Lecture 1

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Transcript Lecture 1

Lecture 13

• Today I plan to cover: – The jansky.

– Photon noise at radio wavelengths?

– Flux calibration.

– A bit more about noise temperatures.

– Polarized radio signals.

– Radio spectroscopy.

NASSP Masters 5003S - Computational Astronomy - 2009

The jansky

• The standard unit of flux density in radio astronomy.

• Symbol Jy .

• Named after a pioneer in the field.

• = 10 -26 W m -2 Hz -1 .

Photon noise..?

• High-energy astronomy usually is dominated by this. But radio υ hugely less!

• Energy of a photon at 1.4 GHz is ~1e -24 J.

• Hence 10 mJy over 1 MHz at this freq • ~ only 100 photons/sec. - a bit unexpected.

NASSP Masters 5003S - Computational Astronomy - 2009

• •

Flux calibration

The bandwidth and gain of a radiometer tend not to be very stable.

There are several methods of calibration. Eg: Switching between the feed and a ‘load’ at a temperature similar to the antenna temperature.

To detector To detector – “Warm load” at

“Warm load” at

But, the required physical resistor can be < 20 K...  temperature of the load need to cool with He.

NASSP Masters 5003F - Computational Astronomy - 2009

More widely used:

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

It is still good, while observing, to look – – occasionally at an astronomical source which has the following properties: Known, stable flux density.

Should also be unresolved (compact).

These are difficult conditions to meet at the same time! Compact sources tend to vary with time.

NASSP Masters 5003S - Computational Astronomy - 2009

Typical noise temperatures

J D Kraus, “Radio Astronomy” 2 nd ed., fig 8-6.(+ 7-25) NASSP Masters 5003F - Computational Astronomy - 2009

Polarized EM waves – conventions:

y x

Left-hand circular polarization according to IEEE convention.

(Physicists use the opposite convention.) Snapshot of a wave moving in the positive

direction.

Direction of rotation of the field vector as seen by an observer.

NASSP Masters 5003F - Computational Astronomy - 2009

Sources of polarized radio waves:

• Thermal? No • Spectral line? No (unless in a strong

field) • Synchrotron? YES .

– And this is the most common astrophysical emission process.

• All jets emit synchrotron – and jets are everywhere.

Magnetic field

Electron moving at speed close to

• Scattering off dust? YES .

Linearly polarized emission.

NASSP Masters 5003F - Computational Astronomy - 2009

How to describe a state of polarization?

axis

Stokes parameters = total intensity.

and

Q U

= intensity of horizontal pol.

= intensity of pol. at 45 °

= intensity of left circular pol.

axis Therefore need 4 measurements to completely define the radiation.

axis Visualize with the “Poincaré sphere.” of radius

Polarization fraction

: 

2 

NASSP Masters 5003F - Computational Astronomy - 2009

Antenna response, and coherency matrices.

• The antenna response is different for different incoming polarization states.

• This may be quantified by 4 ‘Stokes effective areas’

A I , A Q , A U , A V

• But it is more convenient to express both the radiation and the antenna response as coherency matrices :

 1 2

 

U I





iV U I





  and

 1 2

e   

A A U I



A Q



iA V A U A I



iA V



A Q

   • Then the power spectral density detected is

= A e

×Tr(

) (‘Tr’ = the ‘trace’ of the matrix, ie the sum of all diagonal terms.) NASSP Masters 5003F - Computational Astronomy - 2009

Depolarization due to finite resolution

Arrows show the pol arization direction.

Half-power contour of the beam.

Nett polarization observed.

Waves from different areas of the source add incoherently. Result: some degree of depolarization. In general, the finer the resolution, the higher the polarization fraction.

NASSP Masters 5003F - Computational Astronomy - 2009

Faraday rotation.

• Any linear polarized wave can be decomposed into a sum of left and right circularly polarized waves.

• In a magnetized plasma, the LH and RH components travel at slightly different speeds.

• Result: – The plane of polarization rotates.

– The amount of rotation

is proportional to distance travelled x the field strength x the number density of electrons.

–

is also proportional to

2 .

• Most due to Milky Way, but the Earth’s ionosphere also contributes – in a time-variable fashion. The ionosphere is a great nuisance and radio astronomers would abolish it if they could.

NASSP Masters 5003F - Computational Astronomy - 2009

Faraday rotation

J D Kraus, “Radio Astronomy” 2 nd ed., fig 5-4 The slope of the line is called the rotation measure .

