Comptonization RL 7.4, 7.5, 7.6, 7.7
|
|
- Dortha Sims
- 5 years ago
- Views:
Transcription
1 Comptonization RL 7.4, 7.5, 7.6, 7.7
2 Photons scatter off (relativistic) electrons and gain energy hence electrons cool (Inverse Compton cooling, or ICC) We discussed spectra for: Inverse Compton recap / / 0 Single electron energy, single photon energy : [ 0 4 2, 4 2 ], < 1! I /, > 1! I / Power law electron energies c ( ) / U r 0 / p (p 1)/2 with U r 0, single photon energy: the photon energy density Power law electron energies, arbitrary input spectrum: same scaling, except when the integration limits of U r depend on the electron distribution too
3 Comptonization Comptonization is the process of taking an input ( seed ) spectrum and (inverse)-compton-scattering it into a new spectrum The importance of this process is measured by the Compton parameter (in finite media):! mean number average fractional energy y = of scatterings change per scattering! y If y>1 then Comptonization generally changes the spectrum Let s think about the first part first; consider the optical depth for electron scattering (Thomson optical depth) for a constant density electron cloud with size : Mean free path: R T = n e l =(n e T ) 1 T R
4 Number of scatterings T 1 Say the medium is optically thin, value of the number of scatterings is: N T ; then the expectation If the medium is optically thick, the photon takes a random walk, and so scatters around until it reaches the region s edge: d 2 p 1/2 p N = Nl = = p N R n e T T d 2 1/2 = R ) N = 2 T y! mean number So we can write the first part of of scatterings as: = max( T, 2 T)
5 Fractional energy change Now for the second part, the average fractional energy change We already saw its value for a relativistic electron: Now let s consider this more generally; assume a thermal distribution of electrons Non-relativistic means Maxwell-Boltzmann: f(v) = Relativistic means Maxwell-Jüttner: f( )= me 2 k B T 2 K 2 (1/ ) exp 3/2 4 v 2 exp me v 2 with 2k B T k BT m e c 2 So: f NR / 2 exp( / ) and f R / 2 exp( / )
6 Fractional energy change relativistic Now that we have a distribution function, we can calculate an 2 expectation value for : R 2 1 R 2 1 f = 1 R ( )d 4 exp( / )d 1 = R 1 1 f R ( )d R exp( / )d 12 2 So the average fractional energy change is: x x 0 = kb T m e c 2 2 (remember: x h /(m e c 2 ))
7 Fractional energy change non-relativistic You may recall the average kinetic energy of a thermal electron: R m ev 2 f NR (v)dv he k i = R 1 0 f NR (v)dv Some electrons will have a lower energy than the incoming photons and downscatter them, while those with a higher energy scatter them up thermalized electron-photon equilibrium = 3 2 k BT Some unknown parameter determines the balance (fraction of the electron kinetic energy taken by the photon): x x 0 = he ki m e c 2 x 0 = 3 2 x 0 We can find by considering the equilibrium conditions
8 Fractional energy change non-relativistic When thermal electrons only interact with photons through scattering, in equilibrium the photons will follow: f(x) / x 2 exp( Also in equilibrium, we should have x/ ) h xi =0, so: h xi = 3 2 hxi x 2 =0 ) 3 x 2 2 = We calculate the expectation values using f(x) hxi =3 x 2 = 12 2 ) ) 3 2 =4 (Wien distribution, same scaling as relativistic electrons!) hxi just like before: So: x =4 x 0 = 4k BT h 0 x 0 m e c 2
9 We can now write down an expression for the Compton :! mean number y = of scatterings change per scattering y NR = 4k BT 0 ) y = hn sc i Assuming Compton y parameter 0 4k B T x x 0 ) 8 >< >: Per scattering the energy gain is y! average fractional energy m e c 2 max( T, T) 2 2 kb T y R = 16 m e c 2 max( T, T) 2 (so no downscattering) we can write: y [ ]( T + 2 T) [ ] 0 d dn = [ ] 0 ) = 0 e [16 = 0 e y, so differentially:
10 Thermal Compton low optical depth For a power-law electron distribution we got a power-law spectrum; what about for a thermal cloud of electrons? k k A Let s call the photon energy after scatterings and the amplification after one scattering; if the optical depth is low, then: A 1 0 y T +1 Assuming that the starting photon energy is low enough compared to the electrons (i.e /2 me c 2 ), we can write: k = A k 0 e T 1 T The cloud is optically thin, so a fraction escapes without scattering; a fraction scatters only once, etc so: T p( k ) k T (k>0)
