(c) Sketch the ratio of electron to gas pressure for main sequence stars versus effective temperature. [1.5]
|
|
- Thomasina Watkins
- 6 years ago
- Views:
Transcription
1 1. (a) The Saha equation may be written in the form N + n e N = C u+ u T 3/2 exp ( ) χ kt where C = m 3. Discuss its importance in the study of stellar atmospheres. Carefully explain the meaning of each term and explain how u, u + can be obtained. [2.5] (b) A B-type star with a pure hydrogen photosphere has a surface temperature of 15,K and a gas pressure of 1 N m 2. i. What is the electron density and electron pressure? [2] ii. What is the ratio of ionized to neutral hydrogen? [1] (c) Sketch the ratio of electron to gas pressure for main sequence stars versus effective temperature. [1.5] (d) If the B-type star of surface temperature 15,K instead has a pure helium photosphere, and an electron pressure of 5 N m 2, what is the ratio of electron to gas pressure in this case? You will need to use the Saha equation to calculate N(He 2+ )/N(He + ) and N(He + )/N(He). [3] Note: The ionization energies of neutral hydrogen, neutral helium, ionized helium are 13.6eV, 24.6eV and 54.4eV, respectively. The partition functions for neutral, ionized and doubly ionized helium are 1, 2 and 1. 2 CONTINUED
2 2. (a) For an absorption line, define the line depth R λ and equivalent width W λ. Sketch the line profile for an optically thin and an optically thick line. What is the line depth in the core of the thick line? Does LTE hold for the line core or wings of optically thick lines? [2] (b) Briefly discuss the following broadening mechanisms for absorption lines: i. Doppler broadening; ii. Natural broadening; iii. Pressure broadening. Be sure to include a discussion of their associated line profiles. [2.5] (c) The Mg ii (atomic mass 24) line at nm is observed in an late B star with an effetive temperature of T =12,5 K. i. The full width at half maximum (FWHM) for a thermally broadened spectral line, λ D 1/2 in nm, is given by λ D 1/2/λ = (T/µ) where T is the temperature in K, λ is the line wavelength in nm, and µ is the atomic mass in atomic mass units (amu). Calculate the Doppler broadening FWHM of this line in velocity space (m s 1 ). [1] The observed FWHM greatly exceeds the predicted Doppler width. Which other broadening mechanism might be responsible for this observed FWHM? [.5] Would your answers to λ D 1/2 and the alternative broadening mechanism be the same, if instead we were considering the Hβ at 486.1nm in the B star? [1] (d) What is the curve of growth, and how can it be used to determine elemental abundances in stellar photospheres? Explain the abundance dependence of the three distinct parts of the curve of growth. Show graphically examples of line profiles in each of these domains. [3] 3 TURN OVER
3 3. (a) Describe the physical properties of Local Thermodynamic Equilibrium (LTE). Give two astrophysical examples where it is necessary to consider non-lte. [1.5] (b) Energy levels of hydrogen lie 13.6eV/n 2 below the ionization limit. Calculate the threshold energies and wavelengths of the Paschen and Balmer continua. [1.5] Compare the relative number of H atoms and H ions that contribute to the continuous opacity in the photosphere of a star with T =7K on both sides of the Balmer jump. Assume LTE, an electron pressure in the stellar photosphere of 5 N m 2, and identical bound-free cross-sections for atomic hydrogen and H for simplicity. Which absorption or scattering processes dominate at wavelengths shortward and longward of the Balmer jump? [3.5] Sketch the absorption coefficient versus wavelength in the vicinity of the Balmer jump, together with the emergent continuum flux. Is the strength of the Balmer jump sensitive to stellar temperatures and/or electron densities in cool stars? Is your answer the same for hot stars? [2] (c) What is the meaning of a grey atmosphere? Identify one form of continuous opacity in stellar photospheres which is grey. For which types of star is this the dominant opacity source? [1.5] Note: The ionization energy for the negative hydrogen ion is.75ev and neutral hydrogen is 13.6eV. Saha s equation is: log N + N = log u+ u log T 2 T χ log P e CONTINUED
4 4. (a) Define the terms effective temperature and surface gravity. [1] (b) The transfer equation for a plane-parallel stellar atmosphere is cos θ di λ dτ λ = I λ S λ Define each term in this equation, and derive the equation for the surface intensity I(, θ) = If we adopt a linear source function, S λ e τ λ sec θ d(τ λ sec θ) [2.5] S λ (τ λ ) = a λ + b λ τ λ show that I(, θ) = S λ (τ λ = cos θ) You may use the standard integral [1.5] u n e u du = n! Using the above relationship, or otherwise, explain the concept of limb darkening in stellar atmospheres. [1.5] (c) Explain how limb darkening observations can be used to obtain the optical depth dependence of the temperature of the photosphere. How important is this information with regard to identifying the source of continuous opacity in stars? [2] Give two methods used to derive limb darkening information for stars other than the Sun? [1.5] 5 TURN OVER
