extrasolar planets
THE SEARCH FOR HABITABLE WORLDS ELSEWHERE IN THE UNIVERSE
THE SEARCH FOR HABITABLE WORLDS ELSEWHERE IN THE UNIVERSE
COURSE OVERVIEW
For centuries, perhaps even millennia, humankind has been speculating on the possibility of finding worlds beyond the solar system that are potentially safe havens for life. But it is only in the last three decades, with the growing number of discoveries of planets orbiting other stars, that it has finally become possible to address this question in a meaningful way. Extrasolar planets, or exoplanets for short, is a collective term for such planets.
Prior to 1995, the only planetary system that we knew of was our own solar system. In the three decades since then, the number of exoplanets has swelled in numbers to several thousand now. Entire new areas of research have unfolded in this domain, and there is a renewed hope that we are finally ready to take the first crucial step towards answering the most consequential of all questions - are we alone in the universe?
The statistics are compelling. Nearly all the stars that we see in the night sky possibly have one or more planets revolving around them; it is just a matter of finding them. Several ground-based and space-based missions are now in place making those important discoveries gradually changing the way we understand planets around stars and the prospects of life elsewhere in the universe.
This short-term course will, in a quantitative way, discuss how astronomers discover those planets around other stars, how the question of the habitability of those exoplanets is addressed, and what the future holds for research in this field. As an introductory course, it will give you the necessary background for a deeper learning on this topic.
READING REFERENCES
Exoplanets: Hidden Worlds & the Quest for Extraterrestrial Life / Donald Goldsmith
Astrobiology: Understanding Life in the Universe / Charles Cockell
These books are expensive. You need not buy them. The lecture notes and slides from this course will be adequate for an introductory understanding. The above list is only meant as a reference in case you wish to delve deeper into this topic.
Online Resources
Week 1 : challenges in direct imaging / radial velocity method
Week 2 : transit method / direct imaging
Week 3: direct imaging / search for biomarkers / SETI
Problem Sets
1) Problem Set - 1 / Solutions
2) Problem Set - 2 / Solutions
3) Problem Set - 3 / Solutions
4) Problem Set - 4 / Solutions
5) Problem Set - 5 / No solutions for this
Mini-Project 1 / Radial Velocity Method for Finding Exoplanets
TASK 1: Generate a set of synthetic radial velocity curves for the following orbital configurations of the star-exoplanet system.
the angle of inclination of orbit, i = 60 degree
semi-major axis of orbit, a* = 0.05 AU
orbital period, P = 5 years (Earth years)
mass of the star, M* = 1 solar mass
(a) Make four RV curves for e = 0 and omega = 0, 30, 60, and 90 degrees
(b) Make four RV curves for e = 0.7 and omega = 0, 30, 60, and 90 degrees
You can make four separate RV curves for each eccentricity, or in the same plot you can show omega = 0, 30, 60, 90 degree using four different colours
The plot should have the phase of the orbit ranging from 0 to 720 degrees along the X-axis and the radial velocity (km/s) along the Y-axis. The axes should be properly labeled with a suitable choice for the X and Y axes ranges.
Deadline: November 9, 2022 (Wednesday evening class)
TASK 2: Convert the horizontal axis from orbital phase to orbital time for the same exoplanet configuration as TASK 1. Once you accomplish this successfully, generate four different GIF animations that show how the RV signal would change with eccentricity e ranging from 0 to 0.9 in steps of 0.1 for ω values of 0, 30, 60, 90 deg.
See this document on how to correctly bring-in the time axis into the synthetic RV model
Deadline: November 12, 2022 (Saturday class)
TASK 3: Download the radial velocity data for the star 51 Pegasi (the first main-sequence star around which an exoplanet was discovered) from the link given below. The first column is time in terms of a reference Julian date, the second column is the radial velocity in meters per second, and the third column is the uncertainty in radial velocity, also in meters per second. The data is like a time series.
As a first step just plot time vs. radial velocity and see how the data point is scattered. Plot each data point as a big filled circle. From that make a guess-estimate of the time period.
Now estimate the time period of the exoplanet more formally by subjecting the RV data to a Lomb - Scargle periodogram analysis. Scipy module in python already has a Lomb - Scargle periodogram routine.
Based on the periodogram output, try folding this data to the predicted time period and see how the folded radial velocity data plot looks like. [Complete up to this point. In next class we will discuss how to proceed from here]
Mini Project 2 / Transit Duration of an Exoplanet System
Develop a code that would generate the transit duration curve as a function of orbital separation between a planet and its host star for any user-given star-planet system.
Use that code to generate plots of transit duration (in Earth days or Earth hours) vs. orbital radius (in AU) for the following scenarios.
Jupiter size planet in orbit around a Sun-like star, for (a) i = 90 deg, (b) i = 89.9 deg (c) i = 89.5 deg
and (d) 89 deg
Since the question is about a Jupiter-Sun like system, for R∗, Rp, a, P etc use the same values as that of
the Jupiter-Sun system. Look up these quantities from the internet. Make sure to convert everything to
the same units.
The vertical axis should be transit duration in days or hours and X-axis should be the orbital separation
of the planet from the star in units of AU. Put all configurations in a single plot with different curve
styles (dotted, dashed, solid line etc), and in different colours. Clearly label which curve corresponds
to which scenario.