Manuel Gonzalez (IRAM) September 14 th Radiative transfer basics
|
|
- Beverly Sharp
- 5 years ago
- Views:
Transcription
1 Manuel Gonzalez (IRAM) September 14 th 2013 Radiative transfer basics
2 What is radiation? Introduction
3 Introduction In Astrophysics radiation from the sources can give us very important information: - Spatial distribution of the gas -Temperature and density of the gas - Velocity structure - Presence of certain physical or chemical processes -Mass and column density
4 Introduction Two kind of processes: - Continuum: dust, thermic sources - Lines: atoms, ions and molecules
5 Introduction Three kind of interactions with matter: - Emission - Absorption - Scattering
6 Introduction
7 The radiative transfer equation di ν(x, ν,θ)= κ(x, ν) I νds+ j(x, ν,θ)ds destruction terms creation terms
8 The radiative transfer equation di ν(x, ν,θ)= κ(x, ν)iν ds+ j(x, ν,θ)ds destruction terms creation terms I ν(x, ν,θ): Specific intensity. Units (erg s -1 cm -2 Hz -1 sr -1 ) de=i ν( x,ê) nê da d Ω d νdt E is the Energy received!!
9 The radiative transfer equation The radiative transfer equation di ν(x, ν,θ)= κ(x, ν)iν ds+ j(x, ν,θ)ds destruction terms creation terms I ν(x, ν,θ): Specific intensity. Units (erg s -1 cm -2 Hz -1 sr -1 ) Specific intensity is constant along rays, as long as there is no absorption and emission of matter between emitter and receiver
10 The radiative transfer equation di ν(x, ν,θ)= κ(x, ν) I νds+ j(x, ν,θ)ds destruction terms creation terms κ(x, ν): Absorption coefficient. Units (cm -1 ) j(x, ν,θ): Emission coefficient. Units (erg s -1 cm -3 Hz -1 sr -1 )
11 Let's solve this equation...
12 Solution of the equation di ν(x, ν,θ)= κ(x, ν) I ν ds+ j(x, ν,θ)ds
13 Solution of the equation di ν(x, ν,θ)= κ(x, ν) I ν ds+ j(x, ν,θ)ds ds=dx/cos(θ)
14 Solution of the equation di ν(x, ν,θ)= κ(x, ν) I ν ds+ j(x, ν,θ)ds ds=dx/cos(θ) I ν(x, ν,θ)= κ(x, ν) I ν dx /cos(θ)+ j(x, ν,θ)dx /cos(θ
15 Solution of the equation di ν(x, ν,θ)= κ(x, ν) I ν ds+ j(x, ν,θ)ds ds=dx/cos(θ) I ν(x, ν,θ)= κ(x, ν) I ν dx /cos(θ)+ j(x, ν,θ)dx /cos(θ cos(θ)di ν(x, ν,θ)= κ(x, ν) I ν dx+ j(x, ν,θ)dx
16 Solution of the equation di ν(x, ν,θ)= κ(x, ν) I ν ds+ j(x, ν,θ)ds ds=dx/cos(θ) I ν(x, ν,θ)= κ(x, ν) I ν dx /cos(θ)+ j(x, ν,θ)dx /cos(θ cos(θ)di ν(x, ν,θ)= κ(x, ν) I ν dx+ j(x, ν,θ)dx cos(θ) di ν(x, ν,θ) κ(x, ν)dx = I ν+ j(x, ν,θ)dx κ(x, ν)dx
17 Solution of the equation cos(θ) di ν(x, ν,θ) κ(x, ν)dx = I ν+ j(x, ν,θ) κ(x, ν)
