Planetarium

"How can we know what we know about exo-planets?"


I suspect the article about Kepler-452b might have prompted this question. It was mentioned that Kepler-452b is about 6.5 billion years old, five times more massive than Earth, and has a year, which is only slightly longer than our own. This planet is 1,400 light years away and within the habitable zone of its parent star. It seems remarkable that scientists could have worked all this out about a world, which is so far away from us. Especially considering that, astronomers have been unable to resolve this planet separately from its parent star to allow for direct observation. We'll use Kepler-452b as our example to explain how we can know what we know about exo-planets.

EXISTENCE
Yet another metaphysical mind flip. Perhaps the better word would have been "detection." Scientists working with NASA's Kepler mission discovered Kepler-452b just as they have discovered more than 1,00 confirmed planets.* The Kepler probe continuously monitors more than 100,000 stars within Cygnus the Swan to determine if any of them exhibit periodic "dimming" which occurs when planets move in front of their stars. Such passages, called transits,** cause the star to diminish in brightness very slightly. Though sometimes a companion star or irregularities within a star, itself, such as 'star spots' will cause this dimming. These factors can be eliminated, though through more meticulous observation. For instance, a star spot, like Sunspots, will vary in size and be of limited duration so the brightness reduction might vary measurably during each period and then vanish altogether.

THE PLANET'S ORBITAL PERIOD AND MEAN DISTANCE FROM ITS PARENT STAR
Measurements of the time period separating successive transits yields information about the planet's orbital period. The longer the amount of time that elapses between transits the longer the orbital period. The orbital period also provides information about the planet's mean distance through Kepler's third law of planetary motion. This law relates the planet's period to its average distance: if the period is known, the average distance can be calculated.*** So, the transit time provides us with the orbital period, which then give us the distance.

AGE
Perhaps the most astounding determination that astronomers have made about exo-planets such as Kepler-452b is its age. We begin by assuming - quite safely - that stars and their attendant planets are coeval: they form together. If we can determine the parent star's age, we can then know the planet's age, as well. Astronomers employ a couple of age-determination methods, which should be more correctly termed "age-estimation" methods. First, astronomers can determine the star's distance (more on this tomorrow) and can measure its apparent brightness. From this apparent brightness and distance, one can determine its absolute brightness, or luminosity. Spectral analysis (again, tomorrow) of the star yields its spectral type. By this method, astronomers ascertained that the star Kepler-452 was of the same spectral class as the Sun. By comparing the star's luminosity with that of the Sun, they could determine that the star was more luminous than the Sun. Part of this luminosity difference relates to the mass: Kepler-452 is 3.7 percent more massive than the Sun and therefore is intrinsically more luminous.****

Estimating the age from the brightness is not the only method, Another involves 'astroseismology,' or the study of sonic waves within a star. The Sun, like all stars, fuses light elements to form heavier elements. For instance, the Sun fuses hydrogen to form helium. When the Sun first ignited these reactions, the ratio of helium to hydrogen was at its lowest. Over time, the helium reserves increased as the fusion reactions continued. Consequently, the ratio of helium to hydrogen also increased. This ratio can be measured by observations of sonic waves within the stars. Sound waves propagate at different rates depending on the density and pressure of the medium through which they pass. A star's internal density and pressures change as the mass ratio of the constituent material changes. (Think of it this way: waves travel differently through hot water than cold, thick soup.) Measuring the sonic waves of a star yields information about the ratio of helium to hydrogen in a star and from this information we know how long the star has been fusing light elements into heavier ones and this measurement gives us its age and, by extension, the planet's age, as well.

DISTANCE
Yesterday we derived the age of the planet by first determining the age of its parent star. We assumed that the planet formed around the same time its parent star formed. So, the ages would be equal. Similarly, if we can determine the star's distance, we will also know the planet's distance, as well. The distances won't be precisely equal, but the difference is so slight when compared to the system's distance from Earth that we can discard it. The distance to Kepler-452 is estimated to be about 1400 light years: at the outer range of the parallax method, the technique that measures a star's displacement angle relative to background stars. This angle and the star's distance are related: the smaller the angle, the greater the distance. The parallax method is limited, for the accuracy decreases with increasing distance and currently is reliable out to 500-600 parsecs (1620- 950 light years).

