How do we find planets around other stars? David W. Hogg New York University Max-Planck-Institut für Astronomie, Heidelberg Flatiron Institute, New York City 

What is machine learning? • Say you want to find all the kittens in all YouTube videos. • “Learn” a very flexible function that takes a video clip as input and returns kittens! or not-kittens! as output. • Use enormous numbers of labeled videos as a training set. • What does this have to do with science? • In it’s basic form: Not much! 

What are exoplanets? • Planets around other stars. • The first were discovered in the 1990s. Now thousands are known. • A very large fraction of stars have planets. • There are billions of planets in our Galaxy. • How could we know this? 

Astronomy reminders • The Earth orbits the Sun once every 365-ish days. • The Sun is 10 million times the mass of the Earth. • The Sun orbits the Milky Way. • The Milky Way contains tens of billions of stars. • The Solar System is 4.6 billion years old. • The Universe is 13.8 billion years old. 

Planets • In the Solar System, inner planets are made of rock and metal, outer are made of gas. • Inner planets are heated by the Sun, outer planets get sunlight but also have residual heat from formation. • There appears to be a continuum between Jupiter-like planets and stars. 

Planet discovery: Radial velocity • Star–Planet system orbits common center of mass. • The star wobbles. • Radial velocities can be measured as tiny red- and blue-shifts. • Hundreds of discoveries from many telescopes around the world. 

Planet discovery: Transits • If we are very lucky (percent-level): • The planet passes between us and the star. • Planet blots out a tiny fraction of the light. • The signal is periodic. • An Earth-like planet blots out 100 parts per million. • NASA Kepler spacecraft alone found thousands. 

Planet discovery: Direct imaging • Young planets are hot, and shine in the infrared. • Old planets reflect starlight. • Dozens of young planets have been directly imaged. • The Sun is billions of times brighter than Earth. • And yet, we dream! 

Planet discovery: Other methods • Gravitational lensing. • Disturbances in stellar accretion disks. • Tides and dynamical perturbations. • Pulsar or pulsation timing. • Astrometry. • … 

What are exoplanets? • Planets around other stars. 

What are exoplanets? • Exceedingly tiny signals in boring data. 

What aren’t exoplanets? • They sure as h*ck aren’t what you see in artists’ conceptions! 

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NASA Kepler • Incredibly simple mission: • Stare at 150,000 stars, and deliver a brightness measurement for every star every 30 minutes. • 4.1-year mission, 10 billion stellar measurements. • Found thousands of planets. • Followed by the K2 Mission which did even more. And TESS, on now! 

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4000 2000 0 2000 4000 raw: 264 ppm EPIC 201374602; Kp = 11.5 mag 10 20 30 40 50 60 70 80 time [BJD - 2456808] 400 0 400 residuals: 31 ppm relative brightness [ppm] 

10 20 30 40 50 60 70 80 time [BJD - 2456808] 800 400 0 400 relative flux [ppm] 

0.4 0.2 0.0 0.2 0.4 time since transit [days] 600 400 200 0 200 relative flux [ppm] 

NASA Astrophysics data • All data from NASA missions is open and publicly available. • This includes NASA Kepler, K2, and TESS. • Many discoveries have been made by non-professionals. 

NASA Kepler: Results • There are comparable numbers of planets as stars, maybe more! • Many stars have very different planetary systems from our own. • Planets of around twice Earth’s radius are the most common. • Planets with very short periods are common. • Jupiter-like outer planets are very common. 

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Finding an Earth analog • An Earth transit blots out 100 parts per million of the Sun’s light. • It does this for 13 hours every 365.25 days. • Stellar variability, spacecraft issues, and photon noise all are larger in amplitude than the signals we seek. • So, is this an impossible task? 

We have a lot of data! • Common behaviors across many different stars are extremely informative: • We can use the enormous numbers of stars we have • Learn a very flexible model that predicts what a star can do in the future given what it has done in the past… • …and what one star can do in response to spacecraft motions, given what other stars have done. • Remember the kittens? 

Machine learning in science • Many problems in natural science have this character: • The thing we care about has a very predictable, simple form. • The things we don’t care about are stochastic and complicated. • The tools of machine learning can be harnessed for these tasks. • (Commercial entities usually want performance, not understanding.) 

Machine-learning methods • Linear models • Gaussian processes • Deep learning, especially recurrent networks • Generative adversarial networks 

We know what we are looking for • We train flexible models for stellar and spacecraft variations. • We have a very rigid expectation about what a planet transit is! • Periodic, for example. • Very simple shape. • Duration and period are related. • This contrast between the flexible and rigid models is what makes planet discovery possible. 

Radial velocities • Everything I have said about transits carries over to radial-velocity projects. • Trying to measure velocities to better than 1 m/s. • Stellar surface speeds and atmospheric distortions all much larger than this. • Elliptical orbit signature is (once again) very rigid. 

Dirty laundry • The most interesting planets are small (Earth-like) and have long periods (few transits in 4.1 years). • These signals are the hardest to find in the data. • There is no way to independently validate these discoveries. • We’re still pretty confident, but there are limits to what we can know. 

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Astrophysical epistemology • The objects of study are incredibly remote. • No chance of sample return or even radar bounces! • What we find depends heavily on chance. • Photons (light waves) are our only (ish) messengers. • No controlled experiments or counterfactuals. • And yet… 

We know a lot • (In another talk: black holes, expanding Universe, dark matter, etc.) • Planets are common. • Our Solar System is not obviously typical. 

What do I want you to take home? • Planets are plentiful around other stars. • Many of them are very different from the planets around the Sun. • Planets are (mainly) found indirectly, as tiny signals. • New data-science technologies are critical to these discoveries.