harvey lisztarecibo july 2009 harvey s. liszt nrao, charlottesville

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


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


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


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


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


In the optical regime


• How does this difference manifest itself?



linear




saturated




damped



• This is how the difference manifests itself

In the radio regime



Plug in values for HI and expand for small hv/kTexc

H I & the radio regime

H I optical depth



(km/s)

Ugh, radiative transfer!



If the opacity is great



>> 1, TC small

If opacity is small …



TC small

>> 1, TC small

Harvey Liszt Tucson December 2007

3C454.3


3C454.3 in H I

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



3C454.3 in emission


3C454.3 in emission and absorption


~ 0.3

3C454.3 in emission and absorption

Ratio TB and 1-e-


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)



Short Break


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


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


• 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


• 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


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


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)


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


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)


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

Assessing your noise



• This 1990 spectrum of the H I line had Tsys= 36K, now GBT ~ 20 K

How to measure T ?



• The noise level actually varies by a factor 3.5 over this spectrum!

When T is inhomogeneous?


• 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?


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


When might business as usual not be OK?



• AND that T can be read off the spectrum in signal-free channels





• 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




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


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


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.


What was that?

• The number of km/s in one MHz = mm

– 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.

harvey lisztarecibo july 2009 harvey s. liszt nrao, charlottesville

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