the “K2 Mission”, has discovered the youngest exoplanet to date orbiting a brand new star. Follow-up confirmation observations were made using the W. M. Keck Observatory’s twin 10 meter telescopes on Mauna Kea, Hawaii. The 5 – 10 million-year-old star, K2-33 (the 33rd system discovered with the newly reconfigured Kepler Orbiting Observatory), is a brand new M-class (M1-V) red dwarf star with a mass of 0.57 solar, similar to the previous two newly-discovered stars discussed, TRAPPIST-1 and CVSO-30 but somewhat more luminous at 0.14 solar (14% the sun’s luminosity). The M1-V designation is the hottest within class; the next classification is K and then G, the sun’s spectral classification. The system exhibits a toroidal (doughnut) shaped dust and debris ring encircling the star, a remnant from the system’s formation. Over time, this ring will be dispersed from the star’s stellar wind, the outward flow of charged particles exhibited by all stars, a result of the internal hydrogen fusion reactions occurring in their cores. The Earth’s magnetosphere protects us from the sun’s solar wind.
Designated K2-33b, the nascent planet is a Neptune class planet, a gas giant with a mass and size comparable to the planet Neptune in our own solar system. Unlike Neptune though, this planet orbits K2-33 at a blistering distance of 0.05 AU or 5% the distance between the sun and the earth. The Kepler Light Curves for the planet are quite clear, indicating an orbital period of 5.4 days. As a comparison (see diagram below), Mercury orbits the sun at a distance of .39 AU (39% the distance from the Earth to the sun) and completes one orbit in 88 days. A closer examination of the light curves indicates large star spots rotating with the star as well as the possibility of a second planet.
In my discussion of CVSO-30, I established an empirical power law that relates habitable zone extent to stellar luminosity. In comparing these two aspects of any system, it is observed that the habitable zone extent varies as the 1/2 power (square root) of the luminosity, a consequence of the inverse square nature of electromagnetic radiation (light). In other words, the inner and outer limits of the habitable zone are separated by a distance (in AUs, Astronomical Units) equal to the square root of the host star’s luminosity relative to the sun. For example, the habitable zone of the star Sirius, with a luminosity of 25.4 solar, begins at 5.6 AU from the star for an extent of 5 AUs, ending at 10.5 AU. This means that any planet orbiting the star within this 5 AU region could contain liquid water if the only source of energy was the star. Sirius is a winter star and the brightest appearing star in our sky and the closest A-class (A1-V) star at 9 light years. The habitable zone extent for K2-33 of 0.366 AU is consistent with this power law (please see diagram, below).
When considering these aspects of other stars and their planets, it is interesting to note that a modest increase in stellar mass results in a dramatic increase in luminosity. This relationship between stellar mass and luminosity is known as the “Mass-Luminosity” relation and was established through empirical observation and data collection dating back over a century. It codifies the relationship between stellar mass and luminosity where the luminosity varies approximately as the fourth power of the mass measured in terms of the sun’s mass. Again, we can use Sirius as an example. Sirius has a mass of 2.02 solar and thus has a luminosity at least 2.02^4 solar or 17 times greater than the sun. As it turns out, Sirius’ luminosity is 24.5 solar, with other contributing factors beyond the scope of this article in play. As a comparison, a star with 10 solar masses would have a luminosity of 10^4 or 10,000 solar! Spica, the brightest star in Virgo, is such a star. Just to get a sense of the power of a high-mass star and the magnitude of the relationship between mass and luminosity, lets apply these ideas to Spica. At 10.25 solar masses, Spica shines with a luminosity of 11,038 solar! The habitable zone for the star begins at 117 AUs or 3 times the distance to Pluto from the sun and extends for 100 AU, ending at 217 AU! Spica has now evolved to the point where it is producing energy through helium fusion reactions in its core, having depleted its compliment of hydrogen and is thus, on track to end its life in spectacular fashion as a Type-II Supernova. Another instructive example is the subject star of this article, K2-33. With a mass of 0.57 solar, its luminosity is a paltry 0.57^4 or 0.11 solar, a value consistent with the measured luminosity of 0.14 solar.
So what drives this sharp increase in luminosity with modest increase in mass? Every star is a dynamic, self-regulating system, each powered by a huge nuclear fusion reactor in its core. The cores of the sun and other stars in a similar evolutionary state currently produce helium and a tremendous amount of energy. The tens-of-millions of degrees core temperatures produce tremendous outward gas pressures that are balanced by the inward gravitational crush of the star’s hulking mass, measured in terms above 10^29 kg! In order to maintain that dynamic balance between outward gas pressure and gravity, much energy has to be expended, dramatically reducing the star’s productive lifetime. By comparison, our sun, with 1.99 x 10^30 kg of mass has a productive lifespan of over 10 billion years. The star Sirius (2.02 solar masses) or 4 x 10^30 kg has a productive lifespan of less than 2 billion years, illustrating that a two fold increase in mass results in over a five fold decrease in productive lifetime. Conversely, low-mass, small, relatively cool stars such as K2-33 have extraordinarily long lifetimes that can be measured in multiples of the current age of the universe! The estimated productive lifespan of K2-33 is 50 billion years or five times that of the sun. The lifespan of a star such as TRAPPIST-1 is 3 trillion years, 250 times the age of the sun or 217 times the current age of the universe!
All our science, measured against reality, is primitive and childlike-and yet it is the most precious thing we have
An index of all articles in this blog can be found here.
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