Tag: transit method

Nearest Exoplanets

There are 33 confirmed exoplanets within 15 light years of our solar system, with more certainly on the way as a number of unconfirmed exoplanets are under ongoing investigation.

Here’s a table of all known planets within 15 light years of the Sun, including the eight planets of our own solar system for comparison.

Click the link below for a more convenient view of the entire table in a separate tab.

Click to access Nearest-Exoplanets-Confirmed-Planets.pdf

Planet mass and radius are given in terms of Earth’s mass and radius. The reason the radius of all the exoplanets listed here is “unknown” is because all of these planets have been detected using the radial velocity and/or astrometric method. Only the transit method provides a reliable way to measure an exoplanet’s size, but the nearest stars that host transiting exoplanets are 21.3 ly and 22.4 ly distant (HD 219134 and LTT 1445, respectively). Our limit here is 15 ly.

A side note about transiting exoplanets. In order for us to see an exoplanet transiting its host star, the exoplanet’s orbital plane has to be fortuitously aligned quite close to our line of sight. Since even these nearest stars are very far away in comparison to the size of our solar system, we are stuck with the line of sight we have. What percentage of all exoplanets out there might we detect using the transit method? That depends, of course, on the orientation of the exoplanet’s orbital plane but also the size of the star (and the planet if it is large) and the distance of the exoplanet from that star. Roughly, only about 1 in 200 exoplanets or about 0.5% can be detected using the transit method.

Luminosity is the host star’s luminosity in terms of our Sun’s luminosity. Bolometric luminosity is used where available; otherwise, optical luminosity is used.

The average distance of the planet from the star is calculated from the semi-major axis and the orbital eccentricity. We then calculate the incident stellar flux using the average distance of the planet from the star and the luminosity of the star, normalized to what the Earth receives (0.9997 and not 1.oooo because the Earth, on average, is more than 1 AU from the Sun). The relevant equation is:

\frac{\textrm{L}}{\bar{\textrm{d}}^{2}}\cdot\phi_{\oplus }

where L is the luminosity of the star in terms of the Sun’s luminosity
   and d-bar is the average distance of the planet from the star in AU
   and Φ⊕ is the incident stellar flux at Earth’s average distance from the Sun
             in proportional units of solar luminosities per AU2

This calculation, of course, makes no assumptions about the albedo of the planet nor whatever atmosphere the planet may or may not have. It is simply a calculation of stellar radiation per unit area received at the planet’s distance from the star.

Here’s an example from the table. Mercury, on average, receives 6.4 times as much energy per unit area as does the Earth, whereas Neptune receives only 0.0011 as much as the Earth.

Some Key Takeaways

  • The most luminous star that is known to host exoplanets within 15 light years of our solar system, Epsilon Eridani, is only 32% as bright as the Sun.
  • Eight of these exoplanets receive an amount of energy from their star that is comparable to what the Earth receives from the Sun: Gliese 1061 d (0.56), Proxima Centauri b (0.66), Gliese 687 b (0.78), Luyten’s Star b (1.05), Teegarden’s Star b (1.07), Wolf 1061 c (1.37), Gliese 1061 c (1.40), and Ross 128 b (1.42).
  • The most massive of these exoplanets is Epsilon Eridani b, weighing in at 311 earth-masses, comparable to Jupiter in our own solar system (318).

I’d like to conclude by noting that I will do my best to keep this table up-to-date, but if you see something that needs changing before I do, by all means post a comment here and I will make the correction or addition.

Otto Struve & Exoplanets, 1952

It’s too bad the remarkable Russian-born American astronomer Otto Struve (1897-1963) never lived to see the discovery of the first exoplanets, especially considering how he was probably the first to suggest the two main techniques by which they are now discovered.

The first discovery of something that could be called an exoplanet was announced in 1992 by the Polish astronomer Aleksander Wolszczan (1946-) and Canadian astronomer Dale Frail (1961-). They found two planets orbiting a neutron star 2,300 light years away in the constellation Virgo. This neutron star is the pulsar PSR 1257+12, which had only recently been discovered by Wolszczan (1990). The pulsar planets were detected using a variant of the Doppler (radial velocity) method, and a third planet was discovered by the same team in 1994. These planets likely formed from the debris disk formed when two white dwarf stars merged, so they could be considered “exotic” planets, quite unlike anything found in our solar system.

In 1995, the first exoplanet orbiting a “normal” star was announced by Swiss astronomers Michel Mayor (1942-) and Didier Queloz (1966-). Using the Doppler (radial velocity) method, they found a “hot Jupiter” orbiting the star 51 Pegasi at a distance of 51 light years (nice coincidence!).

In 1999, independent teams led by Canadian-American astronomer David Charbonneau (1974-) and American astronomer Gregory W. Henry (1972-) were the first to use the transit method to detect an exoplanet. They confirmed a hot Jupiter orbiting the star HD 209458 (also in Pegasus, another nice coincidence) 157 light years distant that had been discovered using the Doppler (radial velocity) technique only weeks earlier.

