1. Dr. Matt Burleigh 3671 MWA Lecture 2 In this lecture we will review:In this lecture we will review: –Attenuation of radiation by matter –Optical Depth  –Optical Depth  –Mean free path –Blackbody radiation –Wien displacement law (how to measure the wavelength a BB emits most of its energy at)(how to measure the wavelength a BB emits most of its energy at) –Stefan-Boltzmann Law Flux is proportional to T 4Flux is proportional to T 4

2. Dr. Matt Burleigh Optical Depth  Optical Depth  I = I 0 e - I = I 0 e -  E.G. a ray travelling through a star’s atmosphereE.G. a ray travelling through a star’s atmosphere If ray starts at an optical depth   then its intensity will decline by a factor e -1 before escaping the starIf ray starts at an optical depth   then its intensity will decline by a factor e -1 before escaping the star Usually we choose  = 0 to represent the top of a star’s atmosphereUsually we choose  = 0 to represent the top of a star’s atmosphere

3. Dr. Matt Burleigh Optical Depth  Optical Depth  Optical depth can be thought of as the number of mean free paths from a particle’s original position, measured along its pathOptical depth can be thought of as the number of mean free paths from a particle’s original position, measured along its path If  >>1, then cylinder of gas or dust is considered optically thickIf  >>1, then cylinder of gas or dust is considered optically thick If   1, then cylinder of gas or dust is considered optically thinIf   1, then cylinder of gas or dust is considered optically thin Since  is wavelength-dependent, the dust or gas may be optically thick at one wavelength and thin at anotherSince  is wavelength-dependent, the dust or gas may be optically thick at one wavelength and thin at another –Dust blocks optical light but we can see through some of it in the infra-red –Earth’s atmosphere is optically thin in the visible (we see stars) but optically thick at X-rays (we detect none from the ground)

4. Dr. Matt Burleigh A blackbody is an ideal emitter – an object that absorbs all light energy incident upon it & re-radiates it with a characteristic spectrum This radiation is called Blackbody radiation Stars & planets are blackbodies, to a rough approximation A blackbody of temperature T emits a continuous spectrum which peaks at max max moves to shorter with increasing T See Carroll & Ostlie Ch3.4 P.75 “Blackbody Radiation” Blackbody Radiation

5. Dr. Matt Burleigh Wien Displacement Law max T = 2.9x10 6 nm.K ExampleTemp(K) max maxRegime Coronae 10 6 1keVX-ray O star 30,0001000AUV G star (sun) 6,0005000AOptical M star 3,000 1m1m1m1mNear-IR Hot dust 1,500 2m2m2m2mNear-IR Earth300 10  m Mid-IR

6. Dr. Matt Burleigh Other emission processes BB radiation is a thermal processBB radiation is a thermal process –In thermodynamic equilibrium with surroundings Brehmstrahlung – thermalBrehmstrahlung – thermal –“braking radiation” –Free electron experiences a deceleration when it collides with a positive ion, and radiates energy Synchrotron – non-thermalSynchrotron – non-thermal –Electron spinning in a magnetic field –Seen in e.g. Crab Nebula (pulsar has large B field) Electron/photon scattering – non-thermalElectron/photon scattering – non-thermal Inverse Compton scattering – non-thermalInverse Compton scattering – non-thermal –Collision of relativistic electron with a photon –Photon energy changes To learn more about emission processes, attend Graham Wynn’s “Interaction of radiation with matter” courseTo learn more about emission processes, attend Graham Wynn’s “Interaction of radiation with matter” course

7. Dr. Matt Burleigh Summary of lecture 2 From today’s lecture you will need toFrom today’s lecture you will need to –Understand concept of Optical Depth (and derive I=I 0 e -  ) –Understand Blackbody radiation –Remember Wien Law and how to use it  max T = 2.9x10 6 nm.K –Remember Stefan-Boltzmann Law F =  T 4 and L=4  R 2  T 4F =  T 4 and L=4  R 2  T 4 –No need to derive Wien or SB Laws, just remember, understand and know how/when to use!