Transcript Chris_Salter_RadioAst_Tech_2011_REU

Technical
Fundamentals
of
Radio Astronomy
Chris Salter
NAIC/Arecibo Observatory
The Atmospheric Windows
The Full Electromagnetic Spectrum
Cm-wavelength Radio Spectrum
If you can measure it with a ruler, then it's a
RADIO WAVE!
Wavelength Ranges:
Radio: 30 meter →1 millimeter = 3 × 104:1
Optical: 0.3 → 0.75 = 2.5:1
Frequency (GHz)
Observational Astronomy
Q: In what way does Observational (Passive) Astronomy differ
from Other Sciences?
A: It is NOT experimental!
E.g. Zoology: Rats in mazes:
Planetary Radar:
Particle Physics: The Larger Hadron Collider:
→
BUT:
→
In Observational Astronomy, “What
you see in what you get!”
Arecibo 305-m telescope (Puerto Rico)
GBT 100-m telescope (WV, USA)
Single-Dish Radio Telescopes
IRAM 30-m mm-wave telescope (Spain)
Effelsberg 100-m telescope (FRG)
Ooty Radio Telescope 530  30 m (India)
Telescope Beam Pattern
The response of the telescope to signal power arriving from a
direction (θ, Φ) is known as the BEAM PATTERN, or the
POWER POLAR DIAGRAM, P(θ, φ).
We normalize the response such that, P(0,0) = 1.0
The pattern has a MAIN BEAM and SIDELOBES. The
sidelobes in the rear 2π steradians are called the BACK LOBES.
A design requirement is to minimize the sidelobes as they
represent unwanted responses accepting power where you would
like it rejected. The lower the sidelobes, the better the telescope
can detect weak objects near a strong source, giving a higher
DYNAMIC RANGE.
Main-Beam Resolving Power:
This is defined as the angular width of the main beam between
directions where the response has fallen to one half of the
maximum, called the HALF-POWER BEAMWIDTH (HPBW)
or FULL-WIDTH HALF-MAXIMUM (FWHM).
For a single-dish telescope of diameter, D;
HPBW = 1.2 × λ/D radians, where λ is the wavelength.
NOTE: D/λ = Number of wavelengths across the telescope.
HPBW of the Arecibo 305-m Telescope
Wavelength
Frequency
2.3 meter
70 cm
21 cm
13 cm
6 cm
3 cm
130 MHz
430 MHz
1400 MHz
2300 MHz
5000 MHz
10000 MHz
HPBW
37 arcmin
11 arcmin
3.4 arcmin
2.0 arcmin
1.0 arcmin
0.5 arcmin
Specific Intensity or Surface Brightness
Intensity/Surface Brightness is the fundamental observable in
radio astronomy representing the intensity of radio waves
arriving at the Earth.
(x, y)
Considering the energy in a frequency band of width, dυ,
about a central value, υ, arriving per sec from the direction
(x,y) in solid angle, dΩ. Then the Intensity, I(x, y) is given by;
I(x,y,υ,t) =
Solid angle dΩ
Area = dA
lt
dA,dΩ,dυ,dt → 0
dE(x,y,υ,t)
cosθ dA dΩ dυ dt
NOTE: dE/dt is the power received from dΩ on area dA in
bandwidth dυ. So, I is the power per unit area, per Hz from
unit solid angle in the direction (x, y).
The units of I are W m-2 Hz-1 ster-1.
Brightness Temperature: Often Intensity is expressed as a brightness temperature TB,
i.e. if the sky at dΩ were replaced by a black body of temperature TB K, then at our
observing frequency we would measure the same intensity. Luckily, most radio
frequencies are sufficiently low, and TB sufficiently high that the Rayleigh-Jeans
approximation holds, and;
I = 2 k TB υ2 = 2 k TB (where c = speed of light
c2
λ2
and k = Boltzmann's Constant)
Flux Density
We can scan our radio telescope over a radio source such as to measure its
intensity distribution, and in the process produce a “radio photograph” (i.e. an
image) of the source.
To define a global parameter that characterizes the
strength of the emission from our source at observing
frequency υ, we use the power received from the
whole source on unit area, per Hz of bandwidth. This
we call the FLUX DENSITY, S(υ, t).
Integrating over solid angle;
S(υ, t) =
∫ I(x, y, υ, t) dΩ
source
Note that for our tiny piece of sky, dΩ, S = I dΩ =
dE
, so the units are W m-2 Hz-1
dA dυ dt
However, the flux densities of radio sources are so small that a more practical unit has been
adopted. This is the Jansky, where;
1 Jansky (Jy) = 10-26 W m-2 Hz-1
This looks pretty small, but in the 38 years since the Jansky was adopted things have moved
along sufficiently that we can now detect sources whose flux densities are ~10-5 Jy!
Distance Dependencies
Suppose we observe a galaxy of radius, r, at distance, D,
Then we see the galaxy as subtending a solid angle of πr2 / D2.
