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Chapter 6
Radio Astronomy
Robert M. Hjellming
6.1
6.1
Introduction . . . . . . . . . . . . . . . . . . . . . . . . . 121
6.2
Atmospheric Window and Sky Brightness . . . . . . . 123
6.3
Radio Wave Propagation . . . . . . . . . . . . . . . . . 125
6.4
Radio Telescopes and Arrays . . . . . . . . . . . . . . 128
6.5
Radio Emission and Absorption Processes . . . . . . 131
6.6
Radio Astronomy References . . . . . . . . . . . . . . 140
INTRODUCTION
Radio astronomy is defined by three things. First is the range of frequencies that constitute the
radio windows of the Earth’s atmosphere, ranging roughly from 20 MHz to 1000 GHz. Second are
the astronomical objects that emit radio waves with sufficient strength to be detectable at the Earth;
some emit by thermal processes, but most are seen because of the emission from relativistic electrons
(cosmic rays) interacting with local magnetic fields. Third, radio radiation behaves more like waves
than particles (photons), allowing the measurement of both amplitude and phase of the radiation field.
The capability to measure phase gives radio interferometry the capability to do the highest resolution
imaging of astronomical objects currently possible in astronomy.
The variety and number of radio sources is so large that in Table 6.1 we merely summarize a number
of source catalogs devoted to these topics.
121
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Table 6.1. List of radio source catalogs.
Type of Source
Contents
4C Radio Survey [1, 2]
Bologna B2 Sky Survey [3–5]
Bologna B3 Sky Survey [6, 7]
20 cm N. Sky Catalog [8]
6 cm Gal. Plane Survey [9]
6 cm South & Tropical Surveys [10, 11]
11 cm All Sky Catalog [12]
11 cm N. Sky Catalog [13]
Bright Galaxies [14]
20 cm Gal. Plane Survey [15]
21 cm Gal. Plane Survey [16]
Galaxy HI [17, 18]
Atlas of Galactic HI [19]
Molecular lines [20, 21]
Pulsars [22]
Opt. Pos. Radio Stars [23]
20 cm Radio Sources δ > −5◦ [24, 25]
4844 56 cm sources > 2 Jy, −7◦ ≤ δ ≤ 80◦
408 MHz, 21.7◦ ≤ δ ≤ 40◦
408 MHz, 37◦ ≤ δ ≤ 47◦
365, 1400, 4850 MHz, 0 ≤ δ ≤ 75◦
Parkes 64 m, |b| ≤ 2◦ , l = 190◦ − 360◦ − 40◦
Parkes 64 m, −78◦ ≤ δ ≤ −10◦
Bright sources
6483 sources, |b| ≤ 5◦ , 240◦ ≤ l ≤ 357◦
All radio data pre-1975, normal galaxies
VLA B Conf. Survey
Eff. 100m, |b| ≤ 4◦ , 95◦ ≤ l ≤ 357◦
Galaxies, vradial ≤ 3000 km/s
21 cm H emission line profiles
Frequencies, other molecular data
Catalog of known pulsars
221 radio stars
1400 MHz sky atlas
References
1. Pilkington, J.D.H., & Scott, P.F. 1965, Mem. R.A.S., 69, 183
2. Gower, J.F.R., Scott, P.F., & Willis D. 1967, Mem. R.A.S., 71, 144
3. Colla, G. et al. 1970, A&AS, 1, 281
4. Colla, G. et al. 1972, A&AS, 7, 1
5. Colla, G. et al. 1973, A&AS, 11, 291
6. Fanti, C. et al. 1974, A&AS, 18, 147
7. Ficcara, A., Grueff, G., & Tomesetti, G. 1985, A&AS, 59, 255
8. White, R.L., & Becker, R.H. 1992, ApJS, 79, 331
9. Haynes, R.F., Caswell, J.L., & Simons, L.W.J. 1978, Aust. J. Phys. Suppl., 48, 1
10. Griffith, M.R. et al. 1994, ApJS, 90, 179
11. Wright, A.E. et al. 1994, ApJS, 91, 111
12. Wall, J.V., & Peacock, J.A. 1985, MNRAS, 216, 173
13. Fürst, E. et al. 1990, A&AS, 85, 805
14. Haynes, R.F., Caswell, J.L., & Simons, L.W.J. 1978, Aust. J. Phys. Suppl., 45, 1
15. Zoonematkermani, S. et al. 1990, ApJS, 74, 181
16. Reich, W., Reich, P., & Fürst, E. 1990, A&AS, 83, 539
17. Tully, R.B. 1988, Nearby Galaxies Catalog (Cambridge University Press, Cambridge)
18. Huchtmeier, W.K., & Richter, O.-G. 1989, A General Catalog of HI Observations of
Galaxies: The Reference Catalog (Springer-Verlag, New York)
19. Hartman, D., & Burton, W.D. 1995, Atlas of Galactic HI (Cambridge University Press,
Cambridge)
20. Lovas, F.J. 1992, J. Phys. Chem. Ref. Data, 21, 181
21. Lovas, F.J., Snyder, L.E., & Johnson, D.R. 1979, ApJS, 41, 451
22. Taylor, J.H., Manchester, R.N., & Lyne, A.G. 1993, ApJS, 66, 529
23. Réquième, Y. & Mazurier, J.M. 1991, A&AS, 89, 311
24. Condon, J.J., Broderick, J.J., & Seielstad, G.A. 1989, AJ, 97, 1064
25. Condon, J.J., Broderick, J.J., & Seielstad, G.A. 1991, AJ, 102, 2041
Other information and images from surveys can be obtained from Internet pages maintained by the
National Center for Super Computing Applications (NCSA) Astronomy Digital Image Library (ADIL,
http://imagelib.ncsa.uiuc.edu/imagelib.html) and the National Radio Astronomy Observatory (NRAO,
http://info.aoc.nrao.edu). More extensive radio (and other) catalogs can be found from Internet pages
for the NASA Astrophysics Data System (http://adswww.harvard.edu/index.html).
In Figure 6.1 schematic radio spectra representative of a variety of continuum radio sources
are plotted in the form of flux density (in units of Jy = Jansky = 10−23 ergs cm−2 s−1 Hz−1 =
10−26 W m−2 Hz−1 ) as a function of frequency. The sources and spectra in Figure 6.1 are schematic
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6.2 ATMOSPHERIC W INDOW AND S KY B RIGHTNESS / 123
108
Active Sun
107
106
105
Flux Density [Jy]
104
103
Sky
Background
Jupiter
(radiation
belts)
Quiet Sun
Cyg A
Crab
Virgo A Nebula
M31
102
Moon
Cas A
Crab
Pulsar
(unpulsed)
3C295
3C273
101
Orion
Nebula
100
Jupiter
BL Lac
10-1
Mars
SS433
Crab Pulsar
(pulsed)
Cyg X-3 (non-flaring)
10-2
Antares
10-3
10
100
1000
10000
Figure 6.1. Radio spectra of various types of sources in the form of flux density as a function of frequency ν.
indicators of typical behavior for a wide variety of objects. Major solar-system radio sources are
the active Sun, the quiet Sun, the Earth’s Moon, Mars, the surface of Jupiter, and Jupiter’s radiation
belts. Stellar system sources are: pulsars, with the pulsed and unpulsed (dashed line) emission from
the Crab pulsar; the partially ionized coronal emission of the red supergiant Antares; and the X-ray
binaries SS433 and Cyg X-3 (quiescent). The optically thick and thin portions of the radio spectrum
of the ionized gas from an HII region is indicated for the Orion Nebula. Cas A is a remnant of a
supernova explosion in our Galaxy; and the Crab nebula spectrum is representative of the relatively
rare plerion, i.e., nebulosities energized by pulsars. The radio spectrum for M31, the Andromeda
nebula, is representative of spiral galaxy behavior. Strong radio galaxies are represented by Cyg A and
Virgo A; BL Lac is a blazar, while 3C273 and 3C295 are strong quasars.
Defining the convention that the spectral index α is the power law index for the flux density,
Sν ∝ ν α , then positive spectral indices indicate optically thick emission while negative spectral indices
indicate optically thin emission. Spectral indices near zero indicate optically thin emission for thermal
sources, while similarly flat spectra for synchrotron radiation sources indicate optically thick emission
from a wide range of optical depths.
