Dissertation Submitted to the Combined Faculties of the Natural Sciences and Mathematics of the Ruperto-Carola-University of Heidelberg
Total Page：16
File Type：pdf, Size：1020Kb
Dissertation submitted to the Combined Faculties of the Natural Sciences and Mathematics of the Ruperto-Carola-University of Heidelberg. Germany for the degree of Doctor of Natural Sciences Put forward by Mykola G. Malygin born in Cherkasy (Ukraine) Oral examination: 03.02.2016 Gas Opacity in Planet and Star Formation Referees: PD. Dr. Hubert Klahr Prof. Dr. Andreas Quirrenbach Gas Opacity in Planet and Star Formation M G. M T D P A D P A R C U¨ H, B-W¨ F 2016 c 2016 – M G. M . Abstract D G O P- S Die Opazität von Gas und Staub spielt eine Schlüsselrolle bei der Bestimmung von Struktur und Strahlenspektrum von Staub-Gas-Wolken um Sterne (CSM), da hier Strahlentransport den Hauptübertragungsprozess für Energie darstellt. Das Vorherrschen von Staub in Kontinuumabsorbtion und die rechnerische Komplexität bei der Verwendung von molekularen Linienspektren hat bisher verhindert das letztere in den meisten Studien zur Planeten und Sternenentstehung Berücksichtigung fand. Diese Arbeit präsentiert die Berechnung von Gasopazitäten im entscheidenden Parameterraum, eine Methode um diese in Strahlungstransportberechnungen zu nutzen und erste Resultate von Strahlungstransport- und Temperaturausgleichsberechnungen. Die größte Satz an staubfreien CSM-Opazitäten zeigt dank verbesserter Frequenzabtastung bis zu 104 mal größere mittlere Planckopazitäten im Vergleich zu früheren Arbeiten. Mittlere Zweitemperaturplanckopazitäten sind für die Bestimmung vor allem in optisch dünnen angestrahlten Gasen wichtig. Die mittlere Temperatur, mit tabellarisierter Opazitäten bestimmt, in solchen Gasen ist degeneriert und von der Vergangenheit des Mediums abhängig. Das vorgestellte Verfahren zur Bestimmung von Temperaturausgleichszeiten berücksichtigt Stoßwechselwirkung, die den Ausgleich der Temperatur in Regionen mit wenig Gas beschränken. Eine grundsätzliche untere Schranke der Temperaturausgleichszeiten ist durch LTE-Emissionen gegeben. Die Geschwindigkeit des Temperaturausgleich beeinusst wichtige hydrodynamische Instabilitäten die für Turbulenz in magnetisch inaktiven Zonen eine Rolle spielen. G Opacity plays a key role in determining the structure of the heterogeneous circumstellar medium (CSM) and its observable spectrum. Planet and star formation changes dust density on various spatial and time scales through gravity and turbulence, radiation eld and chemistry. The following thesis presents calculations of gas opacity in the suitable parameter space, a methodology of utilising it in hybrid-type radiative transfer schemes, as well as rst results on radiative transfer and thermal relaxation calculations. The largest set of dust-free opacity in the CSM regime is presented. Improved frequency sampling yielded substantially larger (up to a factor of 104 in comparison to some previous works) Planck means. The two-temperature Planck means important for determining the temperatures in the optically thin irradiated gases were tabulated. The equilibrium temperature in such media is degenerate and depends on the thermal history of the gas. The suggested recipe to estimate the thermal relaxation time accounts for collisional coupling, which limits the relaxation in low-density regions. A fundamental lower limit to the relaxation time is set − by the LTE emissivity giving Ωt ∼ 10 4 at the T Tau phase. The locations of onset of linear and the locations of operation of subcritical hydrodynamic instabilities, reckoned as turbulence drivers in magnetically inactive zones, are constrained by the relaxation criterion. Contents A 1 C 2 0 I 6 0.1 Gas Spectroscopy .................................. 6 0.2 Context & Motivation ............................... 7 0.2.1 Radiative Feedback from Star Formation ................. 8 0.2.2 Accretion Discs .............................. 9 0.2.2.1 Transport in Accretion Discs . 10 0.2.2.2 Gravitational Instability .................... 10 0.2.2.3 Core accretion ......................... 13 0.2.2.4 Core migration ........................ 14 0.3 Radiative energy transfer .............................. 14 0.3.1 Radiative transfer and energy evolution equations . 14 0.3.2 LTE .................................... 16 0.3.3 Optically Thin Limit ........................... 18 0.4 Dissertation outline ................................. 18 1 M G O 19 1.1 Motivation & disclaimer .............................. 19 1.2 Calculations .................................... 20 1.3 Line absorption ................................... 21 1.4 Frequency averages ................................. 23 1.5 Results ....................................... 23 1.5.1 Single-temperature Planck mean ..................... 