11 Thermal Compton low optical depth T 2 T 3 T 4 T 5 T 6 T 7 T 8 T power law!
12 Thermal Compton low optical depth For a power-law electron distribution we got a power-law spectrum; what about for a thermal cloud of electrons? Answer: also a power law, through repeated scatterings! I( k ) / I( 0 ) k T Every scattering moves the peak down with another factor, and to the right with another factor A, so: ln T a = ln T ln A = 0 ln T a ln y Note that the bumpiness of the spectrum, caused by the scatterings being discrete, depends on the values of and T A
13 Thermal Compton low optical depth A# A"
14 Thermal Compton low optical depth T # T "
15 Medium optical depth T & 1 For a (slightly) opaque medium,, the photons are diffusing through the electron cloud, and we have to consider more complicated thermodynamics (and quantum effects) The result is the Kompaneets equation (assuming NR electrons): kb K = m e c 2 apple + n + n2 n t K =(n e T c)t x h /k B T is the phase-space density of the photons, is time in units of mean time between scatterings, and For mild optical depths, this can still result in a power law spectrum, now with: a = 3 2 ± r y
16 High optical depth T 1 For a high opacities,, things become a bit easier again: the photons and electrons reach an equilibrium, and the photon spectrum becomes a Wien spectrum (see earlier): I( ) / 3 e h /k BT (To be more precise, the photons distribution becomes Bose- Einstein with a non-zero chemical potential) Note that this spectrum is similar to a blackbody, but harder (i.e. steeper at low frequencies) Since the electrons and photons reach an equilibrium, we call this saturated Comptonization
17 Quasi-saturation Interesting things happen when we consider a scenario in which the seed photons are produced throughout an opaque cloud Almost all near the center will scatter their way to equilibrium, but some near the edge will exit the cloud before that point 1/ T 1/ T 1/ T A fraction will escape without scattering; another fraction escapes after one scattering event; after two, etc. Most photons take a very long time to escape, but after they reach equilibrium they no longer change their spectrum so most exit with the Wien spectrum at some fixed peak energy! Quasi-saturated spectrum: significant part of the spectrum is unsaturated, but for high T most of the energy will be in the saturated part
18 Quasi-saturation / 3 exp[ /(k B T )] / 0 / 2
19 Quasi-saturation T # T "
20 Imagine a magnetized region with relativistic electrons: these will produce synchrotron radiation, but on their way out the photons may interact with the electrons and (inverse) Compton scatter The electrons both produce and scatter the radiation, so we call this synchrotron self-compton (SSC) From last week: for a power-law electron distribution, the synchrotron and IC scattered spectra have the same slope Specifically, if Synchrotron self-compton j syn ( 0 )=j syn,0 0 j ssc ( ) = (4/3) 1 2 then: / n e TKRj syn ( )ln( max / min ) T 1 T ln j syn ( ) =(p 1)/2
21 Synchrotron self-compton T ln
22 Synchrotron self-compton Crab Nebula Next week: atomic lines
Single Particle Spectrum
Single Particle Spectrum Upscattered photons 4 γ ϵ Downscattered photons Multiple Scatterings ( γ h ν m c ) Comptonization Comptonizationparameter parameter Important: Important: IfIf y>1 y>1 then then
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 informationFI 3103 Quantum Physics
FI 3103 Quantum Physics Alexander A. Iskandar Physics of Magnetism and Photonics Research Group Institut Teknologi Bandung General Information Lecture schedule 17 18 9136 51 5 91 Tutorial Teaching Assistant
More informationStatistical Mechanics
Statistical Mechanics Newton's laws in principle tell us how anything works But in a system with many particles, the actual computations can become complicated. We will therefore be happy to get some 'average'
More informationRadiative Processes in Astrophysics
Radiative Processes in Astrophysics 11. Synchrotron Radiation & Compton Scattering Eline Tolstoy http://www.astro.rug.nl/~etolstoy/astroa07/ Synchrotron Self-Absorption synchrotron emission is accompanied
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 information1 The Kompaneets equation
Introduction to Particle Cosmology, Tutorial notes: The Sunyaev-Zeldovich effect 1 The Kompaneets equation Consider evolution of photon phase space density n(, t) in the presence of an electron gas. Assume
More informationThomson scattering: It is the scattering of electromagnetic radiation by a free non-relativistic charged particle.