18 Solution of the equation cos(θ) di ν(x, ν,θ) κ(x, ν)dx = I ν+ j(x, ν,θ) κ(x, ν) cos(θ)=μ
19 Solution of the equation cos(θ) di ν(x, ν,θ) κ(x, ν)dx = I ν+ j(x, ν,θ) κ(x, ν) cos(θ)=μ κ(x, ν)dx=d τ Optical depth
20 Solution of the equation cos(θ) di ν(x, ν,θ) κ(x, ν)dx = I ν+ j(x, ν,θ) κ(x, ν) cos(θ)=μ κ(x, ν)dx=d τ Optical depth j(x, ν,θ) κ(x, ν) =S ν Source function
21 Solution of the equation cos(θ) di ν(x, ν,θ) κ(x, ν)dx = I ν+ j(x, ν,θ) κ(x, ν) cos(θ)=μ κ(x, ν)dx=d τ j(x, ν,θ) κ(x, ν) =S ν μ di ν d τ = I ν+ Sν
22 Radiative transfer equation μ di ν d τ = I ν+ Sν
23 Formal solution μ di ν d τ = I ν+ Sν (for the case µ = 1) 1 st step: Multiply everywhere by e τ ν di ν d τ eτν = I νe τ ν + Sν e τν
24 Formal solution μ di ν d τ = I ν+ Sν Formal solution: 1 st step: Multiply everywhere by e τ ν di ν d τ eτν = I νe τ ν + Sν e τν 2 nd step: We pass to the left the term I ν e τ ν di ν d τ eτν + I ν e τν =S νe τν
25 Formal solution di ν d τ eτν + I ν e τν =Sν e τν a '( x)b( x)+ a( x)b' ( x)=(ab)'
26 Formal solution di ν d τ eτν + I ν e τν =Sν e τν a '( x)b( x)+ a( x)b' ( x)=(ab)' 3 rd step: we change the left side by its value di ν + I νe d τ eτν τν = d( I νeτ ν ) d τν
27 Formal solution di ν d τ eτν + I ν e τν =Sν e τν a '( x)b( x)+ a( x)b' ( x)=(ab)' 3 rd step: we change the left side by its value di ν + I νe d τ eτν τν = d( I νeτ ν ) d τ d (I νe τ ν ) d τ =S νe τ ν
28 Formal solution di ν d τ eτν + I ν e τν =Sν e τν a '( x)b( x)+ a( x)b' ( x)=(ab)' 3 rd step: we change the left side by its value di ν + I νe d τ eτν τν = d( I νeτ ν ) d τ d (I νe τ ν ) d τ =S νe τ ν d(i ν e τ ν )=Sν eτ ν d τ
29 Formal solution d(i ν e τ ν )=Sν eτ ν d τ
30 Formal solution d(i ν e τ ν )=Sν eτ ν d τ 4 th step: we integrate that expression between 0 and the maximum optical depth d(i ν e τ ' )= S ν(τ')e τ ' d τ '
31 Formal solution d(i ν e τ ν )=Sν eτ ν d τ 4 th step: we integrate that expression between 0 and the maximum optical depth d(i ν e τ ' )= S ν(τ')e τ ' d τ ' 5 th step: Solve the integral! I νe τ ' 0 τν = S ν(τ ')e τ ' d τ '
32 Formal solution I νe τ ' 0 τν = S ν(τ ')e τ ' d τ '
33 Formal solution I νe τ ' 0 τν = S ν(τ ')e τ ' d τ ' 6 th step: Fixing some details I ν(τν)e τν =I ν(0)e 0 + Sν(τ ')e τ ' d τ '
34 Formal solution I νe τ ' 0 τν = S ν(τ ')e τ ' d τ ' 6 th step: Fixing some details I ν(τν)e τν =I ν(0)e 0 + Sν(τ ')e τ ' d τ ' Multiply everywhere by: e τ ν I ν(τν)=i ν(0)e τ ν + Sν(τ ' τν) ')e(τ
