based missions.

Let's collaborate!