6.2
6.2.1
ATMOSPHERIC WINDOW AND SKY BRIGHTNESS
Atmospheric Window
The low-frequency end of the radio window is set by ionospheric absorption. Since the ionosphere
has diurnal variations, solar cycle variations, variations depending upon the effect of particle storms
impacting the atmosphere, and variations with Earth latitude and longitude, the lowest frequency where
the atmosphere is transparent varies considerably over the range 10 to 30 MHz. From that lowfrequency cut-off, up to about 22 GHz, the Earth’s atmosphere does not absorb radio waves, although
variation in the index of refraction affects the phase of incoming radio waves at the higher frequencies.
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R ADIO A STRONOMY
1
1
1 mm PWV
8 mm PWV
0
0.01
0
0.1
1
10
100 1000
0
Wavelength [cm]
200
400
600
800
1000
Frequency [GHz]
Figure 6.2. The radio window for the Earth’s atmosphere shown in terms of plots of atmospheric transparency as
a function of both wavelength and frequency. The solid line is for excellent conditions with 1 mm PWV and the
dashed line is for normal conditions with 8 mm PWV.
At the lowest frequencies plasma effects in the ionosphere induce variable Faraday rotation in incoming
radio waves.
In Figure 6.2 we plot models for the transparency of the Earth’s atmosphere for two values
of precipitable water vapor (PWV), 1 and 8 mm, representing extremely low and normal levels,
respectively.
6.2.2
Surface Brightness and Brightness Temperature
All astronomy is based upon measurements of surface brightness on the celestial sphere: Iν (α, δ, t),
where t is time, (α,δ) is position specified by right ascension and declination, ν is frequency, and
I is the specific intensity which can be any of the four Stokes parameters. The surface brightness
of a black body of temperature T is Bν = (2hν 3 /c2 )(1/[ehν/kT − 1]), where h and k are the
Planck and Boltzmann constants. For small values of hν/kT , the Rayleigh–Jeans approximation is
valid, and Bν (T ) ∼
= 2kT /λ2 ; this is valid at longer radio wavelengths. For reasons related to the
antenna measurement equation, radio astronomy often uses brightness temperature rather than surface
brightness to describe measurements, where the brightness temperature is
Tb ≡
λ2
Bν .
2k
(6.1)
Equation (6.1) is often used even when black body or long wavelength approximations are not
applicable. Because of this, the concept of radiation temperature (Tr ≡ [hν/k]/[ehν/kT − 1]) is
commonly used; where T is a “true” physical temperature.
6.2.3
Sources of Background Radiation
At each wavelength there are sources of background radiation detectable by radio telescopes,
principally the Earth’s atmosphere, the cosmic radiation background, and diffuse emission from our
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100000
Galactic
Background
Earth's
Atmosphere
10000
100
1000
Earth's
Atmosphere
100
10
COBE
1
10
Cosmic
Background
Galactic
Background
0.1
0.01
0.001
COBE
Cosmic
Background
0.0001
100
10
1
0.1 100
Wavelength [cm]
10
1
1
Brightness Temperature [K]
15
-2
-1
-1
Brightness x 10 [W cm str cm ]
6.3 R ADIO WAVE P ROPAGATION / 125
0.1
Wavelength [cm]
Figure 6.3. Apparent brightness (left) and brightness temperature (right) plotted as a function of wavelength
for: the Earth’s atmosphere (dashed line, model; open circle, measurements); cosmic background radiation from
COBE (solid line) and other instruments (filled circles); and galactic background radiation (dotted line).
Galaxy. In Figure 6.3 we plot data and models for these sources of radiation. At wavelengths shorter
than ∼ 1 cm the Earth’s atmosphere dominates the background, while above 13 cm the galactic
background dominates. Between 1 and ∼ 13 cm the cosmic background dominates. However, in many
cases man-made interference, or solar radio emission, can be more important “background emission,”
particularly at wavelengths longer than 10 cm.
6.3
6.3.1
RADIO WAVE PROPAGATION
Radiators-Absorbers, Fields, and Coupling Equations
Radiation measurement at radio wavelengths allows direct measurement of the amplitude and phase of
electromagnetic fields; this is the reason radiation field analysis in radio astronomy is usually done in
terms of fields.
If we identify a distant point in a radio source with the vector R, and the location of the oscillating
current element with the vector, the fields between the two points are proportional to the propagator [1]
Pν (r) =
e2πiν|R−r|/c
,
|R − r|
(6.2)
so by Huygens’ Principle, and the fact that all radiation appears as if it originates from the celestial
sphere, the field on the celestial sphere at r is the superposition
E ν (r) =
E(R)
e2πiν|R−r|/c
d S,
|R − r|
(6.3)
where d S is a surface element on the celestial sphere.
The radiation flux for propagating fields is determined by the real part of the Poynting flux averaged
over time, so Sr = E × H
= Re(E θ H φ − E φ Hθ )/2 = E θ Hφ . The power d P at distance r
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R ADIO A STRONOMY
passing through solid angle d = d A/r 2 is the Poynting flux through d A at distance r . From the
field distribution over the surface of an antenna we compute d P/d which allows us to calculate the
important properties of antennas. The normalized antenna pattern is defined by
Pn (θ, φ) =
d P/d
(d P/d)max
(6.4)
so an infinitesimal current element has Pn (θ, φ) = sin2 θ . The beam solid angle of an antenna is
a = 4π Pn (θ, φ) d, and the directivity is D = 4π/ a [2].
For real antennas we integrate over the collecting surface and from that compute d P/d from
which antenna parameters may be computed.
6.3.2
Radio Noise and Detection Limits
The measured quantities for radio telescopes are total power or correlated total power at some point in
the signal path of the electronics. This is one of the sources of the predominance of using temperature
as a measurement variable, because of Nyquist’s law which relates the total power Pa to an antenna
temperature Ta by
Pa = 4kTa ν,
(6.5)
where k ν is the frequency range (or bandwidth) over which the total power measurement is made.
Pa is the measure of the sum of the power due to radiation sources external to the antenna and the
power generated in the antenna and its electronics system. In modern systems the latter is dominated
by the receiver temperature, but is generally called system temperature (Tsys ) which constitutes an
irreducible minimum level of noise in the measured signal. The power being measured is that of a
fluctuating voltage, originally induced by the external electric fields in the form of oscillating currents
in the antenna’s collecting surface, which radiate with a focus on either a feed at the prime focus of the
antenna or on one or more subreflectors directed at a feed. The feed absorbs radiation and produces an
output signal which is transferred to an electronic receiver followed (usually) by a complicated series
of amplifiers, frequency converters, and other electronics elements. Then the fluctuating total power
is then measured over a specific frequency range with a bandwidth (ν), and over a specific time
interval t. For a system temperature Tsys the noise component of the measured signal is
Tnoise = √
Tsys
ν t
,
(6.6)
which indicates how noise changes with bandwidth and integration time. The same principle applies
in the case of interferometry where signals are either added or (almost all the time) correlated (or
multiplied), so it is the correlated power from two antennas that is being measured.
The noise component of the system temperature is usually the limiting factor in the measurements
being made. The fundamental limit to electronic noise temperatures is the quantum limit: hν/k =
0.048νGHz K, where νGHz is the frequency in units of GHz. Real system temperatures must be above
this limit. In the 1990s the state of the art of modern electronics is roughly capable of producing
noise temperatures of 4hν/k. It is expected that at the beginning of the twenty-first century noise
temperatures will be ∼ 2hν/k, but it is unlikely that they will ever get very close to the quantum limit.
6.3.3
Effects of Ionosphere, ISM, and Source Environment
Because radio signals are best dealt with by an analysis based upon electric fields, one should think of
radio sources as three-dimensional regions radiating electric fields. Once radiation that will eventually
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6.3 R ADIO WAVE P ROPAGATION / 127
reach a radio telescope on, or near, the Earth is produced, one then must think of propagation
phenomena which affect these fields. Absorption and re-radiation by free electrons, ions, and atomic
or molecular species can change the original radiation field into one modified by many effects. One
can decompose this process into propagation effects: inside radio sources; in the intergalactic and
interstellar medium (IGM and ISM); in the interplanetary medium of the solar system; and in the
Earth’s atmosphere and ionosphere.