35 Let's come back to physics!!!
36 Physical interpretation I ν(τν)=i ν(0)e τ ν + Sν e( τ ' τ ν) d τ ' Emergent intensity Attenuated background Self attenuated emission by radiatively excited medium
37 Approximate solution: S ν = 0 I ν(τν)=i ν(0)e τ ν + Sν e(τ' τ ν) d τ ' I ν(τν)=i ν(0)e τ ν - Passive medium: there is no emission in the medium - Emergent intensity is the impinging background intensity attenuated by the absorbing medium
38 Approximate solution: S ν = constan I ν(τν)=i ν(0)e τ ν + Sν e( τ ' τ ν) d τ ' I ν(τν)=i ν(0)e τ ν + Sν(1 e τ ν ) - 1 = Attenuated background by the absorbing medium - 2 = Intensity emitted by the medium - 3 = Self attenuation of the medium emission
39 Astronomical observations - Approximate solution S ν is constant - Usually, spectral observations consist in ON (source+background) OFF (background) measurements - ON: I ν = I ν (τ ν ) - OFF I bg = I ν (0) I ν(τν)=i ν(0)e τν + Sν(1 e τν ) I bg =I ν(0) - ON-OFF = I ν - I bg I ν I bg =(Sν I bg )(1 e τ ν )
40 Astronomical observations I ν I bg =(Sν I bg )(1 e τ ν ) - if S ν > I bg => EMISSION LINE - if S ν < I bg => ABSORPTION LINE
41 Astronomical observations I ν I bg =(Sν I bg )(1 e τ ν ) - Optically thin approximation: τ ν << 1 - In that case e τ ~ 1 τ ν I ν I bg τν(sν I bg ) - Optically thick approximation: τ ν >> 1 - In that case e τ ~ 0 I ν I bg (S ν I bg )
42 Brightness temperature - Black body radiation. Planck's law. Bν(T )= 2h ν3 c 2 1 exp(h ν/ K B T ) 1 - h = Planck constant ( erg/s) - c = celerity of light ( cm/s) - Kb = Boltzmann constant ( erg/k)
43 Brightness temperature - Black body radiation. Planck's law. Bν(T )= 2h ν3 c 2 1 exp(h ν/ K B T ) 1 - Wien's limit: hν >> K B T Bν(T )= 2h ν3 c 2 exp( h ν/ K B T ) - Rayleigh-Jeans limit: hν << K B T Bν(T )= 2K B ν2 T c 2
44 Brightness temperature Bν(T )= 2h ν3 c 2 1 exp(h ν/ K B T ) 1 - The brightness temperature T B is a fictitious temperature such that the observed intensity is given by: I ν=bν(t B )
45 Excitation temperature Spontaneous emission Induced emission Collisions
46 Excitation temperature
47 Excitation temperature n u n l = g u g l exp(h ν/ K B T ex ) - The excitation temperature T ex is a fictitious temperature such that the observed population of the levels is given by that expression. - The excitation temperature depends on the transition.
48 Thank you for your attention!
If light travels past a system faster than the time scale for which the system evolves then t I ν = 0 and we have then
6 LECTURE 2 Equation of Radiative Transfer Condition that I ν is constant along rays means that di ν /dt = 0 = t I ν + ck I ν, (29) where ck = di ν /ds is the ray-path derivative. This is equation is the
More information2. NOTES ON RADIATIVE TRANSFER The specific intensity I ν
1 2. NOTES ON RADIATIVE TRANSFER 2.1. The specific intensity I ν Let f(x, p) be the photon distribution function in phase space, summed over the two polarization states. Then fdxdp is the number of photons
More informationI ν. di ν. = α ν. = (ndads) σ ν da α ν. = nσ ν = ρκ ν
Absorption Consider a beam passing through an absorbing medium. Define the absorption coefficient, α ν, by ie the fractional loss in intensity in travelling a distance ds is α ν ds (convention: positive
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 informationTHREE MAIN LIGHT MATTER INTERRACTION
Chapters: 3and 4 THREE MAIN LIGHT MATTER INTERRACTION Absorption: converts radiative energy into internal energy Emission: converts internal energy into radiative energy Scattering; Radiative energy is
More informationComponents of Galaxies Gas The Importance of Gas
Components of Galaxies Gas The Importance of Gas Fuel for star formation (H 2 ) Tracer of galaxy kinematics/mass (HI) Tracer of dynamical history of interaction between galaxies (HI) The Two-Level Atom
