Fundamentals of radio astronomy - Radio Observations of Active

Transcription

Fundamentals of radio astronomy
James Miller-Jones (NRAO Charlottesville/Curtin University)
ITN 215212: Black Hole Universe
Many slides taken from NRAO Synthesis Imaging Workshop
(http://www.aoc.nrao.edu/events/synthesis/2010/)
and the radio astronomy course
Atacama Large Millimeter/submillimeter
of J. Condon and S. Ransom
Array
(http://www.cv.nrao.edu/course/astr534/ERA.shtml)
Expanded Very Large Array
Robert C. Byrd Green Bank Telescope
Very Long Baseline Array
What is radio astronomy?
• The study of radio waves originating from outside the Earth
• Wavelength range 10 MHz – 1 THz
• Long wavelengths, low frequencies, low photon energies
– Low-energy transitions (21cm line)
– Cold astronomical sources
– Stimulated emission (masers)
– Long-lived synchrotron emission
• Sources typically powered by gravity rather than nuclear fusion
– Radio galaxies
– Supernovae
– Pulsars
– X-ray binaries
2nd School on Multiwavelength Astronomy, Amsterdam , June 2010
2
What is radio astronomy?
• Telescope resolution q = 1.02 l/D
– Requires huge dishes for angular resolution
• Coherent (phase preserving) amplifiers practical
– Quantum noise proportional to frequency T = hn/kB
• Precision telescopes can be built s<l/16
• Interferometers are therefore practical: D ≤ 104 km
3
A short historical digression
• Extraterrestrial radio signals first detected in 1932
by Karl Jansky
– Electrical engineer working for Bell Labs
– Attempting to determine origin of radio static at
20.5 MHz
– Steady hiss modulated with a period 23h 56min
– Strongest towards the Galactic Centre
• Discovery ignored by most astronomers, pursued
by Grote Reber
– 1937-1940: Mapped the Galaxy at 160 MHz
– Demonstrated the spectrum was non-thermal
• World War II stimulated rapid progress in radio and
radar technology
4
Why radio astronomy?
• Atmosphere absorbs most of the EM spectrum
– Only optical and radio bands accessible to ground-based
instruments
• Rayleigh scattering by atmospheric dust prevents daytime optical
• Radio opacity from water vapour line, hydrosols, molecular oxygen
– High, dry sites best at high frequencies
• Stars undetectably faint as thermal radio sources
– Non-thermal radiation
– Cold gas emission
– CMB
2hn 3
Bn T   2
c
1
e
hn
k BT
1
2k BTn 2

 0.3Jy
2
c
5
A tour of the radio Universe
6
What are we looking at?
• Synchrotron radiation
– Energetic charged particles accelerating along magnetic field
lines (non-thermal)
• What can we
learn?
• particle energy
• strength of
magnetic field
• polarization
• orientation of
magnetic field
7
• Thermal emission
– Blackbody radiation from cool (T~3-30K) objects
– Bremsstrahlung “free-free” radiation: charged particles
interacting in a plasma at T; e- accelerated by ion
• What can we
• H II regions
learn?
• mass of ionized gas
• optical depth
• density of electrons
in plasma
• rate of ionizing
photons
8
• How to distinguish
continuum mechanisms?
• Look at the spectrum
Spectral index across a SNR
Flux or Flux Density 
Frequency 
From T. Delaney
• Spectral index
Sn  n

