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3671 MWA Lecture 2

3671 MWA Lecture 2. In this lecture we will review: Attenuation of radiation by matter Optical Depth t l 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 T 4.

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3671 MWA Lecture 2

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  1. 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

  2. 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

  3. 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)

  4. 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”

  5. Wien Displacement LawlmaxT = 2.9x106nm.K

  6. 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

  7. 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!

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