As you can see, the 1990s was the decade when exoplanetary science got its start!

Getting back to the prescience of Otto Struve—40 years prior to the discovery of the first exoplanets—Joshua Winn (1972-) in his newly-published The Little Book of Exoplanets writes:

Although the discovery of hot Jupiters came as a surprise, it’s not quite true that nobody foresaw them. In 1952, Otto Struve, an astronomer at the University of California at Berkeley, published a short paper pointing out that the precision of Doppler measurements had become good enough to detect planets—but only if there existed planets at least as massive as Jupiter with orbital periods as short as a few days. Setting aside the question of how such a planet might have formed, he realized there is no law of physics that forbids such planets from existing. In an alternate history, Struve’s paper inspired astronomers to launch a thousand ships and explore nearby stars for hot Jupiters. In fact, his paper languished in obscurity. None of the pioneers—neither Walker, Latham, Mayor, nor Queloz—were influenced by Struve’s paper. The planet around 51 Pegasi probably could have been discovered in the early 1960s, or surely by Walker in the 1980s, had the Telescope Time Allocation Committee allowed him to observe a larger number of stars.

Here is Otto Struve’s 1952 paper in its entirety (references omitted), published in the October 1952 issue of The Observatory.

PROPOSAL FOR A PROJECT OF HIGH-PRECISION STELLAR
RADIAL VELOCITY WORK

By Otto Struve

With the completion of the great radial-velocity programmes of the major observatories, the impression seems to have gained ground that the measurement of Doppler displacements in stellar spectra is less important at the present time than it was prior to the completion of R. E. Wilson’s new radial-velocity catalogue.

I believe that this impression is incorrect, and I should like to support my contention by presenting a proposal for the solution of a characteristic astrophysical problem.

One of the burning questions of astronomy deals with the frequency of planet-like bodies in the galaxy which belong to stars other than the Sun. K. A. Strand’s discovery of a planet-like companion in the system of 61 Cygni, which was recently confirmed by A. N. Deitch at Poulkovo, and similar results announced for other stars by P. Van de Kamp and D. Reuyl and E. Holmberg have stimulated interest in this problem. I have suggested elsewhere that the absence of rapid axial rotation in all normal solar-type stars (the only rapidly-rotating G and K stars are either W Ursae Majoris binaries or T Tauri nebular variables, or they possess peculiar spectra) suggests that these stars have somehow converted their angular momentum of axial rotation into angular momentum of orbital motion of planets. Hence, there may be many objects of planet-like character in the galaxy.

But how should we proceed to detect them? The method of direct photography used by Strand is, of course, excellent for nearby binary systems, but it is quite limited in scope. There seems to be at present no way to discover objects of the mass and size of Jupiter; nor is there much hope that we could discover objects ten times as large in mass as Jupiter, if they are at distances of one or more astronomical units from their parent stars.

But there seems to be no compelling reason why the hypothetical stellar planets should not, in some instances, be much closer to their parent stars than is the case in the solar system. It would be of interest to test whether there are any such objects.

We know that stellar companions can exist at very small distances. It is not unreasonable that a planet might exist at a distance of 1/50 astronomical unit, or about 3,000,000 km. Its period around a star of solar mass would then be about 1 day.

We can write Kepler’s third law in the form V^{3} \sim \frac{1}{P}. Since the orbital velocity of the Earth is 30 km/sec, our hypothetical planet would have a velocity of roughly 200 km/sec. If the mass of this planet were equal to that of Jupiter, it would cause the observed radial velocity of the parent star to oscillate with a range of ± 0.2 km/sec—a quantity that might be just detectable with the most powerful Coudé spectrographs in existence. A planet ten times the mass of Jupiter would be very easy to detect, since it would cause the observed radial velocity of the star to oscillate with ± 2 km/sec. This is correct only for those orbits whose inclinations are 90°. But even for more moderate inclinations it should be possible, without much difficulty, to discover planets of 10 times the mass of Jupiter by the Doppler effect.

There would, of course, also be eclipses. Assuming that the mean density of the planet is five times that of the star (which may be optimistic for such a large planet) the projected eclipsed area is about 1/50th of that of the star, and the loss of light in stellar magnitudes is about 0.02. This, too, should be ascertainable by modern photoelectric methods, though the spectrographic test would probably be more accurate. The advantage of the photometric procedure would be its fainter limiting magnitude compared to that of the high-dispersion spectrographic technique.

Perhaps one way to attack the problem would be to start the spectrographic search among members of relatively wide visual binary systems, where the radial velocity of the companion can be used as a convenient and reliable standard of velocity, and should help in establishing at once whether one (or both) members are spectroscopic binaries of the type here considered.

Berkeley Astronomical Department, University of California.
1952 July 24.