The ionized component of the intervening medium between a radio source and an observing
telescope affects propagation by introducing time delays and Faraday rotation. The time of arrival
L
of a pulse of radiation is tpulse = 0 ds/vgroup where L is the propagation path length, ds is a segment
of the line of sight, and vgroup is the group velocity. The delay per unit frequency introduced by the
electron concentration Ne is approximated by
L
dtpulse ∼
e2
Ne ds.
(6.7)
=
dν
4π 0 mcν 3 0
The pulsed emission of radio pulsars allows the measurement of the changing time of arrival of a pulse
L
with frequency, so the dispersion measure, Dm = 0 Ne ds, is routinely measured for the lines of sight
to pulsars in our galaxy. If coexistent with magnetic fields, the same electrons that cause propagation
delays induce Faraday rotation of the field vectors by an angle φ = λ2 Rm where λ is the wavelength.
Rm is the rotation measure, which depends on the product of the local electron density, Ne , and the
component of the magnetic field parallel to the line of sight, B|| , and is given by
Rm = 8.1 × 105 Ne B|| ds
(6.8)
in units of radians/m2 , where B|| is in Gauss, Ne is in cm−3 , ds is in parsecs, and the integral is over
the path length along the line of sight. An estimate for the magnitude of these effects in can be made
using mean values for the Galactic ISM such as Ne ∼
= 0.003 cm−3 , B|| ∼
= 2 µG, and typically
◦
2
Rm ∼ −18| cot b| cos(l − 94 ) radians/m , where l and b are the galactic longitude and latitude.
The scattering of radiation from electrons in the ISM, which produces interstellar scintillation,
also has the effect of increasing the apparent size of point sources of radio emission. This effect
produces an angular size due to scintillation which is roughly 7.5λ11/5 milliarcsec for |b| ≤ 0.◦ 6,
0.5(| sin b|)−3/5 λ11/5√milliarcsec for 0.◦ 6 < |b| < 4◦ , 13(| sin b|)−3/5 λ11/5 milliarcsec for 15◦ >
|b| > 4◦ , and 15λ2 / | sin b| milliarcsec for |b| > 15◦ , where b is the galactic latitude and λ is the
wavelength in meters.
At long wavelengths, and for source line of sights close to the Sun, the solar corona and solar
wind contribute very strongly to propagation delay, Faraday rotation, and scintillation. This can be
estimated from the above formulas by Ne ∼
= (1.55R −6 + 2.99R −16 ) × 1014 m−3 for R < 4, and
11
−2
−3
∼
Ne = 5 × 10 R m for 4 < R < 20, where R is the radial distance from the center of the Sun.
The scattering size for an unresolved radio source due to the interplanetary medium is approximately
50(λ/R)2 arcmin where λ is in meters.
The ionosphere of the Earth is a major, and highly variable, contributor of electrons along the line
of sight that affects the propagation of radio waves at long wavelengths. Figure 6.4 shows typical, but
idealized, distributions of the ionospheric electron density for night and day, during sunspot maximum,
and at temperate latitudes.
The troposphere of the Earth’s atmosphere also has the effect of absorbing the radiation from distant
sources. If I0,ν is the surface brightness of a source seen from outside the Earth’s atmosphere, and τ0,ν
is the optical depth at the zenith, then at a zenith angle (z)
I (z, ν) = I0,ν e−τ0,ν X (z) ,
(6.9)
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R ADIO A STRONOMY
F2
Day
-3
Electron Concentration [m ]
1012
F
F1
1011
E
1010
Night
109
E
D
108
100
1000
Height [km]
Figure 6.4. The electron concentration profile of the Earth’s ionosphere for day and night plotted against height
above the Earth’s surface, at solar maximum, and at mid-latitudes.
where X (z) is the relative air mass in units of the air mass at the zenith. To first order, X (z) ∼
= sec(z) =
1/ cos z. For X < 5 the formula X (z) = −0.0045+1.00672 sec z−0.002234 sec2 z−0.000 624 7 sec3 z
has an error less than 6 × 10−4 . Also, τ0,ν ∼
= 0.12, 0.05, and 0.04 at 20, 6, and 2 cm, but can be very
large and variable at mm wavelengths.
Even more important than air mass in affecting radio observations are the delay and scattering
effects in the Earth’s troposphere that produce the radio equivalent of seeing disks. However, since
the 1970s radio astronomers have devised algorithms that allow so-called self-calibration of phase
variations produced by the troposphere for radio interferometry measurements with four or more
antennas in an array. Phase self-calibration by interferometric arrays are methods by which one can,
for any observed field with a strong source, solve for the differences in atmospheric phase variations
over each antenna, and then remove these phase variations from interferometric data.
6.4
6.4.1
RADIO TELESCOPES AND ARRAYS
Properties of Antennas
The normalized antenna pattern Pn (θ, φ) (Equation (6.4)) is used to define many of the important
antenna properties. Although real antenna patterns cannot be exactly described by a mathematical
function, many are close to that for a uniformly illuminated circular aperture of diameter D for which
2

πD

 2J1

sin θ 


λ
Pn (θ ) =
,
(6.10)
πD






sin θ
λ
where J1 is a first-order Bessel function. In Table 6.2 we list various definitions of antenna and source
properties that depend upon the antenna pattern, and give the approximate values for uniform circular
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6.4 R ADIO T ELESCOPES AND A RRAYS / 129
apertures. Since some of the directly measured quantities for radio sources are dependent upon the
antenna pattern, some of these are also listed in Table 6.2 [2].
Table 6.2. Antenna properties.
Quantity
Source solid angle
Effective source solid angle
Surface brightness
Half power beam width
Beam width at first nulls
Beam solid angle
Uniform Circular Ap.
s = source Pn (θ, φ) d
Bν (θ, φ)Pn d
Bν = main lobe
main lobe Pn d
HPBW = 1.02(λ/D) = 58◦ (λ/D)
Pn (HPBW ) = 1/2
Pn (BWFN ) = 0
A = 4π Pn (θ, φ) d
BWFN = 2.44(λ/D) = 140◦ (λ/D)
Directivity
M = main lobe Pn (θ, φ) d
4π/ A
Effective area
A e = λ2 / A
Aperture efficiency
Beam efficiency
A = Ae /(π D 2 /4)
M = M / A
Main beam solid angle
6.4.2
Definition
s = source d
Major Radio Telescopes and Arrays
There are many tens of radio telescope systems in the world that are, have been, or are about to be,
important in radio astronomy. Many are listed in Table 6.3, where the size of the telescope or array, its
main operational wavelengths, and its type or specialized role may be listed in abbreviated form. For a
complete list of most of these telescopes and arrays, see [3].
Table 6.3. Radio observatories.
Name of Observatory/Inst.
Location
Description
Australia Tel. Nat. Facility
Basovizza-Solar Radio Stn.
Bleien Radio Ast. Obs.
Culgoora, Australia
Parkes, Australia
Trieste, Italy
Zurich, Switzerland
Caltech Submillimeter Obs.
Crawford Hill Obs.
Mauna Kea, Hawaii
Holmdel, New Jersey
Decameter Wave Radio Obs.
Deep Space Network Sta.
Gauribidanur, India
Goldstone, California
Deep Space Network Sta.
Robledo, Spain
Deep Space Network Sta.
Tidbinbilla, Australia
6 km EW Arr. 1 + (6) 22 m; 0.3–24 cm
64 m; 0.7–75 cm
10 m; 38–130 cm solar
5 m; 30–300 cm solar
7 m; 10–300 cm solar
10.4 m; 1.3 mm–350 µm
7 m Horn Tunable; 21 cm
7 m Tunable; 1.3–3 mm
1.5 km T Arr.; 200–900 cm
34 m; 3.6–13 cm
70 m; 3.6–13 cm
34 m; 3.6–13 cm
70 m; 3.6–13 cm
34 m; 3.6–13 cm
70 m; 3.6–13 cm
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Table 6.3. (Continued.)
Name of Observatory/Inst.
Location
Description
Dominion Radio Astro. Obs.
Penticton, BC, Canada
Dwingeloo Radio Obs.
Eur. Incoh. Scatt. Fac.
Dwingeloo, Netherlands
Kiruna, Sweden
Fleurs Radio Tel.