Thomson scattering: It is the scattering of electromagnetic radiation by a free non-relativistic charged particle. The electric and magnetic components of the incident wave accelerate the particle. As
More informationCompton Scattering II
Compton Scattering II 1 Introduction In the previous chapter we considered the total power produced by a single electron from inverse Compton scattering. This is useful but limited information. Here we
More informationSpecial relativity and light RL 4.1, 4.9, 5.4, (6.7)
Special relativity and light RL 4.1, 4.9, 5.4, (6.7) First: Bremsstrahlung recap Braking radiation, free-free emission Important in hot plasma (e.g. coronae) Most relevant: thermal Bremsstrahlung What
More information1/30/11. Astro 300B: Jan. 26, Thermal radia+on and Thermal Equilibrium. Thermal Radia0on, and Thermodynamic Equilibrium
Astro 300B: Jan. 26, 2011 Thermal radia+on and Thermal Equilibrium Thermal Radia0on, and Thermodynamic Equilibrium 1 Thermal radiation is radiation emitted by matter in thermodynamic equilibrium. When
More informationStep 1. Step 2. g l = g v. dg = 0 We have shown that over a plane surface of water. g v g l = ρ v R v T ln e/e sat. this can be rewritten
The basic question is what makes the existence of a droplet thermodynamically preferable to the existence only of water vapor. We have already derived an expression for the saturation vapor pressure over
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. 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 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 informationWe start with a reminder of a few basic concepts in probability. Let x be a discrete random variable with some probability function p(x).
1 Probability We start with a reminder of a few basic concepts in probability. 1.1 discrete random variables Let x be a discrete random variable with some probability function p(x). 1. The Expectation
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 informationExplain how Planck resolved the ultraviolet catastrophe in blackbody radiation. Calculate energy of quanta using Planck s equation.
Objectives Explain how Planck resolved the ultraviolet catastrophe in blackbody radiation. Calculate energy of quanta using Planck s equation. Solve problems involving maximum kinetic energy, work function,
More informationMITOCW watch?v=wr88_vzfcx4
MITOCW watch?v=wr88_vzfcx4 PROFESSOR: So we're building this story. We had the photoelectric effect. But at this moment, Einstein, in the same year that he was talking about general relativity, he came
More informationGamma-ray flares from 3C454 and PKS 1830 in late 2010: electron energization in the jet is not enough!
Gamma-ray flares from 3C454 and PKS 1830 in late 2010: electron energization in the jet is not enough! Name Affiliation A. Bulgarelli INAF-IASF Bologna A.W. Chen INAF-IASF Milano I. Donnarumma INAF-IASF
More informationCompton Scattering. hω 1 = hω 0 / [ 1 + ( hω 0 /mc 2 )(1 cos θ) ]. (1) In terms of wavelength it s even easier: λ 1 λ 0 = λ c (1 cos θ) (2)
Compton Scattering Last time we talked about scattering in the limit where the photon energy is much smaller than the mass-energy of an electron. However, when X-rays and gamma-rays are considered, this
More informationCHAPTER 3 The Experimental Basis of Quantum Theory
CHAPTER 3 The Experimental Basis of Quantum Theory 3.1 3.2 3.3 3.4 3.5 3.6 3.7 3.8 3.9 Discovery of the X Ray and the Electron Determination of Electron Charge Line Spectra Quantization As far as I can
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 information5. Light-matter interactions: Blackbody radiation
5. Light-matter interactions: Blackbody radiation The electromagnetic spectrum Sources of light Boltzmann's Law Blackbody radiation why do hot things glow? The cosmic microwave background The electromagnetic
More information4/14/2015. Models of the Atom. Quantum Physics versus Classical Physics The Thirty-Year War ( ) Classical Model of Atom
Quantum Physics versus Classical Physics The Thirty-Year War (1900-1930) Models of the Atom Interactions between Matter and Radiation Models of the Atom Bohr s Model of the Atom Planck s Blackbody Radiation
More informationAstrophysical Radiation Processes
PHY3145 Topics in Theoretical Physics Astrophysical Radiation Processes 3: Relativistic effects I Dr. J. Hatchell, Physics 407, J.Hatchell@exeter.ac.uk Course structure 1. Radiation basics. Radiative transfer.