5 5. (a) Write down the formal definitions of the mean intensity and flux. Why can we only measure flux rather than intensity for most stars? Does either obey the inverse square law? [1.5] If there is no azimuthal dependence on I λ, the surface flux F λ () is given by 1 F λ () = 2π I λ (, θ) cos θd(cos θ). Assuming a linear source function, S λ (τ λ ) = a λ + b λ τ λ, we obtain I λ (, θ) = a λ + b λ cos θ. Hence, derive the Eddington-Barbier relation, and explain its significance. [2] (b) For a grey atmosphere in LTE, using the Eddington approximation, the source function becomes S τ = 3 4π (τ + 3 )F () 4 Derive the surface temperature in terms of the effective temperature. [2.5] (c) The radiation pressure, P ν, at frequency ν can be expressed as P ν = 1 I ν cos 2 θdω c Use the Eddington approximation to show that for a grey atmosphere in LTE the total radiation pressure, P R, is equal to P R = 4σ 3c T 4 Briefly discuss how radiation pressure can drive winds in earlytype stars. [2.5] (d) The Eddington parameter, Γ e, can be written as Γ e = q L/L M/M where q is the number of free electrons per atomic mass unit. Explain the meaning of Γ e and derive the Eddington luminosity for a completely ionized hydrogen atmosphere of mass 1M. [1.5] END OF QUESTION PAPER 6
Opacity and Optical Depth
Opacity and Optical Depth Absorption dominated intensity change can be written as di λ = κ λ ρ I λ ds with κ λ the absorption coefficient, or opacity The initial intensity I λ 0 of a light beam will be
More information6. Stellar spectra. excitation and ionization, Saha s equation stellar spectral classification Balmer jump, H -
6. Stellar spectra excitation and ionization, Saha s equation stellar spectral classification Balmer jump, H - 1 Occupation numbers: LTE case Absorption coefficient: κ ν = n i σ ν$ à calculation of occupation
More information2. Stellar atmospheres: Structure
2. Stellar atmospheres: Structure 2.1. Assumptions Plane-parallel geometry Hydrostatic equilibrium, i.e. o no large-scale accelerations comparable to surface gravity o no dynamically significant mass loss
More information6. Stellar spectra. excitation and ionization, Saha s equation stellar spectral classification Balmer jump, H -
6. Stellar spectra excitation and ionization, Saha s equation stellar spectral classification Balmer jump, H - 1 Occupation numbers: LTE case Absorption coefficient: = n i calculation of occupation numbers
More information6. Stellar spectra. excitation and ionization, Saha s equation stellar spectral classification Balmer jump, H -
6. Stellar spectra excitation and ionization, Saha s equation stellar spectral classification Balmer jump, H - 1 Occupation numbers: LTE case Absorption coefficient: = n i calculation of occupation numbers
More informationAstronomy 421. Lecture 14: Stellar Atmospheres III
Astronomy 421 Lecture 14: Stellar Atmospheres III 1 Lecture 14 - Key concepts: Spectral line widths and shapes Curve of growth 2 There exists a stronger jump, the Lyman limit, occurring at the wavelength
More informationSISD Training Lectures in Spectroscopy
SISD Training Lectures in Spectroscopy Anatomy of a Spectrum Visual Spectrum of the Sun Blue Spectrum of the Sun Morphological Features in Spectra λ 2 Line Flux = Fλ dλ λ1 (Units: erg s -1 cm -2 ) Continuum
More informationStars AS4023: Stellar Atmospheres (13) Stellar Structure & Interiors (11)
Stars AS4023: Stellar Atmospheres (13) Stellar Structure & Interiors (11) Kenneth Wood, Room 316 kw25@st-andrews.ac.uk http://www-star.st-and.ac.uk/~kw25 What is a Stellar Atmosphere? Transition from dense
More informationTHE OBSERVATION AND ANALYSIS OF STELLAR PHOTOSPHERES
THE OBSERVATION AND ANALYSIS OF STELLAR PHOTOSPHERES DAVID F. GRAY University of Western Ontario, London, Ontario, Canada CAMBRIDGE UNIVERSITY PRESS Contents Preface to the first edition Preface to the
More informationThe Sun as a Typical Star. Stellar Spectra. Stellar Spectroscopy
Stellar Spectroscopy Resolved observa7ons of the sun allow us to look at varia7ons across the surface, but we can only look at (almost all) other stars in integrated light. In the visible, we see the photosphere
More informationLimb Darkening. Limb Darkening. Limb Darkening. Limb Darkening. Empirical Limb Darkening. Betelgeuse. At centre see hotter gas than at edges
Limb Darkening Sun Betelgeuse Limb Darkening Stars are both redder and dimmer at the edges Sun Limb Darkening Betelgeuse Limb Darkening Can also be understood in terms of temperature within the solar photosphere.