Five College Radio Ast. Obs.
Giant Metrewave Radio Tel.
Hat Creek Radio Ast. Obs.
Haystack Obs.
Hiraiso Solar-Terr. Res. Ctr.
Humain Radio Ast. Stn.
Fleurs, NSW, Aus.
Quabbin Res., Mass.
Pune District, India
Cassel, California
Westford, Massachusetts
Nakaminato, Ibaraki, Japan
Humain, Belgium
High Time Resolving Tel.
Interplanetary Scint. Obs.
Instituto Argentino de Rad.
Inst. de Radio Astron. Mill.
IPS Fleurs Solar Obs.
Itapetinga Radio Obs.
Nanjing, China
Toyakawa, Japan
Parque Pereya Iraola, Arg.
Plateau de Bure, France
Pico Veleta, Spain
Fleurs, NSW, Aus.
Atibaia, Brazil
James Clerk Maxwell Tel.
Kashima Space Res. Ctr.
Kisaruzu College Obs.
Maryland Point Obs.
Staz. Rad. di Medicina
Mauna Kea, Hawaii
Kashima, Japan
Kisaruza chiba, Japan
Riverside, Maryland
Medicina, Italy
Metsahovi Obs. Radio Sta.
Molonglo Obs. Synth. Tel.
Mount Pleasant Radio Obs.
Metsähovi, Finland
Hoskinstown, NSW, Aus.
Cambridge, Tasmania, Aus.
Mullard Radio Ast. Obs.
National Astro. and Ion. Obs.
National Obs. Ast. Center
National Radio Ast. Obs.
Cambridge, England
Arecibo, Puerto Rico
Yebes, Spain
Green Bank, West Va.
NRAO mm Telescope
Very Large Array
Very Long Baseline Array
Netherlands Found. Res. Ast.
Nobeyama Solar Radio Obs.
Kitt Peak, Arizona
Socorro, New Mexico
Socorro, New Mexico
Dwingeloo, Netherlands
Nobeyama, Japan
Nobeyama Radio Obs.
Nobeyama, Japan
Nobeyama, Japan
Noto, Sicily
England
Jodrell Bank, Cheshire
Jodrell Bank, Cheshire
Wardle, Cheshire
Defford, Worchestershire
Darnhall, Cheshire
Knockin, Shropshire
Pickmere, Cheshire
Jodrell Bank, Cheshire
Floirac, France
Plateau de Bure, France
600 m EW Arr. 4 9 m; 21,90 cm
26 m; 18–21 cm
25 m; 6–29 cm
32 m; 32 cm
4 40 × 120 m; 130 cm
EW Arr. 32 5.8 m + 6 14 m; 21 cm
13.7 m; 1–7 mm
25 km Irr. Arr. 36 45 m; 21–790 cm
3 + (3) T Arr. 6 m; 1–7 mm
36 m; 0.7–18 cm
2 10 m + 6 m + 1 m; 300–950 cm
7.5 m; 50 cm solar
T Arr. 48 4 m; 74 cm solar
2 m; 3.2 cm solar
100 × 20 m; 92 cm
2 30 m; 17–21 cm
0.4 km T Arr. (3) 15 m; 1.3–4 mm
30 m; 0.8–4 mm
2.5 m + 12-Yagi; 6,11,20, 120 cm
13.7 m; 0.3–28 cm
1.5 m; 4.3 cm solar
15 m; 1.3 mm-300 µm
26 m; 3–150 cm
1.5 m; CO 2.6 mm Line
26 m; 0.7–90 cm
32 m; 1.3–20 cm VLBI
T Parab. Cyl.; 74 cm
14 m; 0.3–1.3 cm
1570 × 12 m EW Cyl. Par.; 36 cm
14 m; 30–50 cm pulars
26 m; 2.5–50 cm
5 km EW Arr. (4) 13 m; cm λ
305 m; λ > 6 cm
14 m; mm λ
43 m; 1.3–600 cm
100 m; 0.7–90 cm
12 m; 0.9–7 mm
1–35 km Y Arr. (27) 25 m; 0.7–90 cm
5000 km Arr. 10 25 m; 0.7–90 cm VLBI
22 m Ant.
0.5 km T Arr. 16 1.2 m, 1.8 cm solar
T Arr 17 6 m, 190 cm
45 m, 0.26–3 cm
0.7 km T Arr. (5) 10 m, 0.25–1.3 cm
32 m; 0.3–1.3 cm VLBI
134 km Irr. MERLIN Arr. 7 Ant.:
76 m; 5–200 cm
38 × 26 m Par.; 1.3–200 cm
38 × 26 m; 17–370 cm
25 m; 6–200 cm
25 m; 1.3–200 cm
25 m; 1.3–200 cm
25 m; 1.3–200 cm
13 m; 20–50 cm pulsars
2.5 m; 2.5–4 mm
2.5 m; 1.3 mm
Noto Radio Ast. Sta.
Nuffield Radio Ast. Labs.
Obs. de Bordeaux
Obs. de Grenoble
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6.5 R ADIO E MISSION AND A BSORPTION P ROCESSES / 131
Table 6.3. (Continued.)
Name of Observatory/Inst.
Location
Description
Obs. für Solare Astr.
Obs. Radioastron. de Maipú
Ohio State Radio Obs.
Ondrejov Ast. Obs.
Tremsdorf, Germany
Maipú, Chile
Delaware, Ohio
Ondrejov, Czech.
Onsala Space Obs.
Onsala, Sweden
Ooty Radiotelescope
Ooty Synthesis Radiotelescope
Owens Valley Radio Obs.
Ootacamund, India
Big Pine, California
Purple Mountain Obs.
Purple Mt. Obs. Solar Fac.
Delingha, China
Nanjing, China
Puschino Radio Ast. Sta.
Puschino, Russia
Radioobs. Effelsberg
RATAN-600
Solar Radiospec. Obs.
Sta. de Rad. de Nancay
Effelsberg, Germany
Zelenchukskaya, SU
Ravensburg, Germany
Nancay, France
Swedish-ESO Submm. Tel.
Tonantzintla Solar Radio Int.
Toyokaya Obs.
La Silla, Chile
Puebla, Mexico
Toyokawa, Japan
U. of Mich. Radio Obs.
URAN-1 Interferometer
UTR-2 Array
Westerbork Synth. Rad. Tel.
Yunnan Obs.
Dexter, Michigan
Kharkov, SU
Kharkov, SU
Westerbork, Netherlands
Kunming, China
1.5 + 4 + 10.5 m + Yagi; 3.2–750 cm
160 × 73 m; 670 cm
100 × 30 m; 1.9 cm
3 m; 1.5–3 cm solar
7.5 m; 37–120 cm solar
7.5 m; 25–300 cm solar
20 m; 3.7–270 cm
25 m; 30–260 cm
530 × 30 m Par. Cyl.; 90 cm
(ORT) + 8 23 × 9 m; 90 cm
0.4 km T Arr. (4) 10 m; 1.3–3 mm
40 m; 0.7–90 cm
Arr. of 2 27 m; 4–30 cm
13.7 m; 0.3,1.3 cm
1.5 m; 3.2–11 cm solar
2 m; 6 cm solar
22 m Tel.
