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Radial Velocity Method for Extrasolar Planet Detection

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Radial Velocity Method for Extrasolar Planet Detection How many civilizations are there in the Galaxy? Codified as the Drake Equation Number of stars in the Milky Way galaxy ~1011 (100 billion) Nciv = N* " f HP " f life " f civ " f alive Distance from the Sun to the galactic Center is about 25,000 light years Frank Drake ! Nciv is the number of civilizations alive today N is the number of stars in the Galaxy (~1011) Number of civilizations `alive’ now depends upon: * fHP is the fraction of stars with habitable planets • fraction of stars with habitable planets f is the fraction of habitable planets that develop life • fraction of habitable planets that develop life life fciv is the fraction of planets on which life becomes • fraction of time that life becomes intelligent intelligent • fraction of civilizations that still exist falive is the fraction of once intelligent civilizations that are still alive Extraterrestrial Life: Spring 2008 Extraterrestrial Life: Spring 2008 Not so much a traditional `equation’ - more a framework An example: for thinking about SETI… Assume: fHP: astronomical question • fHP = 0.1 • flife = 1 11 #4 #5 -4 Nciv =10 " 0.1"1"10 "10 =10 flife / fciv: biological / evolutionary questions • fciv = 10 -5 • falive = 10 falive: sociological question Easy to come up with optimistic estimates that suggest The age of the Galaxy (and the oldest planets in the nearest !civ ilization is close by - can also pick numbers it) is ~10 billion years. If, on average, a civilization that make us alone in the Galaxy (or even the Universe) survives for 100,000 years before destroying itself: First two factors can be addressed via astronomy and biology in a normal `scientific’ way - last two can only 105 years f ~ ~ 10"5 realistically be determined by finding other civilizations… alive 1010 years Extraterrestrial Life: Spring 2008 Extraterrestrial Life: Spring 2008 ! Detecting extrasolar planets Contrast between star and planet is the main problem d R E e.g. brightest stars in this image are around 18th magnitude Fraction of total Solar luminosity that is reflected is: flux " area of Earth as seen from Sun " A f = solar luminosity 1380 watts / m2 " #R2 " A = E 3.9 "1026 watts 6 Earth radius is RE = 6.4 x 10 m 3.5 arcseconds -10 ! f = 1.4 x 10 Seen from another star, Earth is ~10 billion times dimmer than the Sun No direct detections of extrasolar planets… Extraterrestrial Life: Spring 2008 Extraterrestrial Life: Spring 2008 1 Indirect detection methods Radial velocity searches for planets Most successful method so far is based on the fact that Sun wobbles slightly in response to the gravity from orbiting a planet does not (strictly) orbit the star, but rather the planets (in the Solar System mostly from Jupiter): center of mass of the star + planet system. Small effect - center of mass of the Solar System (Sun plus center of mass planets) is within the Sun itself e.g. in an equal mass binary star system each star orbits But detectable - either by at the same distance from the looking for the motion of the common center of mass star on the sky or by looking for changes in the radial velocity of a star Extraterrestrial Life: Spring 2008 Extraterrestrial Life: Spring 2008 How large is the radial velocity signal caused by a planet? The orbital velocity of the planet is given by the formula: ap a* GM* v p = Mp M* a center of mass …where G = 6.67 x 10-11 m3 kg-1 s-2 (Newton’s gravitational constant) Suppose the star-planet separation is a e.g. for !th e Earth: If the star has mass M and the planet M , the distances * p 11 of the star and planet from the center of mass are: • a = 1.5 x 10 m 30 • M* = 2 x 10 kg M p ap = M*a* Orbital velocity = 29,800 ms-1 (about 30 km per second) M p a* = ap M* Extraterrestrial Life: Spring 2008 Extraterrestrial Life: Spring 2008 ! During one planetary orbit, the star also does one orbit How large is the effect? around the center of mass M p GM* Distance the star travels is smaller than the distance the v* = planet travels by the ratio of their distances from the M* a center of mass: a / a << 1 * p Jupiter: Stellar velocity caused by the orbiting planet is: • a = 7.8 x 1011 m • M = 1.9 x 1027 kg -1 M GM p! v*=12.5 ms p * • M = 2 x 1030 kg v* = * M* a Very small - but measurable! -1 For the Earth, v* = 0.1ms - not detectable… ! Extraterrestrial Life: Spring 2008 Extraterrestrial Life: Spring 2008 2 Radial velocity is measured via the Doppler shift: light is slightly blueshifted when the star moves toward us, redshifted when it moves away Extraterrestrial Life: Spring 2008 3.
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