nassp masters 5003f - computational astronomy - 2009 lecture 10 today i plan to cover: –a bit more...

NASSP Masters 5003F - Computational Astronomy - 2009

Lecture 10

• Today I plan to cover:– A bit more about noise temperatures;– Polarized radio signals;– Radio spectroscopy.


Typical noise temperatures

J D Kraus, “Radio Astronomy” 2nd ed., fig 8-6.(+ 7-25)


Polarized EM waves – conventions:

z

x

y Left-hand circular polarizationaccording to IEEE convention.(Physicists use the oppositeconvention.)

Direction of rotation ofthe field vector as seenby an observer.

Snapshot of a wave moving in thepositive z direction.


Sources of polarized radio waves:• Thermal? No• Spectral line? No (unless in a strong B field)• Synchrotron? YES.

– And this is the most common astrophysical emission process.

• All jets emit synchrotron – and jets are everywhere.

Magnetic field B

Electron moving atspeed close to c

Linearlypolarizedemission.


How to describe a state of polarization?

Visualize with the “Poincaré sphere.” of radius I.

Stokes parameters I, Q, U and V.I = total intensity.Q = intensity of horizontal pol.U = intensity of pol. at 45°V = intensity of left circular pol.

Q axis

U axis

V axis

Polarization fraction d:

I

VUQd

222

Therefore need 4measurements tocompletely definethe radiation.


Antenna response, and coherency matrices.

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

• This may be quantified by 4 ‘Stokes effective areas’ AI, AQ, AU, AV.

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

• Then the power spectral density detected is

QIiVU

iVUQI

I2

1S

QIVU

VUQI

AAiAA

iAAAA

Ae2

1Aand

w = AeI×Tr(AS) (‘Tr’ = the ‘trace’ of the matrix, ie the sum of all diagonal terms.)


Depolarization due to finite resolution

Half-power contourof the beam.

Arrows show the pol-arization direction.

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

Nettpolarization

observed.


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 θ is proportional to distance

travelled x the field strength x the number density of electrons.

– θ is also proportional to λ2.

• 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.


Faraday rotation

J D Kraus, “Radio Astronomy” 2nd ed., fig 5-4

The slope of the line is calledthe rotation measure.

Why is there progressive depolarization with increase in wavelength?


Faraday rotation - depolarizationBecause the rotation measure is not uniform and may vary within the beam. Eg:

Half-power contourof the beam.


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


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.

S


Broad-band emitters

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

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


HII 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.

• 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 (braking radiation.)

+

-e


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 λ2.

• Effective temperature Teff = T(1-e-τ).

– Long λ - high τ - Teff ~ T – thus α = -2.

– Short λ - low τ - Teff proportional to λ2 - means flux density S is constant, or α = 0.


Some more about synchrotron• Already covered the

basics in slide 4.• 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 < 1012 K by inverse Compton scattering.

J D Kraus, “Radio Astronomy” 2nd ed., fig 10-10

PKS 1934-63


Narrow-band spectra• Molecular transitions:

– Hundreds now known.– Interstellar chemistry.– Tracers of star-forming regions.– Doppler shift gives velocity information.

• Masers:– Eg OH, H2O, NH3.– 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.


HI

• The I indicates the degree of ionization. I means none – just the neutral atom. Hydrogen has only 1 electron so the highest it can go is HII – which is just a bare proton.

• The neutral atom has a very weak (lifetime ~ 107 years!) transition between 2 closely spaced energy levels, giving a photon of wavelength 21 cm (1420 MHz).

• But because there is so much hydrogen, the line is readily visible.


HI

• 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.

• Concept of column density in atoms per square cm.

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


HI – 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 HI – we can see galaxies behind it at 21 cm, whereas visible light is strongly absorbed.

• Cosmic Doppler red shift z is given by

cv

c

v

cv

cvz

for 1

1

12

true

trueobs


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 2403Credit: F Walter et al (2008).

(Courtesy Erwin de Blok.)

nassp masters 5003f - computational astronomy - 2009 lecture 10 today i plan to cover: –a bit more...

Documents

radio astronomy

polarized waves

radio astronomers

antenna response

different areas

calledthe rotation measure

intensity of left circular

intensity of horizontal