Galactic AstronomyGalactic Astronomy

Radio observationRadio observation

Dong-hyun LeeDong-hyun Lee2007/08/152007/08/15

Radio obs.sRadio obs.s Radio telescope : most powerful diagnostics of ISMRadio telescope : most powerful diagnostics of ISM analysis : radiation interact with material (path)analysis : radiation interact with material (path) Specific intensitiySpecific intensitiy

n_i ^(nu) : no. density of atoms (emit :i=2 , absorb : i=1)n_i ^(nu) : no. density of atoms (emit :i=2 , absorb : i=1)photon of freq. nuphoton of freq. nu

Einstein coeff. : A_21 – prob. for spontaneous em. Einstein coeff. : A_21 – prob. for spontaneous em. B_21 - for stimulated em. B_12 – for absorb.B_21 - for stimulated em. B_12 – for absorb.

Radio obs.Radio obs.

☞ ☞

Tau : optical depth , S : source func. Tau : optical depth , S : source func. In case S is const. along the l.o.sIn case S is const. along the l.o.s

Radio obs.Radio obs. assume : thermodynamic equil. at temp Tassume : thermodynamic equil. at temp T

→ → Then I must tend to Planck intensityThen I must tend to Planck intensity

Limit tau -> inf. Limit tau -> inf. S = B in T.D.equil. S = B in T.D.equil.

Replace S to BReplace S to B

g : no. of quantum states (E. level i)g : no. of quantum states (E. level i)

Radio obs.Radio obs. Einstein’s rel.s Einstein’s rel.s

At radio freq. , generally in Rayleigh-Jeans regimeAt radio freq. , generally in Rayleigh-Jeans regime

hnu << kThnu << kT

We obtainWe obtain

Brightness temp. Brightness temp.

Radio obs.Radio obs.

Optically-thin limit Optically-thin limit

T_B is proportional to column density along the l.o.sT_B is proportional to column density along the l.o.s Optically-thick, T_B measures temp. rather than its col. DensitOptically-thick, T_B measures temp. rather than its col. Densit

yy ISM optically thin in 21cm atomic H ISM optically thin in 21cm atomic H

& optically thick in 2.6 mm carbon monoxide& optically thick in 2.6 mm carbon monoxide Antenna temp : T_A = alpha T_B - beam dilutionAntenna temp : T_A = alpha T_B - beam dilution

21cm line of atomic H21cm line of atomic H Ground state of atomic H split into 2 hyperfine levelsGround state of atomic H split into 2 hyperfine levels

spins of electron & proton : 6 * 10^-6 eV spins of electron & proton : 6 * 10^-6 eV antiparallel lower than parallelantiparallel lower than parallel Photon freq. : 1.4204 GHz or lambda : 21.105cmPhoton freq. : 1.4204 GHz or lambda : 21.105cm F=0 , F=1 states no electric dipole momentF=0 , F=1 states no electric dipole moment abs. or em. of 21cm photon : forbiddenabs. or em. of 21cm photon : forbidden lifetime of excited level is long(1.1*10^7 yr)lifetime of excited level is long(1.1*10^7 yr)

& A_21 , B_ij are extremely small& A_21 , B_ij are extremely small

T equl to kin. temp. of gasT equl to kin. temp. of gas Calc. the optical depth in 21cm lineCalc. the optical depth in 21cm line

dfdf

21cm line of atomic H21cm line of atomic H N_1 : col. Density of H atoms of abs. at freq. nu N_1 : col. Density of H atoms of abs. at freq. nu N_1 determined by dist. Of atoms over radial-vel.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)F(v) dv : frac. of all atoms on the l.o.s with rad.vel in range (v+dv, v)

21cm line of atomic H21cm line of atomic H 3 factor detemine f(v)3 factor detemine f(v)

1.1. Rand. thermal motions with TRand. thermal motions with T

2.2. Rand. vel.s diff. macroscopic vol.s of gas (ISM is turbulent) Rand. vel.s diff. macroscopic vol.s of gas (ISM is turbulent)

3.3. Large scale ordered vel grad.s in ISM (diff. Gal. rotation)Large scale ordered vel grad.s in ISM (diff. Gal. rotation)

Thermal motion : char. Width ~ 1km/s to f(v) Thermal motion : char. Width ~ 1km/s to f(v)

21cm em. From face-on gal. s : turbulence contributes 21cm em. From face-on gal. s : turbulence contributes

a width of order 7km/sa width of order 7km/s Width contri. By Gal rotation varies enor. With longituWidth contri. By Gal rotation varies enor. With longitu

de l of l.o.sde l of l.o.s Fig 8.12 : center & anticenter directionFig 8.12 : center & anticenter direction

21cm line of atomic H21cm line of atomic H Total neutral H col. Den. N_HTotal neutral H col. Den. N_H

If optically thin, replace T_tau by T_B(brightness temp)If optically thin, replace T_tau by T_B(brightness temp)

T_B is dir. Measured (cf. T & tau not easily determine)T_B is dir. Measured (cf. T & tau not easily determine)

When we observe ext. gal. , we can determine N_H by integrating When we observe ext. gal. , we can determine N_H by integrating the HI col. Den. Over the surf. Area of sys.the HI col. Den. Over the surf. Area of sys.

dS = D^2 d omega : D – dist. To gal. & omega – solid angledS = D^2 d omega : D – dist. To gal. & omega – solid angle

dfdf

21cm line of atomic H21cm line of atomic H Corresponding mass of HCorresponding mass of H

M_H & total lum. L of gal. are prop. To D^2 , so that M_H / L 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.is indep. Of uncertain dist. To ext. gal.

