Some Radiation Theory - Lecture Notes | ASTRO 342, Study notes of Astronomy

Download Some Radiation Theory - Lecture Notes | ASTRO 342 and more Study notes Astronomy in PDF only on Docsity! Some Radiation Theory Why? ¢ The average temperature of a planet depends on how much energy a planet receives, and how it stores it. Variations, like seasons and climate, also depend on heat is stored and transported. ¢ We also need basic radiation theory to understand the temperature and luminosity of stars (including the sun). To begin... Three ways to transport heat... ¢ Conduction: random molecular motion. oy a oe ¢ Convection: larger scale circulations and turbulence e Radiation... what is radiation? We need a little more theory. Ill. Particle Aspect of Electromagnetic Radiation: Tn addition to its wave nature, electromagnetic radiation also seems to come in discrete bundles of energy called “photons”. The energy of a photon depends on the frequency of the radiation via Planck's law: €=hv =he/A. This relation connects the wave-particle dual characteristics of em. radiation. The particle aspect is most relevant at high energies, or very low light levels, i.e. where there are few photons. The Loppler Effect Offen opined 4y an analy bp send or Waler- Waves, See Ss uce ed Wave dhagram below Full special polebivisfhe aposn Jor Wave - lensth of leh trom a Man Source (S) € f+ We 17. Ake 1 = E 1-% | When Yo<s? , om approximate tis by : Mo x (144 &)(1- (4%) * 14 Ye 3) a = And ee, a 8.3 SPECTROSCOPY 151 a server Figure 8.17 The Doppler effect. Wi Tf & Werte Ee i Intensity and Flux To describe the flow (and scaterig) of hr lation we need te concepls of intensity wl Fux, which quality the idea a a dreclal density of radiation, Monochromatic intensily - js the amcutl of cnehy in Frequency interval 6 % yeoy) Slowing tarouyh a unit area, per unt time, into a cone of unit cold angle, in a qiver pipet an: ee v Av s4 at 22 Som. fz. ster 2-5 Continuous Thermal, EWU SS1Dn Consider he special, case of an wdhealjzed 2quilibriur Hera, rad Mier or Black body, a fe a a oe = Cand emt: “mg ) couvily, The redialion Ip the cavily iS IN @ wilhbyrrum with the walk (which ave pared. black d abserd, Noj t reflect rf Ia ti “on ho Secill a je Gf “Ud Abyy0i ton), Wel are insulated oa ad slyly b compensa @ for bsses through te peephole. % Properties of Thermal Rdeton @ 8 Thermal, radation has a Continuous spect: tum. D utensil 4; lye & << i= ly ° Ked: ab on IS conslanliy shectet deel reewtal, ; ae in Le cauily’ ad LL Man ny EM SSiom Poets invelye collisions belueen pies or electrons , Photon Cnty denends on coll’ ‘S$/0n CME4Ys an there Is -@ wide dispersion. of LMNs, ® When's Jew te poiter Le cavily, the pluer the peak ware lengta i, : nal hi er averaye oe Li hte.) ty = ae pe - dione ) - 027 TOQ \o> 8 Stetan- Boltemann Law when the Cavily fee Joffer- the ote! CHErgy i use WICK EASES AS = *sfars — 2a. a RE" @ Reyles igh - Jeans Law «- coe At low Frequencies Exdrapole th on of Lis lw Prec itesed a crisis in ph (Sits. All ai dese jus are confined yillen fie thd Epuction fer black bay rathtation I(A) = "(eV Ecee-] Why are We sO eee ed jn He “Special lo of HAdbd radials halion? Syars are ayratinade Bés | The universe was once a BB! XU -2 Ww) Orbits (shells ) balance Coicdonl alraction and centripetal Spree. i _G@ele 3 eo Fe The discreteness comes trom the assumplion thf orbital ata r Momentum is funtived, | myr = BA = yh @ Notes especialy the Cxish CHILE a a buest, or ground state orbil, n=7. This doeswt exist classically , 1S Mnbyinsi- caly quan am, @) The 7 het Ween ae gel- iS smaller tor lige A. tS ae ee r Car mr = jee Scubstituteng For- Y. i = (nh) nv jee i 2 arate — Im = Gnbex) Leni — 0] 2utf Ae EL, See ie se eye rp: Chery — z i Ss ye = ee ae aes ee i = r Znh mel Zz ey hy loge - a] JE -4 () There exists a coutimum, EO, where € lectvons are Ho longer Asad © The sir uclure of ave /'s d brent tr ach clement The orbits are drawn closer im for elements with ure frotens, bayer A. (6) Wi Ure shelk there Can be subchole (anion numbers n,m... The number of Llectrons | in the cuter shell determmnes the chemistry y, ? The Paul} exclusion principle slates Uh? | No more than 2 electrons Can Occupy Qa piven orbit ;  IVE -7 some ot He relbve binete nergy ot the coll’sion Is useal to boost the chibred low T° (Maxwellen dist.) <> few til collsicns. tig 7 fi => Mary test collisions. i eroush energy is imparted to the electron in the colfrsion it May be pred. tree, a = s © ie Coll’sional, lization O Photo absorption Cc a Electron whet: ploten with anergy epee! b Ye Wiermee between levels, for phetojenization need Cphebon > [Ebel dWl-5 We Cir POW under siand, K, op hod bus trem a MICKOSCapic int 2_microscopic point of Viel. ViEW. @ low a. (ot -pague C that ; eS hot fm to excite ee levels Bf (0H: Wy => emission Ines D lery pol, Tf 7 7 me yith much ion vallion, excilali (On, - po = ilo oe => continuum LMSsiCn. @ Gl ae platoabsonption => re- emission ito random = directions + abserp fon lines M Sorsuar abvection. Optical Depth and the Transfer of Radiation To begin, the photon scattering probability is formalized by defining the optical depth. The differential optical depth and the differential scattering probability are essentially the same, At=no, Al, where optical depth is conventionally measured from the outside-in. Integral form: C= Jn(x) o,dx path We also have, At, =o, Al=k, p Al, (m) where <m> is the mean particle mass, and ky is ths opac ty in units of m2/kg. XXL —8 Limd Larkening Can see deun to an optical depih ot abouL 76 (because ew xt) anywhere on Ue tae of sun. Assume no » const,, then ar= % Corresponds bo a ted jut A és serves as a constant mel? sbickh tr Lyping? ino the Sun abny te Jne a sight. ——  Ee, dabue opie Wher there I'S Em[SSton As we/f as absorplion/callerig in @ volume of almospherc, fi FAR S, fa G becomes. sO & = I, -S, with Sy ce er ? the ” source Jade kp and a the Enssion BE, Levent (in wuts of ly | Bee sohfin of transfer F 2 6-11) fees eS Lic = ae oe CSO — Wher Sy &O, we have He y bil ae Loin val solution. (beed tor plenels,) os — PUN WANYAI When cos = 1, aod we heve « GR sleb wrth Oy * const and. Mo Slax 70) geltng tired Urewoh , we ave / ly= S&S (4/4 e*) (with KeO, nor) 2 . es Sys the bhckbedy mn tnsily for? |