Cross-type 1 km decimetric array
18 acre decimetric phased array
100 m; 0.6–49 cm
0.6 cm circle of 895 elem.; 0.8–30 cm
7 m + 8 dipoles; 30–1000 cm
16 1 m Parab.; 3.2 cm
24 Parab.; 67–200 cm solar
16 + 2 Parab.; 67–200 cm solar
299 × 40 m; 9–21 cm
144 Con. Log. Per.; 380–2000 cm
15 m; 0.8–3 mm
2 1.1 m Parab.; 4 cm solar
0.85 m; 3.2 cm solar
1.5 m; 8 cm solar
2 m; 14 cm solar
3 m; 2.8 cm solar
3 arrays; 3.2,7.8 cm solar
25 m; cm λ
Linear Arr, Xed dipoles; 1200–3000 cm
T Arr 1800 × 54 m + 900 × 54 m; 1200–3000 cm
4 km EW Arr. 10 + (4) 25 m; 6–90 cm
2.5, 3, 3.2, & 10 m; 8.1–130 cm
6.5
6.5.1
RADIO EMISSION AND ABSORPTION PROCESSES
Source Models and Prediction of Observables
The relationship between the emission and absorption coefficients, which are used to describe
the microphysics of radiation processes, and the theoretical quantities corresponding to the direct
observables, is important in discussing the principle physical processes in radio astronomy. There
are three principal observables: surface brightness Bν (and the related brightness temperature Tb,ν ),
the integrated flux density Sν for a source with a closed boundary of solid angle source , and Vν the
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R ADIO A STRONOMY
coherence (or visibility) function measured by radio interferometers. All are computed as integrals
over the true sky brightness, or specific intensity, Iν , and are given by
Iν dsource
Bν = source
,
(6.11)
source dsource
2k
Sν =
Iν dsource ∼
Tb dsource ,
(6.12)
= 2
λ source
source
(where the approximation is valid for the Rayleigh–Jeans limit and most radio wavelengths) and
Vν (u, v) =
Iν (α, δ)Pn (α − α0 , δ − δ0 )e−2πi/λ[L j −Lk ]·[s(α,δ)−s0 (α0 ,δ0 )] d,
(6.13)
where L j and Lk are vector locations of antennas j and k, and s is a unit vector pointing to locations
on the celestial sphere such as (α, δ) or the reference position (α0 , δ0 ). For a spherically symmetric
brightness distribution the latter equation simplifies to a Hankel transform:
Vν (u, v) =
Iν (θ )Pn (θ )J0 (2πqθ)2π θ dθ,
(6.14)
where (L j − Lk ) · (s − s0 )/λ = ux + vy + wz, q = (u 2 + v 2 + w 2 )1/2 ∼
= (u 2 + v 2 )1/2 , and
2
2
2
1/2
2
2
1/2
∼
θ = (x + y + z ) = (x + y ) .
In Table 6.4 a number of models and the associated observables are listed.
Table 6.4. Observables for simple source models.
Model
Tb (θ )/Tb,max
2
Gaussian
e−4 ln 2(θ/θH )
Uniform disk
1, θ ≤ θH /2
0, θ > θH /2
Limb-brightened
2 − θ 2 ),
2θH /(θH
(shot glass)
“Thin” ring
θ ≤ θH /2
0, θ > θH /2
δ(θ − θH /2)
Sν (J y)
Vν (q)/Sν
2 (arcsec)
Tb,max (K )θH
1360λ2 (cm)
2
2
e−(π 4 ln 2)(qθH )
2 (arcsec)
Tb,max (K )θH
1961λ2 (cm)
2 (arcsec)
Tb,max (K )θH
981λ2 (cm)
2 (arcsec)
420Tb,max (K )θH
λ2 (cm)
2J1 (πqθH )/(πqθH )a
sin(πqθH )/(πqθH )
J0 (πqθH )
Note
a J is a Bessel function of order n, and assuming that source is at the center of the field, then
n
θ = r/d (d is the distance to the object) and θH is the half-intensity point in these spherically
symmetric models.
The resolution of an instrument of size D is set by diffraction theory to be λ/D, and for radio
astronomy the best resolution of an antenna is determined by its diameter (Dm in units of meters)
and the shortest wavelength it can observe (∼ [surface rms]/16). For arrays the size is the maximum
separation of antennas (Dkm in units of km). Thus
resolution =
λcm
λcm
λ
= 2
.
= 34
D
Dm
Dkm
(6.15)
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6.5 R ADIO E MISSION AND A BSORPTION P ROCESSES / 133
The resolution of the instrument and the characteristics of the radio source, which we will discuss
in terms of the models in Table 6.4, together with the other parameters determining the sensitivity of
the antenna or array, determine the minimum surface brightness that can be detected. For modern
paraboloid-shape antennas the 5σ detection level for flux density during a time interval tsec is
20Tsys
1
σdetection =
Jy,
(6.16)
√
2
FK/Jy Dm
νMHz tsec
where FK/Jy is a fixed, empirically determined constant for each antenna–receiver combination, while
for an array of N antennas of this size,
2.5Tsys
1
σdetection =
Jy,
(6.17)
√
2
ηc a D m
νMHz tsec N (N − 1)/2
where ηc is the correlator efficiency (0.82 for 3-level correlations), a is the aperture efficiency (∼ 0.5
for simple paraboloids, but 0.6–0.7 for specially designed antennas), νMHz is the bandwidth in MHz,
and tsec is the integration time in seconds.
6.5.2
Thermal Free–Free and Free–Bound Transitions
For thermal bremsstrahlung radiation, the emission and absorption coefficients jν ρ and κν ρ are
proportional to ρ 2 , where ρ is the mass density. The source function jν /κν , at radio wavelengths,
is the Planck function for an electron temperature Te . Thermal bremsstrahlung or free–free radiation
processes are caused by interactions between free electrons and positive ions in a partially or fully
ionized plasma. The emission coefficient for free–free emission is given by
jff,ν ρ = 5.4 × 10−39 Ne2 Te
1/2
gff ehν/kTe ∼
= 7.45 × 10−39 Ne2 Te0.34 ν −0.11 ,
(6.18)
where we have used
3/2 31/2
Te
−0.11
∼
gff (ν, Te ) =
17.7 + ln
= 1.38 × Te−0.34 νGHz
π
ν
(6.19)
for the free–free Gaunt factor, with an approximation valid at radio wavelengths [4, 5]. In (6.18)–
(6.19), Ne is the electron concentration in units of cm−3 , and Te is the electron temperature. The
Planck function relates the emission and absorption coefficients for black body radiation, i.e.,
ν 2
ν 2
1
jν
2hν 3
∼
Sν =
= 2 hν/kT
,
(6.20)
2kTe
≡ 2kTr
=
e −1
κν
c
c
c e
∼ Te is valid for longer radio wavelengths,
where the approximation that the radiation temperature Tr =
but becomes invalid at mm wavelengths.
For bound–free transitions the emission coefficient and Gaunt factor are given by
−3/2
jfb,ν ρ = 1.72 × 10−33 Ne2 Te
∞
n −3 gfb (ν, Te , n)e157890/n
2T
e
,
(6.21)
n=m
where n is the principal quantum number and m is the integer portion of (3.789 89 × 1015 Hz/ν) and
gbf (ν, Te , n) = 1 +
0.1728(u n − 1) 0.0496(u 2n + 43 u n + 1)
−
,
n(u n + 1)2/3
n(u n + 1)4/3
where u n = n 2 (ν/3.289 89 × 1015 Hz) [6].
(6.22)
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134 / 6
6.5.3
R ADIO A STRONOMY
Spectral Lines—Thermal Bound–Bound Transitions
For bound–bound transitions between any two levels with energies E n = E 1 , ..., E ionization and
statistical weights gn , radiation absorption and emission involves photons of energy hνnm = E m − E n .
The properties of a line transition are determined by the Einstein coefficients Amn , Bmn , and Bnm ,
which are related by
Bmn =
c2
Amn
2hν 3
and
Bnm =
gm
Bmn .
gn
(6.23)
The emission and absorption coefficients for line transitions are
jbb,νnm =
hνnm
Nm Amn φmn (νnm )
4π
(6.24)
κbb,νnm =
hνnm
Nn gn φmn (νmn )
Nm Bnm φmn (νnm ) 1 −
,
4π
Nm gm φmn (νnm )
(6.25)
and
where φnm (νmn ) and φmn (νmn ) are absorption and emission “line” profile functions, which are usually
equal to each other. Note that in general the source function can be expressed as


Sνnm =

1
jbb,νnm
2hν 3 
.
= 2 


N
g
φ
(ν
)
κbb,νnm
c
n n mn mn
−1
Nm gm φmn (νnm )
(6.26)
If the line is in Local Thermodynamic Equilibrium (LTE) with temperature T , then Nn /Nm =
(gn /gm ) exp(hνnm /kT ) and S = Bν so
κbb,LTE,νnm =
hνnm
Nm Bnm φmn (νnm ) 1 − e−hνnm /kT .
4π
(6.27)
Most of the known spectral lines from molecules in the interstellar medium have been detected at
radio wavelengths. Many are in Table 6.5. For current lists and information about the parameters of
various molecular species see the Internet URL http://spec.jpl.nasa.gov.
Table 6.5. Known interstellar molecules.