9
• Spectral line emission (discrete transitions of atoms and molecules)
– Spin-flip 21-cm line of HI
– Recombination lines
– Molecular rotational/vibrational modes
• What can we
learn?
• gas physical
conditions
• kinematics (Doppler
effect)
10
The Sun
• Brightest discrete
radio source
• Atmospheric dust
doesn‟t scatter
radio waves
Image courtesy of NRAO/AUI
11
The planets
•
•
•
•
Thermal emitters
No reflected solar radiation detected
Jupiter is a non-thermal emitter (B field traps electrons)
Also active experiments: radar
Jupiter
Mars (radar)
Saturn
Images courtesy of NRAO/AUI
12
Stars
• Coronal loop resolved in the Algol system
• Tidally-locked system, rapid rotation drives magnetic dynamo
Credit: Peterson, Mutel, Guedel, Goss (2010, Nature)
13
Black holes and neutron stars
Blundell & Bowler (2004)
Mirabel & Rodriguez (1994)
Dhawan et al. (2000)
Dhawan et al. (2006)
Gallo et al. (2005)
Dubner et al. (1998)
14
Center of our Galaxy
VLA 20cm
VLA 1.3cm
VLA 3.6cm
1 LY
Credits: Lang, Morris, Roberts, Yusef-Zadeh, Goss, Zhao
SgrA* - 4 milliion Mo
black hole source
15
Radio Spectral Lines: Gas in galaxies
16
Jet Energy via Radio Bubbles in Hot
Cluster Gas
1.4 GHz VLA contours over Chandra X-ray image (left) and optical (right)
6 X 1061 ergs ~ 3 X 107 solar masses X c2 (McNamara et al. 2005, Nature, 433, 45)
17
Resolution and Surface-brightness
Sensitivity
18
The Cosmic Microwave Background
• 2.73 K radiation from z~1100
• Angular power spectrum of brightness fluctuations constrains
cosmological parameters
19
Definitions
2
In (or Bn ) = Surface Brightness : erg/s/cm /Hz/sr
(= intensity)
Sn = Flux density : erg/s/cm 2 /Hz
 In 
 In n
P = Power received : erg/s  In nA
E = Energy : erg  In nA t
S = Flux : erg/s/cm
2
tel
tel
20
Radio astronomy: instrumentation
• Antennas convert electromagnetic
radiation into electrical currents in
conductors
• Average collecting area of any lossless
antenna
2
l
Ae 
4
– Long wavelength: dipoles sufficient
– Short wavelength: use reflectors to
collect and focus power from a large
area onto a single feed
• Parabola focuses a plane wave to
a single focal point
Prime focus
(GMRT)
Offset cassegrain
(EVLA)
Beam waveguide
offset (NRO)
Cassegrain
(ATCA)
Naysmith
(OVRO)
Dual offset
(GBT)
21
Types of antennas
• Wire antennas
(l  1m)
– Dipole
– Yagi
– Helix
– Small arrays of the above
• Reflector antennas
(l  1m)
• Hybrid antennas
– Wire reflectors (l  1m)
– Reflectors with dipole feeds
22
Fundamental antenna equations
P(q ,  ,n )  A(q ,  ,n ) I (q ,  ,n )n
• Effective collecting
area A(qn) m2
• On-axis response
Ao=hA
• Normalized pattern
(primary beam)
A(qn) = A(qn)/Ao
• Beam solid angle
A= ∫∫ A(n,q,) d
all sky
• AoA = l2
23
Aperture-Beam Fourier Transform Relationship
• Aperture field distribution
and far-field voltage
pattern form FT relation
f l   
aperture
g (u )e 2ilu du
• u = x/l
• lsin q
• Uniformly-illuminated
aperture gives sinc
function response
 qD 
P(q )  sinc 

 l 
2
• qHPBW  l/D
24
Antenna efficiency
On axis response: A0 = hA
Efficiency: h = hsf . hbl  hs  ht  hmisc
rms error s
hsf = Reflector surface efficiency
Due to imperfections in reflector surface
hsf = exp[(4s/l)2] e.g., s = l/16 , hsf = 0.5
hbl = Blockage efficiency
Caused by subreflector and its support structure
hs = Feed spillover efficiency
Fraction of power radiated by feed intercepted by subreflector
ht = Feed illumination efficiency
Outer parts of reflector illuminated at lower level than inner part
hmisc= Reflector diffraction, feed position phase errors, feed match and loss
25
Interferometry
• Largest fully-steerable dishes have D~100m
– l/D ≤ 10-4 at cm wavelengths
• Sub-arcsecond resolution impossible
• Confusion limits sensitivity
– Collecting area limited to D2/4
• Tracking accuracy limited to s~1”
– Gravitational deformation
– Differential heating
– Wind torques
– Must keep s < l/10D for accurate imaging/photometry
• Interferometers consisting of multiple small dishes mitigate these
problems
26
Interferometry
• Interferometry = Aperture Synthesis
– Combine signals from multiple small apertures
– Technique developed in the 1950s in England and Australia.
– Martin Ryle (University of Cambridge) earned a Nobel Prize for
his contributions.
• Basic operation:
Correlation = multiply and average separate voltage outputs
27
Interferometry
• We seek a relation between the characteristics of the product of the
voltages from two separated antennas and the distribution of the
brightness of the originating source emission.
• To establish the basic relations, consider first the simplest
interferometer:
–
–
–
–
–
–
Fixed in space – no rotation or motion
Quasi-monochromatic
Single frequency throughout – no frequency conversions
Single polarization (say, RCP).
No propagation distortions (no ionosphere, atmosphere …)
Idealized electronics (perfectly linear, perfectly uniform in frequency and
direction, perfectly identical for both elements, no added noise, …)
28
The two-element interferometer
• Radiation reaching 1 is
delayed relative to 2
• Output voltage of antenna
1 lags by geometric delay
tg = b.s/c
• Multiply outputs:
V1V2  V 2 cos t cost  t g 