More informationRadiation in the Earth's Atmosphere. Part 1: Absorption and Emission by Atmospheric Gases
Radiation in the Earth's Atmosphere Part 1: Absorption and Emission by Atmospheric Gases Electromagnetic Waves Electromagnetic waves are transversal. Electric and magnetic fields are perpendicular. In
More informationde = j ν dvdωdtdν. (1)
Transfer Equation and Blackbodies Initial questions: There are sources in the centers of some galaxies that are extraordinarily bright in microwaves. What s going on? The brightest galaxies in the universe
More information1 Radiative transfer etc
Radiative transfer etc Last time we derived the transfer equation dτ ν = S ν I v where I ν is the intensity, S ν = j ν /α ν is the source function and τ ν = R α ν dl is the optical depth. The formal solution
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 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 informationCHAPTER 26. Radiative Transfer
CHAPTER 26 Radiative Transfer Consider an incoming signal of specific intensity I ν,0 passing through a cloud (i.e., any gaseous region). As the radiation transits a small path length dr through the cloud,
More informationThe Electromagnetic Spectrum
Astr 102: Introduction to Astronomy Fall Quarter 2009, University of Washington, Željko Ivezić Lecture 4: The Electromagnetic Spectrum 1 Understanding Stellar and Galaxy Properties, and Cosmology Four
More informationCHAPTER 27. Continuum Emission Mechanisms
CHAPTER 27 Continuum Emission Mechanisms Continuum radiation is any radiation that forms a continuous spectrum and is not restricted to a narrow frequency range. In what follows we briefly describe five
More informationLecture 2: Transfer Theory
Lecture 2: Transfer Theory Why do we study transfer theory? The light we detect arrives at us in two steps: - first, it is created by some radiative process (e.g., blackbody, synchrotron, etc etc ) -
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 informationSome fundamentals. Statistical mechanics. The non-equilibrium ISM. = g u
Some fundamentals Statistical mechanics We have seen that the collision timescale for gas in this room is very small relative to radiative timesscales such as spontaneous emission. The frequent collisions
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 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 informationRadiation Processes. Black Body Radiation. Heino Falcke Radboud Universiteit Nijmegen. Contents:
Radiation Processes Black Body Radiation Heino Falcke Radboud Universiteit Nijmegen Contents: Planck Spectrum Kirchoff & Stefan-Boltzmann Rayleigh-Jeans & Wien Einstein Coefficients Literature: Based heavily
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 information3 Some Radiation Basics
12 Physics 426 Notes Spring 29 3 Some Radiation Basics In this chapter I ll store some basic tools we need for working with radiation astrophysically. This material comes directly from Rybicki & Lightman
More informationQuantum Electronics/Laser Physics Chapter 4 Line Shapes and Line Widths
Quantum Electronics/Laser Physics Chapter 4 Line Shapes and Line Widths 4.1 The Natural Line Shape 4.2 Collisional Broadening 4.3 Doppler Broadening 4.4 Einstein Treatment of Stimulated Processes Width
More informationLecture 2 Line Radiative Transfer for the ISM
Lecture 2 Line Radiative Transfer for the ISM Absorption lines in the optical & UV Equation of transfer Absorption & emission coefficients Line broadening Equivalent width and curve of growth Observations
More informationChapter 2 Bremsstrahlung and Black Body
Chapter 2 Bremsstrahlung and Black Body 2.1 Bremsstrahlung We will follow an approximate derivation. For a more complete treatment see [2] and [1]. We will consider an electron proton plasma. Definitions:
More informationBlackbody radiation. Main Laws. Brightness temperature. 1. Concepts of a blackbody and thermodynamical equilibrium.
