Reflections on Spectra and Spectral Line Work

1
Reflections on Spectra andSpectral Line Work

• Harvey S. Liszt
• NRAO, CHARLOTTESVILLE

2
Why spectral lines?

• From profile velocities and widths
• Gas flows in local clouds and the Hubble flow
• Galaxy rotation curves and (dark) masses
• Cloud dynamics, collapse, turbulence
• From intensities
• Gas temperatures, cloud masses
• Chemical composition chemistry
• Atomic/molecular physics

3
What does it take to see one?

• Medium that isnt completely transparent
• Finite optical depth photon mean free path
• Implies radiative interaction with environment
• Medium that stands out
• Its existence must either brighten or dim the
  radiation heading in our direction
• Background may be the cmb
• A medium at the temperature of the cmb is
  invisible against the cmb no matter how opaque

4
Spectral lines

• Spectral lines connect discrete internal states
• One, labelled l is lower in energy, u higher
• States are typically degenerate with weights gl ,
  gu
• Radiated energy appears at E hv (duh)
• For radio hv/k is quite small, 0.048 K/GHz
• hv/k isnt necessarily gt 2.73K
• More likely (than optical) to be near LTE
• Arbitrarily define excitation temperature
  nu/nl (gu/gl) e-hv/kTexc

5
Radio v. Optical

• By optical standards, radio lines may seem very,
  very weak in terms of f-values,
• For Lyman-a line of H I, f 0.48
• For 21 cm line of H I, f hv/2mec2 5.75.10-12
• Indeed, radio astronomy can only detect
  relatively large amounts of H I (1018 cm-2 vs
  1012 cm-2)
• Nonetheless, RA sees the H I line easily,
  everywhere in the sky

6
Radio v. Optical

• And the Einstein Aul are langorous
• For Lyman-a line of H I, Aul 109/s
• For 21 cm line of H I, Aul 2.7.10-15/s
• For TK lt 500 K, Texc TK
• For CO J1-0 at 2.6mm, Aul 7.2.10-8/s
• Small Aul low hv/k result in peculiarities of
  radiative transfer in the radio

7
In the optical regime

• How does this difference manifest itself?

8
In the optical regime

• How does this difference manifest itself?

9
In the optical regime

• How does this difference manifest itself?

10
In the optical regime

• How does this difference manifest itself?

linear
11
In the optical regime

• How does this difference manifest itself?

saturated
12
In the optical regime

• How does this difference manifest itself?

damped
13
In the optical regime

• How does this difference manifest itself?

14
In the radio regime

• This is how the difference manifests itself

15
In the radio regime

• This is how the difference manifests itself

16
In the radio regime

• This is how the difference manifests itself

17
In the radio regime

• This is how the difference manifests itself

18
H I the radio regime

• This is how the difference manifests itself

Plug in values for HI and expand for small
hv/kTexc
19
H I optical depth

• This is how the difference manifests itself

(km/s)
20
Ugh, radiative transfer!

• This is how the difference manifests itself

21
If the opacity is great

• This is how the difference manifests itself

t gtgt 1, TC small
22
If opacity is small

• This is how the difference manifests itself

t gtgt 1, TC small
t ltlt 1,TC small
23
3C454.3
24
3C454.3
25
3C454.3 in H I
26
H I vs. dust

• Integral of TBdv 385.5 K km/s
• Equivalent to N(H) 7.0x1020 cm-2
• E(B-V) 0.11 mag
• From Copernicus, gt N(H) 6.4x1020 cm-2
• Most of the extincting material is seen H I

27
3C454.3 in emission
28
3C454.3 in emission and absorption
29
3C454.3 in emission and absorption
t 0.3
30
Ratio TB and 1-e-t
31
Ratio TB and 1-e-t
32
Ratio TB and 1-e-t
33
Ratio TB and 1-e-t

• Inhomogeneity in TK
• Colder narrow-line clouds coexist with a
  warmer,more diffuse gas, broader- lined gas
  (inter-cloud medium)
• Two phase model cf. Clark (1965)

34
Short Break
35
Short Break
36
Better epistemolgy through radiometry

• Something (nature?) emits some radiation
• Manifested to us as a flux or burst of energy
  crossing our telescope
• Which we measure through radiometry
• By accumulating incident radiation until there is
  a detectable amount of energy
• Which we relate to some (celestial) phenomenon by
  deconvolving from the measurement the
  conditions of making it

37
Conditions?

• One aspect of conditions is physics of spectral
  line formation in the source
• Thats more or less my original book article,
  which back in the day was followed by a 2nd
  lecture
• Another aspect is what happens to these cosmic
  emanations in our equipment
• And another is how we maul, er, excuse me,
  manipulate spectra afterward

