Galactic Astronomy

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Galactic Astronomy

• Radio observation

Dong-hyun Lee 2007/08/15
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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 i2 ,
  absorb i1)
• photon of freq. nu
• Einstein coeff. A_21 prob. for spontaneous
  em.
• B_21 - for stimulated em. B_12 for absorb.

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Radio obs.

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

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Radio obs.

• assume thermodynamic equil. at temp T
• ? Then I must tend to Planck intensity
• Limit tau -gt inf. ? S B in T.D.equil.
• Replace S to B
• g no. of quantum states (E. level i)

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Radio obs.

• Einsteins rel.s
• At radio freq. , generally in Rayleigh-Jeans
  regime
• hnu ltlt kT
• We obtain
• Brightness temp.

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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

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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
• F0 , F1 states no electric dipole moment
• ? abs. or em. of 21cm photon forbidden
• ? lifetime of excited level is long(1.1107
  yr)
• A_21 , B_ij are extremely small
• ? T equl to kin. temp. of gas
• Calc. the optical depth in 21cm line
• df

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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 (vdv, v)

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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

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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 D2 d omega D dist. To gal. omega
  solid angle
• df

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21cm line of atomic H

• Corresponding mass of H
• M_H total lum. L of gal. are prop. To D2 , so
  that M_H / L is indep. Of uncertain dist. To ext.
  gal.

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Rot. Transitions of heteronuclear mol.s

• Spectra of mol.s mm- band lines -gt 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

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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/(mR2) 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

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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

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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

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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 104 K, significant no. of
  free electrons will be captured by protons into
  states principal quantum no. ngt 50k
• Highly excited H atoms formed are subsequently to
  decay by cascading down through states of smaller
  n , atom emits a photon of freq.

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Radio-freq. bremsstrahlung recombination lines

• Estimate of plasmas temp can be obtained from
  the ratio
• Where I_l peak intensity of the line
• I_c intensity of the bremsstrahlung continuum
  at lines central freq.
• b/c ratio of lines 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

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Dispersion rotation measures

• When plane polarized radiation of lambda
  propagates through a plasma ? radiations plane
  of polarization slowly rotates Faraday rotation
• R_M rotation measure of path
• Refractive index of plasma

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Dispersion rotation measures

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