More informationOptical Depth & Radiative transfer
University of Naples Federico II, Academic Year 2011-2012 Istituzioni di Astrofisica, read by prof. Massimo Capaccioli Lecture 8 Optical Depth & Radiative transfer Learning outcomes The student will :
More informationLecture 6: Continuum Opacity and Stellar Atmospheres
Lecture 6: Continuum Opacity and Stellar Atmospheres To make progress in modeling and understanding stellar atmospheres beyond the gray atmosphere, it is necessary to consider the real interactions between
More informationEnergy transport: convection
Outline Introduction: Modern astronomy and the power of quantitative spectroscopy Basic assumptions for classic stellar atmospheres: geometry, hydrostatic equilibrium, conservation of momentum-mass-energy,
More informationSpectral Line Shapes. Line Contributions
Spectral Line Shapes Line Contributions The spectral line is termed optically thin because there is no wavelength at which the radiant flux has been completely blocked. The opacity of the stellar material
More informationLecture 4: Absorption and emission lines
Lecture 4: Absorption and emission lines Senior Astrophysics 2018-03-13 Senior Astrophysics () Lecture 4: Absorption and emission lines 2018-03-13 1 / 35 Outline 1 Absorption and emission line spectra
More informationLecture 2 Solutions to the Transport Equation
Lecture 2 Solutions to the Transport Equation Equation along a ray I In general we can solve the static transfer equation along a ray in some particular direction. Since photons move in straight lines
More informationShort/Simple Definitions:
Eric Joseph Bubar Stellar Atmosphere/Interiors Portfolio CHAPTER : CURVES OF GROWTH Short/Simple Definitions: Curve of Growth: Plot of equivalent widths versus number of absorbing atoms that created that
More informationStellar Astrophysics: The Classification of Stellar Spectra
Stellar Astrophysics: The Classification of Stellar Spectra Temperature and Color The intensity of light emitted by three hypothetical stars is plotted against wavelength The range of visible wavelengths
More informationAssignment 4 Solutions [Revision : 1.4]
Assignment 4 Solutions [Revision : 1.4] Q9.7 We typically see a optical distance τ 2/3 through an opaque medium. Using τ = κρs, for constant κ = 0.03 m 2 kg 1 and ρ = 1.2 kgm 3, gives a physical distance
More informationSIMPLE RADIATIVE TRANSFER
ASTR 511/O Connell Lec 4 1 SIMPLE RADIATIVE TRANSFER The theory of radiative transfer provides the means for determining the emergent EM spectrum of a cosmic source and also for describing the effects
More informationObservational Appearance of Black Hole Wind Effect of Electron Scattering
Observational Appearance of Black Hole Wind Effect of Electron Scattering Kazuyuki OGURA Astronomical Institute Osaka Kyoiku Univ. 29 Jun 2013 Meeting of BH Horizon Project @Nagoya Univ. Contents Introduction
More informationThe Classification of Stellar Spectra Chapter 8
The Classification of Stellar Spectra Chapter 8 Star Clusters in the Large Magellanic Cloud http://www.seds.org/hst/ NGC850.html The Classification of Stellar Spectra Classification scheme developed before
More informationElectromagnetic Spectra. AST443, Lecture 13 Stanimir Metchev
Electromagnetic Spectra AST443, Lecture 13 Stanimir Metchev Administrative Homework 2: problem 5.4 extension: until Mon, Nov 2 Reading: Bradt, chapter 11 Howell, chapter 6 Tenagra data: see bottom of Assignments
More informationChapter 3C. 3-4C. Ionization
Chapter 3C The excitation ratio N B /N A increases as the excitation potential get smaller. Also, as T increases, the higher energy levels become more populated. One should see that as T goes to infinity,
More informationLecture 2: Formation of a Stellar Spectrum
Abundances and Kinematics from High- Resolution Spectroscopic Surveys Lecture 2: Formation of a Stellar Spectrum Eline Tolstoy Kapteyn Astronomical Institute, University of Groningen I have a spectrum:
More informationModel Atmospheres. Model Atmosphere Assumptions
