Today in Astronomy 111: Planet Formation and Exoplanets

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Today in Astronomy 111: exoplanet detection The successful search for 1.E+10 extrasolar planets around Number of transistors 1.E+08 in new microprocessors ordinary stars doubles every Radial-velocity planet 24 months 1.E+06 detection Exoplanetary transits and 1.E+04 With Kepler planet eclipses candidates Number of extrasolar Measurement of mass, 1.E+02 planets doubles every 29 months radius and surface 1.E+00 temperature of exoplanets 1970 1980 1990 2000 2010 Exoplanetary atmospheres Year Exponential progress: Moore’s law compared to exoplanet discovery. (Data from Intel, AMD, IBM, Zilog, Motorola, Sun Microsystems, Kepler and exoplanet.eu.) 6 December 2011 Astronomy 111, Fall 2011 1 The bad news Exam #2 takes place here next Tuesday. To the test bring only a writing instrument, a calculator, and one 8.5”×11” sheet on which you have written all the formulas and constants that you want to have at hand. • No computers, no access to internet or to electronic notes or stored constants in calculator. The best way to study is to work problems like those in homework and recitation, understand the solutions and reviews we distributed, refer to the lecture notes when you get stuck, and make up your cheat sheet as you go along. Try the Practice Exam on the web site. Under realistic conditions, of course. 6 December 2011 Astronomy 111, Fall 2011 2 The successful search for extrasolar planets By which we mean, mature planets around normal stars. The first four extrasolar planets were observed around neutron stars (Wolszczan & Frail 1992, Backer et al. 1993.) In the early 1990s, groups in San Francisco and Geneva were gearing up for long searches for giant planets around normal stars by Doppler-velocity techniques. The idea: detect the relatively small, but periodic, Dopper shift in the spectrum of a star due to its orbital motion around the center of mass of a star-planet system. The new part of the idea: simultaneously to use thousands of stellar spectral lines in a broad wavelength range, always viewed through a cell filled with a gas (iodine) which has many spectral lines but which is rare in stars. 6 December 2011 Astronomy 111, Fall 2011 3 Example: orbital speeds of Sun and Jupiter Recall, from our discussion of the two-body system on 29 September 2011, applied to Jupiter and the Sun: MM J 30 Reduced mass: µ ==×≅1.897 10 gm ( MJ ) MM + J Orbital speeds, dictated by momentum conservation: µ GM -1 v = = 13.044 km sec J Mr J µ GM MJ vv= = = 0.012 km sec-1 MrJ M The best planet-search spectrometers can measure stellar − Doppler velocities as small as 0.0002 km sec-1 = 20 cm sec1 . 6 December 2011 Astronomy 111, Fall 2011 4 The successful search for extrasolar planets (continued) The observers thought they were going to detect Jupiters like this, so they were prepared to do observations over the course of many years. (Recall that Jupiter’s orbital period is 11.9 years.) So it was much to their surprise that they detected their first planets in a matter of days: • 51 Peg b: msini = 0.46MJ, P = 4.2 days (Mayor & Queloz 1995, Marcy & Butler 1995) • 70 Virginis b: msini = 6.5MJ, P = 117 days (Marcy & Butler 1996) • 47 Ursae Majoris b: msini = 2.5MJ, P = 1100 days (Butler & Marcy 1996) Jupiter-size planets, in terrestrial-planet-size orbits (or smaller)? 6 December 2011 Astronomy 111, Fall 2011 5 The successful search for extrasolar planets (continued) In 1999, after several more exoplanets had been detected, two more milestones in the search were reached: One planet detected by radial velocity, HD 209458 b, was seen to transit: to eclipse a tiny portion of the star (Henry et al. 2000). • Thus its orbit is viewed close to edge on ( i ≈° 90 ) and its mass can be determined precisely: Deeg and Garrido 2000 mM=0.69 ± 0.05J . 6 December 2011 Astronomy 111, Fall 2011 6 The successful search for extrasolar planets (continued) Also in 1999, the first multiple exoplanetary system was detected: υ Andromedae c and υ Andromedae d (periods 242 and 1275 days), to go with the previously- detected υ Andromedae b (4.6 days). Top: from Butler et al. 1999 Bottom: animation by Sylvain Korzennik (CfA) 6 December 2011 Astronomy 111, Fall 2011 7 The successful search for extrasolar planets (continued) Later (in 2005) the Spitzer Space Telescope detected the eclipse of HD 209458b (the planet) by HD 209458 (the star) – meaning that the light from the planet is directly detected at mid- infrared wavelengths Animation by Robert Hurt, SSC when not in eclipse (Deming et al. 2005). 6 December 2011 Astronomy 111, Fall 2011 8 The successful search for extrasolar planets (continued) 2008 saw two historic firsts: an image of a planet orbiting the bright, nearby star Fomalhaut, which truncates the remains of the disk from which it formed. This planet’s orbit was correctly predicted two years earlier (by Alice Quillen, on the basis of the disk truncation) – the first time since Le Verrier and Galle (1846, Neptune) that anyone has Paul Kalas, UC Berkeley/STScI/NASA accomplished such a feat. 6 December 2011 Astronomy 111, Fall 2011 9 The successful search for extrasolar planets (continued) and an image of three planets in orbit around another 0.49 HR 8799 IRAS bright nearby star, HR 8799. 0.39 Another reported in 2010. 0.29 HR 8799 was previously Total subtracted flux subtracted density (Jy) 0.19 known to have two debris - 35 K belts (Chen et al. 2006), 0.09 Spitzer-IRS 152 K which turn out to lie inside Photosphere -0.01 and outside the orbits of the 5 15 25 35 45 55 65 planets. The resemblance to Wavelength (μm) our Solar system’s giant planets, asteroid belt and C. Marois and B. Macintosh, Keck Observatory Kuiper belt is striking. 6 December 2011 Astronomy 111, Fall 2011 10 The successful search for extrasolar planets (continued) And this year, 2011, has seen, among many other results, the first detection of a planet in orbit around a binary star, Kepler 16AB b… The stars are K and M type in a 41-day period; the planet is Saturn-like in a 229-day period (Doyle et al. 2011). So the stars and the planet’s orbital distance are about right for Tatooine, but the planet’s mass is way too large. (Lucasfilm ) 6 December 2011 Astronomy 111, Fall 2011 11 The successful search for extrasolar planets (continued) …and the first detection – via imaging – of an infant giant planet orbiting in the gap of a transitional disk, LkCa 15. Planet (blue) seems to be accompanied by a streamer of material (red) which shows up at longer wavelengths. Andrews et al. 2011 Kraus & Ireland 2011 6 December 2011 Astronomy 111, Fall 2011 12 Today’s exoplanets Today there are 708 objects listed as exoplanets: 181 by radial velocity and transits. • You can take 177 of them to the bank, as we’re 100% sure they’re of planetary mass. 471 others by radial velocity alone. Something like 5-10% of these may prove to be brown dwarfs eventually. • e.g. the earliest discovery on the list, HD 114762 b. These 652 planets live in 534 planetary systems: there are 78 multiple-planet RV or RV+T systems so far. • 24 have three or more planets. • The most populous systems have six confirmed planets each: HD 10180, Kepler 11. 6 December 2011 Astronomy 111, Fall 2011 13 Exosolar systems with three or more planets 47 UMa 55 Cnc 61 Vir GJ 581 GJ 876 HD 10180 HD 125612 HD 136352 HD 181433 HD 20794 HD 31527 HD 37124 HD 39194 HD 40307 HD 69830 HIP 14810 HIP 57274 HR 8799 Kepler-11 Kepler-18 Kepler-9 KOI-730 µ Ara υ And Sun 0.01 0.1 1 10 100 Orbital semimajor axis (AU) 6 December 2011 Astronomy 111, Fall 2011 14 Today’s exoplanets (continued) 14 others, in 9 systems, have been discovered by timing pulsars (neutron stars) or pulsating giant stars. 42 more have been found by direct imaging (29) or gravitational micro-lensing (13). Many of those imaged might be brown dwarfs. The official list currently includes only transit events which have been confirmed by RV measurements to be planets. But the planetary-transit satellites, COROT (ESA) and Kepler (NASA), have produced a huge number of candidates for RV followup, the vast majority of which are expected to turn out to be planets. Kepler’s current list of 2326 candidates includes candidate planets as small as RR = 0.6⊕ . (!!) 6 December 2011 Astronomy 111, Fall 2011 15 Radial-velocity planet detection and msini measurement …in which one makes a series of accurate measurements of tiny periodic variations in the Doppler shift of the host star. For help in visualizing how this works, click here. Steps: measure P and K. Measure the period P of the Doppler shift’s variation. This determines the length of the semimajor axis of the planet- star separation via Kepler’s third law: From exoplanets.org GM( + m) GM a3= PP 22≅ 22 44ππ 6 December 2011 Astronomy 111, Fall 2011 16 Radial-velocity planet detection and msini measurement (continued) Measure also the amplitude K (maximum Doppler shift with respect to the average) of the star’s radial velocity: KV= sin i Observer’s view Side view Orbital axis m Line of VKr = 90 − i sight Vt Vt V Orbit Orbit i 6 December 2011 Astronomy 111, Fall 2011 17 Radial-velocity planet detection and msini measurement (continued) If the orbital eccentricity is close to zero, the radial velocity varies sinusoidally with time.
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  • An Explanation of Stability of Extrasolar Systems Based on the Universal Stellar Law