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 informationNotes on x-ray scattering - M. Le Tacon, B. Keimer (06/2015)
Notes on x-ray scattering - M. Le Tacon, B. Keimer (06/2015) Interaction of x-ray with matter: - Photoelectric absorption - Elastic (coherent) scattering (Thomson Scattering) - Inelastic (incoherent) scattering
More informationMinimum Bias Events at ATLAS
Camille Bélanger-Champagne Lehman McGill College University City University of New York Thermodynamics Charged Particle and Correlations Statistical Mechanics in Minimum Bias Events at ATLAS Statistical
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 informationRecall: The Importance of Light
Key Concepts: Lecture 19: Light Light: wave-like behavior Light: particle-like behavior Light: Interaction with matter - Kirchoff s Laws The Wave Nature of Electro-Magnetic Radiation Visible light is just
More informationPhotoelectric Effect & Bohr Atom
PH0008 Quantum Mechanics and Special Relativity Lecture 03 (Quantum Mechanics) 020405v2 Photoelectric Effect & Bohr Atom Prof Department of Physics Brown University Main source at Brown Course Publisher
More informationThe Bohr Model of Hydrogen
The Bohr Model of Hydrogen Suppose you wanted to identify and measure the energy high energy photons. One way to do this is to make a calorimeter. The CMS experiment s electromagnetic calorimeter is made
More informationis the minimum stopping potential for which the current between the plates reduces to zero.
Module 1 :Quantum Mechanics Chapter 2 : Introduction to Quantum ideas Introduction to Quantum ideas We will now consider some experiments and their implications, which introduce us to quantum ideas. The
More informationWith certain caveats (described later) an object absorbs as effectively as it emits
Figure 1: A blackbody defined by a cavity where emission and absorption are in equilibrium so as to maintain a constant temperature Blackbody radiation The basic principles of thermal emission are as follows:
More informationRadiative processes in GRB (prompt) emission. Asaf Pe er (STScI)
Radiative processes in GRB (prompt) emission Asaf Pe er (STScI) May 2009 Outline Historical approach Synchrotron: pro s and co s Compton scattering in prompt emission (and why it is different than in afterglow)
More informationSynchrotron Radiation II
Synchrotron Radiation II Summary of Radiation Properties Thermal Blackbody Bremsstrahlung Synchrotron Optically thick YES NO Maxwellian distribution of velocities YES YES NO Relativistic speeds YES Main
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 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 informationIntroduction to Modern Physics NE 131 Physics for Nanotechnology Engineering
Introduction to Modern Physics NE 131 Physics for Nanotechnology Engineering Dr. Jamie Sanchez-Fortún Stoker Department of Physics, University of Waterloo Fall 2005 1 Introduction to Modern Physics 1.1
More informationRadiation processes and mechanisms in astrophysics I. R Subrahmanyan Notes on ATA lectures at UWA, Perth 18 May 2009
Radiation processes and mechanisms in astrophysics I R Subrahmanyan Notes on ATA lectures at UWA, Perth 18 May 009 Light of the night sky We learn of the universe around us from EM radiation, neutrinos,
More informationThe perfect quantal gas
The perfect quantal gas Asaf Pe er 1 March 27, 2013 1. Background So far in this course we have been discussing ideal classical gases. We saw that the conditions for gases to be treated classically are
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 informationPlanck s Quantum Hypothesis Blackbody Radiation
Planck s Quantum Hypothesis Blackbody Radiation The spectrum of blackbody radiation has been measured(next slide); it is found that the frequency of peak intensity increases linearly with temperature.