Lecture 4 lackbody radiation. Main Laws. rightness temperature. Objectives: 1. Concepts of a blackbody, thermodynamical equilibrium, and local thermodynamical equilibrium.. Main laws: lackbody emission:
More informationThe formation of stars and planets. Day 1, Topic 2: Radiation physics. Lecture by: C.P. Dullemond
The formation of stars and planets Day 1, Topic 2: Radiation physics Lecture by: C.P. Dullemond Astronomical Constants CGS units used throughout lecture (cm,erg,s...) AU = Astronomical Unit = distance
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 informationpoint, corresponding to the area it cuts out: θ = (arc length s) / (radius of the circle r) in radians Babylonians:
Astronomische Waarneemtechnieken (Astronomical Observing Techniques) 1 st Lecture: 1 September 11 This lecture: Radiometry Radiative transfer Black body radiation Astronomical magnitudes Preface: The Solid
More informationLecture 3: Specific Intensity, Flux and Optical Depth
Lecture 3: Specific Intensity, Flux and Optical Depth We begin a more detailed look at stellar atmospheres by defining the fundamental variable, which is called the Specific Intensity. It may be specified
More informationRadiation in the atmosphere
Radiation in the atmosphere Flux and intensity Blackbody radiation in a nutshell Solar constant Interaction of radiation with matter Absorption of solar radiation Scattering Radiative transfer Irradiance
More informationDescription of radiation field
Description of radiation field Qualitatively, we know that characterization should involve energy/time frequency all functions of x,t. direction We also now that radiation is not altered by passing through
More information= (fundamental constants c 0, h, k ). (1) k
Introductory Physics Laboratory, Faculty of Physics and Geosciences, University of Leipzig W 12e Radiation Thermometers Tasks 1 Measure the black temperature T s of a glowing resistance wire at eight different
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 informationν is the frequency, h = ergs sec is Planck s constant h S = = x ergs sec 2 π the photon wavelength λ = c/ν
3-1 3. Radiation Nearly all our information about events beyond the Solar system is brought to us by electromagnetic radiation radio, submillimeter, infrared, visual, ultraviolet, X-rays, γ-rays. The particles
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 information5. Light-matter interactions: Blackbody radiation
5. Light-matter interactions: Blackbody radiation REMINDER: no lecture on Monday Feb. 6th The electromagnetic spectrum Sources of light Boltzmann's Law Blackbody radiation The cosmic microwave background
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 informationRadiation Transport in a Gas
Radiation Transport in a Gas By analogy to a particle gas, define a photon distribution function by, f ν ν, Ω; r, t)dvdωd r = Number of photons of a frequency in ν, ν + dν), in a volume at rd r), with
More information1. Why photons? 2. Photons in a vacuum
Photons and Other Messengers 1. Why photons? Ask class: most of our information about the universe comes from photons. What are the reasons for this? Let s compare them with other possible messengers,
More informationINTRODUCTION Radiation differs from conduction and convection in that it does not require the presence of a material medium to take place.
RADIATION INTRODUCTION Radiation differs from conduction and convection in that it does not require the presence of a material medium to take place. Radiation: The energy emitted by matter in the form
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 informationAST 301, Lecture 2. James Lattimer. Department of Physics & Astronomy 449 ESS Bldg. Stony Brook University. January 29, 2019
AST 301, Lecture 2 James Lattimer Department of Physics & Astronomy 449 ESS Bldg. Stony Brook University January 29, 2019 Cosmic Catastrophes (AKA Collisions) james.lattimer@stonybrook.edu Properties of
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 informationSome recent work I. Cosmic microwave background, seeds of large scale structure (Planck) Formation and evolution of galaxies (Figure: Simpson et al.
Radio astronomy Radio astronomy studies celestial objects at wavelengths longward of λ 100 µm (frequencies below ν 3 THz) A radio telecope can see cold gas and dust (Wien s displacement law of BB emision,
More informationAstrochemistry and Molecular Astrophysics Paola Caselli
School of Physics and Astronomy FACULTY OF MATHEMATICS & PHYSICAL SCIENCES Astrochemistry and Molecular Astrophysics Paola Caselli Outline 1. The formation of H 2 2. The formation of H 3 + 3. The chemistry
More informationWhat is it good for? RT is a key part of remote sensing and climate modeling.
Read Bohren and Clothiaux Ch.; Ch 4.-4. Thomas and Stamnes, Ch..-.6; 4.3.-4.3. Radiative Transfer Applications What is it good for? RT is a key part of remote sensing and climate modeling. Remote sensing:
More informationBeer-Lambert (cont.)
The Beer-Lambert Law: Optical Depth Consider the following process: F(x) Absorbed flux df abs F(x + dx) Scattered flux df scat x x + dx The absorption or scattering of radiation by an optically active
More informationSome HI is in reasonably well defined clouds. Motions inside the cloud, and motion of the cloud will broaden and shift the observed lines!
