nassp masters 5003f - computational astronomy - 2009 lecture 9 – radio astronomy fundamentals...

NASSP Masters 5003F - Computational Astronomy - 2009

Lecture 9 – Radio Astronomy FundamentalsS

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Types of electron acceleration:• Thermal (random jiggling)• Synchrotron (spiral)• Spectral line (resonant sloshing)


Noise power spectrum• Analyse the signal into Fourier

components. jth component is:

• The Fourier coefficient Vj is in general complex-valued. Power in this component is:

• Closely related to the ‘power spectrum’ we’ve already encountered in Fourier theory.

Vj(t) = Vj exp(-iωjt) = Vj (cos[ωjt] + i sin[ωjt])

Pj = Vj*(t)Vj(t)/R = Vj *Vj/R (cos2[ωjt] + sin2[ωjt]) = Vj *Vj/R


Averaging the power spectrumt = 1 t = 16

t = 64t = 4


Total noise power output by the antenna.

• “Noise is noise”: signal from an astrophysical source is indistinguishable from contamination from– Background thermal radio noise.– Ditto from intervening atmosphere.– Noise generated in the receiver system.

• Each of these makes a contribution to the total. Thus the total noise power is

Ptotal = Psource + Pbackground + Patmosphere + Psystem


On-and-off source comparison• The simplest way to determine the source

contribution is to make 1 measurement pointing at the source, then a second pointing away from (but close to) the source, then subtract the two.

• Scanning over the source is also popular.• Uncertainty in total power measurements is:

– Note the Poisson-like character: σP is proportional to P.

• A low-pass filter with a time constant t is another way of ‘averaging’.

t

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Antenna detection efficiency

• The source radiates at S W m-2 Hz-1.

• The antenna has an effective area Ae in the direction of the source. (Eg for a dish antenna pointed to the source, this is close to the actual area of the dish.)

• Thus the power per unit frequency interval picked up by the antenna is:

• However, antennas are only sensitive to one polarisation...

w = AeS watts per herz.


Decomposition into polarised components

The total power in the signal is the sum of the power in eachpolarization. An antenna can only pick up 1 polarization though.


Dependence on source polarisation

• If the source is unpolarized, the antenna will only pick up ½ the power, regardless of orientation.

• If the source is 100% polarized, the antenna will pick up between 0 and 100% of the power, depending on orientation (and type of detector – eg is detector sensitive to linear polarization, or circular).

• Obviously all values in between will be encountered. Thus measurement of source polarization is important.


Directionality of antennas.A radio telescope often (not always) incorporates a mirror.

Parkes

GMRT

Ok as long as the roughness is << λ.

An optically ‘smooth’ surface

These are supposed to be smoothmirrors?


Directionality of antennas.

Reflector

Focal plane

Point Spread Function

Radio telescopes with a mirror can be analysed likeany other reflecting telescope...


A more usual treatment:B

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It is often conceptually easier to imaginethat the antenna is emitting radiation tothe sky rather than absorbing it.

Beam width ~λ/D, same as for any other reflector.Eg Parkes 64m dish at 21 cm, beam width ~ 15’.


Going into a little more detail...

• Essential quantities:– The distribution of brightness B(θ,φ) over the

celestial sphere. (See next slide for definition of θ,φ.) The units of this are W m-2 Hz-1 sr-1 (watts per square metre per herz per steradian).

– The effective area Ae of the antenna, in m2. (This is something which must be measured as part of the antenna calibration.)

– The relative efficiency f(θ,φ) of the antenna, which is normalized such that it has a maximum of 1. (This shape must also be calibrated.)

– The received power spectrum w (units: W Hz-1).



J D Kraus, “RadioAstronomy” 2nd ed.,

Fig 3-2.

Pointing direction of theantenna – NOT the zenith.

Kraus uses Pwhere I have f.



• The general relation between these quantities is:

Remember that the ½ only applies where B is unpolarized.

• Further useful relations:

• It can be shown that ΩA = λ2/Ae.

,BdS

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1e BfdAw

,A fd


Going into a little more detail...• Let’s consider two limiting cases:

– B(θ,φ) = B (ie, uniform over the sky);– B(θ,φ) = S δ(θ-0,φ-0) (ie, a point source of

flux=S, located at beam centre).

f f

B

B(θ,φ)=Sδ

w = ½ λ2 B w = ½ Ae S

...the ½ still applies only for unpolarized B.


Conversion of everything to temperatures.

• Suppose our antenna is inside a cavity with the walls at temperature T (in kelvin).

• It can be shown that the power per unit frequency picked up by the antenna is

• Because of this linear relation between a white noise power spectrum and temperature, it is customary in radio astronomy to convert all power spectral densities to ‘temperatures’. Hence:

w = kT watts per herz.


System temperature

• Tsource only says something about the real temperature of the source if– The source area is >>ΩA, and

– The physical process producing the radio waves really is thermal.

• Tatmosphere is a few kelvin at about 1 GHz.

• Tbackground may be as much as 300 K if the antenna is seeing anything of the surroundings! Therefore avoid this.

• Tsystem again says nothing about the real temperature of the receiver electronics. Rather it is a figure of merit – the lower the better.

Ttotal = Tsource + Tbackground + Tatmosphere + Tsystem


The more usual way to write the measurement uncertainty:

• Thus the minimum detectable flux is

• and the minimum detectable brightness:

• Note:1. Bmin not dependent on Ae.2. Factors of 2 only for unpolarized case.

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A more realistic system:R M Price, “Radiometer Fundamentals”,

Meth. Exp. Phys. 12B (1976),Fig 1, section 3.1.4.

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Jargon• The ‘antenna’:

– the reflecting surface (ie the dish).

• The ‘feed’:– usually a horn to

focus the RF onto the detector.

• The ‘front end’:– electronics near the

Rx (shorthand for receiver).

• The ‘back end’:– electronics near the

data recorder.• The LO:

– local oscillator.

A 38 GHz feed horn. Thecorrugations are good

for wide bandwidth.

•RF:–Radio Frequency.

•IF:–Intermediate Frequency.


Flux calibration• The bandwidth and gain of the radiometer tend

not to be very stable.• There are several methods of calibration. Eg:

1. Switching between the feed and a ‘load’ at a temperature similar to the antenna temperature. But, this can be < 20 K...

2. Periodic injection of a few % of noise into the feed. Noise sources can be made much more stable than noise detectors.

• Still good to look occasionally at an astronomical source of known, stable flux. Should also be unresolved (compact).

– Difficult conditions to meet all together! Compact sources tend to vary with time.

nassp masters 5003f - computational astronomy - 2009 lecture 9 – radio astronomy fundamentals...

Documents

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total noise power isptotal

total noise power output

total power measurements

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