More informationAddition of Opacities and Absorption
Addition of Opacities and Absorption If the only way photons could interact was via simple scattering, there would be no blackbodies. We ll go into that in much more detail in the next lecture, but the
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 informationOrder of Magnitude Astrophysics - a.k.a. Astronomy 111. Photon Opacities in Matter
1 Order of Magnitude Astrophysics - a.k.a. Astronomy 111 Photon Opacities in Matter If the cross section for the relevant process that scatters or absorbs radiation given by σ and the number density of
More informationAnnouncements. One more bit of vocabulary about waves
Announcements Homework 5 now available; due on Sunday, Nov. 16 before midnight No class on Tuesday, Nov. 11 (Veteran s Day) Midterm 2 on Wednesday, Nov. 12 Study materials now available on class web page;
More informationModern Physics, summer Modern physics. Historical introduction to quantum mechanics
1 Modern physics 2 Gustav Kirchhoff (1824-1887) Surprisingly, the path to quantum mechanics begins with the work of German physicist Gustav Kirchhoff in 1859. Electron was discovered by J.J.Thomson in
More informationPoS(MQW7)007. X-ray spectral states of microquasars
and Renaud Belmont CESR, Toulouse, France E-mail: Julien.Malzac@cesr.fr, Renaud.Belmont@cesr.fr We discuss the origin of the dramatically different X-ray spectral shapes observed in the Low Hard State
More informationAstrophysical Radiation Processes
PHY3145 Topics in Theoretical Physics Astrophysical Radiation Processes 5:Synchrotron and Bremsstrahlung spectra Dr. J. Hatchell, Physics 406, J.Hatchell@exeter.ac.uk Course structure 1. Radiation basics.
More information8.044 Lecture Notes Chapter 5: Thermodynamcs, Part 2
8.044 Lecture Notes Chapter 5: hermodynamcs, Part 2 Lecturer: McGreevy 5.1 Entropy is a state function............................ 5-2 5.2 Efficiency of heat engines............................. 5-6 5.3
More informationaka Light Properties of Light are simultaneously
Today Interaction of Light with Matter Thermal Radiation Kirchhoff s Laws aka Light Properties of Light are simultaneously wave-like AND particle-like Sometimes it behaves like ripples on a pond (waves).
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 informationThermal Equilibrium in Nebulae 1. For an ionized nebula under steady conditions, heating and cooling processes that in
Thermal Equilibrium in Nebulae 1 For an ionized nebula under steady conditions, heating and cooling processes that in isolation would change the thermal energy content of the gas are in balance, such that
More informationCHAPTER 3 The Experimental Basis of Quantum
CHAPTER 3 The Experimental Basis of Quantum 3.1 Discovery of the X Ray and the Electron 3.2 Determination of Electron Charge 3.3 Line Spectra 3.4 Quantization 3.5 Blackbody Radiation 3.6 Photoelectric
More informationParticles and Waves Particles Waves
Particles and Waves Particles Discrete and occupy space Exist in only one location at a time Position and velocity can be determined with infinite accuracy Interact by collisions, scattering. Waves Extended,
More informationDARK HEAT. By Kadir Aydoğdu student from MIDDLE EAST TECHNICAL UNIVERSITY DEPARTMENT OF PHYSICS
DARK HEAT By Kadir Aydoğdu student from MIDDLE EAST TECHNICAL UNIVERSITY DEPARTMENT OF PHYSICS e-mail: kadir.aydogdu@metu.edu.tr or elkadir@hotmail.com New Heat Theory Remodeling of Black Body Radiation
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 informationBose-Einstein Condensation and Intermediate State of the. Photon Gas. Abstract
Bose-Einstein Condensation and Intermediate State of the Photon Gas Levan N. Tsintsadze Venture Business Laboratory, Hiroshima University, Higashi-Hiroshima, Japan (July 19, 2002) Abstract Possibility
More informationPhys 344 Ch 7 Lecture 6 April 6 th, HW29 51,52 HW30 58, 63 HW31 66, 74. w ε w. π ε ( ) ( )
Phys Ch 7 Lecture 6 April 6 th,009 1 Mon. /6 Wed. /8 Fri. /10 Mon. /1 Review 7. Black Body Radiation he Rest 7. Debye Solids 7.6 Bose-Einstein Condensate HW9 1, HW0 8, 6 HW1 66, 7 HW6,7,8 HW9,0,1 Equipment:
More informationExternal (differential) quantum efficiency Number of additional photons emitted / number of additional electrons injected
Semiconductor Lasers Comparison with LEDs The light emitted by a laser is generally more directional, more intense and has a narrower frequency distribution than light from an LED. The external efficiency
More informationHIGH ENERGY ASTROPHYSICS - Lecture 7. PD Frank Rieger ITA & MPIK Heidelberg Wednesday
HIGH ENERGY ASTROPHYSICS - Lecture 7 PD Frank Rieger ITA & MPIK Heidelberg Wednesday 1 (Inverse) Compton Scattering 1 Overview Compton Scattering, polarised and unpolarised light Di erential cross-section
More informationFundamentals. Statistical. and. thermal physics. McGRAW-HILL BOOK COMPANY. F. REIF Professor of Physics Universüy of California, Berkeley
Fundamentals of and Statistical thermal physics F. REIF Professor of Physics Universüy of California, Berkeley McGRAW-HILL BOOK COMPANY Auckland Bogota Guatemala Hamburg Lisbon London Madrid Mexico New
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 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 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 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 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 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 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 informationChapter 37 Early Quantum Theory and Models of the Atom. Copyright 2009 Pearson Education, Inc.
