Planets outnumber stars

 kw: book reviews, nonfiction, astronomy, astrometry, exoplanets

We have so far detected about 5,000 exoplanets (planets of other stars). Since the first confirmed detection in January 1992, astronomers have developed five methods to detect exoplanets, over most of the range of plausible sizes, and quite a range of orbital periods. That's enough to learn a few things.

In Worlds Without End: Exoplanets, Habitability, and the Future of Humanity, author Chris Impey describes the most common type of planet: Diameter larger than Earth but smaller then Neptune, in an orbit on the warm side of the habitability zone, or inside of it. These are called "super-Earths" and "mini-Neptunes", with the dividing line about twice the diameter of Earth. Neptune weighs just over 17 times as much as Earth, so variations in density increase the range of masses from about 17:1 to perhaps 25:1 (or 20:0.8).

The technology of exoplanet discovery makes up the first of four sections of the book. The other three sections consider habitability, how we might search for life on exoplanets, and the possibilities for us or our machines to visit them.

I hadn't known that there are five ways to detect an exoplanet. In particular, I didn't know that astrometry can be used for that. Astrometry means "star measurement", and in this application, it refers to precise measurements of a star's location or position. While quite a number of exoplanets have been detected by the doppler shift in stellar spectra, using telescopes on Earth's surface, the use of a star's position is many times more delicate, and can only be done from telescopes in space. A bit of figuration will illustrate the difference.

Considering the mass of Earth as a basis, and calling it 1, the mass of Jupiter is 317.8 and that of the Sun is 332,946. The Sun's diameter is 1,392,000 km, the average distance of Earth from the Sun is 149.6 million km, and the average distance between Jupiter and the Sun is 778.3 million km. The orbital velocity of Earth is 29.78 km/sec = 107,200 km/hr and that of Jupiter is 13.1 km/sec = 47,160 km/hr.

The doppler shift caused by the Sun's reaction to the planetary motions is calculated by mass and distance ratios. Thus, for Jupiter, the mass ratio is 317.8/332,946 = 0.000 954 5; so the Sun's velocity is that times 13.1 km/sec = 0.0125 km/sec = 12.5 m/s. It takes a very precise spectroscope to measure the doppler shift caused by this motion, but it has now been done many times. 

The closer Jupiter is to the Sun, the faster it goes, and therefore the faster the Sun goes. Let's put Jupiter in Earth's orbit and check the consequences: 0.000 954 5 x 29.78 = 0.0284 or 28.4 m/s. This is more than twice the earlier figure. This is much easier to detect, and explains why the first exoplanets to be detected were "hot Jupiters" that orbited very close to their host stars. Also, doppler shift is the same from any distance, as long as you can gather enough light to get a good and precise spectrum.

Now we consider hyper-precision astrometry. The diffraction limit of the Hubble Space Telescope in visible wavelengths is around 0.02 milli-arc-seconds (5.5 billionths of a degree). It would be the same for any space telescope of equal size. However, even though star images are enlarged by diffraction to that degree, the position of a star can be measured with greater precision than this. One must magnify star images to cover many pixels of the detector, and the centroid of the star image can be calculated with great precision, in the range of millionths of an arc second (trillionths of a degree). The longer the exposure (the more photons captured), the more precisely this can be done, as the statistics of the "shot noise" of photon detection reduce the errors that would cause.

Specialized orbiting telescopes are being planned that can do this for a number of stars in a field of view. The positions of many stars would be measured again and again over long periods, looking for tiny shifts. How tiny?

For Jupiter again, when the planet moves from one side of its orbit to the other, it moves 1.56 billion km. The Sun moves 1.56 billion × 317.8 / 332,946 = 1.49 million km, or 1.07 times the Sun's diameter! However, this motion requires six years...starting at the right place.

How far away can we detect the shift? One millionth of an arc second has a tangent of 0.000 000 0159; dividing this into 1.49 million km yields 93.6 trillion km. That's almost ten light years (9.9). To reach a reasonable number of stars with this technique requires astrometric measurements with a relative precision from star to star of a ten millionth of an arc second, or smaller if possible. This takes big telescopes and long exposure times. But it has been done!

OK, that's a long discussion of two methods: Doppler Shift (the first method to work) and High Precision Astrometry (the most recent). To round out the methods, the third is the most prolific to date: the Transit method, which measures the little dip in brightness that occurs when a planet passes in front of a star. The fourth is Microlensing, for which stars are watched for brightening that occurs during the period (measured in days) that one passes in front of another and its gravity magnifies the star behind; a small extra glimmer signals that the star in front has a planet. The fifth is Direct Imaging, which works best for large planets farther from their host stars. Each method has a useful range of planetary size and orbital distance, which means we are getting a more and more complete overview of what is out there.

I will give rather short shrift to the latter three sections of the book. They are very interesting, but secondary to my interest in the subject. Only a small percentage of exoplanets so far detected are at a suitable distance from their host stars to have a chance of having liquid water at or near the surface. Thus, the discussion of habitability and life are more speculative. The author does bring up an interesting subject: Could the Earth be detected by any of these methods, from suitably placed stars in "nearby" space, the nearest few hundred light years? Very possibly!

The statistics of what we now know indicate something even more interesting: Nearly every star seems to have at least one planet, and wherever the viewpoint and associated method(s) are favorable we find a few planets, usually 3, 4 or 5. Precision timing of Transits is beginning to reap a harvest of added planets in many of the systems initially found using that method, for example. That means that there are more planets than stars, overall.

Furthermore, the Solar System has, so far discovered, 200 moons, most of them around Jupiter and Saturn. BUT! Although the surface temperature of satellites that distant from the Sun is far too cold to allow liquid water, the interiors of several larger satellites could hold a large liquid ocean, which could then host life. It may be that the greatest number of objects in the Universe that host living beings (microbes, at least) will prove to be satellites of large planets!

That in itself made the book worth reading.