Some HI is in reasonably well defined clouds. Motions inside the cloud, and motion of the cloud will broaden and shift the observed lines Idealized 21cm spectra Example observed 21cm spectra HI densities
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 informationWhat are Lasers? Light Amplification by Stimulated Emission of Radiation LASER Light emitted at very narrow wavelength bands (monochromatic) Light
What are Lasers? What are Lasers? Light Amplification by Stimulated Emission of Radiation LASER Light emitted at very narrow wavelength bands (monochromatic) Light emitted in a directed beam Light is coherenent
More informationProblem 1. Hyperfine Emission from Neutral Hydrogen
Ay 201 Radiative Processes Problem Set 4 Solutions Linda Strubbe and Eugene Chiang October 2, 2003 Problem 1. Hyperfine Emission from Neutral Hydrogen This problem is an exercise in learning more astronomy
More informationProperties of Electromagnetic Radiation Chapter 5. What is light? What is a wave? Radiation carries information
Concepts: Properties of Electromagnetic Radiation Chapter 5 Electromagnetic waves Types of spectra Temperature Blackbody radiation Dual nature of radiation Atomic structure Interaction of light and matter
More informationAdvanced Heat and Mass Transfer by Amir Faghri, Yuwen Zhang, and John R. Howell
Advanced Heat and Mass Transfer by Amir Faghri, Yuwen Zhang, and John R. Howell 9.2 The Blackbody as the Ideal Radiator A material that absorbs 100 percent of the energy incident on it from all directions
More informationa few more introductory subjects : equilib. vs non-equil. ISM sources and sinks : matter replenishment, and exhaustion Galactic Energetics
Today : a few more introductory subjects : equilib. vs non-equil. ISM sources and sinks : matter replenishment, and exhaustion Galactic Energetics photo-ionization of HII assoc. w/ OB stars ionization
More informationRelations between the Einstein coefficients
Relations between the Einstein coefficients Additional reading: Böhm-Vitense Ch 13.1, 13.2 In thermodynamic equilibrium, transition rate (per unit time per unit volume) from level 1 to level 2 must equal
More informationAstro 305 Lecture Notes Wayne Hu
Astro 305 Lecture Notes Wayne Hu Set 1: Radiative Transfer Radiation Observables From an empiricist s point of view there are 4 observables for radiation Energy Flux Direction Color Polarization Energy
More informationGoal: The theory behind the electromagnetic radiation in remote sensing. 2.1 Maxwell Equations and Electromagnetic Waves
Chapter 2 Electromagnetic Radiation Goal: The theory behind the electromagnetic radiation in remote sensing. 2.1 Maxwell Equations and Electromagnetic Waves Electromagnetic waves do not need a medium to
More informationOBSERVATIONAL ASTROPHYSICS AND DATA ANALYSIS. Vitaly Neustroev
OBSERVATIONAL ASTROPHYSICS AND DATA ANALYSIS Vitaly Neustroev Contact details Location: FY 272 Telephone: 5531930 Email: vitaly.neustroev@oulu.fi Web: http://cc.oulu.fi/~vneustro/ Content Observational
More informationOpacity 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 informationII. HII Regions (Ionization State)
1 AY230-HIIReg II. HII Regions (Ionization State) A. Motivations Theoretical: HII regions are intamitely linked with past, current and future starforming regions in galaxies. To build theories of star-formation
More informationATMOS 5140 Lecture 7 Chapter 6
ATMOS 5140 Lecture 7 Chapter 6 Thermal Emission Blackbody Radiation Planck s Function Wien s Displacement Law Stefan-Bolzmann Law Emissivity Greybody Approximation Kirchhoff s Law Brightness Temperature
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 informationModern Physics. Unit 6: Hydrogen Atom - Radiation Lecture 6.5: Optical Absorption. Ron Reifenberger Professor of Physics Purdue University
Modern Physics Unit 6: Hydrogen tom - Radiation Lecture 6.5: Optical bsorption Ron Reifenberger Professor of Physics Purdue University 1 We now have a simple quantum model for how light is emitted. How
More informationChemistry 795T. Lecture 7. Electromagnetic Spectrum Black body Radiation. NC State University
Chemistry 795T Lecture 7 Electromagnetic Spectrum Black body Radiation NC State University Black body Radiation An ideal emitter of radiation is called a black body. Observation: that peak of the energy
More informationChemistry 795T. Black body Radiation. The wavelength and the frequency. The electromagnetic spectrum. Lecture 7
Chemistry 795T Lecture 7 Electromagnetic Spectrum Black body Radiation NC State University Black body Radiation An ideal emitter of radiation is called a black body. Observation: that peak of the energy
More informationLecture 2: principles of electromagnetic radiation
Remote sensing for agricultural applications: principles and methods Lecture 2: principles of electromagnetic radiation Instructed by Prof. Tao Cheng Nanjing Agricultural University March Crop 11, Circles
More informationElectromagnetic Radiation.