Why is there progressive depolarization with increase in wavelength?

NASSP Masters 5003F - Computational Astronomy - 2009

Faraday rotation – another cause of depolarization

Because the rotation measure is not uniform and may vary within the beam. Eg:

Half-power contour of the beam.

NASSP Masters 5003F - Computational Astronomy - 2009

Radio spectroscopy

• The variation of flux with wavelength contains a lot of information about the source.

• We can pretty much divide sources into – Broad-band emitters, eg • Synchrotron emitters • HII regions (ie ionized hydrogen) • Thermal emitters – Narrow-band emitters (or absorbers), eg • HI (ie neutral hydrogen) • Masers • Neutral molecular clouds NASSP Masters 5003F - Computational Astronomy - 2009

Broad-band emitters

• Most of these have spectra which, over large ranges of wavelength, can be described by a simple power law , ie

   • For thermal sources, the Rayleigh-Jeans approximation to the black-body radiation law gives a spectral index α = -2.

• Synchrotron sources have +ve α , averaging around +0.8.

• HII regions exhibit a broken power law.

NASSP Masters 5003F - Computational Astronomy - 2009

Wavelength or frequency?

• Since

, a power-law spectrum

     implies

    • Ie, the sign of the spectral index depends whether you give the spectrum as a function of wavelength or frequency.

• Make sure you know which convention is intended before using a spectral index (and always record this convention in your own reports).

NASSP Masters 5003F - Computational Astronomy - 2009

Broad-band emitters

J D Kraus, “Radio Astronomy” 2 nd ed., fig 8-9(a) Mostly synchrotron .

Steep-spectrum source Reversed-spectrum sources: mostly thermal, ie slope = 2.

Log-log plot so all straight lines are power-laws .

One spectrum , many spectra .

Note too that nearly all broad band spectra are quite smooth.

NASSP Masters 5003F - Computational Astronomy - 2009

H

regions

• The gas here is ionized and hot (10,000 K is typical) – usually as a result of intense irradiation from a massive young star.

• The radiation comes from electrons accelerated (diverted) as they come close to a positive ion.

+ -e • This radiation mechanism is called free-free , because the electron being accelerated is not bound to an atom either before its encounter or after. But it is basically a thermal process.

• Otherwise known as bremsstrahlung (German for “braking radiation”. Yes spellt with 2 esses.) NASSP Masters 5003F - Computational Astronomy - 2009

Optical depth

• Whenever you have a combination of radio waves and plasma, optical depth τ plays a role.

– High τ = opaque – behaves like a solid body.

– Low τ = transparent.

• τ for a plasma is proportional to

2 .

• Effective temperature

eff – Long

- high τ -

eff ~

(1-e – thus α τ = -2.

– Short

- low τ -

eff proportional to means flux density

τ is constant, or , thus α = 0.

2 •  Flat-spectrum source.

– The troposphere is a good example of a thermal radiator which is optically thin at dm wavelengths.

NASSP Masters 5003F - Computational Astronomy - 2009

Some more about synchrotron

• Already covered the basics in slide 7.

• Also subject to optical depth effects: – At low frequencies, opacity is high, the radiation is strongly self-absorbed: • α ~ -2.5.

• Effective temperature limited to < 10 12 K by inverse Compton scattering .

J D Kraus, “Radio Astronomy” 2 nd ed., fig 10-10 PKS 1934-63 NASSP Masters 5003F - Computational Astronomy - 2009

Narrow-band spectra

• Molecular transitions: – Hundreds now known.

– Interstellar chemistry.

– Tracers of star-forming regions.

– Doppler shift gives velocity information.

• Masers: – Eg OH, H 2 O, NH 3 .

– Like a laser – a molecular energy transition which happens more readily if another photon of the same frequency happens to be passing  radiation is amplified, coherent.

– Spatially localized, time-variable.

• Recombination lines.

NASSP Masters 5003F - Computational Astronomy - 2009

H

I • The I indicates the degree of ionization.

– Subtract 1 from this number to get the number of electrons stripped from the atom.

• Eg Fe VII , ‘iron seven’, means iron which has lost 6 electrons. Hence I means minus 0 electrons – just the neutral atom. Hydrogen has only 1 electron so the highest it can go is H II – which is just a bare proton .

• The neutral H atom has a very weak (lifetime ~ 10 7 years!) transition between 2 closely spaced energy levels, giving a photon of wavelength 21 cm (1420 MHz).