Model Atmospheres Problem: Construct a numerical model of the atmosphere to estimate (a) Variation of physical variables (T, P) with depth (b) Emergent spectrum in continuum and lines Compare calculated
More informationLecture 3: Emission and absorption
Lecture 3: Emission and absorption Senior Astrophysics 2017-03-10 Senior Astrophysics Lecture 3: Emission and absorption 2017-03-10 1 / 35 Outline 1 Optical depth 2 Sources of radiation 3 Blackbody radiation
More informationStellar atmospheres: an overview
Stellar atmospheres: an overview Core M = 2x10 33 g R = 7x10 10 cm 50 M o 20 R o L = 4x10 33 erg/s 10 6 L o 10 4 (PN) 10 6 (HII) 10 12 (QSO) L o Photosphere Envelope Chromosphere/Corona R = 200 km ~ 3x10
More informationAtomic Spectral Lines
Han Uitenbroek National Solar Observatory/Sacramento Peak Sunspot, USA Hale COLLAGE, Boulder, Feb 18, 216 Today s Lecture How do we get absorption and emission lines in the spectrum? Atomic line- and continuum
More informationM.Phys., M.Math.Phys., M.Sc. MTP Radiative Processes in Astrophysics and High-Energy Astrophysics
M.Phys., M.Math.Phys., M.Sc. MTP Radiative Processes in Astrophysics and High-Energy Astrophysics Professor Garret Cotter garret.cotter@physics.ox.ac.uk Office 756 in the DWB & Exeter College Radiative
More informationA Stellar Spectra 3. Stars shine at night (during the day too!). A star is a self-luminous sphere of gas. Stars are held together by gravity.
Stellar Spectra Relativity and Astrophysics Lecture 12 Terry Herter Outline What is a star? Stellar Spectra Kirchhoff s Laws Spectral Classification Spectral Types: O B A F G K M L T Stellar Photometry
More informationSubstellar Atmospheres II. Dust, Clouds, Meteorology. PHY 688, Lecture 19 Mar 11, 2009
Substellar Atmospheres II. Dust, Clouds, Meteorology PHY 688, Lecture 19 Mar 11, 2009 Outline Review of previous lecture substellar atmospheres: opacity, LTE, chemical species, metallicity Dust, Clouds,
More informationEquilibrium Properties of Matter and Radiation
Equilibrium Properties of Matter and Radiation Temperature What is it? A measure of internal energy in a system. Measure from (1) velocities of atoms/molecules () population of excited/ionized states (3)
More informationThe Stellar Opacity. F ν = D U = 1 3 vl n = 1 3. and that, when integrated over all energies,
The Stellar Opacity The mean absorption coefficient, κ, is not a constant; it is dependent on frequency, and is therefore frequently written as κ ν. Inside a star, several different sources of opacity
More informationTRANSFER OF RADIATION
TRANSFER OF RADIATION Under LTE Local Thermodynamic Equilibrium) condition radiation has a Planck black body) distribution. Radiation energy density is given as U r,ν = 8πh c 3 ν 3, LTE), tr.1) e hν/kt
More informationSpectroscopy Lecture 2
Spectroscopy Lecture 2 I. Atomic excitation and ionization II. Radiation Terms III. Absorption and emission coefficients IV. Einstein coefficients V. Black Body radiation I. Atomic excitation and ionization
More informationFIA0221: Taller de Astronomía II. Lecture 14 Spectral Classification of Stars
FIA0221: Taller de Astronomía II Lecture 14 Spectral Classification of Stars Spectral types along the stellar CMD. Oh, Be A Fine Girl Kiss Me! Classification of Stellar spectra: The MK system: strong He+
More informationThe Sun. Basic Properties. Radius: Mass: Luminosity: Effective Temperature:
The Sun Basic Properties Radius: Mass: 5 R Sun = 6.96 km 9 R M Sun 5 30 = 1.99 kg 3.33 M ρ Sun = 1.41g cm 3 Luminosity: L Sun = 3.86 26 W Effective Temperature: L Sun 2 4 = 4πRSunσTe Te 5770 K The Sun
More informationWINDS OF HOT MASSIVE STARS III Lecture: Quantitative spectroscopy of winds of hot massive stars
WINDS OF HOT MASSIVE STARS III Lecture: Quantitative spectroscopy of winds of hot massive stars 1 Brankica Šurlan 1 Astronomical Institute Ondřejov Selected Topics in Astrophysics Faculty of Mathematics
More informationCHAPTER 22. Astrophysical Gases
CHAPTER 22 Astrophysical Gases Most of the baryonic matter in the Universe is in a gaseous state, made up of 75% Hydrogen (H), 25% Helium (He) and only small amounts of other elements (called metals ).