V2

cos 2t  t g   cos t g 
2
• Time-average the result
V2
R  V1V2 
cos t g 
2
multiply
average
29
V2
R  V1V2 
cos t g 
2
• Sinusoidal variation with
changing source direction:
fringes
  t g 
b cos q
c
d
 b sin q 
 2 

dq
 l 
• Fringe period l/bsinq
• Phase measures source
position (for large b)
30
V2
R  V1V2 
cos t g 
2
• Sensitivity to a single
Fourier component of sky
brightness, of period
l/bsinq
• Antennas are directional
• Multiply correlator output
by antenna response
(primary beam)
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Adding more elements
• Treat as N(N-1)/2
independent two-element
interferometers
• Average responses over all
pairs
• Synthesized beam
approaches a Gaussian
• For unchanging sources,
move antennas to make
extra measurements
32
Extended sources
V2
• Point source response of our cosine correlator: R  V1V2 
cos t g 
2
2
•
V
1/ 2
 Sn  A1 A2 
2
Treat extended sources as the sum of individual point sources
– Sum responses of each antenna over entire sky, multiply, then
average
Rc 
 V d  V d
1
• If emission is spatially incoherent
1
2
2
n R1 n * R 2   0 for R1  R 2
• Then we can exchange the integrals and the time averaging
b.s 

Rc   In s  cos 2n
d
c 

33
Odd and even brightness distributions
b.s 

• Response of our cosine correlator: Rc   In s  cos 2n
d
c 

• This is only sensitive to the even (inversion-symmetric) part of the
source brightness distribution I = IE+IO
• Add a second correlator following a 90o phase shift to the output of
one antenna
2
V
sin t g 
2
b.s 

Rs   In s sin 2n
d
c 

Rs  V1V2 
I
IE
=
IO
+
34
Complex correlators
• Define complex visibility V = Rc-iRs = Aei
• Thus response to extended source is
A = (Rc2+Rs2)1/2
 = tan-1(Rs/Rc)
b.s 

Vn   In s  exp   2i
d
l 

• Under certain circumstances, this is a Fourier transform, giving us a
well established way to recover I(s) from V
– 1) Confine measurements to a plane
– 2) Limit radiation to a small patch of sky
• Use an interferometer to measure the spatial coherence function Vn
and invert to measure the sky brightness distribution
35
Digression: co-ordinate systems
• Baseline b measured in wavelengths: the (u,v,w) co-ordinate system
– w points along reference direction so
– (u,v) point east and north in plane normal to w-axis
– (u,v,w) are the components of b/l along these directions
• In this co-ordinate system, s = (l,m,n)
– l,m,n are direction cosines
– n = cos q = (1-l2-m2)1/2
b.s 

Vn   In s  exp   2i
d
dldm
l 

d 
1  l 2  m2
In (l , m)
Vn u, v, w  
exp  2iul  vm  wn dldm
2
2
1 l  m
36
Measurements confined to a plane
• All baselines b lie in a plane, so b = r1-r2 = l(u,v,0)
• Components of s are then l , m, 1  l 2  m2


Vn u, v, w  0   In (l , m)
•
•
•
e 2i (ulvm )
dldm
1 l  m
This is a Fourier-transform relationship between Vn and In, which we
know how to invert
Earth-rotation synthesis (so is Earth‟s rotation axis): 1  l 2  m2  cos q  sec 
– E-W interferometers
– ATCA, WSRT
VLA snapshots
2
2
37
All sources in a small region of sky
• Radiation from a small part of celestial sphere: s = so+s
• n = cos q = 1 – (q2/2)
Vn u, v, w  e
 2iw

