Practical Numerical Training UKNum

Transcription

1 Practical Numerical Training UKNum Conclusions PD. Dr. C. Mordasini Max Planck Institute for Astronomy, Heidelberg Programm: 1) Weiterführende Vorlesungen 2) Fragebogen 3) Eigene Forschung 4) Bachelor/Masterarbeiten

2 1 Weitereführende Vorlesungen

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9 Weiterführende Vorlesungen Numerische Strömungsmechanik -Equations of fluid dynamics -Hyperbolic systems of equations -Advection algorithms -Classical hydrodynamics solve WS 2012/2013: Springel & Dullemond num_fluid_2012/index.shtml

10 Weiterführende Vorlesungen Radiative transfer in astrophysics (Master/ PhD Course) basics of radiative transfer theory Advanced radiative transfer theory different kinds of transfer problems numerical methods for solving LTE and non-lte radiative transfer problems work with an actual radiative transfer code A particular emphasis will be on hands-on exercises using a radiative transfer code. SS, 2013, Dullemond

11 2 Fragebogen

12 3 Eigene Forschung

13 Galaxies, stars and planets 10 billion galaxies How many harbor life? 100 billion stars how many planets? How frequent? Life? First generation of human beings with technology to answer this.

14 Ways to understanding Herschel s 1789 For many centuries Cloud collapse Hertzsprung Russel Nuclear Fusion Stellar Mass Funct. Sun Stars Solar System La Silla Obs. ESO Darwin ESA For a decade In a decade? Formation in disks Collisions Gas accretion Migration Exoplanets Astrobiology Habitable Zone Biomarkers Complex Life Life Extraterrestrial Life?

15 Planet formation: The paradigm Gravitational Core - remote observations - in-situ measurements - sample returns - laboratory analysis - theoretical modeling Minority line Party line Accretion Instability A satisfactory theory should explain the formation of planets in the solar system as well as around other stars.

16 Planet formation: Sequential picture in presence of gas in absence of gas dust 10 7 years 10 7 years Star & protoplanetary disk planetesimals protoplanets migration giant planets giant impacts 10 8 years type I type II terrestrial planets dynamical rearrangement

17 Planet formation is a complex process Huge dynamical range in size/mass: grains to giant planets Multiple input physics: gravity, hydrodynamics, radiative transport, [ thermodynamics, magnetic fields, impact physics, material properties,... Strong non-linear mechanisms (e.g. runaway growth) Feedbacks and interactions (e.g. protoplanetary disk-planet: orbital migration) dσ dt = 3 r r [ ] r 1/2 ) r νσr1/2 + Σ w (r) + Q planet (r). dm dr =4πr2 dp ρ dr = Gm ρ r ( ) 2 dl dr =4πr2 ρ ɛ T S dt t dr = T dp P dr = d ln T d ln P =min( ad, rad ) rad = 3 0 = q h 2 2 p r 2 p 2 p dr p dt = 2r p tot J p 64πσG d P dt κlp T 4 m = (3M ) 1/3 dm Z 6 a 2 B L M 1/3 dt 3 4 H R H + 50 qr 1 dm Z dt ρ(p )=ρ 0 + cp n. = p R 2 captf G (e, i) 1/3 Mp r H = r p 3M H Planet formation and evolution difficult to understand from first principles alone.

18 Magnetohydrodynamic disk models around young stars

19 Instabilities in disks

20 Orbital migration of planets

21 High mass star formation models

22 Fig. III.1.1: Two of the most important statistical observational constraints for planet formation theory. The left panel shows the semimajor axis mass diagram of the extrasolar planets. The different colors indicate the observational detection technique. mass-radius lines for planets of different compositions. In both panels, the planets of the Solar System are also shown. Note that these figures are not corrected for the various observational biases, which favor for the radial velocity and the transit tech- Exoplanets: statistical tests for theory Mass Mass [Earth [M mass] ] Jupiter Saturn Neptune Uranus 5 Radial velocity Venus Earth & Transits Earth 1 Microlensing Venus Direct imaging Neptune , Semimajor axis [AU] Mass [Earth masses] Radius [R Earth ] Uranus Saturn Jupiter ice rocky jovian Credit: C. Mordasini

23 Extrasolar planet population synthesis

24 General planet formation model Core struct. Interpolation Migration Planet-Planet Diff. Eq. Infalling Diff. Eq. Envelope Bisection Diff. Eq. Accretion rate Diff. Eq. Bisection Atmosphere Vert. str. Interpolation Rad. str. Lin. Equations (Part. Diff. Eq.) Evaporation Solid disk

25 Exoplanets: statistical tests for theory 46 Credit: C. Mordasini 0.08 III. Selected Research Areas 100 Normalized Fraction Number of planets KOI 423b 0.04 CoRoT 9b HD 17156b Normalized Fraction Fig. III.1.4: Comparison of the observed and the synthetic planetary mass distribution. The left panel shows the distribution of planetary masses as found with high precision radial 0.06 velocity observations (Mayor et al. 2011). The blue line gives the raw count, while the red line corrects for the observational bias against the detection of low-mass planets. The right panel 0.04 Credit: C. Mordasini Msin i [MEarth] [R!] radius] Radius R [Earth Jupiter Kepler 9b Kepler 9c 10 Saturn Msin i [MEarth] Kepler 18d 103 Credit: C. Mordasini III. Selected Research Areas HD 80606b CoRoT 10b 104 shows the planetary mass function as found in a population synthesis calculation. The black line gives the full underlying 5 Kepler 11e population, while the blue, red, and green lines are the detecturanus able synthetic planets at a low, high, and very high radial velockepler 11d Neptune ity precision. Kepler 11c Kepler 10c the fact that always exactly the same formation model is planetary disk disappears exactly during the short time used. This is a basic outcome similar to the observational during which the planet is transformed from a Neptunian Kepler 11f result. In Figure III.1.3, one can for example find tracks into a Jovian planet. This makes that planets with inter0 that0.02 lead to the formation of hot Jupiters. Most embryos mediate masses! 30 MEarth are less frequent ( planetary however remain at low masses, since they cannot accrete desert, cf. Ida & Lin 2004). The dryness of the desert M [M Mass [Earth mass]!] a sufficient amount of planetesimals to start rapid gas ac- is directly given by the rate at which planets can accrete cretion and become a giant planet. gas, while the mass where the frequency drops represents Fig. III.1.6: Mass-radius diagram of synthetic planets with a the synthetic planets. The black symbols (bottom) 0 the where runaway starts.with We thus correspond to solid-dominated low-mass planets w primordial H mass / He envelope at an agegas of accretion 5 Gyrs together all see how the comparison of synthetic and actual mass funcplanets in- and outside of the Solar System with a known mass at most 1 % of H / He, while the most massive pla Msin i [MEarth] tion constrains the theory formation. Wethe further Comparison with observations top) consist of at least 99 % H / He. and radius, and a semimajor axis ofofatplanet least 0.1 AU (as in

26 Exoplanets: observations Telescope Vaccum chamber Control room

27 4 Verfügbare Bachelor/ Masterarbeiten

28 Current Batchelor/Master projects diploma_phd/dipl/dipl.php

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