More informationASTRONOMY QUALIFYING EXAM August Possibly Useful Quantities
L = 3.9 x 10 33 erg s 1 M = 2 x 10 33 g M bol = 4.74 R = 7 x 10 10 cm 1 A.U. = 1.5 x 10 13 cm 1 pc = 3.26 l.y. = 3.1 x 10 18 cm a = 7.56 x 10 15 erg cm 3 K 4 c= 3.0 x 10 10 cm s 1 σ = ac/4 = 5.7 x 10 5
More information3. Stellar Atmospheres: Opacities
3. Stellar Atmospheres: Opacities 3.1. Continuum opacity The removal of energy from a beam of photons as it passes through matter is governed by o line absorption (bound-bound) o photoelectric absorption
More informationInterstellar Astrophysics Summary notes: Part 2
Interstellar Astrophysics Summary notes: Part 2 Dr. Paul M. Woods The main reference source for this section of the course is Chapter 5 in the Dyson and Williams (The Physics of the Interstellar Medium)
More informationFundamental Stellar Parameters
Fundamental Stellar Parameters Radiative Transfer Specific Intensity, Radiative Flux and Stellar Luminosity Observed Flux, Emission and Absorption of Radiation Radiative Transfer Equation, Solution and
More information23 Astrophysics 23.5 Ionization of the Interstellar Gas near a Star
23 Astrophysics 23.5 Ionization of the Interstellar Gas near a Star (8 units) No knowledge of Astrophysics is assumed or required: all relevant equations are defined and explained in the project itself.
More informationStellar Spectra ASTR 2120 Sarazin. Solar Spectrum
Stellar Spectra ASTR 2120 Sarazin Solar Spectrum Solar Prominence Sep. 14, 1999 Solar Activity Due to rotation, convection, and magnetic field (Section 7.2 review) Charged Particles in Magnetic Fields
More informationAtomic Physics 3 ASTR 2110 Sarazin
Atomic Physics 3 ASTR 2110 Sarazin Homework #5 Due Wednesday, October 4 due to fall break Test #1 Monday, October 9, 11-11:50 am Ruffner G006 (classroom) You may not consult the text, your notes, or any
More informationProperties of Stars (continued) Some Properties of Stars. What is brightness?
Properties of Stars (continued) Some Properties of Stars Luminosity Temperature of the star s surface Mass Physical size 2 Chemical makeup 3 What is brightness? Apparent brightness is the energy flux (watts/m
More informationAy Fall 2004 Lecture 6 (given by Tony Travouillon)
Ay 122 - Fall 2004 Lecture 6 (given by Tony Travouillon) Stellar atmospheres, classification of stellar spectra (Many slides c/o Phil Armitage) Formation of spectral lines: 1.excitation Two key questions:
More informationStellar Atmospheres: Basic Processes and Equations
Stellar Atmospheres: Basic Processes and Equations Giovanni Catanzaro Abstract The content of this chapter is a very quick summary of key concepts that concern the interaction between photons created in
More information7. Non-LTE basic concepts
7. Non-LTE basic concepts LTE vs NLTE occupation numbers rate equation transition probabilities: collisional and radiative examples: hot stars, A supergiants 10/13/2003 Spring 2016 LTE LTE vs NLTE each
More informationInterstellar Medium Physics
Physics of gas in galaxies. Two main parts: atomic processes & hydrodynamic processes. Atomic processes deal mainly with radiation Hydrodynamics is large scale dynamics of gas. Start small Radiative transfer
More informationAstronomy 421. Lecture 13: Stellar Atmospheres II. Skip Sec 9.4 and radiation pressure gradient part of 9.3
Astronomy 421 Lecture 13: Stellar Atmospheres II Skip Sec 9.4 and radiation pressure gradient part of 9.3 1 Announcements: Homework #4 is due Oct 3 Outline is due October 8 See example on the class web
More informationStellar Astrophysics: Heat Transfer 1. Heat Transfer
Stellar Astrophysics: Heat Transfer 1 Heat Transfer Update date: September 3, 21 We discuss various energy transfer mechanisms in stars: radiative, conductive, and convective. 1 Radiative Transfer 1.1
More informationASTROPHYSICS. K D Abhyankar. Universities Press S T A R S A ND G A L A X I E S
ASTROPHYSICS S T A R S A ND G A L A X I E S K D Abhyankar Universities Press Contents Foreword vii Preface ix 1 Introduction 1 1.1 ' Astronomy and astrophysics 1 1.2 Importance of astronomy 2 1.3 Methods