In (l , m)
1 l  m
2
2



exp  2i ul  vm  wq 2 / 2 dldm
• If wq 2 << 1, i.e. q~(l/b)1/2 then we can ignore last term in brackets
Vnu, v, w  e 2iw 
In (l , m)
1  l 2  m2
e 2i (ulvm ) dldm
• Let Vn u, v, w  e 2iwVn(u, v, w)
In (l , m) 2i (ulvm )
Vn u, v   
e
dldm
2
2
1 l  m
• Again, we have recovered a Fourier transform relation
• Here the endpoints of the vectors s lie in a plane
• Break up larger fields into multiple facets each satisfying wq 2 << 1
38
All sources in a small region of sky
• This assumption is valid since antennas are directional
Vn u, v    An (l , m) In (l , m)e 2i (ulvm) dldm
• Primary beam of interferometer elements An gives sensitivity as a
function of direction
• Falls rapidly to 0 away from pointing centre so
• Holds where field of view is not too large
– centimetre-wavelength interferometers
• EVLA
• MERLIN
• VLBA
• EVN
• GMRT
39
Visibility functions
• Brightness and
Visibility are
Fourier pairs.
• Some simple and
illustrative
examples make
use of „delta
functions‟ –
sources of
infinitely small
extent, but finite
total flux.
40
Visibility functions
• Top row: 1-dimensional even brightness distributions.
• Bottom row: The corresponding real, even, visibility functions.
Inq
Vn(u)
41
Inverting the Fourier transform
• Fourier transform relation between measured visibilities and sky
brightness
In (l , m) 2i (ulvm )
Vn u, v   
e
dldm
2
2
1 l  m
• Invert FT relation to recover sky brightness
In l , m
  Vn (u, v)e 2i (ulvm ) dudv
1  l 2  m2
• This assumes complete sampling of the (u,v) plane
• Introduce sampling function S(u,v)
InD l , m
  Vn (u, v)Sn (u, v)e 2i (ulvm ) dudv
1  l 2  m2
D
• Must deconvolve to recover In : In  In  B
• See Katherine Blundell‟s lecture for details
42
Seems simple?
• We have discovered a beautiful, invertible relation between the
visibility measured by an interferometer and the sky brightness
• BUT:
• Between the source and the correlator lie:
– Atmosphere
– Man-made interference (RFI)
– Instrumentation
• The visibility function we measure is not the true visibility function
• Therefore we rely on:
– Editing: remove corrupted visibilities
– Calibration: remove the effects of the atmosphere and
instrumentation
Vijobs  Gij Vijtrue  Gi G*j Vijtrue
43
What about bandwidth?
• Practical instruments are not
monochromatic
G
• Assume:
– constant source brightness
– constant interferometer
response
over the finite bandwidth, then:
n
n0
n
1 n c  n / 2

Vn   n  
In (s) exp  2int g dvd


n c  n / 2
• The integral of a rectangle function is a sinc function:
Vn   In (s)sinc(nt g ) exp( 2in ct g )d
• Fringe amplitude is reduced by a sinc function envelope
• Attenuation is small for ntg<< 1, i.e. nq  qsn
44
What about bandwidth?
• For a square bandpass, the bandwidth attenuation reaches a null at
an angle equal to the fringe separation divided by the fractional
bandwidth: nn0
• Depends only on baseline and bandwidth, not frequency
Fringe Attenuation
function:
 b n 
sinc
q
l n 
sin q 
c
bn
45
Delay tracking
• Fringe amplitude reduced by
sinc function envelope
• Eliminate the attenuation in any
one direction so by adding extra
delay t0 = tg
• Shifts the fringe attenuation
function across by sin q = ct0/b
to centre on source of interest
• As Earth rotates, adjust t
continuously so | t0 - tg| < (n-1
• nq  qsn
• Away from this, bandwidth
smearing: radial broadening
• Convolve brightness with
rectangle nqn
46
Field of view
• Bandwidth smearing
– Field of view limited by
bandwidth smearing to
q  qsnn
– Split bandwidth into many
narrow channels to widen
FOV
• Time smearing
– Earth rotation should not
move source by 1 synthesized
beam in correlator averaging
time
– Tangential broadening
– q  Pqs2t where
P=86164s (sidereal day)
Source
q
e
NCP
l/D
Interferometer
Fringe Separation
l/b
Primary Beam
Half Power
47
What about polarization?
• All the above was derived for a scalar electric field (single
polarization)
• Electromagnetic radiation is a vector phenomenon:
– EM waves are intrinsically polarized
– monochromatic waves are fully polarized
• Polarization state of radiation can tell us about:
– the origin of the radiation
• intrinsic polarization, orientation of generating B-field
– the medium through which it traverses
• propagation and scattering effects
– unfortunately, also about the purity of our optics
• you may be forced to observe polarization even if you do not want to!
48
The Polarization Ellipse
•
From Maxwell‟s equations E•B=0 (E and B perpendicular)
– By convention, we consider the time behavior of the E-field in
a fixed perpendicular plane, from the point of view of the
receiver.
k E  0
transverse wave
•
For a monochromatic wave of frequency n, we write
Ex  Ax cos2n t   x 
E y  Ay cos 2n t   y 
– These two equations describe an ellipse in the (x-y) plane.
•
The ellipse is described fully by three parameters:
– AX, AY, and the phase difference,  = Y-X.
Elliptically Polarized Monochromatic Wave
The simplest description
of wave polarization is in
a Cartesian coordinate
frame.
In general, three parameters
are needed to describe the
ellipse.
If the E-vector is rotating:
– clockwise, wave is „Left
Elliptically Polarized‟,
– counterclockwise, is
„Right Elliptically
Polarized‟.
equivalent to 2 independent Ex and Ey oscillators
Polarization Ellipse Ellipticity and P.A.
• A more natural description is
in a frame (xh), rotated so
the x-axis lies along the
major axis of the ellipse.
• The three parameters of the
ellipse are then:
Ah : the major axis length
tan c  AxAh : the axial ratio
 : the major axis p.a.
• The ellipticity c is signed:
c > 0  REP
c < 0  LEP
c = 0,90°  Linear (=0°,180°)
c = ±45°  Circular (=±90°)
Circular Basis
• We can decompose the E-field into a circular basis, rather than a (linear)
Cartesian one:


