Astrofysikaliska Dynamiska Processer

Transcription

1 Astrofysikaliska Dynamiska Processer VT 2008 Susanne Höfner

2 Aims of this Course - understanding the role and nature of dynamical processes in astrophysical contexts and how to study such phenomena - getting familiar with the basic concepts and equations of fluid dynamics (incl. gravitation and magnetic fields) and commonly used approximations - studying examples of astrophysical objects where dynamical processes play an important role - understanding which physical and mathematical methods can be applied to specific astrophysical environments - learning how to make simple estimates for dynamical time scales and stability of astrophysical objects - understanding how the effects of dynamical processes can be measured and observed in astronomical contexts - creating a basis for more specialized astrophysics courses

3 Course Contents and Format The course consists of a series of lectures on the following topics: - introduction and basic concepts of fluid dynamics - fluid equations and gravitation, virial theorem - energy equation, fluid dynamics vs. kinetic theory - hydrostatic equilibrium and stellar structure - sound waves and shocks - blast waves, supernova remnants - spherical accretion, stellar winds and jets - fluid instabilities, convection, gravitational collapse - viscous flows, turbulence - accretions discs in astrophysics - plasmas, basics of magnetohydrodynamics together with hand-in exercises, a computer lab (discussed in extra sessions) and a short presentation by each student on a topic related to dynamical processes in astrophysics

4 Practical Matters Literature - Principles of Astrophysical Fluid Dynamics, C.J. Clarke & R.F. Carswell, Cambridge University Press, 2007 (also available as e-book) - some extra lecture notes (will be posted on-line and/or handed out) Format - detailed schedule & more information online: Course Requirements - problem sets handed in on respective due dates (see web page) - results of computer lab handed in on due date (to be determined) - short presentation on selected topic - final exam

5 Astrofysikaliska Dynamiska Processer 1.1 Introduction

6 The Cosmic Matter Cycle Interstellar medium Stars - form out of interstellar gas - show convection and pulsation - return gas to the ISM through winds and SN explosions

7 The Cosmic Matter Cycle Interstellar medium Fraction of elements heavier than H and He (metallicity) increases in the ISM with every generation of stars Stars enrich the interstellar medium with newly-produced elements heavier than H and He Dynamical processes in stars and the ISM play a crucial role for the chemical evolution of galaxies!

8 The Cosmic Matter Cycle The stellar life cycle... in real life: stars of different mass born from the same cloud evolve on different time scales stars influence the surrounding interstellar medium, triggering or prohibiting further star formation in a certain region material ejected from stars is mixed in the ISM The galactic nebula NGC 3603 (source: hubblesite.org)

9 The Local ISM and the Heliosphere Structure and dynamics of the local ISM: Local Bubble (LB): region of low-density gas, extending to about 100 pc from the sun, irregular shape. Local ISM: hot, warm and cold gas located inside the LB; shaped by SN explosions and winds of massive stars; heated by radiation from hot stars. Dynamics of clouds in the local ISM (Linsky & Redfield 2007) - Dynamics of cloud-cloud interactions (shocks?) - Dynamical structure of the local ISM: direct influence on the heliosphere

10 The Local ISM and the Heliosphere Structure and dynamics of the heliosphere: The solar system sits inside a bubble of gas (about four times wider than the orbit of Neptune) created by the solar wind, called the heliosphere. Voyager 1 (started 1977) reached the beginning of the transition zone to the ISM in 2006, measuring an unexpectedly slow velocity of the solar wind in the heliosheath. science.nasa.gov/headlines/y2006/21sep_voyager.htm Simulating the heliosheath in the kitchen sink.

11 Measuring Velocities of Astrophysical Objects vt = 4.74 µ d [km/s] v vt µ: proper motion [arcseconds/year] d: distance [parsec] vr vr/c = (λ λ0) / λ0 d λ: observed wavelength λ0: rest wavelength (lab) c: speed of light velocities: observed as - movements on the sky: tangential velocities vt - Doppler shift in light: radial velocities vr

12 Measuring Velocities of Astrophysical Objects Example: Barnard's star vt = 4.74 µ d [km/s] = 89.4 km/s µ = [arcseconds/year] d = 1.82 [parsec] v2 = vt2 + vr2 v = 143 km/s vr = c (λ λ0) / λ0 = 111 km/s λ = nm λ0 = nm c = km/s (iron line)

13 Measuring Velocities of Astrophysical Objects towards observer vwind material ejected from a star in all directions (wind, supernova remnant): superposition of different radial velocities (projected velocity components towards observer) from different parts of the envelope leads to complicated line profiles (e.g. P Cygni profiles for stellar winds)

14 Measuring Velocities of Astrophysical Objects Example: Wind of fast moving star interacting with ISM NASA's Galaxy Evolution Explorer (Galex) discovered an exceptionally long (13 light years) tail of material trailing behind the cool giant star Mira (o Ceti). The tail is only visible in ultraviolet light (top left), and does not show up in visible light (bottom left).

15 Measuring Velocities of Astrophysical Objects towards observer vwind material ejected from a star in all directions (wind, supernova remnant) fast expanding envelopes: change of size in tangential direction may be measurable superposition of different radial velocities (projected velocity components towards observer) from different parts of the envelope leads to complicated line profiles (e.g. P Cygni profiles for stellar winds)

16 Measuring Velocities of Astrophysical Objects Example: Expansion of the Crab Nebula Positive and negative photographs of the Crab Nebula taken 14 years apart (by Walter Baade) do not superimpose exactly, indicating that the gaseous filaments are still moving away from the site of the explosion.

17 Measuring Velocities of Astrophysical Objects Example: Jet produced by a young stellar object jet movie obtained with HST Patrick Hartigan (hartigan@sparky.rice.edu)

18 Astrofysikaliska Dynamiska Processer 1.2 Basic Concepts of Fluid Dynamics

19 Basic Concepts of Fluid Dynamics Definition of fluid element: A region over which we can define local variables (density, temperature, etc.) The size of this region is assumed to be such that it is (i) small enough that we can ignore systematic variations across it for any variable q we are interested in: l region << l scale q / q (ii) large enough to contain sufficient particles to ignore fluctuations due to the finite number of particles (discreteness noise): n l3region >> 1 In addition, collisional fluids must satisfy: (iii) l region >> mean free path of particles

20 Mean Free Path - Examples Mean Free Path - depends on number density and cross section - elastic scattering cross section of neutral atoms: cm2 Examples gas in density MFP size -3 [cm ] [cm] [cm] typical room HI region (ISM)

21 Basic Concepts of Fluid Dynamics - frequent collisions, small mean free path compared to the characteristic length scales of the system coherent motion of particles - definition of fluid element: mean flow velocity u (bulk velocity) - particle velocity = mean flow velocity u + random velocity component w

22 Basic Concepts of Fluid Dynamics Fluid element: coherent motion of particles

23 Basic Concepts of Fluid Dynamics Fluid element: coherent motion of particles

24 Basic Concepts of Fluid Dynamics Frame of reference: Lagrangian vs. Eulerian description DQ Q = u Q Dt t Q t