    An Explanation of Stability of Extrasolar Systems Based on the Universal Stellar Law

    Chaotic Modeling and Simulation (CMSIM) 4: 513-529, 2017 An explanation of stability of extrasolar systems based on the universal stellar law Alexander M. Krot1 1 Laboratory of Self-Organization Systems Modeling, United Institute of Informatics Problems of National Academy of Sciences of Belarus, Minsk, Belarus (E-mail: [email protected]) Abstract: This work investigates the stability of exoplanetary systems based on the statistical theory of gravitating spheroidal bodies. The statistical theory for a cosmogonical body forming (so-called spheroidal body) has been proposed in our previous works. Starting the conception for forming a spheroidal body inside a gas-dust protoplanetary nebula, this theory solves the problem of gravitational condensation of a gas-dust protoplanetary cloud with a view to planetary formation in its own gravitational field. This work develops the equation of state of an ideal stellar substance based on conception of the universal stellar law (USL) connecting temperature, size and mass of a star. This work also shows that knowledge of some orbital characteristics for multi-planet extrasolar systems refines own parameters of stars based on the combined Kepler 3rd law with universal stellar law (3KL–USL). The proposed 3KL–USL predicts statistical oscillations of circular motion of planets around stars. Thus, we conclude about a possibility of presence of statistical oscillations of orbital motion, i.e. the oscillations of the major semi-axis and the orbital angular velocity of rotation of planets and bodies around stars. Indeed, this conclusion is completely confirmed by existing the radial and the axial orbital oscillations of bodies for the first time described by Alfvén and Arrhenius.