Mellinger Lesson 2 Radiative transfer & emission from single electron Toshihiro Handa Dept. of Phys. & Astron., Kagoshima University 鹿児島大学／愛媛大学 Galactic Radio Astronomy 銀河電波天文学特論

Mellinger Ray R dA 1 d1d1 dA 2 d2d2

Mellinger Effect of EM wave to a matter ▶ radiative transfer ■ analysis on EM wave travel in a matter ■ phenomenological consideration ■ 1 dimension model along a single ray ▶ Two effects ■ Matter absorbs the light. ■ Matter emits the light.

Mellinger Modeling of the radiative transfer ▶ absorption: absorption coeffisent  ■ proportional to the column density of the matter ■ proportional to the intensity of the ray ▶ emission: emissivity j ■ proportional to the column density of the mater

Mellinger Radiative transfer equation

Mellinger Simplest solution: absorption only

Mellinger Simple solution: emission only

Mellinger Simplest solution: thermal equilibrium

Mellinger General solution

Mellinger Physical meaning of the solution ▶ General solution for uniform media I = I 0 e -  + S (1- e -  ) ■ It gives I = (I 0 –S) e -  + S ▶ In the case of  →0: I = I 0 uniform ray ▶ In the case of  →∞: I =S brightness of media ▶ In the general cases, the result is between them

Mellinger Brightness temperature

Mellinger 1st order approximation and Taylor’s expansion

Mellinger Rayleigh-Jeans approximation

Mellinger Radiative transfer with brightness temperature ▶ General solution of the rad. trans. eq. I = I 0 e -  + S (1- e -  ) ▶ In thermal equilibrium, S= B (T) ■ Define T from S in the opposite way. ■ It is not always equal to thermodynamical temp. ▶ Using the brightness temperature, T B = T B,0 e -  + T (1- e -  )

Mellinger Basis of emission & absorption

Mellinger Radiation of a single electron(1) d

Mellinger Radiation of a single electron(2)

Mellinger Fourier transformation

Mellinger Delta function & complex conjugate

Mellinger Radiation of a single electron(3)