Hanno Rein

My name is Hanno Rein and this is my academic website. Since 2013, I am an Assistant Professor at the University of Toronto. I am a member of the Department for Physical and Environmental Sciences. My graduate appointments are at the Department of Astronomy and Astrophysics and the Department of Physics. My research interests are broad. They include planet formation, stochastic processes, planet migration, celestial mechanics, Saturn's rings, N-body codes, hydrodynamics, code development and high performance computing. Numerical methods are a big passion of mine.

Make sure to check out my REBOUND code. It is an open source N-body code which gives you access to the world's fastest and most accurate numerical integrators. You can do almost anything with it from long-term symplectic orbit integrations to collisional shearing-sheet simulations of Saturn's rings. The installation takes literally 30 seconds and it comes with an easy to use python interface. It's really cool and I'm very proud of it.

You also don't want to miss the Exoplanet App. It is a free smartphone application for the iPhone/iPad that I wrote. It let's you explore almost the entire universe, including the cosmic microwave background, galaxy clusters, our Milky Way, the Solar System and all discovered extra-solar planets. Several million people have downloaded it already!

Contact details

You want to contact me? Awesome!

My mailing address is:
University of Toronto at Scarborough
DPES Physics and Astrophysics
1265 Military Trail
Toronto, Ontario M1C 1A4
Telephone (office):
(+1) 416-287-7206 (UTSC)
(+1) 416-978-4582 (UTSG)
hanno.rein (-at-) utoronto.ca
Office (Scarborough Campus):
Science Wing, SW504C
Office hours: Mon+Wed, 1-2pm
Office (St George Campus):
McLennan Physical Laboratories, MP1203C

Research News:

Second order variational equations

For chaotic systems, one often uses variational equations to study the evolution of nearby trajectories. Variational equations have better numerical properties as shadow particles and have been implemented in REBOUND for a while.

Dan Tamayo and I recently published a paper in which we describe how to generalize the conept of variational equations to second order. We provide an implementation for the IAS15 integrator in REBOUND that lets you use second order variational equations very easily. The possible applications are very exciting, ranging from better orbit fitting methods for explanets to spacecraft trajectory optimization methods.

The fastest and most accurate symplectic integrator: WHFast

Newton's Law of universal gravitation describes how any two objects in the universe attract each other. Among many applications, it allows astronomers to calculate how planets, asteroids and comets move through the Solar System. Although this law and the corresponding mathematical equations have been known for over three hundred years, how to calculate the solutions has been an active field of research for both astronomers and mathematicians alike ever since.

The equations are what mathematicians call transcendental, in other words, they have no simple solutions. With the advent of computers, scientists were finally able to solve the equations at least approximately for a wide range of problems. However, because the solutions are not exact, they cannot be used to predict the positions of planets very long into the future. This is because the relatively small errors made on short timescales (say 1 year) quickly add up to large errors after long time scales (100 years). Very much like the weather report might give a fairly good prediction for the weather tomorrow, but not so for the weather a year from now. Astronomers are often interested in very long timescales, billions of years! So you see the problem, even a tiny error after 1 year, will have a dramatic effect after 1000000000 years.

Using various tricks from mathematics and computer-science, we were able to improve the standard method used for the last 30 years. It's a powerful class of algorithms that's called symplectic integrators. We made two significant improvements. First we were able to speed it up by a factor of 2 to 5. Second, we were able to reduce the errors. We made sure that the errors don't add up as fast as they did in previous algorithms. Previously the error was growing by a factor of 100 by going from 1 year to 100 years. With our improvements, we can go from 1 year to 100 years and only improve the error by a factor of 10. We achieve a fundamental limit which says that what we have achieved is the most accurate algorithm possible. We cannot be any more accurate on a present day computer processors.

The paper describing WHFast is published in MNRAS and can also be found on the arXiv server. The algorithm is part of the REBOUND package and can be downloaded at github. My university has also written a press release about our results.

Hanno Rein

All-purpose high order integrator IAS15

We also developed a new, high order integrator for gravitational dynamics that can handle both conservative and non-conservative forces. We ran a lot of tests and all results seem to show that our algorithm is superior to other integrators, including mixed variable symplectic integrators such as the one by Wisdom and Holman and other high order non-symplectic integrators, for example Bulirsch-Stoer. We took great care when implementing the scheme and achieve Brouwer's law (accuracy up to machine precision) for at least a billion orbits, equivalent to 10^11 timesteps. The scheme comes with adaptive timestepping and works extremely well on a wide range of problems with out-of-the-box setting and no fine-tuning of any parameters. This includes long term integrations of planetary systems, close encounters, Kozai cycles, migrating planets and dust undergoing PR-drag. You can find the preprint at http://arxiv.org/abs/1409.4779.