Chapter 37 Early Quantum Theory and Models of the Atom Planck s Quantum Hypothesis; Blackbody Radiation Photon Theory of Light and the Photoelectric Effect Energy, Mass, and Momentum of a Photon Compton
More informationRadiative Processes in Astrophysics
Radiative Processes in Astrophysics 9. Synchrotron Radiation Eline Tolstoy http://www.astro.rug.nl/~etolstoy/astroa07/ Useful reminders relativistic terms, and simplifications for very high velocities
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 informationX-ray and Gamma-ray. Emission Pulsars and Pulsar Wind Nebulae. K.S. Cheng Department of Physics University of Hong Kong Hong Kong, China
X-ray and Gamma-ray Emission Pulsars and Pulsar Wind Nebulae K.S. Cheng Department of Physics University of Hong Kong Hong Kong, China X-ray luminosity (L x ) vs spin-down power (L sd ) Becker and Trumper
More informationSlowing down the neutrons
Slowing down the neutrons Clearly, an obvious way to make a reactor work, and to make use of this characteristic of the 3 U(n,f) cross-section, is to slow down the fast, fission neutrons. This can be accomplished,
More informationCHAPTER 3 Prelude to Quantum Theory. Observation of X Rays. Thomson s Cathode-Ray Experiment. Röntgen s X-Ray Tube
CHAPTER Prelude to Quantum Theory.1 Discovery of the X Ray and the Electron. Determination of Electron Charge. Line Spectra.4 Quantization.5 Blackbody Radiation.6 Photoelectric Effect.7 X-Ray Production.8
More informationBlackbody radiation The photoelectric effect Compton effect Line spectra Nuclear physics/bohr model Lasers Quantum mechanics
Blackbody radiation The photoelectric effect Compton effect Line spectra Nuclear physics/bohr model Lasers Quantum mechanics Phys 2435: Chap. 38, Pg 1 Blackbody radiation New Topic Phys 2435: Chap. 38,
More informationQM all started with - - The Spectrum of Blackbody Radiation
QM all started with - - The Spectrum of Blackbody Radiation Thermal Radiation: Any object, not at zero temperature, emits electromagnetic called thermal. When we measure the intensity of a real object,
More informationChemical Reaction Engineering Prof. JayantModak Department of Chemical Engineering Indian Institute of Science, Bangalore
Chemical Reaction Engineering Prof. JayantModak Department of Chemical Engineering Indian Institute of Science, Bangalore Module No. #05 Lecture No. #29 Non Isothermal Reactor Operation Let us continue
More informationPSI AP Physics How was it determined that cathode rays possessed a negative charge?