More informationTheory of optically thin emission line spectroscopy
Theory of optically thin emission line spectroscopy 1 Important definitions In general the spectrum of a source consists of a continuum and several line components. Processes which give raise to the continuous
More informationOutline. Today we will learn what is thermal radiation
Thermal Radiation & Outline Today we will learn what is thermal radiation Laws Laws of of themodynamics themodynamics Radiative Radiative Diffusion Diffusion Equation Equation Thermal Thermal Equilibrium
More informationThe Formation of Spectral Lines. I. Line Absorption Coefficient II. Line Transfer Equation
The Formation of Spectral Lines I. Line Absorption Coefficient II. Line Transfer Equation Line Absorption Coefficient Main processes 1. Natural Atomic Absorption 2. Pressure Broadening 3. Thermal Doppler
More informationt KH = GM2 RL Pressure Supported Core for a Massive Star Consider a dense core supported by pressure. This core must satisfy the equation:
1 The Kelvin-Helmholtz Time The Kelvin-Helmhotz time, or t KH, is simply the cooling time for a pressure supported (i.e. in hydrostatic equilibrium), optically thick object. In other words, a pre-main
More informationPHAS3135 The Physics of Stars
PHAS3135 The Physics of Stars Exam 2013 (Zane/Howarth) Answer ALL SIX questions from Section A, and ANY TWO questions from Section B The numbers in square brackets in the right-hand margin indicate the
More informationProblem set: solar irradiance and solar wind
Problem set: solar irradiance and solar wind Karel Schrijver July 3, 203 Stratification of a static atmosphere within a force-free magnetic field Problem: Write down the general MHD force-balance equation
More information2 The solar atmosphere
1 The solar atmosphere 1.1 Introduction The solar atmosphere may be broadly defined as that part of the Sun extending outwards from a level known as the photosphere where energy generated at the Sun s
More informationTHIRD-YEAR ASTROPHYSICS
THIRD-YEAR ASTROPHYSICS Problem Set: Stellar Structure and Evolution (Dr Ph Podsiadlowski, Michaelmas Term 2006) 1 Measuring Stellar Parameters Sirius is a visual binary with a period of 4994 yr Its measured
More information6. Interstellar Medium. Emission nebulae are diffuse patches of emission surrounding hot O and
6-1 6. Interstellar Medium 6.1 Nebulae Emission nebulae are diffuse patches of emission surrounding hot O and early B-type stars. Gas is ionized and heated by radiation from the parent stars. In size,
More informationStellar Astrophysics Chapter 3: Heat Transfer
Stellar Astrophysics Chapter 3: Heat Transfer Q. Daniel Wang Astronomy Department University of Massachusetts While we have crudely obtained the Fick s law in Chapter 1, we will here derive it more precisely,
More informationRadiative Transfer Plane-Parallel Frequency-Dependent
4 Radiative Transfer Plane-Parallel Frequency-Dependent variables I ν J ν H ν K ν in astronomy 4. Basic Equations After Fukue, J. 2, PASJ, 63, in press We here assume the followings: i) The disk is steady
More informationASTRONOMY QUALIFYING EXAM August 2014
ASTRONOMY QUALIFYING EXAM August 2014 L = 3.9 10 33 erg s 1 M = 2 10 33 g M bol = 4.74 R = 7 10 10 cm 1 AU = 1.5 10 13 cm 1 pc = 3.26 Ly. = 3.1 10 18 cm a = 7.56 10 15 erg cm 3 K 4 c = 3 10 10 cm s 1 σ
More informationPHYS 231 Lecture Notes Week 3
PHYS 231 Lecture Notes Week 3 Reading from Maoz (2 nd edition): Chapter 2, Sec. 3.1, 3.2 A lot of the material presented in class this week is well covered in Maoz, and we simply reference the book, with
More informationSection 11.5 and Problem Radiative Transfer. from. Astronomy Methods A Physical Approach to Astronomical Observations Pages , 377
Section 11.5 and Problem 11.51 Radiative Transfer from Astronomy Methods A Physical Approach to Astronomical Observations Pages 365-375, 377 Cambridge University Press 24 by Hale Bradt Hale Bradt 24 11.5
More informationInfluence of Mass Flows on the Energy Balance and Structure of the Solar Transition Region
