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Harvey Liszt Arecibo July 2009
Reflections on Spectra and Spectra andSpectral 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:– Gas temperatures, cloud masses– Chemical composition & chemistry– Atomic/molecular physics
Harvey Liszt Arecibo July 2009
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
Harvey Liszt Arecibo July 2009
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
Harvey Liszt Arecibo July 2009
Radio v. Optical
• By optical standards, radio lines may seem very, very weak; in terms of f-values, – For Lyman- 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
Harvey Liszt Arecibo July 2009
Radio v. Optical
• And the Einstein Aul are langorous
– For Lyman- 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
Harvey Liszt Arecibo July 2009
Harvey Liszt Arecibo July 2009
• How does this difference manifest itself?
linear
In the optical regime
Harvey Liszt Arecibo July 2009
• How does this difference manifest itself?
saturated
In the optical regime
Harvey Liszt Arecibo July 2009
• How does this difference manifest itself?
damped
In the optical regime
Harvey Liszt Arecibo July 2009
• This is how the difference manifests itself
Plug in values for HI and expand for small hv/kTexc
H I & the radio regime
H I optical depth
Harvey Liszt Arecibo July 2009
• This is how the difference manifests itself
(km/s)
Ugh, radiative transfer!
Harvey Liszt Arecibo July 2009
• This is how the difference manifests itself
If the opacity is great
Harvey Liszt Arecibo July 2009
• This is how the difference manifests itself
>> 1, TC small
If opacity is small …
Harvey Liszt Arecibo July 2009
• This is how the difference manifests itself
TC small
>> 1, TC small
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
Harvey Liszt Arecibo July 2009
Ratio TB and 1-e-
• 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)
Harvey Liszt Arecibo July 2005
Harvey Liszt Arecibo July 2009
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
Harvey Liszt Arecibo July 2009
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
Harvey Liszt Arecibo July 2009
• 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) = 10-26 W m-2 Hz-1
– Accumulate the energy falling across the area of the telescope, over some bandwidth
Energy
Harvey Liszt Arecibo July 2009
• 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 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
Area
Harvey Liszt Arecibo July 2009
Area?
• Telescope (effective) area Aeff ~D2/4– D is diameter of the illuminated area– No telescope is perfectly efficient– 75% is very good, 55% is more typical
• Beam solid angle Aeff 2– For a very good antenna ofis in a main
lobe– For an isotropic antenna , Aeff 2/– This is 0 dBi gain, used for RFI calculations
Harvey Liszt Arecibo July 2009
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)
Harvey Liszt Arecibo July 2009
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 v
T = T/(v t)1/2
Harvey Liszt Arecibo July 2009
But at what ‘T’?
• What is T in the radiometer equation?
T = (Tsys+ TA)/(v 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)
Harvey Liszt Arecibo July 2005
• When strong lines are observed with sensitive radiometers the noise level across a spectrum is inhomogeneous
Assessing your noise
Harvey Liszt Arecibo July 2005
• 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
How to measure T ?
Harvey Liszt Arecibo July 2005
• 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!
When T is inhomogeneous?
Harvey Liszt Arecibo July 2005
• 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
What’s in it for you?
Harvey Liszt Arecibo July 2005
• The usual assumption is that T 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
When might business as usual not be OK?
Harvey Liszt Arecibo July 2005
• The usual assumption is that T is the same across the spectrum
• AND that T 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
When might business as usual not be OK?
Harvey Liszt Arecibo July 2005
• The usual assumption is that T is the same across the spectrum
• AND that T 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
When might business as usual not be OK?
Harvey Liszt Arecibo July 2005
When data are smoothed/oversampled!
• When data are oversampled by a factor q>1, the rms of an N-channel sum is q1/2 larger than the naive result, N1/2 x the single-channel rms
Harvey Liszt Arecibo July 2005
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
Harvey Liszt Arecibo July 2009
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.