OSSERVAZIONI SZ con ALMA

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OSSERVAZIONI SZ con ALMA

• SZ-ALMA Meeting
• Trieste, 13 Aprile 2005
• Paola Andreani
• INAF-OAT

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SZ Interferometric observations

• SZ large angular scale feature on the sky high
  resolution detrimental
• Improvements in the control of systematic
  offsets
• structures on the sky modulated by a fringe
  pattern at a ? rate than most of the
  contaminating sources (rejection of signals from
  astronomical sources)
• loss of coherence away from the pointing center
  ground spill-over terrestrial interferences
  other spurious sources attenuated
• allow simultaneous observations of confusing,
  small angular scale, variable sources

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Interferometric observations

• Time averaged correlation of the signals from a
  pair of antennas (collection of n(n-1)/2
  2-element interferometer)
• Multiplies sky brightness at ? by a cosine,
  integrates and outputs the time average amplitude
• Output is the visibility (signals are split and
  correlations are performed with a 90 phase shift)
  which is the complex Fourier transform of the sky
  brightness.

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Interferometric observations

• The correlated output R
• R ? A I cos (2p b/? ?? cos(?0))
• 
  I energy received per unit area
• 
  A area of each antenna
• 
  ?0 is a reference direction
• 
  b is the baseline
• Sky structures on larger angular scales will not
  modulate R with ?0 (time) and wont produce a
  detectable signal

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Interferometric observations

• Stability and spatial filtering
• Only sensitive to angular scale
• (spatial frequencies) b/?
• (bbaselineprojected
  separation seen by the source)
• Insensitive to atmospheric emission gradient and
  large scale emission features
• Only correlated signal between array elements
  contribute to detection (sky noise, amplification
  instability do not lead to false detection)
• Offsets, drifts and spurious noise correlation
  removed with modulation of the signal phase and
  demodulation of the correlator output.

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Sources of contamination and confusion

• Anisotropy of CMB
• thermal SZ spectral behaviour
• kinetic SZ only with small spectral
  distortion due to relativistic effects
• not a problem for very small angular scales

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Sources of contamination and confusion

• Radio sources (underestimates)
• radio sources are variable
• observations at high-?
• S? ?-a (radio source) and S?2 (RJ SZ)
• Radio sources (overestimates) radio sources in
  the reference fields

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Sources of contamination and confusion

• Gravitational lensing increased efficiency of
  detecting point sources toward the cluster center
  (overestimate of the SZE signal)
• more important at higher ? (steeper count
  slope)
• dn/dS ?µ?-2S-? ? if µ ? and ?gt2
• Bulk peculiar velocities of Lya absorbers
• ?T/T 10-6 OLya ltv2400gt1/2
• OLya is O in ionized
  gas in Lya absorbers
• ltv2400gt1/2 rms los peculiar velocity of these
  systems at z 3

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Relative amplitude of 1s confusion noise with
and without lensing
lensing more pronounced if ?b 2?E
?450,850µm 1.2mm,2mm
arsec
(model 1) (model 2)
Blain, 1998
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Sources of contamination and confusion

• Dust from extragalactic sources S? ?(2ß)
• (SCUBA source ß1.5-2.5)
• S(350GHz)10mJy ? ?T 345 µK
• at 270GHz ?T 140 µK
• or y6 10-5
  
• At SZE thermal null S(218GHz) 85 µK
• uncertainties in the cluster peculiar velocity
  te0.01, Te10keV ?vpec930km/s !
• More severe for less massive clusters
• ?vpec te-1 R2/M M-1/3 Te-1/2
• Contamination scales as 1/beam

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Sources of contamination and confusion

• Dust from galactic ISM
• P(k) 4.8 105 (NHI/1020)2.1 (k/0.01)-3
  (B?/B100)2
• s2 ? P(k) 2pk dk Jy2/sr2
• _at_ 350 GHz s 40nJy in 9'' FOV
• should be then negligible (although lower-?
  measurements lack)

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Separate point sources from SZE

• either High dynamic angular range
• or Large spectral coverage
• or both
• (see later in the proposed observations)