Links to scientific publications

All of my publication are listed on this website. Alternatively, they can be found on the NASA Astrophysics Data System (ADS) or the arXiv preprint server.

I feel very strongly about open access. All my publication are on the arXiv and you can access them free of charge. If you also think publicly funded research should be freely available for everyone on this planet, please do the same. Please also consider signing a petition against Elsevier.

Research Group

Group Some of the CPS faculty, postdocs and students (I'm in the back on the left, Aleksandar Rachkov and Rejean Leblanc are next to me, Ari Silburt and Dan Tamayo are sitting at the table.

Current postdocs I'm closely working with: Dan Tamayo (CITA/CPS).
Current students: Chin Chen (undergraduate research project), Rejean Leblanc (working towards a MSc), Ekin Ozturk (undergraduate research project), Aleksandar Rachkov (working towards a PhD), Vismay Shah (undergraduate research project), Ari Silburt (working towards a PhD).
Past students: Caden Armstrong, Bryce Bolin, Jade Checlair, Alice Chen, Sunny Chen, Eric Dapp, Taylor Esch, Patrick Fraser, Shang-Fei Liu, Srivathsan Morkonda, Jasmeer Sangha, Pengshuai Shi, Natasha Urbancic, Trevor Vincent, Quentin Xue, Eric Yeung.


New students

There are funding opportunities available for students interested in a MSc or PhD. Please talk to me to get a list of possible projects.


Short academic curriculum vitae

Assistant Professor
2013 - now, University of Toronto, Canada
Member at the Institute for Advanced Study
2010 - 2013, Institute for Advanced Study, Princeton, US
PhD, Doctor of Philosophy
2007 - 2010, University of Cambridge, DAMTP, England
Thesis: The effects of stochastic forces on the evolution of planetary systems and Saturn's rings
Supervisor: Professor John C. B. Papaloizou
MASt, Master of Advanced Study, Part III of the Mathemtical Tripos
2006 - 2007, University of Cambridge, DAMTP, England
With distinction
Exams: General Relativity, String Theory, Quantum Field Theory, Advanced Quantum Field Theory, Black Holes
Essay: Finite time singularities (with Stephen J. Cowley)
Undegratuate studies in both Mathematics and Physics
2003 - 2006, University of Tuebingen, Germany



Connaught New Researcher Award (2014)
Funded by: The Connaught Fund
NSERC Discovery Grant (2014-2020)
Funded by: The Natural Sciences and Engineering Research Council of Canada
Exoplanet Smartphone App (2012)
Funded by: The Royal Astronomical Society, London
Principal investigator: Hanno Rein
Propellers, Frogs, and Random Walks (2012)
Funded by: NASA, ROSES-11, Outer Planets Research Program
Principal investigator: Eugene Chiang
Collaborators: Hanno Rein, Matthew Tiscareno, Margaret Pan



This is a screenshot of my collisional N-body code REBOUND. It can do so many things, there wasn't enough space on the main page to describe it. You therefore need to click on the link below. Or even better: just go over to github and try it out.

Find out more about REBOUND!

Open Exoplanet Catalogue

Check out the Open Exoplanet Catalogue! It's a new kind of astronomical database: open, community driven and decentralized. Send me a message if you have any question or want to contribute to it but don't know how!

Hanno Rein

Exoplanet App

Over the last few years, I developed a very successful smartphone application called Exoplanet. It has attracted almost ten million (!) users and received outstandingly positive reviews. The application lists all extra-solar planets, features three dimensional visualizations and an interactive model of the Milky Way. The user can zoom out from the solar system all the way to the cosmic microwave background. An enormous amount of supplementary data from the Hipparcos catalogue, the 2MASS survey, WMAP and other missions is included in the app. This is like Google Earth, but for the entire universe. When a new planet is found and added to the database users receive a push notification. With about one million users already signed up for these notifications, it is a huge driving force in announcing new discoveries to the public. I was recently awarded an outreach grant from the Royal Astronomical Society in London specifically for the Exoplanet App.

Download the Exoplanet app now!