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Reflections on Spectra and Spectral Line Work

Reflections on Spectra and Spectral Line Work. Harvey S. Liszt NRAO, CHARLOTTESVILLE. 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:

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Reflections on Spectra and Spectral Line Work

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  1. Reflections on Spectra andSpectral Line Work Harvey S. Liszt NRAO, CHARLOTTESVILLE Arecibo July 2009

  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 Arecibo July 2009

  3. What does it take to see one? • Medium that isn’t 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 Arecibo July 2009

  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 isn’t necessarily > 2.73K • More likely (than optical) to be near LTE • Arbitrarily define “excitation temperature” nu/nl= (gu/gl) e-hv/kTexc Arecibo July 2009

  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 Arecibo July 2009

  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 < 500 K, Texc ~ TK • For CO J=1-0 at 2.6mm, Aul~ 7.2.10-8/s • Small Aul + low hv/k result in peculiarities of radiative transfer in the radio Arecibo July 2009

  7. In the optical regime • How does this difference manifest itself? Arecibo July 2009

  8. In the optical regime • How does this difference manifest itself? Arecibo July 2009

  9. In the optical regime • How does this difference manifest itself? Arecibo July 2009

  10. In the optical regime • How does this difference manifest itself? linear Arecibo July 2009

  11. In the optical regime • How does this difference manifest itself? saturated Arecibo July 2009

  12. In the optical regime • How does this difference manifest itself? damped Arecibo July 2009

  13. In the optical regime • How does this difference manifest itself? Arecibo July 2009

  14. In the radio regime • This is how the difference manifests itself Arecibo July 2009

  15. In the radio regime • This is how the difference manifests itself Arecibo July 2009

  16. In the radio regime • This is how the difference manifests itself Arecibo July 2009

  17. In the radio regime • This is how the difference manifests itself Arecibo July 2009

  18. H I & the radio regime • This is how the difference manifests itself Plug in values for HI and expand for small hv/kTexc Arecibo July 2009

  19. H I optical depth • This is how the difference manifests itself (km/s) Arecibo July 2009

  20. Ugh, radiative transfer! • This is how the difference manifests itself Arecibo July 2009

  21. If the opacity is great • This is how the difference manifests itself t >> 1, TC small Arecibo July 2009

  22. If opacity is small … • This is how the difference manifests itself t >> 1, TC small t << 1,TC small Arecibo July 2009

  23. 3C454.3 Tucson December 2007

  24. 3C454.3 Tucson December 2007

  25. 3C454.3 in H I Tucson December 2007

  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, => N(H) ~ 6.4x1020 cm-2 • Most of the extincting material is seen H I Arecibo July 2009

  27. 3C454.3 in emission Tucson December 2007

  28. 3C454.3 in emission and absorption Tucson December 2007

  29. 3C454.3 in emission and absorption t ~ 0.3 Tucson December 2007

  30. Ratio TB and 1-e-t Arecibo July 2005

  31. Ratio TB and 1-e-t Arecibo July 2005

  32. Ratio TB and 1-e-t Arecibo July 2005

  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) Arecibo July 2005

  34. Short Break Tucson December 2007

  35. Short Break Tucson December 2007

  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 Arecibo July 2009

  37. Conditions? • One aspect of ‘conditions’ is physics of spectral line formation in the source • That’s 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 Arecibo July 2009

  38. Energy • E = k T (energy, ergs, Joules) • k = Boltzmann’s 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) = 10-26W m-2Hz-1 • Accumulate the energy falling across the area of the telescope, over some bandwidth Arecibo July 2009

  39. Area • E = k T (energy, ergs, Joules) • k = Boltzmann’s constant 10-23 Joules/K • k = k . Hz-1 s-1 • So Joules = W Hz-1 • That is why we talk about powerfluxdensity • Sv (Jy) = 10-26Wm-2Hz-1 • Accumulate the energy falling across the area of the telescope, over some bandwidth Arecibo July 2009

  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 AeffW = 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 Arecibo July 2009

  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 K’s • 12m ALMA antennas need ~30 Jy/K but have 1’ beam at 115 GHz (vs 3’-8’ w/Arecibo or GBT H I) Arecibo July 2009

  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 Arecibo July 2009

  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) Arecibo July 2009

  44. Assessing your noise • When strong lines are observed with sensitive radiometers the noise level across a spectrum is inhomogeneous Arecibo July 2005

  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 Arecibo July 2005

  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! Arecibo July 2005

  47. What’s 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 Arecibo July 2005

  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 Arecibo July 2005

  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 Arecibo July 2005

  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 Arecibo July 2005

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