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Fundamentals of Radio
Astronomy
Lyle Hoffman, Lafayette College
ALFALFA Undergraduate WorkshopUnion College, 2005 July 06
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Outline
Sources in brief
Radiotelescope components
Radiotelescope characteristics
Useful Texts
Burke & Graham-Smith, An Introduction to Radio AstronomyRohlfs, Tools of Radio Astronomy
Stanimirovic et al., Single-dish Radio Astronomy: Techniques
and Applications
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Sources of Radio Emission
Blackbody (thermal)
Continuum sources Spectral line sources
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Blackbody Sources
Peak in cm-wave radio requires very lowtemperature: lmT = 0.2898 cm K
Cosmic Microwave Background is aboutthe only relevant blackbody source
Ignored in most workessentially constant
source of static (same in all directions) andmuch weaker than static produced byinstrumentation itself
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Continuum Sources
Due to relativistic electrons:
Synchrotron radiation
Bremsstrahlung Quasars, Active Galactic Nuclei, Pulsars,
Supernova Remnants, etc.
Used by ALFALFA for calibration
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Spectral Line Sources
Neutral hydrogen (H I ) spin-flip transition
Recombination lines (between high-lyingatomic states)
Molecular lines (CO, OH, etc.)
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Doppler effect: frequency shift of spectral
line due to relative motion of source andobserver
Closely related: redshift due to expansion
of universe
Customarily report velocity as
cz = c(fo-f)/f
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H I spectral line from galaxy shifted by
expansion of universe (recession velocity)
and broadened by rotation
Frequency
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Radiotelescope Components
Reflector(s)
Feed horn(s)
Low-noise
amplifier
Filter
Downconverter
IF Amplifier
Spectrometer
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Feedhorns
4 GHz feedhorn
on LCRT
Typical cm-wave
feedhorn
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Signal Path
FilterDown-
converter
Low-Noise
Amplifier
Local
Oscil-
lator
IF AmplifierSpectro-
meter
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Autocorrelation Spectrometer
Special-purpose hardware computes
autocorrelation function:
Rn =N-1 S1
N [u(tj)u(tj+ndt)]
where dt is lag and u is signal voltage;
integer n ranges from 0 to (dt df)-1 if
frequency channels of width df are required
Power spectrum is discrete Fourier
transform (FFT) of Rn
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Nyquist theorem: must sample at rate 2B to
achieve spectrum of bandwidth B withoutaliassing
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Gain & effective area
Received power Prec Flux (energy per unit area per unit time) S
Effective area Aeff= Prec / S
Gain G for transmitter is ratio of emittedflux in given direction to P/(4pr2)
Most emitted (received) within central
diffraction max, angle ~ l/ D So G = 4p Aeff/l
2
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Beam & sidelobes
Essentially diffraction
pattern of telescope
functioning astransmitter
Uniformly illuminated
circular aperture:central beam &
sidelobe rings
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Obstructions, non-uniform illumination by
feedhorn asymmetry and alter strengthsof sidelobes vs. central beam
Emission received from pattern outside first
sidelobe ring often called stray radiation FWHM of central beam is beamwidth
Integrated solid angle of central beam is Wo
Gain related to beam via G = 4p /Wo
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Sensitivity
Limited by noisemostly thermal noise
within electronics but also from ground
reflected off telescope structure intofeedhorn and CMB
System temperature: temperature of
blackbody producing same power astelescope + instrumentation produces when
there is no source in beam
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Often give brightness of source in
temperature units: difference in effectiveblackbody temperature when source is in
beam vs. when no source is in beameven
when source is spectral line or synchrotronradiation and brightness has little to do with
actual temperature of the source
Preferred unit (requires calibration) isJansky:
1Jy = 10-26 W m-2 Hz-1
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Limiting sensitivity for unpolarized source set
by requiring signal added by source to equal rmsuncertainty in Tsys:
DS = 2kTsys Aeff-1 (Bt)-1/2
(k: Boltzmanns constant; t: integration time) For spectral line work, B is set by velocity
resolution required; Tsys and Aeffset by telescope
and instumentation increase sensitivity byintegrating longerbut need 4 times integration
time to increase sensitivity by factor of 2
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Polarization
H I sources unpolarized, but synchrotronsources are often polarized to some extent
E in plane of electrons acceleration Single receiver (LNA) can respond to only
single polarization at any instanteither onecomponent of linear polarization or one
handedness of circular polarization
So two receivers required to receive bothpolarizations
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Linear Ex and Ey with phase difference f
Stokes parameters:
I = Ex2 + Ey
2
Q = Ex
2- Ey
2
U = 2ExEycosf
V = 2ExEysinf
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Unpolarized source: Ex = Ey and f = 0
So Q = 0, V = 0, and I = U for H I; usuallyreport only Stokes I or total flux = sum of
fluxes of x and y polarizations
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