Rot. Transitions of heteronuclear mol.sRot. Transitions of heteronuclear mol.s Spectra of mol.s : mm- band lines -> powerful probes of Spectra of mol.s : mm- band lines -> powerful probes of

denser & colder components of ISMdenser & colder components of ISM Important line of CO : 2.6mm & 1.3 mmImportant line of CO : 2.6mm & 1.3 mm Diff b/w H_2 & heteronuclear mol.(CO)Diff b/w H_2 & heteronuclear mol.(CO)

Hetero. Has net dipol moment Hetero. Has net dipol moment radiate when it spins radiate when it spins Diff b/w relevant Einstein const. for CO & HIDiff b/w relevant Einstein const. for CO & HI

Lifetimes for rot. Excited levels of CO are rel. shortLifetimes for rot. Excited levels of CO are rel. short Smaller col. Den. Of CO than of HI is required to establish a giSmaller col. Den. Of CO than of HI is required to establish a gi

ven optical depth in the relevn linesven optical depth in the relevn lines Table 8.1 & fig 8.13Table 8.1 & fig 8.13

Rot. Transitions of heteronuclear mol.sRot. Transitions of heteronuclear mol.s

Mass of a mol. Cloud will be prop. To its val. Of I_COMass of a mol. Cloud will be prop. To its val. Of I_CO Suppose cloud has rad. R & each cloudlet has mass m Suppose cloud has rad. R & each cloudlet has mass m

M/m cloudlets & along a l.o.s through the center of cloud M/m cloudlets & along a l.o.s through the center of cloud there are M/(mR^2) cloudlets per unit area there are M/(mR^2) cloudlets per unit area let delta be let delta be vel. Dispersion , then shadowing will be importantvel. Dispersion , then shadowing will be important

11stst factor : mean no. of cloudlets & 2 factor : mean no. of cloudlets & 2ndnd factor : prob. Vel ranges of 2 cloudlet ov factor : prob. Vel ranges of 2 cloudlet overlaperlap

Synchrotron rad.Synchrotron rad. Charged ptcl move in B-field spirals around field lins & rCharged ptcl move in B-field spirals around field lins & r

adiates (Lorentz force)adiates (Lorentz force) If ptcl is at sub rel. vel If ptcl is at sub rel. vel Cyclotron rad. & gyro-freq Cyclotron rad. & gyro-freq

If ptcl is at rel. vel If ptcl is at rel. vel broad-band rad. broad-band rad. Critcal freq. Critcal freq.

Pitch angle Pitch angle

Synchrotron rad.Synchrotron rad. Power radiatedPower radiated

This power is prop.to (q/m)^2 : electrons are more than 3 millioThis power is prop.to (q/m)^2 : electrons are more than 3 million more eff. Protons & 13 million more eff. Other nuclein more eff. Protons & 13 million more eff. Other nuclei

Total E dinsity : E is concentrated in lowest-E ptcl.s, whiTotal E dinsity : E is concentrated in lowest-E ptcl.s, which most midly rel. ch most midly rel. cosmic rays should be thought of as cosmic rays should be thought of as comprising suprathermal ptcl.scomprising suprathermal ptcl.s

Radio-freq. bremsstrahlung & recombination linesRadio-freq. bremsstrahlung & recombination lines Comparatively densce ionized gas(that of HII regions) is provComparatively densce ionized gas(that of HII regions) is prov

ided by observations of radio-freq. bremstrahlungided by observations of radio-freq. bremstrahlung Observed radio-freq. spectrum will be flat if the plasma is optObserved radio-freq. spectrum will be flat if the plasma is opt

ically thinically thin Sufficiently low freq. , every thermal plasma must become opSufficiently low freq. , every thermal plasma must become op

tically thicktically thick In a plasm with T ~ 10^4 K, significant no. of free electrons In a plasm with T ~ 10^4 K, significant no. of free electrons

will be captured by protons into states principal quantum no. will be captured by protons into states principal quantum no. n>~ 50kn>~ 50k

Highly excited H atoms formed are subsequently to decay by cascadiHighly excited H atoms formed are subsequently to decay by cascading down through states of smaller n , atom emits a photon of freq.ng down through states of smaller n , atom emits a photon of freq.

Radio-freq. bremsstrahlung & recombination linesRadio-freq. bremsstrahlung & recombination lines Estimate of plasma’s temp can be obtained from the ratioEstimate of plasma’s temp can be obtained from the ratio

Where I_l : peak intensity of the line Where I_l : peak intensity of the line

I_c : intensity of the bremsstrahlung continuum at line’s central freq.I_c : intensity of the bremsstrahlung continuum at line’s central freq.

b/c : ratio of line’s vel.-width to speed of lightb/c : ratio of line’s vel.-width to speed of light

Precise temp. dep. Of q is not easy to calc. Precise temp. dep. Of q is not easy to calc. it is sensitive t it is sensitive to departures from T.D equil. In the plasma o departures from T.D equil. In the plasma q prop. to 1/T q prop. to 1/T

Dispersion & rotation measuresDispersion & rotation measures When plane polarized radiation of lambda propagates When plane polarized radiation of lambda propagates

through a plasma through a plasma radiation’s plane of polarization radiation’s plane of polarization slowly rotates : Faraday rotationslowly rotates : Faraday rotation

R_M : rotation measure of pathR_M : rotation measure of path Refractive index of plasma Refractive index of plasma

Dispersion & rotation measuresDispersion & rotation measures Group vel.Group vel.

Time for pulse of central freq. to arrive from a source at DTime for pulse of central freq. to arrive from a source at D

Where D_M : dipersion measureWhere D_M : dipersion measure