STAR TYPE
The one issue that has raised the hopes of alien admirers is that Kepler-452 is a Sun-like star. In other words, it has the same spectral type as our Sun. Astronomers have divided stars into a series of spectral types based on absorption lines with their spectra. As electromagnetic radiation (light) travels from a star's core through its outer layers, gases within these layers absorb the light at different wavelength. Chemicals absorb light at specific wavelengths so this absorption spectrum serves as a chemical signature. Each spectral type exhibits its own specific spectra. So, by observing a star's spectrum, an astronomer can determine its spectral type, which, in turn, yields information pertaining to a star's temperature.

[For more information about this concept, visit our brand new web-page "Fly-By Astrophysics," devoted to elucidating astrophysical concepts: http://usm.maine.edu/planet/fly-astrophysics Look for the first entry: Simplified Spectral Classification.]

STAR'S MASS
Here, we are helped by something called the "mass-luminosity" relation. First, astronomers can know the star's apparent brightness by observing it directly. Secondly, if the distance is also known, then the star's actual brightness can be determined through the distance modulus. If we know how bright a star appears and we also know its distance, we can calculate it intrinsic brightness. If we know the actual brightness, we can know the star's luminosity, or energy output. The star's luminosity depends on its mass through what we call the mass-luminosity relation. Through knowledge of the star's luminosity, Kepler-452 was found to be about 3.7 percent more massive than the Sun.

PLANET RADIUS
Yesterday we discussed the transit method. As a planet moves in front of the star, the star dims slightly. We call this passage of a planet in front of a star as a 'transit.' The transit yields some information pertaining to this planet. First, the time period separating successive transitions indicates the planet's orbital period. The longer the orbital period, the longer the lapse between transits. Also, the amount by which the brightness decreases relates to the planet's size: the larger the planet the greater the occultation area and brightness reduction. The brightness reduction yields an estimate of the planet's size, or radius.

PLANET MASS
Measuring mass is a bit trickier, especially for smaller Earth-sized planets. One technique involves measuring the gravitational tug that a planet induces on its parent star. While astronomers employed this technique to discover the highly massive Jupiter sized worlds, it is much more difficult, but still possible, to use this method for find smaller worlds. The technique is always called the "radial velocity" method because the star will be "tugged" slightly forward when the planet is between us and the star. It will be tugged backward when the planet is on the other side of it. This technique yields an approximate mass. When a star is known to have multiple planets, the masses of the individual planets can be measured based on the gravitational influence they exert on each other. Astronomer measure this influence by measuring the slight timing difference between successive transits as a result of this gravitational tugging and pushing.

PLANET DENSITY
If we have the radius and the mass, calculating the density is rather straightforward. The radius gives us the volume as we assume the body is spherical.***** Density is then just mass over volume.

While we still have much to learn about exo-planets and especially their suitability for life, we can learn quite a lot about a planets size, mass, density, and even its age. If nothing else, it is a great start in our search for other life in the galaxy.


*As of this moment, the number of Kepler's confirmed planets is 1030, a number that will likely increase by the time this article is finished, damnit.

**Here on Earth, we can occasionally see transits of Mercury and Venus. The next Venus transit won't happen until December 2117. The next transit of Mercury occurs on May 9, 2016. (And, yes, if the skies are clear, we'll see this event.)

***The square of a planet's orbital period (P) (or P x P) is proportional to the cube of its mean distance (a) (or a x a x a.)

****The Mass-Luminosity Relation relates a star's mass and energy output, which are related by different factors depending on the star type.

*****The gravitational molding of a massive body will make it spherical if its diameter is more than 600 kilometers. (400 kilometers if the object is largely composed of ices.)