23 1.5.2 Two-temperature Planck mean ...................... 25 2 CONTENTS Page 3 of 111 1.5.3 Metallicity ................................. 25 1.5.4 Connection to low temperature atmospheric opacity . 26 1.5.5 Comparison to other studies ....................... 28 2 E T D O T G 31 2.1 Radiative Instability In Optically Thin Limit .................... 32 2.2 Illustrative example ................................. 33 2.3 Equilibrium gas temperature as a function of radiation temperature . 35 2.4 Discussion ..................................... 36 3 T R T 38 3.1 Denition ..................................... 38 3.2 Optically thin relaxation regime .......................... 39 3.3 Optically thick relaxation regime .......................... 40 3.4 Set-up ........................................ 41 3.4.1 Density model ............................... 41 3.4.2 Temperature model ............................ 42 3.4.3 Opacities ................................. 42 3.5 Results ....................................... 44 3.5.1 Relaxation regimes: recipe verication . 44 3.5.2 Constituent times ............................. 46 3.5.3 Perturbation wavelength ......................... 47 3.5.4 Radial and vertical modes ......................... 50 3.5.5 Dust-to-gas mass ratio ........................... 52 3.5.6 Disc mass ................................. 54 3.6 Discussion ..................................... 55 3.6.1 Temperature relaxation, not disc cooling . 55 3.6.2 On ux limiter .............................. 57 3.6.3 Stochastic nature of density perturbations . 58 3.6.4 The method: thin and thick ........................ 59 4 C H & G I 61 4.1 Birthplaces of hydrodynamic instabilities ...................... 61 4.1.1 Zombie vortices instability (ZVI) ..................... 62 4.1.2 Vortices: an instability growing from linear convective overstability (COV) 62 4.1.3 Vertical shear instability (VSI) ....................... 63 4.2 Uniform Q = 1 disc ................................. 64 3 CONTENTS Page 4 of 111 4.2.1 Setup ................................... 64 4.2.2 Thermal relaxation in a Q = 1 disc .................... 65 4.2.3 Comparisons to other studies ....................... 67 5 F- G O 69 5.1 Motivation & challenge ............................... 69 5.2 Opacity probability distribution function ..................... 71 5.3 Opacity sampling .................................. 71 5.4 Planck & Rosseland bin averaging ......................... 72 6 S 75 A 78 A A O 80 A.1 Basic equations ................................... 80 A.2 Linear analysis ................................... 82 A.3 Energy or temperature evolution time? ....................... 83 A B O 85 B.1 Thermal emission time ............................... 85 B.2 Collisional coupling ................................ 86 B.3 Dust-to-gas collisions ................................ 86 B.4 Gas-to-gas collisions at low temperatures ...................... 86 N 88 L 90 R 94 4 CONTENTS Page 5 of 111 T . 5 The secret of getting ahead getting started. Mark Twain 0 Introduction 0.1 G S William Hyde Wollaston was the rst one to publish a notice of absorption features in dispersed light from the Sun as well as from candle re, which he revealed during his foreshadowing experiments with prisms [Wollaston, 1802, p. 378]. Shortly aferwards, Joseph Fraunhofer duly noted 574 “starke¨ und schwache vertikale Linien” he observed in a difracted solar light [Fraunhofer, 1817, p. 279]. A complementary information from later experiments held in Heidelberg by Gustav Robert Kirchhof and Robert Wilhelm Bunsen on candle light spectrum [Kirchhof & Bunsen, 1860], established a new eld in physics: spectroscopy. Balmer identied a series of spectral lines from Hydrogen [Balmer, 1885]. Hydrogen and Helium absorption lines in solar spectrum [Lockyer, 1869, pp.432-434] as well as both absorption and emission lines from other objects [Pickering et al., 1901; Pickering, 1901d,c] and other phenomena [Pickering, 1901b]. Observations of absorption lines in binary stars [“spectroscopic binaries” Pickering, 1901a] enabled mass estimate and the radial velocity measurements, now in heart of the main ground-based exoplanet search method. It was not until ∗ 1913, when Bohr made a genuine intuitive step that founded quantum mechanics [Bohr, 1913a,b,c] . Spectroscopy became a revolutionary technique in astrophysics. Spectra turned to be ’biometric’ ∗ The story tells that Bohr’s interpretation was anticipated by three years in a 1910 work by an Austrian physi- cist Arthur Erich Haas, but the publication got rejected. 6 0.2. CONTEXT & MOTIVATION Page 7 of 111 databases of stellar properties allowing deciphering such information as efective, kinetic and excitation temperatures, gravitational attraction in photospheres, abundances of various species, microturbulent (non-thermal) motions, rotational velocities,