38
Energy

• E k T (energy, ergs, Joules)
• k Boltzmanns constant 10-23 Joules/K
• k k . s-1 . Hz-1
• So Joules W Hz-1
• That is why we talk about power flux density
• Sv (Jy) 10-26 W m-2 Hz-1
• Accumulate the energy falling across the area of
  the telescope, over some bandwidth

39
Area

• E k T (energy, ergs, Joules)
• k Boltzmanns constant 10-23 Joules/K
• k k . Hz-1 s-1
• So Joules W Hz-1
• That is why we talk about power flux density
• Sv (Jy) 10-26 W m-2 Hz-1
• Accumulate the energy falling across the area of
  the telescope, over some bandwidth

40
Area?

• Telescope (effective) area Aeff h . pD2/4
• D is diameter of the illuminated area
• No telescope is perfectly efficient
• h 75 is very good, 55 is more typical
• Beam solid angle Aeff W l2
• For a very good antenna 90 of W is in a main
  lobe
• For an isotropic antenna W 4p, Aeff l2/4p
• This is 0 dBi gain, used for RFI calculations

41
Flux as temperature

• Define antenna temperature Sv 2 kTA/Aeff
• In terms of the effective area of the telescope
• Sv/TA (or TA/Sv) is the gain
• 2 Kelvins/Jy at the GBT, 14 K/Jy for ART
• Each Jy heats the surface EM field by some Ks
• 12m ALMA antennas need 30 Jy/K but have 1 beam
  at 115 GHz (vs 3-8 w/Arecibo or GBT H I)

42
Phooey, noise

• Radiometers have an intrinsic property
• An irreducible rms fluctuation level
• When measuring a source of radiation whose
  ambient flux is equivalent to that of a black
  body at temperature T, during a time t, over a
  bandwidth Dv
• DT T/(Dv t)1/2

43
But at what T?

• What is T in the radiometer equation?
• DT (Tsys TA)/(Dv t)1/2
• Where
• Tsys is inherent in the equipment
• TA is what is added by incident flux
• Our signal is usually just additional noise,
  devoid of character (modulation)

44
Assessing your noise

• When strong lines are observed with sensitive
  radiometers the noise level across a spectrum is
  inhomogeneous

45
How to measure DT ?

• When strong lines are observed with sensitive
  radiometers the noise level across a spectrum is
  inhomogeneous
• This 1990 spectrum of the H I line had Tsys 36K,
  now GBT 20 K

46
When DT is inhomogeneous?

• When strong lines are observed with sensitive
  radiometers the noise level across a spectrum is
  inhomogeneous
• The noise level actually varies by a factor 3.5
  over this spectrum!

47
Whats in it for you?

• Notice how the software you use treats the rms
  noise it is probably taken to be homogeneous at
  the level of the line-free channels which may
  be OK if your lines are suitably weak

48
When might business as usual not be OK?

• The usual assumption is that DT is the same
  across the spectrum

• Notice how the software you use treats the rms
  noise it is probably taken to be homogeneous at
  the level of the line-free channels which may
  be OK if your lines are suitably weak

49
When might business as usual not be OK?

• The usual assumption is that DT is the same
  across the spectrum
• AND that DT can be read off the spectrum in
  signal-free channels

• Notice how the software you use treats the rms
  noise it is probably taken to be homogeneous at
  the level of the line-free channels which may
  be OK if your lines are suitably weak

50
When might business as usual not be OK?

• The usual assumption is that DT is the same
  across the spectrum
• AND that DT can be read off the spectrum in
  signal-free channels
• AND that the rms of an N-channel sum grows as
  N1/2

• Notice how the software you use treats the rms
  noise it is probably taken to be homogeneous at
  the level of the line-free channels which may
  be OK if your lines are suitably weak

51
When data are smoothed/oversampled!

• When data are oversampled by a factor qgt1, the
  rms of an N-channel sum is q1/2 larger than the
  naive result, N1/2 x the single-channel rms

52
When data are smoothed/oversampled!

• When data have q channels/resolution element, the
  rms of an N-channel sum is asymptotically q1/2
  larger than the naive result, N1/2 x the
  single-channel rms

53
History

• Since 1970 when CO was detected at 2.6mm, Tsys
  for 21cm H I work has fallen from 70 K to 20 K
  and Tsys for 3mm work has fallen from 5000 K to
  sub-100 K!

• In terms of the radiometer equation, the ratio
  (100 GHz/1.42GHz)1/2 now outweighs the higher
  system temperature at 100 GHz.

54
What was that?

• The number of km/s in one MHz lmm
• For H I, 1 MHz 211.1 km/s
• For CO, 1 MHz 2.6 km/s
• Advantage grows with sqrt(v)

• In terms of the radiometer equation, the ratio
  (100 GHz/1.42GHz)1/2 now outweighs the higher
  system temperature at 100 GHz.