• But because there is so

much

line is readily visible.

hydrogen, the NASSP Masters 5003F - Computational Astronomy - 2009

H

I • Because the transition is so weak, and also because of Doppler broadening, hydrogen is practically always optically thin (ie completely transparent).

• Thus the intensity of the radiation is directly proportional to the number of atoms.

– For a cloud of mass

distance

solar masses at a megaparsecs, the measured flux

(in W m -2 ) is  ~ 6  10  23

M D

(I think.) NASSP Masters 5003F - Computational Astronomy - 2009

H

I • Concept of column density square cm.

in atoms per Distribution of atoms this way makes no difference.

Observer • Hydrogen will be seen in emission if it is warmer than the background, in absorption otherwise.

NASSP Masters 5003F - Computational Astronomy - 2009

H

– Doppler information

• Hubble relation between distance and recession velocity allows distance of far galaxies to be estimated.

– Hence: 3D information about the large-scale structure of the universe.

• Our Milky Way is transparent to H I – we can see galaxies behind it at 21 cm, whereas visible light is strongly absorbed.

• Cosmic Doppler red shift

is given by

   obs  true  true  1 

v c

1    2  1 

v c

for



NASSP Masters 5003F - Computational Astronomy - 2009

HI – Doppler information

• Within galaxies: – Doppler broadening tells about the distribution of velocities within a cloud of hydrogen.

– the Doppler shift of the HI line maps the rotation curve of the galaxy, eg: NGC 2403 Credit: F Walter et al (2008).

(Courtesy Erwin de Blok.) NASSP Masters 5003F - Computational Astronomy - 2009

Model of galactic hydrogen

• A good model for many galaxies is a disk of uniform surface density

within a radius

, rotating with a uniform speed |

– Such decoupling of speed from radius is not what is observed in eg planetary systems and is one of the indicators for large dominance of dark matter.

• With distance

and inclination angle

this leads to a predicted spectral shape of

  

0 2   2

sin 2 2    



centre  2 – Here I have used

instead of with velocity

. ( Caveat!

to avoid confusion This is my own derivation.) NASSP Masters 5003F - Computational Astronomy - 2009

Diagram of HI spectrum

NASSP Masters 5003F - Computational Astronomy - 2009

An example exercise

• You have an antenna of diameter 12 m, efficiency

=70%. The feed is linearly polarized and the detection chain has a noise temperature of 45 kelvin. How long do you have to observe to see an unresolved HI source of average flux density 2 Jy in a channel width of 15 kHz?

– The relation between source flux density

and equivalent noise temperature

, for an unresolved source, is



kT pA

effective – where

is the fraction of signal the polarised detector is picking up.

NASSP Masters 5003F - Computational Astronomy - 2009

An example exercise

– HI emission is unpolarised, so

case.

is 0.5 in the present – The effective area is the true area times the efficiency; =

πr

= in the present problem.

– Hence

source  

• We need to observe long enough that the uncertainty in the total noise temperature (source plus instrumental) is equal to the source noise temperature.

– A common trick: assume figures!

source <<

inst .

– This is valid because we don’t need to know our observing time to more than a couple of significant NASSP Masters 5003F - Computational Astronomy - 2009

An example exercise

• We can therefore write, to a reasonable approximation: 



total   

inst   

• Setting this equal to the source temperature allows us to derive: 

 4    

inst 

k S

  2 • = 41 s. (Don’t forget to convert Jy to MKS!) NASSP Masters 5003F - Computational Astronomy - 2009

Spectra - baselines

• The spectrum of interest sits on top of a high ‘mesa’ due to system and background ‘temperature’ (ie noise).

• We usually want to subtract the mesa and just leave the spectrum.

• We

could

do that by alternating between on and off-source observations, and subtracting the two: – But this needs 4 times as much observing time to reach the same SNR!

NASSP Masters 5003F - Computational Astronomy - 2009

Spectra - baselines

• More commonly, the mesa is slowly varying compared to the spectrum, so one can fit some fairly smooth function to the mesa, then subtract it.

• The examples (for which this has

already

been done) show it is not always so simple!

• These show the infamous ‘Parkes ripple.’ NASSP Masters 5003F - Computational Astronomy - 2009

The ‘Parkes ripple’

A weak Fabry-Perot resonance occurs between the dish and the feed.

n λ

= (

+1)(

λ-

) => Δ ν ~ 5.5 MHz.

~ 26 m NASSP Masters 5003F - Computational Astronomy - 2009