E  AR eR  AL eL
– where AR and AL are the amplitudes of two counter-rotating unit
vectors, eR (rotating counter-clockwise), and eL (clockwise)
– NOTE: R,L are obtained from X,Y by a phase shift
• In terms of the linear basis vectors:
1
AR 
AX2  AY2  2 AX AY sin  XY
2
1
AL 
AX2  AY2  2 AX AY sin  XY
2
Circular Basis Example
• The black ellipse can be
decomposed into an xcomponent of amplitude
2, and a y-component of
amplitude 1 which lags
by ¼ turn.
• It can alternatively be
decomposed into a
counterclockwise
rotating vector of length
1.5 (red), and a
clockwise rotating vector
of length 0.5 (blue).
Stokes parameters
• Stokes parameters I,Q,U,V
– defined by George Stokes (1852)
– scalar quantities independent of basis (XY, RL, etc.)
– units of power (flux density when calibrated)
– form complete description of wave polarization
– Total intensity, 2 linear polarizations and a circular polarization
• I
= EX2 + EY2
= ER2 + EL2
• Q = I cos 2c cos 2y = EX2 - EY2
= 2 ER EL cos RL
• U = I cos 2c sin 2y
= 2 EX EY cos XY = 2 ER EL sin RL
• V = I sin 2c
= 2 EX EY sin XY = ER2 - EL2
• Only 3 independent parameters:
– I2 = Q2 + U2 + V2 for fully-polarized emission
– If not fully polarized, I2 > Q2 + U2 + V2
Stokes parameters
• Linearly Polarized Radiation: V = 0
– Linearly polarized flux:
P  Q2  U 2
– Q and U define the linear polarization position angle:
tan 2  U / Q
– Signs of Q and U:
Q>0
U>0
Q<0
U<0
Q<0
U<0
U>0
Q>0
Polarization example
• VLA @ 8.4 GHz
– Laing (1996)
• Synchrotron radiation
– relativistic plasma
– jet from central
“engine”
– from pc to kpc scales
– feeding >10kpc
“lobes”
• E-vectors
– along core of jet
– radial to jet at edge
3 kpc
Sensitivity
• The radiometer equation for point source sensitivity:
sS 
2k BTsys
Aeff N ( N  1)tintn
• Increase the sensitivity by:
• Increasing the bandwidth
• Increasing the integration time
• Increasing the number of antennas
• Increasing the size/efficiency of the antennas
• Surface brightness sensitivity is MUCH worse
• synthesized beam << beam size of single dish of same effective
area
57
Summary: why should I use radio
telescopes?
• Unparalleled resolution
– Astrometry: positions, velocities, distances
– High-resolution imaging
• Unique probe
– Radio waves not scattered by dust: probe inner Galaxy
– Low-energy, long-lived non-thermal emission
– Spectral lines probe physical conditions of gas
• Signature of high-energy processes; link to X-ray emission
• Exotic phenomena
– Coherent emission (pulsar phenomenon)
• New “Golden Age”
– New telescopes opening up new parameter space
58
Radio Astronomy: A Golden Age!
EVLA
WSRT
EVN
LOFAR
GMRT
VLBA
ATCA
SKA?
ALMA
MeerKAT
LBA
ASKAP
59
Equations to take away
• Resolution of an interferometer
q
• Field of view of an interferometer
q
l
bmax
l
D
• Sensitivity of an interferometer
sS 
2k BTsys
Aeff N ( N  1)tintn
• Relation between visibility and sky brightness
Vn u, v   
In (l , m)
1  l 2  m2
e 2i (ulvm ) dldm
60

Fundamentals of radio astronomy - Radio Observations of Active

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