PSI AP Physics 2 Name Chapter Questions 1. How was it determined that cathode rays possessed a negative charge? 2. J. J. Thomson found that cathode rays were really particles, which were subsequently named
More information3. Particle-like properties of E&M radiation
3. Particle-like properties of E&M radiation 3.1. Maxwell s equations... Maxwell (1831 1879) studied the following equations a : Gauss s Law of Electricity: E ρ = ε 0 Gauss s Law of Magnetism: B = 0 Faraday
More informationPH300 Spring Homework 07
PH300 Spring 2011 Homework 07 Total Points: 30 1. (1 Point) Each week you should review both your answers and the solutions for the previous week's homework to make sure that you understand all the questions
More informationOVERVIEW OF A 3C279 s FLARE and SIMULATION OF AGNs
Gamma-ray Large Area Space Telescope OVERVIEW OF A 3C279 s FLARE and SIMULATION OF AGNs Alessandro Buzzatti Università degli Studi di Torino / SLAC Alessandro Buzzatti 1 Outline Overview of 3C279 flare
More informationModern Physics (Lec. 1)
Modern Physics (Lec. 1) Physics Fundamental Science Concerned with the fundamental principles of the Universe Foundation of other physical sciences Has simplicity of fundamental concepts Divided into five
More informationThermal radiation (a.k.a blackbody radiation) is the answer to the following simple question:
Thermal radiation (a.k.a blackbody radiation) is the answer to the following simple question: What is the state of the electromagnetic (EM) field in equilibrium with its surroundings at temperature T?
More informationPhysics 102: Lecture 23
Physics 102: Lecture 23 De Broglie Waves & Compton Scattering Physics 102: Lecture 23, Slide 1 Early Indications of Problems with Classical Physics Blackbody radiation Photoelectric effect Wave-particle
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 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 informationLecture 8. The Second Law of Thermodynamics; Energy Exchange
Lecture 8 The Second Law of Thermodynamics; Energy Exchange The second law of thermodynamics Statistics of energy exchange General definition of temperature Why heat flows from hot to cold Reading for
More informationCHAPTER 9 Statistical Physics
CHAPTER 9 Statistical Physics 9.1 9.2 9.3 9.4 9.5 9.6 9.7 Historical Overview Maxwell Velocity Distribution Equipartition Theorem Maxwell Speed Distribution Classical and Quantum Statistics Fermi-Dirac
More informationTable of Contents [ttc]
Table of Contents [ttc] 1. Equilibrium Thermodynamics I: Introduction Thermodynamics overview. [tln2] Preliminary list of state variables. [tln1] Physical constants. [tsl47] Equations of state. [tln78]
More information22. Lasers. Stimulated Emission: Gain. Population Inversion. Rate equation analysis. Two-level, three-level, and four-level systems
. Lasers Stimulated Emission: Gain Population Inversion Rate equation analysis Two-level, three-level, and four-level systems What is a laser? LASER: Light Amplification by Stimulated Emission of Radiation
More informationParticle acceleration and generation of high-energy photons
Particle acceleration and generation of high-energy photons For acceleration, see Chapter 21 of Longair Ask class: suppose we observe a photon with an energy of 1 TeV. How could it have been produced?
More informationSet 3: Thermal Physics
Set 3: Thermal Physics Equilibrium Thermal physics describes the equilibrium distribution of particles for a medium at temperature T Expect that the typical energy of a particle by equipartition is E kt,
More information12/04/2012. Models of the Atom. Quantum Physics versus Classical Physics The Thirty-Year War ( )
Quantum Physics versus Classical Physics The Thirty-Year War (1900-1930) Interactions between Matter and Radiation Models of the Atom Bohr s Model of the Atom Planck s Blackbody Radiation Models of the
More informationLecture 12. Measurements in Astronomy. Using Light. ASTR 111 Section 002. In astronomy, we need to make remote and indirect measurements
Lecture 12 ASTR 111 Section 002 Measurements in Astronomy In astronomy, we need to make remote and indirect measurements Think of an example of a remote and indirect measurement from everyday life Using
More informationAlan Mortimer PhD. Ideas of Modern Physics
Alan Mortimer PhD Ideas of Modern Physics Electromagnetic Waves Last Week Special Relativity General Relativity The Quantum World Index Planck s Law Atomic Structure and emission lines Matter waves Uncertainty
More informationAST 105 Intro Astronomy The Solar System. MIDTERM II: Tuesday, April 5 [covering Lectures 10 through 16]
AST 105 Intro Astronomy The Solar System MIDTERM II: Tuesday, April 5 [covering Lectures 10 through 16] REVIEW Light as Information Bearer We can separate light into its different wavelengths (spectrum).
More information