**TITLE** ASP Conference Series, Vol. **VOLUME***, **YEAR OF PUBLICATION** **NAMES OF EDITORS** Influence of Mass Flows on the Energy Balance and Structure of the Solar Transition Region E. H. Avrett and
More informationToday. Kirchoff s Laws. Emission and Absorption. Stellar Spectra & Composition. Doppler Effect & Motion. Extrasolar Planets
Today Kirchoff s Laws Emission and Absorption Stellar Spectra & Composition Doppler Effect & Motion Extrasolar Planets Three basic types of spectra Continuous Spectrum Intensity Emission Line Spectrum
More informationSources of radiation
Sources of radiation Most important type of radiation is blackbody radiation. This is radiation that is in thermal equilibrium with matter at some temperature T. Lab source of blackbody radiation: hot
More informationRadiative transfer equation in spherically symmetric NLTE model stellar atmospheres
Radiative transfer equation in spherically symmetric NLTE model stellar atmospheres Jiří Kubát Astronomický ústav AV ČR Ondřejov Zářivě (magneto)hydrodynamický seminář Ondřejov 20.03.2008 p. Outline 1.
More informationVII. Hydrodynamic theory of stellar winds
VII. Hydrodynamic theory of stellar winds observations winds exist everywhere in the HRD hydrodynamic theory needed to describe stellar atmospheres with winds Unified Model Atmospheres: - based on the
More informationSpectral Line Intensities - Boltzmann, Saha Eqs.
Spectral Line Intensities - Boltzmann, Saha Eqs. Absorption in a line depends on: - number of absorbers along the line-of-sight, and -their cross section(s). Absorp. n a σl, where n a is the number of
More informationProblem Set 4 is due Thursday. Problem Set 5 will be out today or tomorrow. Launch Latest from MASCOT
1 Problem Set 4 is due Thursday. Problem Set 5 will be out today or tomorrow. Launch Latest from MASCOT 3 Continuous Spectra: Thermal Radiation The equations below quantitatively summarize the light-emitting
More informationExercise: A Toy Model for Dust-driven Winds
Astrofysikalisk dynamik, VT 00 Exercise: A Toy Model for Dust-driven Winds Susanne Höfner Department of Physics and Astronomy, Uppsala University Cool luminous giants stars, in particular pulsating AGB
More informationAstronomy II (ASTR-1020) Homework 2
Astronomy II (ASTR-1020) Homework 2 Due: 10 February 2009 The answers of this multiple choice homework are to be indicated on a Scantron sheet (either Form # 822 N-E or Ref # ABF-882) which you are to
More informationSubstellar Atmospheres. PHY 688, Lecture 18 Mar 9, 2009
Substellar Atmospheres PHY 688, Lecture 18 Mar 9, 2009 Outline Review of previous lecture the Kepler mission launched successfully results P < 1 month planets by September 09 giant planet interiors comparison
More informationEnvironment of the Radiation Field ...
Copyright (2003) Geroge W. Collins, II 11 Environment of the Radiation Field... Thus far, we have said little or nothing about the gas through which the radiation is flowing. This constitutes the second
More informationDiffuse Interstellar Medium
Diffuse Interstellar Medium Basics, velocity widths H I 21-cm radiation (emission) Interstellar absorption lines Radiative transfer Resolved Lines, column densities Unresolved lines, curve of growth Abundances,
More informationASTR-1020: Astronomy II Course Lecture Notes Section III
ASTR-1020: Astronomy II Course Lecture Notes Section III Dr. Donald G. Luttermoser East Tennessee State University Edition 4.0 Abstract These class notes are designed for use of the instructor and students
More informationASTRONOMY AND ASTROPHYSICS Theoretical X-ray spectra of hot H-rich white dwarfs. Impact of new partition functions of iron, Fe V through Fe VII
Astron. Astrophys. 343, 531 535 (1999) ASTRONOMY AND ASTROPHYSICS Theoretical X-ray spectra of hot H-rich white dwarfs. Impact of new partition functions of iron, Fe V through Fe VII J. Madej 1, J. Halenka
More informationExample: model a star using a two layer model: Radiation starts from the inner layer as blackbody radiation at temperature T in. T out.
