Modeliranje plimskega trenja v dvozvezdju

Vehovar, Jon (author), Prša, Andrej (mentor)

V dvojnih sistemih razlika v privlaku ene zvezde na drugo v različnih delih druge povzroči plimske izbokline na bližnjem in daljnem delu zvezde. V kolikor sta orbitalna in rotacijska kotna hitrost različni, izboklini povzročita navor in se izmenjata rotacijska ter orbitalna vrtilna količina. V ekscentričnih orbitah je ta neenakost vedno prisotna in izmenjava vrtilne količine poteka, dokler sistem ne pride v stanje, kjer zvezdi potujeta po krožni orbiti in sta rotacijska ter orbitalna kotna hitrost enaki. Analitični pristopi to izmenjavo opišejo le s parametrom notranje strukture, vendar ni znano, kako sama notranja struktura zvezde vpliva na izmenjavo vrtilne količine. Razumevanje dinamike prenos pripomore k boljšemu razumevanju razvoja dvojnic z znatno plimsko interakcijo. Najbolj preprosti gostotni profili so Lane-Emdenovi, ki zvezdo obravnavajo kot kroglo politropne tekočine pod vplivom lastnega gravitacijskega privlaka. Ti podajo približno ustrezne gostotne profile, vendar sedaj obstajajo tudi bolj napredni pristopi z uporabo enodimenzionalnih simulacij zvezdne strukture, ki so implementirani v knjižnici MESA. V tem magistrskem delu sta predstavljena dva pristopa k ovrednotenju vpliva radialnih profilov gostote na prenos vrtilne količine. Prvi pristop modelira zvezdo kot nabor razsežnih delcev, ki jih veže gravitacijska sila, na krajših razdaljah pa izkusijo odbojno ter disipativno silo. S tem model poskuša modelirati plimsko trenje preko mikroskopskih zakonov. Model deluje, vendar ni praktičen, ker je zahteva po številu delcev za kakovostne rezultate $\mathcal{O}\left(\left(a/R\right)^9\right)$, kjer je $a$ velika polos orbite ter $R$ radij zvezde. Drugi model ne upošteva dinamike, temveč izračuna plimsko deformacijo zvezde v mirovni legi in nato računa profile kotnega pospeška v odvisnosti od rotacije zvezde okoli osi, ki poteka skozi njeno težišče. To stori preko izračuna oblike ovojnice zvezde, ki ohranja volumen, v prilagojenem Rochevem potencialu nato pa izračuna porazdelitev mase znotraj nje. Ob predpostavki, da je gostota enaka na ekvipotencialnih ploskvah, lahko uporabimo gostotni profil za sferično zvezdo za določanje mase delcev, ki vzorčijo gostotno porazdelitev deformirane zvezde. Z višanjem resolucije modela ni mogoče doseči poljubne natančnosti kotnega pospeška, vendar proizvede zanesljive oblike profilov. Za dvojnice v tesni orbiti, kjer imata obe zvezdi enako maso, ni znatne variacije v obliki profilov. Enako velja za večje tirnice, kjer spreminjamo masno razmerje para. Ta ugotovitev podpira ustreznost analitičnih pristopov. Pri obeh modelih je uporabljen SPH (ang. $\it{smoothed \ particle \ hydrodynamics}$) formalizem za določanje mase delcev glede na želeno gostoto.

• Language: Slovenian
• Keywords: zvezdna struktura, zvezdna evolucija, dvojne zvezde, plimsko trenje, numerično modeliranje, Lane-Emdenove enačbe, MESA
• Work type: Master's thesis/paper
• Typology: 2.09 - Master's Thesis
• Organization: FMF - Faculty of Mathematics and Physics
• Year: 2024
• PID: 20.500.12556/RUL-161238
• COBISS.SI-ID: 207134211
• Publication date in RUL: 08.09.2024

Secondary language

• Language: English
• Title: Modeling of tidal friction in a binary star system

Abstract

In binary systems, the difference in the gravitational pull of one star on different parts of the other causes the appearance of tidal bulges in the near and far part of the star with respect to the location of the other star. If the orbital and rotational angular velocities differ, the bulges induce a torque that leads to the exchange of the rotational and orbital angular momentum. This inequality is always present in eccentric orbits and the angular momentum exchange perisists until the rotational and orbital angular velocities become equal. Analytical approaches rely on the internal structure parameter to describe this exchange, but it is not known how the internal structure of the star influences the exchange of angular momentum. Understanding of the dynamics of the transfer would contribute to a more complete description of binaries with notable tidal interaction. Lane-Emden's density profiles are the simplest and treat the star as a self-gravitating sphere of polytropic fluid. These profiles are adequate, but modern approaches use one-dimensional simulations of stellar structure such as those implemented in the MESA library. This thesis presents two approaches to evaluate the influence of different density radial profiles to the transfer of angular momentum. The first approach models a star as a collection of extended particles which are bound by the gravitational force while they experience repulsion and viscous damping at close range. Using these processes the model attempts to simulate tidal friction through microscopic phenomena. The model works, but it is not useful as it is not practical as the number of particles, necessary to adequately model the system, increases as $\mathcal{O}\left(\left(a/R\right)^9\right)$, where $a$ is the semi-major axis of the orbit and $R$ the stellar radius. The second model doesn't follow the dynamics but rather computes the tidal deformation of the star in the steady state and then computes profiles of the angular acceleration as a function of rotation of a star about an axis that goes through its center of mass. To do this it computes the equipotential surface of the star which preserves its volume in an adapted Roche potential and then computes the mass distribution within. Using the assumption that density is constant along equipotential surfaces and that volume is conserved it uses an arbitrary spherically symmetric density radial profile to compute particle masses which sample the density distribution of the deformed star. It is not possible to achieve arbitrarily high accuracy of the angular acceleration by increasing the resolution, but the shape of the profiles is reliable. Close binaries with equal masses do not show notable variation in the shape of the profiles. The same is true for not necessarily close binaries where the binary mass ratio is varied. This conclusion supports the adequacy of analytical approaches. Both models use SPH (smoothed particle hydrodynamics) formalism to determine particle masses according to the specified density.

• Keywords: stellar structure, stellar evolution, binary stars, tidal friction, numerical modeling, Lane-Emden equations, MESA