Galactic Astronomy

Galactic Astronomy Radio observation Dong-hyun Lee 2007/08/15

Radio obs.s • Radio telescope : most powerful diagnostics of ISM • analysis : radiation interact with material (path) • Specific intensitiy • n_i ^(nu) : no. density of atoms (emit :i=2 , absorb : i=1) photon of freq. nu • Einstein coeff. : A_21 – prob. for spontaneous em. B_21 - for stimulated em. B_12 – for absorb.

Radio obs. ☞ • Tau : optical depth , S : source func. • In case S is const. along the l.o.s

Radio obs. • assume : thermodynamic equil. at temp T → Then I must tend to Planck intensity • Limit tau -> inf.  S = B in T.D.equil. • Replace S to B g : no. of quantum states (E. level i)

Radio obs. • Einstein’s rel.s • At radio freq. , generally in Rayleigh-Jeans regime hnu << kT • We obtain • Brightness temp.

Radio obs. • Optically-thin limit • T_B is proportional to column density along the l.o.s • Optically-thick, T_B measures temp. rather than its col. Density • ISM optically thin in 21cm atomic H & optically thick in 2.6 mm carbon monoxide • Antenna temp : T_A = alpha T_B - beam dilution

21cm line of atomic H • Ground state of atomic H split into 2 hyperfine levels  spins of electron & proton : 6 * 10^-6 eV antiparallel lower than parallel • Photon freq. : 1.4204 GHz or lambda : 21.105cm • F=0 , F=1 states no electric dipole moment  abs. or em. of 21cm photon : forbidden  lifetime of excited level is long(1.1*10^7 yr) & A_21 , B_ij are extremely small  T equl to kin. temp. of gas • Calc. the optical depth in 21cm line • df

21cm line of atomic H • N_1 : col. Density of H atoms of abs. at freq. nu • N_1 determined by dist. Of atoms over radial-vel. F(v) dv : frac. of all atoms on the l.o.s with rad.vel in range (v+dv, v)

21cm line of atomic H • 3 factor detemine f(v) • Rand. thermal motions with T • Rand. vel.s diff. macroscopic vol.s of gas (ISM is turbulent) • Large scale ordered vel grad.s in ISM (diff. Gal. rotation) • Thermal motion : char. Width ~ 1km/s to f(v) 21cm em. From face-on gal. s : turbulence contributes a width of order 7km/s • Width contri. By Gal rotation varies enor. With longitude l of l.o.s • Fig 8.12 : center & anticenter direction

21cm line of atomic H • Total neutral H col. Den. N_H • If optically thin, replace T_tau by T_B(brightness temp) T_B is dir. Measured (cf. T & tau not easily determine) • When we observe ext. gal. , we can determine N_H by integrating the HI col. Den. Over the surf. Area of sys.  dS = D^2 d omega : D – dist. To gal. & omega – solid angle df

21cm line of atomic H • Corresponding mass of H • M_H & total lum. L of gal. are prop. To D^2 , so that M_H / L is indep. Of uncertain dist. To ext. gal.

Rot. Transitions of heteronuclear mol.s • Spectra of mol.s : mm- band lines -> powerful probes of denser & colder components of ISM • Important line of CO : 2.6mm & 1.3 mm • Diff b/w H_2 & heteronuclear mol.(CO) • Hetero. Has net dipol moment  radiate when it spins • Diff b/w relevant Einstein const. for CO & HI • Lifetimes for rot. Excited levels of CO are rel. short • Smaller col. Den. Of CO than of HI is required to establish a given optical depth in the relevn lines • Table 8.1 & fig 8.13

Rot. Transitions of heteronuclear mol.s • Mass of a mol. Cloud will be prop. To its val. Of I_CO • Suppose cloud has rad. R & each cloudlet has mass m  M/m cloudlets & along a l.o.s through the center of cloud there are M/(mR^2) cloudlets per unit area  let delta be vel. Dispersion , then shadowing will be important 1st factor : mean no. of cloudlets & 2nd factor : prob. Vel ranges of 2 cloudlet overlap

Synchrotron rad. • Charged ptcl move in B-field spirals around field lins & radiates (Lorentz force) • If ptcl is at sub rel. vel  Cyclotron rad. & gyro-freq • If ptcl is at rel. vel  broad-band rad. • Critcal freq. • Pitch angle

Synchrotron rad. • Power radiated • This power is prop.to (q/m)^2 : electrons are more than 3 million more eff. Protons & 13 million more eff. Other nuclei • Total E dinsity : E is concentrated in lowest-E ptcl.s, which most midly rel.  cosmic rays should be thought of as comprising suprathermal ptcl.s

Radio-freq. bremsstrahlung & recombination lines • Comparatively densce ionized gas(that of HII regions) is provided by observations of radio-freq. bremstrahlung • Observed radio-freq. spectrum will be flat if the plasma is optically thin • Sufficiently low freq. , every thermal plasma must become optically thick • In a plasm with T ~ 10^4 K, significant no. of free electrons will be captured by protons into states principal quantum no. n>~ 50k • Highly excited H atoms formed are subsequently to decay by cascading down through states of smaller n , atom emits a photon of freq.

Radio-freq. bremsstrahlung & recombination lines • Estimate of plasma’s temp can be obtained from the ratio • Where I_l : peak intensity of the line I_c : intensity of the bremsstrahlung continuum at line’s central freq. b/c : ratio of line’s vel.-width to speed of light • Precise temp. dep. Of q is not easy to calc.  it is sensitive to departures from T.D equil. In the plasma  q prop. to 1/T

Dispersion & rotation measures • When plane polarized radiation of lambda propagates through a plasma  radiation’s plane of polarization slowly rotates : Faraday rotation • R_M : rotation measure of path • Refractive index of plasma

Dispersion & rotation measures • Group vel. • Time for pulse of central freq. to arrive from a source at D • Where D_M : dipersion measure

Galactic Astronomy