Next, consider an optically thick source: Already shown that in the interior, radiation will be described by the Planck function. Radiation escaping from the source will be modified because the temperature
More informationCharacteristic temperatures
Characteristic temperatures Effective temperature Most sources are only roughly blackbodies (if that). So we integrate the flux over frequency and define: F = I cosθ dω d = σ T e 4 i.e. a source of effective
More informationPhysics 160: Stellar Astrophysics. Midterm Exam. 27 October 2011 INSTRUCTIONS READ ME!
Physics 160: Stellar Astrophysics 27 October 2011 Name: S O L U T I O N S Student ID #: INSTRUCTIONS READ ME! 1. There are 4 questions on the exam; complete at least 3 of them. 2. You have 80 minutes to
More informationReview of Star Intro. PHYSICS 162 Lecture 7a 1
Review of Star Intro Parallax - geometric method of determining star distance Absolute and apparent luminosity. Temperature Spectrum: What characterizes the star s surface Is related to its temperature
More informationOpacity. requirement (aim): radiative equilibrium: near surface: Opacity
(Gray) Diffusion approximation to radiative transport: (assumes isotropy valid only in the deep stellar interior) - opacity is a function of frequency (wave length ). - aim: to reduce the (rather complex)
More informationOverview of Astronomical Concepts III. Stellar Atmospheres; Spectroscopy. PHY 688, Lecture 5 Stanimir Metchev
Overview of Astronomical Concepts III. Stellar Atmospheres; Spectroscopy PHY 688, Lecture 5 Stanimir Metchev Outline Review of previous lecture Stellar atmospheres spectral lines line profiles; broadening
More informationReview: Properties of a wave
Radiation travels as waves. Waves carry information and energy. Review: Properties of a wave wavelength (λ) crest amplitude (A) trough velocity (v) λ is a distance, so its units are m, cm, or mm, etc.
More informationLines of Hydrogen. Most prominent lines in many astronomical objects: Balmer lines of hydrogen
The Family of Stars Lines of Hydrogen Most prominent lines in many astronomical objects: Balmer lines of hydrogen The Balmer Thermometer Balmer line strength is sensitive to temperature: Most hydrogen
More informationProblem Set 2 Solutions
Problem Set 2 Solutions Problem 1: A A hot blackbody will emit more photons per unit time per unit surface area than a cold blackbody. It does not, however, necessarily need to have a higher luminosity,
More information7. Non-LTE basic concepts
7. Non-LTE basic concepts LTE vs NLTE occupation numbers rate equation transition probabilities: collisional and radiative examples: hot stars, A supergiants 1 Equilibrium: LTE vs NLTE LTE each volume
More informationV. Stars.
V. Stars http://sgoodwin.staff.shef.ac.uk/phy111.html 0. The local HR diagram We saw that locally we can make an HR diagram of absolute luminosity against temperature. We find a main sequence, giants and
More informationLecture Notes: Basic Equations
Basic Equations Lecture Notes: INTRODUCTION TO NON-LTE RADIATIVE TRANSFER AND ATMOSPHERIC MODELING Eugene H. Avrett Harvard-Smithsonian Center for Astrophysics July 2008 The specific intensity of radiation
More informationScales of solar convection
Solar convection In addition to radiation, convection is the main form of energy transport in solar interior and lower atmosphere. Convection dominates just below the solar surface and produces most structures
More informationPlasma Spectroscopy Inferences from Line Emission
Plasma Spectroscopy Inferences from Line Emission Ø From line λ, can determine element, ionization state, and energy levels involved Ø From line shape, can determine bulk and thermal velocity and often
More information12. Physical Parameters from Stellar Spectra. Fundamental effective temperature calibrations Surface gravity indicators Chemical abundances
12. Physical Parameters from Stellar Spectra Fundamental effective temperature calibrations Surface gravity indicators Chemical abundances 1 Fundamental Properties of Stars Temperature (T) Radius (R) Chemical
More information11.1 Local Thermodynamic Equilibrium. 1. the electron and ion velocity distributions are Maxwellian,
Section 11 LTE Basic treatments of stellar atmospheres adopt, as a starting point, the assumptions of Local Thermodynamic Equilibrium (LTE), and hydrostatic equilibrium. The former deals with the microscopic
More information