Name of
molecule
Chemical
symbol
Wavelength
region
Date and telescope
of discovery
methyladyne
cyanogen radical
methyladyne ion
hydroxyl radical
ammonia
water
formaldehyde
carbon monoxide
hydrogen cyanide
cyanoacetylene
hydrogen
methanol
formic acid
formyl radical ion
CH
CN
CH+
OH
NH3
H2 O
H2 CO
CO
HCN
HC3 N
H2
CH3 OH
HCOOH
HCO+
4 300 Å
3 875 Å
4 232 Å
18 cm
1.3 cm
1.4 cm
6.2 cm
2.6 mm
3.4 mm
3.3 cm
1013–1108 Å
36 cm
18 cm
3.4 mm
1937 – Mt. Wilson 2.5 m
1940 – Mt. Wilson 2.5 m
1941 – Mt. Wilson 2.5 m
1963 – Lincoln Lab. 26 m
1968 – Hat Creek 6 m
1968 – Hat Creek 6 m
1969 – NRAO 43 m
1970 – NRAO 11 m
1970 – NRAO 11 m
1970 – NRAO 43 m
1970 – NRL rocket
1970 – NRAO 43 m
1970 – NRAO 43 m
1970 – NRAO 11 m
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6.5 R ADIO E MISSION AND A BSORPTION P ROCESSES / 135
Table 6.5. (Continued.)
Name of
molecule
Chemical
symbol
Wavelength
region
Telescope of
discovery
formamide
carbon monosulfide
silicon monoxide
carbonyl sulfide
methyl cyanide
isocyanic acid
methyl acetylene
acetaldehyde
thioformaldehyde
hydrogen isocyanide
hydrogen sulfide
methanimine
sulfur monoxide
diazenylium
ethynyl radical
methylamine
NH2 CHO
CS
SiO
OCS
CH3 CN
HNCO
CH3 CCH
CH3 CHO
H2 CS
HNC
H2 S
CH2 NH
SO
N2 H+
C2 H
CH3 NH2
dimethyl ether
ethanol
sulfur dioxide
silicon sulfide
vinyl cyanide
methyl formate
nitrogen sulfide
cyanamide
cyanodiacetylene
formyl radical
acetylene
cyanoethynyl radical
ketene
cyanotriacetylene
nitrosyl radical
confirmed
ethyl cyanide
cyano-octatetra-yne
methane
nitric oxide
butadiynyl radical
methyl mercaptan
isothiocyanic acid
thioformyl radical ion
protonated carbon dioxide
ethylene
cyanotetraacetylene
silicon dicarbide
propynylidyne
methyl diacetylene
methyl cyanoacetylene
tricarbon monoxide
silane
protonated HCN
(CH3 )2 O
CH3 CH2 OH
SO2
SiS
CH2 CHCN
CH3 OCHO
NS
NH2 CN
HC5 N
HCO
C2 H2
C3 N
H2 CCO
HC7 N
HNO
6.5 cm
2.0 mm
2.3 mm
2.7 mm
2.7 mm
3.4 mm
3.5 mm
28 cm
9.5 cm
3.3 mm
1.8 mm
5.7 cm
3.0 mm
3.2 mm
3.4 mm
3.5 mm
4.1 mm
9.6 mm
2.9–3.5 mm
3.6 mm
2.8, 3.3 mm
22 cm
18 cm
2.6 mm
3.7 mm
3.0 cm
3.5 mm
infrared
3.4 mm
2.9 mm
2.9 cm
3.7 mm
1.9 mm
2.7–4.0 mm
2.9 cm
infrared
2.0 mm
2.6–3.5 mm
3 mm
3 mm
3 mm
3 mm
infrared
many (cm)
many (mm)
many (3 mm)
several (cm)
several (cm)
2 cm
infrared
3, 2, 1 mm
cyclopropynylidene
—
hydrogen chloride
protonated water
confirmed
C3 H2
H2 D+ ?
HCl ?
H3 O+
1971 – NRAO 43 m
1971 – NRAO 11 m
1971 – NRAO 11 m
1971 – NRAO 11 m
1971 – NRAO 11 m
1971 – NRAO 11 m
1971 – NRAO 11 m
1971 – NRAO 43 m
1971 – Parkes 64 m
1971 – NRAO 11 m
1972 – NRAO 11 m
1972 – Parkes 64 m
1973 – NRAO 11 m
1974 – NRAO 11 m
1974 – NRAO 11 m
1974 – NRAO 11 m
1974 – Tokyo 6 m
1974 – NRAO 11 m
1974 – NRAO 11 m
1975 – NRAO 11 m
1975 – NRAO 11 m
1975 – Parkes 64 m
1975 – Parkes 64 m
1975 – Texas 5 m
1975 – NRAO 11 m
1976 – Algonquin 46 m
1976 – NRAO 11 m
1976 – KPNO 4 m
1976 – NRAO 11 m
1976 – NRAO 11 m
1977 – Algonguin 46 m
1977 – NRAO 11 m
1990 – FCRAO 14 m
1977 – NRAO 11 m
1977 – Algonguin 46 m
1977 – KPNO 4 m
1978 – NRAO 11 m
1978 – NRAO 11 m
1979 – BTL 7 m
1979 – BTL 7 m
1980 – BTL 7 m
1980 – BTL 7 m
1980 – KPNO 4 m
1981 – Algonquin 46 m
1984 – BTL 7 m
1984 – BTL 7 m
1984 – Haystack 37 m
1984 – Haystack 37 m
1984 – Haystack 37 m
1984 – KPNO 4 m
1984 – NRAO 12 m
1984 – Texas 5 m
1985 – many
1985 – KAO
1985 – KAO
1986 – NRAO 12 m
1990 – CSO 10 m
CH3 CH2 CN
HC9 N
CH4
NO
C4 H
CH3 SH
HNCS
HCS+
HOCO+
C2 H4
HC11 N
SiC2
C3 H
CH3 C4 H
CH3 C3 N
C3 O
SiH4
NCNH+
3, 2 mm
0.62 mm
0.48 mm
1.0 mm
0.8 mm
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R ADIO A STRONOMY
Table 6.5. (Continued.)
6.5.4
Name of
molecule
Chemical
symbol
Wavelength
region
Telescope of
discovery
pentynylidyne radical
hexatriynyl radical
phosphorus nitride
C5 H
C6 H
PN
radio
radio
3, 2, 1 mm
—
—
acetone
sodium chloride
aluminum chloride
potassium chloride
aluminum fluoride
methyl isocyanide
cyanomethyl radical
C2 S
C3 S
(CH3 )2 CO ?
NaCl
AlCl
KCl
AlF
CH3 NC
CH2 CN
silicon carbide
propynal
SiC
HCCCHO
—
phosphorus carbide
propadienylidene
SiC4
CP
H2 CCC
butatrienylidene
silicon nitride
silylene (pend. conf.)
—
carbon suboxide
H2 CCCC
SiN
SiH2 ?