Electromagnetic Radiation http://apod.nasa.gov/apod/astropix.html CLASSICALLY -- ELECTROMAGNETIC RADIATION Classically, an electromagnetic wave can be viewed as a self-sustaining wave of electric and magnetic
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 3 Energy Balance and Temperature. Astro 9601
Chapter 3 Energy Balance and Temperature Astro 9601 1 Topics to be covered Energy Balance and Temperature (3.1) - All Conduction (3..1), Radiation (3.. and 3...1) Convection (3..3), Hydrostatic Equilibrium
More informationWavelength λ Velocity v. Electric Field Strength Amplitude A. Time t or Distance x time for 1 λ to pass fixed point. # of λ passing per s ν= 1 p
Introduction to Spectroscopy (Chapter 6) Electromagnetic radiation (wave) description: Wavelength λ Velocity v Electric Field Strength 0 Amplitude A Time t or Distance x Period p Frequency ν time for 1
More informationRecap Lecture + Thomson Scattering. Thermal radiation Blackbody radiation Bremsstrahlung radiation
Recap Lecture + Thomson Scattering Thermal radiation Blackbody radiation Bremsstrahlung radiation LECTURE 1: Constancy of Brightness in Free Space We use now energy conservation: de=i ν 1 da1 d Ω1 dt d
More informationChapter 13. Phys 322 Lecture 34. Modern optics
Chapter 13 Phys 3 Lecture 34 Modern optics Blackbodies and Lasers* Blackbodies Stimulated Emission Gain and Inversion The Laser Four-level System Threshold Some lasers Pump Fast decay Laser Fast decay
More informationChapter 7: Quantum Statistics
Part II: Applications SDSMT, Physics 2013 Fall 1 Introduction Photons, E.M. Radiation 2 Blackbody Radiation The Ultraviolet Catastrophe 3 Thermal Quantities of Photon System Total Energy Entropy 4 Radiation
More informationφ(ν)dν = 1. (1) We can define an average intensity over this profile, J =
Ask about final Saturday, December 14 (avoids day of ASTR 100 final, Andy Harris final). Decided: final is 1 PM, Dec 14. Rate Equations and Detailed Balance Blackbodies arise if the optical depth is big
More informationPreliminary Examination: Astronomy
Preliminary Examination: Astronomy Department of Physics and Astronomy University of New Mexico Spring 2017 Instructions: Answer 8 of the 10 questions (10 points each) Total time for the test is three
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 informationLaser Types Two main types depending on time operation Continuous Wave (CW) Pulsed operation Pulsed is easier, CW more useful
What Makes a Laser Light Amplification by Stimulated Emission of Radiation Main Requirements of the Laser Laser Gain Medium (provides the light amplification) Optical Resonator Cavity (greatly increase
More informationGeneral Considerations 1
General Considerations 1 Absorption or emission of electromagnetic radiation results in a permanent energy transfer from the emitting object or to the absorbing medium. This permanent energy transfer can
More informationLasers PH 645/ OSE 645/ EE 613 Summer 2010 Section 1: T/Th 2:45-4:45 PM Engineering Building 240
Lasers PH 645/ OSE 645/ EE 613 Summer 2010 Section 1: T/Th 2:45-4:45 PM Engineering Building 240 John D. Williams, Ph.D. Department of Electrical and Computer Engineering 406 Optics Building - UAHuntsville,
More informationChapter 3 Energy Balance and Temperature. Topics to be covered
Chapter 3 Energy Balance and Temperature Astro 9601 1 Topics to be covered Energy Balance and Temperature (3.1) - All Conduction (3..1), Radiation (3.. and31) 3...1) Convection (3..3), Hydrostatic Equilibrium
More informationLecture 2 Blackbody radiation
Lecture 2 Blackbody radiation Absorption and emission of radiation What is the blackbody spectrum? Properties of the blackbody spectrum Classical approach to the problem Plancks suggestion energy quantisation
More informationThermal Bremsstrahlung