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Sensitivity

• ?S? J Tsys / ?Q v2Nbase ??
  tint
• J 2k/(?aA)
  33 Jy/K antenna gain
• 
  Nbase N(N-1)/2
• 
  primary beam O and effective collecting area A
  OA?a?2
• ?T Tsys / vNbase ?? tint ( ?p/?s)2
• In continuum ??16GHz
• 1h integration time 13 µJy/beam 0.13mK/beam
• 1s integration time 0.8mJy/beam
• Compact Configuration
• Good image fidelity at intermediate d
• 1 resolution at 350GHz
• Full UV coverage in snapshot

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Beam "antidilution"

• beam pattern
• G(?) 1/2ps2 exp (?2/2s2)
• Average signal
• Y(?') 2p ??d? 1/2pL2 exp(-?2/2L2) Y(?)
  
• where LDas and ? angular radius from the
  cluster center
• The Y profile for a spatially resolved cluster
  is
• f(x)-1 (kTe/mec2)sTne(0)DA ?cvpG(a-0.5)/2G(a)
  (1?2/?c2)(0.5-a)
• ?c?(1-2a)/(1-2a) ?c/2 (1?2/?c2)
  ?-(12a)/(12a)
• ?21Rmax/Rc a-3ß/2

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Y profile for a spatially resolved cluster
to detect most of the cluster signal spatial
integration until 4?c
? 350GHz
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Beam "antidilution"

• beam pattern
• G(?) 1/2psb2 exp (?2/2sb2)
• sb ?FWHM /(8ln2)0.5
• ? is the angle from the beam
  axis
• the beam smeared profile of the cluster is
• S obs?(?) y0 ?2c j? G?/?c, sb/?c
• this profile is subject to detection criteria
• object image above a flux density of qspix
  covering a
• minimum solid angle ONminOpix
• G?/?c, sb/?c qspix / y0 ?2c j? y/y0
  (sb/?c)2

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detection criteria
?det cluster angular size above detection
threshold Sobs?(?det) qspix ?c characteristic
cluster size (model dependent) I?(?)?
(1?2/?2c)a ?b beam FWHM
?det/?c
Bartlett,2000
?c/?b
y0
?c/?bltlt1 point sources source profile beam
object sinks below the detection threshold
cutoff at low ?c/?b
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Variation of the beam averaged y with beam size
Massive young galaxies
effective y average of y in different shells weig
hted by the corresponding projected area
convolved with beam profile
5 1012M?
1011M?
Rosa-Gonzalez et al., 2004
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Proposed observations

• Compact Array (150m), complete sampling (u,v)
  sampling total power mosaicing high-?
  observations 1'' resolution at 350 GHz
• Mosaicing 0.1arcmin2 250 areas for ?c50'' (less
  for lower ?)
• Drift scanning arrayapertures kept stationary
  wrt environment
• Larger baselines to subtract compact sources
• No effect of source confusion (but lensed obj?)

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Correlated signals

• R d? cos(2p?bso/c) ?skyA(?0)I(?0) cos(2p?b?0/c)
  dO
• d? sin(2p?bso/c) ?skyA(?0)I(?0)sin(2p?bso/c) dO
• Power received from a sky area dO in direction s
  A(?0)I(?0)dOd?
• Complex Visibility V Ve iF?
  ?skyA(?0)I(?0)e(-2ip?bso/c) dO
• Correlator output is proportional to the
  visibility amplitude
• V and its phase
• R d? cos(2p?bso/c) Vcos(F?) - d?
  sin(2p?bso/c) )
• Vsin(F?)

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Sources of contamination and confusion

• Dust from extragalactic sources
• S? ?(2ß) (SCUBA ß1.5-2.5)
• _at_ 350GHz 10mJy
• ?T 345 µK
• _at_ 270GHz
• ?T 140 µK
• (1 beam) or y6 10-5
• _at_ SZE thermal null
• S(218GHz) 85 µK
• uncertainties in the cluster vpec
• te0.01, Te10keV ?vpec930km/s!
• More severe for less massive clusters
• ?vpec te-1 R2/M M-1/3 Te-1/2
• Contamination scales as 1/beam