UgradALFALFA Hoffman

7/31/2019 UgradALFALFA Hoffman

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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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