HCCN
C2 O
isocyanoacetylene
sulfur oxide ion
ethinylisocyanide
magnesium isocyanide
protonated HC3 NH+
—
carbon monoxide ion
sodium cyanide
—
nitrous oxide
magnesium cyanide
prot. formaldehyde
octatetraynyl radical
octatetraynyl radical
protonated hydrogen
hexapentaenylidene
ethylene oxide
hydrogen flouride
HCCNC
SO+
HNCCC
MgNC
NC3 H+
NH2
CO+
NaCN
CH2 D+
N2 O
MgCN
H2 COH+
C8 H
C7 H
H+
3
H2 C6
c − C2 H4 O
HF
3, 7 mm
3, 7 mm
3.4 mm
2, 3 mm
2, 3 mm
2, 3 mm
2, 3 mm
3 mm
6.5 mm
1.3 cm
2 mm
8 mm
1.6 cm
3.5, 7.5 mm
1.2, 3.0 mm
3 mm
1.4 cm
many (3 mm)
1.1, 1.4 mm
0.8, 1.0 mm
3 mm
7 mm
1.3 cm
7 mm
1.3, 3 mm
1.1, 0.8, 0.64 cm
radio
radio
0.645 mm
1.3, 0.8 mm
3, 2.4 mm
0.8–4.0 mm
2.0–4.0 mm
radio
radio
radio
radio
IR-3.67 µm
K-band
K, Q, 3 mm,1 mm
121.7 µm
1986 – IRAM 30 m
1986 – IRAM 30 m
1986 – NRAO 12 m
1986 – FCRAO 14 m
1986 – Nobeyama 45 m
1986 – Nobeyama 45 m
1987 – IRAM 30 m
1987 – IRAM 30 m
1987 – IRAM 30 m
1987 – IRAM 30 m
1987 – IRAM 30 m
1987 – IRAM 30 m
1988 – Nobeyama 45 m
1988 – NRAO 43 m
1989 – IRAM 30 m
1989 – Nobeyama 45 m
1989 – NRAO 43 m
1989 – Nobeyama 45 m
1989 – IRAM 30 m
1990 – IRAM 30 m
1990 – NRAO 43 m
1990 – IRAM 30 m
1990 – NRAO 12 m
1990 – CSO 10 m
1991 – IRAM 30 m
1991 – Nobeyama 45 m
1991 – NRAO 43 m
1992 – Nobeyama 45 m
1992 – NRAO 12 m
1992 – Nobeyama 45 m
1992 – Nobeyama 45 m
1993 – Nobeyama 45 m
1993 – CSO
1993 – NRAO 12 m, CSO
1993 – NRAO 12 m
1993 – NRAO 12 m, CSO
1994 – NRAO 12 m
1995 – NRAO 12 m
1995 – Nobeyama 45 m
1996 – IRAM 30 m
1996 – IRAM 30 m
1996 – UKIRT
1997 – NASA 34 m
1997 – NRO, SEST, Haystack
1997 – ISO
Magneto-Bremsstrahlung Emission and Absorption
The other radiation process of dominant importance in radio astronomy is magneto-bremsstrahlung
emission and absorption which results from the interaction between fast-moving electrons and the
ambient magnetic field. There are three major varieties of magneto-bremsstrahlung emission. When
the moving electrons are very relativistic, the emission process is the very efficient, highly beamed
synchrotron emission which dominates the emission from many galactic and most extragalactic ra-
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6.5 R ADIO E MISSION AND A BSORPTION P ROCESSES / 137
dio sources. However, in some stars and certain solar system environments, two other magnetobremsstrahlung processes occur when the moving electrons are nonrelativistic or only mildly relativistic. When mildly relativistic (γLorentz ≡ (1 − (v/c)2 )−1/2 ∼
= 2–3) electrons undergo interactions
with magnetic fields, the emission process is called gyro synchrotron, which is much less beamed and
much less efficient at producing radio emission than synchrotron processes; however, it tends to be
highly circularly polarized, a characteristic commonly found in stellar radio emission. Even less efficient is the magneto-bremsstrahlung resulting from less relativistic particles, with γLorentz ≤ 1, which
is called cyclotron or gyro resonance emission. The details of nonrelativistic (cyclotron) and mildly
relativistic (gyro synchrotron) emission and absorption processes are more complicated than the highly
relativistic case. They are summarized by [7], and extensively discussed by [8] and [9].
Much of the analysis of radio source data uses very simple models for the behavior of synchrotron
radiating sources. This section summarizes formulas used in such analysis. We assume that the density
of relativistic electrons can be described by a power law distribution in energy, N (E) = K E −γ in
the energy range E to E + d E, where γ is a constant. If these electrons are mixed in with a uniform
distribution of magnetic fields of strength H , which can be described as having uniformly random
directions on a large scale, then the emission and absorption coefficients are given by
jν ρ = 1.35 × 10
and
−22
a(γ )K H
(γ +1)/2
6.36 × 1018
ν
(γ −1)/2
(6.28)
κν ρ = 0.019g(γ )(3.5 × 109 )γ K H (γ +2)/2 ν −(γ +4)/2 ,
(6.29)
where H is in gauss and all other variables are in cgs units, so that the source function is
Sν =
a(γ ) γ /2 −1/2 5/2
jν
= 2.84 × 10−30
ν erg s−1 cm−3
2 H
κν
g(γ )
(6.30)
[10]. Table 6.6 gives some of the values of the functions a(γ ), g(γ ), the brightness temperature source
function Ts , and the angular size (0 ) of a uniform source with flux density S0 and magnetic field HmG
in units of milligauss.
Table 6.6. Incoherent synchrotron emission constants.
γ
a(γ )
g(γ )
α
1.0
15
2.0
2.5
3.0
4.0
5.0
0.283
0.147
0.103
0.0852
0.0742
0.0725
0.0922
0.96
0.79
0.70
0.66
0.65
0.69
0.83
0.0
0.25
0.50
0.75
1.0
1.5
2.0
−1/2
1/2
Ts νGHz HmG
1.9 × 1012
1.0 × 1012
6.6 × 1011
4.9 × 1011
3.6 × 1011
2.3 × 1011
1.7 × 1011
−1/2
0 S0
K
K
K
K
K
K
K
−1/4 5/4
HmG νGHz
0.015 mas
0.021 mas
0.026 mas
0.030 mas
0.035 mas
0.044 mas
0.051 mas
The specific intensity is given by
Iν =
0
L
Sν (1 − exp(−τν )) dτν ,
where dτν = κν ρ ds in the above integral, which is along the line of sight of length L.
(6.31)
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R ADIO A STRONOMY
We see from (6.30) that the important case where jν /κν is constant occurs if the magnetic field
is uniform in strength and geometry. Equations (6.28)–(6.30) also tell us that for the optically thick
and thin limits, Iν is proportional to H −1/2 ν 5/2 and K H (γ +1)/2 ν −(γ −1)/2 L, respectively, where L is a
line-of-sight path length. Defining the spectral index α by Sν ∝ ν α , then α = 2.5 and −(γ − 1)/2 in
the optically thick and thin limits, respectively. The values of α in the latter case for various values of
γ are listed in Table 6.6.
The evolution of the relativistic electron energy distribution N (E, t) is the primary factor in the
evolution or synchrotron radiation sources. In its most general form this evolution is described by
∂ N (E, t)
∂
dE
+
N (e, t)
= (E, T ) − (E, t),
(6.32)
∂t
∂E
dt
where (E, T ) and (E, t) are functions describing particle “injection” and “escape,” with escape
time scales T , respectively. Usually and are zero, as they will be for all models discussed
below, or applies to only small portions of the radio sources. The equation for evolution of N (E, t) is
supplemented by the energy loss equation:
dE
= φ(E) = −ζ − ηE − ξ E 2 ,
dt
(6.33)
where the first two terms are due to losses by ionization in the ambient, medium, and free–free
interaction with this medium. The last term, which is usually the most important, includes both energy
loss due to synchrotron radiation and energy loss due to inverse Compton scattering off photons in the
local radiation field. The coefficients of the first two terms in (6.33) are:
E
E
−20
ζ ≈ 3.33 × 10−20 n H 6.27 + ln
+
1.22
×
10
73.4
ln
−
ln
n
(6.34)
n
e
e
mc2
mc2
and
E
η ≈ 8 × 10−16 n H n e 0.36 + ln
,
(6.35)
mc2
where n H is the concentration of neutral hydrogen atoms and n e is the concentration of thermal
electrons.
For synchrotron radiation losses ξsynch ∼
= 2.37 × 10−3 H⊥2 , where H⊥ is the magnetic field
perpendicular to the velocity vector of the radiating relativistic electron. The time scale for synchrotron
losses is tsynch ≡ E/(−d E/dt) = 1/(ζsynch E) ∼ (5.1 × 108 /H⊥2 )(mc2 /E) s. Synchrotron radiation
losses dominate in regions with large magnetic fields and low radiation fields.
For inverse Compton losses ξIC ≈ 3.97 × 10−4 u rad , where u rad is the radiation energy density.
Inverse Compton losses dominate when brightness temperature approaches Tb ≤ 1012 K. Above 1012 K
all relativistic electrons loss their energy rapidly due to this process.
For steady-state synchrotron radiation sources where one assumes (E, t) = (E), and
N (E, t) = N (E), and ∂ N /∂t = 0, the relativistic particle energy equation has the solution N (E) =
φ −1 (E) (E) d E. So if one can assume a power law for the particle injection, (E) = 0 E −γ ,
then
N (E) = 0 (γ − 1)−1 E −γ (ζ E −1 + η + ζ E)−1 .