Thermal Bremsstrahlung ''Radiation due to the acceleration of a charge in the Coulomb field of another charge is called bremsstrahlung or free-free emission A full understanding of the process requires
More informationLecture 7: Molecular Transitions (2) Line radiation from molecular clouds to derive physical parameters
Lecture 7: Molecular Transitions (2) Line radiation from molecular clouds to derive physical parameters H 2 CO (NH 3 ) See sections 5.1-5.3.1 and 6.1 of Stahler & Palla Column density Volume density (Gas
More informationObservations 3: Data Assimilation of Water Vapour Observations at NWP Centres
Observations 3: Data Assimilation of Water Vapour Observations at NWP Centres OUTLINE: Data Assimilation A simple analogy: data fitting 4D-Var The observation operator : RT modelling Review of Radiative
More informationTake away concepts. What is Energy? Solar Radiation Emission and Absorption. Energy: The ability to do work
Solar Radiation Emission and Absorption Take away concepts 1. 2. 3. 4. 5. 6. Conservation of energy. Black body radiation principle Emission wavelength and temperature (Wien s Law). Radiation vs. distance
More informationAerothermodynamics of high speed flows
Aerothermodynamics of high speed flows AERO 0033 1 Lecture 9 Thierry Magin Thierry.Magin@vki.ac.be Aeronautics and Aerospace Department von Karman Institute for Fluid Dynamics Aerospace and Mechanical
More informationElectromagnetic Radiation. Physical Principles of Remote Sensing
Electromagnetic Radiation Physical Principles of Remote Sensing Outline for 4/3/2003 Properties of electromagnetic radiation The electromagnetic spectrum Spectral emissivity Radiant temperature vs. kinematic
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 informationMie vs Rayleigh. Sun
Mie vs Rayleigh Sun Chemists Probe Various Energy Levels of Molecules With Appropiate Energy Radiation It is convenient (and accurate enough for our purposes) to treat a molecule or system of molecules
More informationRADIO SPECTRAL LINES. Nissim Kanekar National Centre for Radio Astrophysics, Pune
RADIO SPECTRAL LINES Nissim Kanekar National Centre for Radio Astrophysics, Pune OUTLINE The importance of radio spectral lines. Equilibrium issues: kinetic, excitation, brightness temperatures. The equation
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 informationLecture 10. Lidar Effective Cross-Section vs. Convolution
Lecture 10. Lidar Effective Cross-Section vs. Convolution q Introduction q Convolution in Lineshape Determination -- Voigt Lineshape (Lorentzian Gaussian) q Effective Cross Section for Single Isotope --
More informationBremsstrahlung Radiation
Bremsstrahlung Radiation Wise (IR) An Example in Everyday Life X-Rays used in medicine (radiographics) are generated via Bremsstrahlung process. In a nutshell: Bremsstrahlung radiation is emitted when
More informationTemperature Scales and Telescope Efficiencies
Temperature Scales and Telescope Efficiencies Jeff Mangum (NRAO) April 11, 2006 Contents 1 Introduction 1 2 Definitions 1 2.1 General Terms.................................. 2 2.2 Efficiencies....................................
More informationInteraction X-rays - Matter
Interaction X-rays - Matter Pair production hν > M ev Photoelectric absorption hν MATTER hν Transmission X-rays hν' < hν Scattering hν Decay processes hν f Compton Thomson Fluorescence Auger electrons
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 informationElectron temperature is the temperature that describes, through Maxwell's law, the kinetic energy distribution of the free electrons.
10.3.1.1 Excitation and radiation of spectra 10.3.1.1.1 Plasmas A plasma of the type occurring in spectrochemical radiation sources may be described as a gas which is at least partly ionized and contains
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 information