So, dΩ α D-2
Now, the energy, dE received from the galaxy α D-2 (inverse square law)
And as I = dE / (dA dΩ dυ dt) , I is Distance Independent.
(i.e. while a distant source looks smaller than a similar nearby one, it
has the same intensity/surface brightness.
In contrast, the flux density, S = dE / (dA dυ dt) so, S falls as the
inverse-square of the distance.
D
2×r
Effective Area of a Telescope
A Point Source is one that has an angular size, θs << HPBW of the antenna.
Its flux density is S(υ) = dE/(dA dυ dt), so the power collected by our telescope
can be written as S(υ) Aeff(υ) Δυ, where Δυ is the receiver bandwidth, and Aeff(υ)
is called the Effective Area of the telescope.
Note that a single radio receiver can only collect the power from one of the two
polarizations of the incoming signal. Hence it can only collect ½ S(υ) Aeff(υ) Δυ.
Suppose that after observing a point source, we replace the receiving dipole by a
resistor whose temperature is adjusted to a value TA, where the noise power from
the resistor equals the power previously received from the point source. Now the
power received from a resistor at a temperature T = k T Δυ. Hence;
k TA Δυ = ½ S(υ) Aeff(υ) Δυ
and, Aeff (υ) = 2 k TA ,where TA is called the Antenna Temperature.
S(υ)
Hence, if we measure a source of known flux density, we can calculate Aeff.
If AP is the physical area of the antenna, we define its Aperture Efficiency to be;
ηA = Aeff/AP < 1.0
A Simple Radio Receiver
The celestial source provides a “noise-power”
giving Antenna Temperature = TA.
Front-end
IF Stage
Back-end
The preamplifier is very important as it provides
most of the noise against which we are trying to
detect a radio source!
The mixer changes the frequency of the received
signal to a (usually) lower frequency. Most
amplification occurs at the IF Stage, and a
“Standard IF” can be used for received signals of
all frequencies.
A Square-Law Detector is used so:
Output voltage α(Input Voltage)2
α Input Power
The integrator sums up the detector output,
“beating down” the noise level in the process.
The data are recorded for subsequent analysis.
Receiver Noise
RECEIVER NOISE TEMPERATURE , TR,
is given by PR = k TR Δυ
PR
SYSTEM NOISE TEMPERATURE ,
TS, is given by TS = TR +TA
Q: “How weak a source can we detect with our receiver?”
A: The answer is provided by the RADIOMETER EQUATION: Trms = Tsys ,
(Δυ τ)0.5
where Δυ is the receiver bandwidth (Hz), and τ is the integration time (sec).
A good rule-of-thumb is that a source will be detected if it provides TA > 5 × Trms
Interferometry
If the biggest telescope in the World (Arecibo) has a resolution of ~1 arcmin, can we
ever discover what the radio sky looks like at arsecond resolution, or finer?
Yes — Thanks to radio interferometery! Despite dealing with the longest wavelength
electromagnetic waves, radio astronomy has provided our most detailed images of the
Universe, achieving not only arcsec resolution, but even sub-milliarcsec resolution!
Combining the voltages from 2 telescopes separated by a
distance, b, there is a phase difference between them of;
φ = (2π b cos θ) / λ , where λ is the wavelength.
This produces a fringe pattern, with maxima at cos θ = n λ / b
If b = 30 km and λ = 3 cm, fringe maxima are separated by
~0.2 arcsec. If b = 6000 km, then the fringe separation is
~1 milliarcsec!
While two antennas will give you a fringe pattern, combining the signals from many
(N) telescopes separated by large distances, and allowing the Earth's rotation to move a
radio source through their mutual N(N – 1)/2 fringe patterns, allows us to make images
of the sky with the angular resolution obtainable by a “virtual” single telescope whose
diameter is that of the widest separation of any pair of telescopes present.
GMRT (India)
Angular Resolution = ( / Separation) radians
VLBA (USA)
VLA (ΝΜ, USA)
Radio
Interferometers
(1 arcsec = a Quarter
at 3.5 miles)
(1 milliarcsec = a Quarter
at 3500 miles)
VLA
Telescope (NM,
Arrays
USA)
Very Long Baseline Interferometry
When the telescopes in an interferometer array are separated by large distances, it
was for many years impossible to directly combine their signals. The voltages from
each telescope were recorded on magnetic tapes, and later disc packs, which are
Fed-Exed to a central location where the signals from each antenna pair are crossmultiplied in a special Very Long Baseline Interferometry (VLBI) correlator.
In recent years, real-time correlation has become possible by transmitting the
signals directly to the correlation center via the internet — eVLBI.
A number of major VLBI arrays have come into being;
Very Long Baseline Array
(VLBA; USA)
European VLBI Network
(EVN; EEC)
VLBI Space Observatory
Project (VSOP; Japan)