(6.36)
The relativistic particle spectra and observable radio spectrum for such steady-state radio sources can
be described by three segments of power laws as shown in Figure 6.5. The principle effect of more
complex models is replacement of the sharp spectral breaks with smooth transitions.
Sp.-V/AQuan/1999/10/07:17:14
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6.5 R ADIO E MISSION AND A BSORPTION P ROCESSES / 139
α = − (γ − 1)/2
γ−1
γ
log N(E)
γ+1
log E
ionization losses
free-free losses synchrotron + inverse
compton losses
α − 1/2
α
log S
ν
α + 1/2
absorption
absorption
log ν
Figure 6.5. Relativistic particle (top), and observable flux density (bottom), spectrum for steady-state synchrotron
radiation sources. The changes in slope indicate regions where ionization, free–free, and synchrotron (+ inverse
Compton) losses dominate. By each curve segment is the power law index for the energy and flux density spectra.
External or self-absorption can occur at any point in the flux density spectrum; two possibilities are indicated in
the figure.
A synchrotron radio source with losses only due to synchrotron radiation has an energy loss
equation d(E −1 )/dt = ζsynch which leads to a spectrum described by E = E 0 /[1 + ζsynch (t − t0 )E 0 ].
Then if at t = t0 , N (E) = N0 E −γ , then at later times N (E) = N0 E −γ (1 − ζsynch Et)γ −1 for
E < E T (t), and N (E, T ) = 0 for E > E T (t), where E T (t) = 1/(ζsynch t). The frequency above
−3
−2 GHz.
which synchrotron losses dominate is νb ≈ BGauss
tyear
Time-dependent synchrotron radiation source models with complex geometry and complex energy
loss mechanisms require extensive computation. However in the case of simple geometries and only
adiabatic losses the evolution of the flux density of a radio source can be expressed in analytic or nearanalytic equations. For a spherical region which “suddenly” has a distribution of relativistic particles
given by N0 = K 0 E −γ and which expands with an outer radius r2 (t) the flux density of the source is
described by the quantities in Table 6.7 [11–13]. An analogous model can be expressed for a conical
jet with ejection of adiabatically expanding plasma [13]. The jet ejection parameters are such that at
an initial distance z 0 the radius of the cross section of the jet is r0 (jet Mach number M0 = z 0 /r0 )
and the relativistic particle density is N0 . The quantities that determine the flux density for an observer
for whom the jet is oriented at an inclination angle are in Table 6.7; for a continuous jet z 2 = ∞
and z 1 = z 0 ; however, a time-dependent jet which starts ejection with velocity v2 at time tstart and
ends ejection with velocity v1 at time tstop is described by the same equations with the necessary time
dependence in the limits of integral for the flux density.
Table 6.7. Radio source models—only adiabatic energy losses.
Expanding sphere
Conical jet
E = E 0 (r2 /r0 )−1
H = H0 (r2 /r0 )−2
K = K 0 (r2 /r0 )−(γ +2)
E = E 0 [r2 (z 2 )/r0 ]−2/3
H = H0 [r2 (z 2 )/r0 ]−1
K = K 0 [r (z 2 )/r0 ]−2(γ +2)/3
(γ +2)/2
τ0 = 0.038g(γ )(3.5 × 109 )γ K 0 H0
r0
same
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140 / 6
R ADIO A STRONOMY
Table 6.7. (Continued.)
Expanding sphere
Conical jet
ξ(τ ; τ > 20) = 1
ξ(τ ; τ < 20) = 0.66584 + 0.09089τ
− 0.009989τ 2 + 0.0005208τ 3
− 0.00001268τ 4 + 0.000000115τ 5
ξ(τ ; τ > 20) = 1
ξ(τ ; τ < 20) = 0.78517 + 0.06273τ
− 0.007242τ 2 + 0.0003905τ 3
− 0.00000973τ 4 + 0.00000009τ 5
−(γ +4)/2 r2 (z 2 ) −(7γ +8)/6
ν
τ0
τν =
sin()
ν0
r0
τν = τ0
r −(2γ +3) ν −(γ +4)/2
r0
ν0
−1/2 5/2
Sν = 1.42e−0.65γ H0,mG νGHz 3mas
× 1 − exp(−τν ) × ξ( τν )
r2 (t; free exp.) = r0
r2 (t; E cons.) = r0
r2 (t; Mom. cons.) = r0
t
t0
ν 5/2
sin()
ν0
z (t)
× z 2(t) ζ 3/2 1 − exp(−τν ) ξ(τν ) dζ
Sν = S0 M0
1
r2 (t; free exp.) = r0
t 2/5
t0
r2 (t; E cons.) = r0
t 1/4
t0
r2 (t; Mom. cons.) = r0
z2
z0
z 2 1/2
z0
z 2 1/3
z0
z 2 = v2 (t − tstart )
z 1 = v1 (t − tstop )
6.6
RADIO ASTRONOMY REFERENCES
Table 6.8 gives further references for radio astronomy.
Table 6.8. List of radio astronomy references.
Topic
Reference
Radio astronomy research field reviews
Properties of radio telescopes
Interferometry and aperture synthesis
Aperture synthesis
Observation-oriented radio astronomy textbooks
Synchrotron radiation physics
Radio astrophysical theory
General astrophysical theory
[1]
[2]
[3]
[4, 5]
[6, 7]
[8]
[9]
[10]
References
1. Verschuur, V.L., & Kellermann, K.I. 1988, Galactic and Extragalactic Radio Astronomy (Springer-Verlag, New York)
2. Christiansen, W.N., & Högbom, J.A. 1985, Radio Telescopes (Cambridge University Press, Cambridge)
3. Thompson, A.R., Moran, J.M., & Swenson, G.W. 1986, Interferometry and Synthesis in Radio Astronomy (Wiley,
New York)
4. Perley, R.A., Schwab, F.R., & Bridle, A.H. 1989, Synthesis Imaging in Radio Astronomy, A.S.P. Conference Series, 6
5. Cornwell, T.J., & Perley, R.A. 1991, Radio Interferometry: Theory, Techniques, and Applications, A.S.P. Conference
Series, 19
6. Rohlfs, K. 1986, Tools of Radio Astronomy (Springer-Verlag, Berlin)
7. Krause, J.D. 1986, Radio Astronomy, 2nd ed. (Cygnus-Quasar Books, Powell)
8. Ginzburg, V.L., & Syrovatskii, S.I. 1965, Ann. Rev. Astron. Astrophys., 3, 297
9. Pacholczyk, A.G. 1970, Radio Astrophysics (W.H. Freeman, San Francisco)
10. Longair, M.S. 1981, High Energy Astrophysics: an informal introduction for students of physics and astronomy
(Cambridge University Press, Cambridge)
Sp.-V/AQuan/1999/10/07:17:14
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6.6 R ADIO A STRONOMY R EFERENCES / 141
REFERENCES
1. Clark, B.G. 1989, Synthesis Imaging in Radio Astronomy, A.S.P. Conference Series, 6, p. 1
2. Christiansen, W.N., & Högbom, J.A. 1985, Radio Telescopes (Cambridge University Press, Cambridge)
3. Price, R.M. et al. 1989, Radio Astronomy Observatories
(National Academy Press, Washington, DC)
4. Karzas W.J., & Latter, R. 1961, ApJS, 6, 167
5. Hjellming, R.M., Wade, C.M., Vandenberg, N.R., &
Newell, R.T. 1979, AJ, 84, 1619
6. Aller, L.H. & Liller, W. 1968, Nebulae and Interstellar
Matter, edited by B. Middlehurst & L.H. Aller (Univer-
sity of Chicago Press, Chicago), Chapter 9
7. Dulk, G.A. 1985, ARA&A, 23, 169
8. Kundu, M.R. 1965, Solar Radio Astronomy (Interscience, New York)
9. Zheleznyakov, V.V. 1970, Radio Emission of the Sun
and Planets (Pergamon Press, Oxford)
10. Ginzburg, V.L., & Syrovatskii, S.I. 1965, ARA&A, 3,
297
11. van der Laan, H. 1966, Nature, 211, 1131
12. Kellermann, K.I. 1966, ApJ, 146, 621
13. Hjellming, R.M., & Johnston, K.J. 1988, ApJ, 328, 600
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