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3671 MWA Lecture 2 • In this lecture we will review: – Attenuation of radiation by matter – Optical Depth tl – Mean free path – Blackbody radiation – Wien displacement law • (how to measure the wavelength a BB emits most of its energy at) – Stefan-Boltzmann Law • Flux is proportional to T4 Dr. Matt Burleigh Optical Depth tl • Il = Il0 e-tl • E.G. a ray travelling through a star’s atmosphere • If ray starts at an optical depth tl=1 then its intensity will decline by a factor e-1 before escaping the star • Usually we choose tl = 0 to represent the top of a star’s atmosphere Dr. Matt Burleigh Optical Depth tl • Optical depth can be thought of as the number of mean free paths from a particle’s original position, measured along its path • If tl>>1, then cylinder of gas or dust is considered optically thick • If tl<<1, then cylinder of gas or dust is considered optically thin • Since tl 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) Dr. Matt Burleigh Blackbody Radiation • 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 lmax • lmax moves to shorter l with increasing T • See Carroll & Ostlie Ch3.4 P.75 “Blackbody Radiation” Dr. Matt Burleigh Wien Displacement Law lmaxT = 2.9x106nm.K Example Coronae O star G star (sun) M star Hot dust Earth Dr. Matt Burleigh Temp(K) 106 30,000 6,000 lmax 1keV 1000A 5000A Regime X-ray UV Optical 3,000 1,500 300 1mm 2mm 10mm Near-IR Near-IR Mid-IR Other emission processes • BB radiation is a thermal process – In thermodynamic equilibrium with surroundings • Brehmstrahlung – thermal – “braking radiation” – Free electron experiences a deceleration when it collides with a positive ion, and radiates energy • Synchrotron – non-thermal – Electron spinning in a magnetic field – Seen in e.g. Crab Nebula (pulsar has large B field) • Electron/photon scattering – non-thermal • Inverse 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” course Dr. Matt Burleigh Summary of lecture 2 • From today’s lecture you will need to – Understand concept of Optical Depth (and derive I=I0e-t) – Understand Blackbody radiation – Remember Wien Law and how to use it lmaxT = 2.9x106 nm.K – Remember Stefan-Boltzmann Law • F = sT4 and L=4pR2sT4 – No need to derive Wien or SB Laws, just remember, understand and know how/when to use! Dr. Matt Burleigh