Misure del CMB. Intrinsic CMB measurements limits 20/11/2017. Come si misurano le osservabili CMB?

Transcription

1 0//07 Misure del CMB Come si misurano le osservabili CMB? Spettro Anisotropia Polarizzazione Limitazioni di origine fondamentale Strategie di misura Metodi di modulazione del segnale (cm - ) wavenumber he spectrum echniques? h B(, ) c e.7k CMB CMB h k CMB 6 GHz ien ma ma e ma.8 ma 9 GHz ( ma. cm ) B(, ) B(, ) ma. 06 mm RJ ma ma ma 60 GHz 60 GHz 60 GHz RJ ien coherent detectors bolometers??? Intrinsic CMB measurements limits Is the fundamental limit of any measurement. Photon noise reflects the particle-wave duality of photons. It is the sum of Poisson noise (particles) PLUS interference noise (waves) Poisson noise: E h his is a typical random-walk process (variance prop.to time). Using Einstein s generalization kbt f 4 we get the power spectrum and the variance of radiative power fluctuations: h h h h ht f kb

2 0//07 Orders of magnitude eample: A He-e m laser beam has a perfect Poisson statistics, so f h. 0 Hz otice the power spectrum units (remember that the integral of the PS over frequency is the variance). In this case the intrinsic fluctuations per unit bandwidth are >7 orders of magnitude smaller than the signal. It is useless to build a comple detector with a noise of 0 / Hz for this measurement: the precision of the measurement will be limited at a level of.0 / Hz anyway. hermal radiation (like the CMB) has also wave interference noise: the correct statistics is Bose-Einstein. e ; ( E ) g g Poisson noise d d ave interference noise, V For a blackbody g ; g 4Vd ( E ) e c 8 Vd h c e h e Poisson noise, important at short wavelengths ave interference noise, Important at low frequencies E.77 0 h e h h h e e h h e 8 A cm sr Hz K 4 e d e h CMB observables he spectrum h B(, ) c e he angular distribution h k e B(, ) B(, ) e he polarization state e BP (, ) B(, ) e he noise (, ) d P CMB (MKS units) 4 e e d =.7 K (m sr Hz) -/ Hz -/ m - sr - Hz - average brightness anisotropy (rms) polarization (E rms) photon noise (rms) polarization (B rms) m - sr - Hz - m - sr - Hz Frequency (Hz) oise and integration time Any detector has a response time which limits its sensitivity at high post-detection frequencies. Data taken at intervals shorter than will not be independent. he error on the estimate of in the observation time t, is t fma fmin, the average power where is the number of independent measurements. In the integration time t, it will be =t/ t

3 0//07 / / oise and integration time t / f ma f min t t / t / t he noise decreases as the square root of the integration time. otice that this is applies equally to detector noise and to intrinsic radiation noise. f ma f min oise and integration time umerical eample: CMB anisotropy (or polarization) measurement limited only by radiation noise: B (, ) 4 k e 4 k e B (, ) d B A e B (, ) d e 4 A e 4 e 4 e ( e ) d d t he ultimate sensitivity plot!! Development of thermal detectors for far IR and mm-waves error per piel (K) 0 0. CMB BLIP 0 GHz,0% B, 0 GHz, 0% B, cm sr 0 GHz, 0% B, time required to make a measurement (seconds) 0 7 Langley's bolometer Golay Cell 0 Golay Cell Boyle and Rodgers bolometer 0 7 year F.J.Low's cryogenic bolometer day Composite bolometer hour Composite bolometer at 0.K 0 second Spider web bolometer at 0.K Spider web bolometer at 0.K integration time (s) year ' ' e For a grey-body with emissivity relevant cases: Radiation emitted by a mirror) Radiation emitted by the atmosphere in the atmospheric windows ' h A 4 ( e ) d e ' ' e For a grey-body with emissivity relevant cases: Radiation emitted by a mirror Radiation emitted by the atmosphere in the atmospheric windows ' h A 4 ( e ) d e

4 0//07 arxiv: arxiv: Measurement strategy Importance of a differential detection technique Detectors have drifts, due to the fact that their parameters and the environment are not perfectly stable. hese drifts are very slow low level fluctuations of the output signal independent of the input signal. As a result the spectrum of the detector output has a /f component, diverging at f=0. detector drift (no signal) Sky chopper Sky signal Cold Reference signal Detector mirror detector drift plus modulated signal Differential Radiometer S( t) ( sky ref )sin( t) n( t) High-passed modulated signal (drift removal) Cold Reference Source S( t)sin( t) ( sky ref ) 4

5 0//07 Reference source In the case of Penzias and ilson, the em waves were collected by an off-ais, low s antenna, and propagated in a waveguide. he chopper was a ferrite Dicke switch he reference source was a cold load cooled at 4.K with liquid helium. he detector was a low-noise maser amplifier. Importance of low s he power detected is the integral of the brightness Brightness from direction () A B(, ), ) d 4 ypical telescope response ) elescope response in direction () s ) FHM=/D Importance of low s he power detected is the integral of the brightness Importance of low s he power detected is the integral of the brightness Brightness from direction () elescope response in direction () Brightness from direction () elescope response in direction () A B(, ), ) d 4 ypical telescope response ) )= A B(, ), ) d 4 ypical telescope response ) )< s s Importance of low s he power detected is the integral of the brightness Importance of low s he power detected is the integral of the brightness Brightness from direction () elescope response in direction () Brightness from direction () elescope response in direction () A B(, ), ) d 4 A B(, ), ) d 4 ypical telescope response ) s )<< ypical telescope response ) s )<<

6 0//07 Importance of low s In the case of CMB observations, the detected brightness is the sum of the brightness from the sky (dominant for the solid angles directed towards the sky, in the ) and the Brightness from ground (dominant for the solid angles directed towards ground, in the s). A B s ) FHM=/D (, ) RA (, ) d B Ground (, ) RA (, d s sky ) A Importance of low s B sky (, ) RA (, ) d BGround (, ) RA (, ) d s signal of interest disturbance signal A Bsky(, ), ) BGround(, ) RA (, ) s K srad Obtaining : signal of interest >> disturbance signal requires, ) RA (, ) s 00K s srad signal of interest disturbance signal A Bsky(, ), ) BGround(, ) RA (, ) s RA s K (, ) RA srad (, ) s FHM <RA s > 0 o 0 - srad <<40 - o 0-4 srad << srad <<0-8 s 00K srad ( srad) Bsky(, ) BGround(, ) srad <<0-0!!! hat is )? Fraunhofer diffraction from a circular aperture (radius a) (at large distances from shield) he incident wave is an infinite plane wave (wavevector k in parallel to the z ais). he outgoing wave is not infinite, and for this very reason it will have components with wavevectors k in different directions. So it is not a plane wave. e want to find out which are the amplitudes of the different components of the outgoing wave. a z k in r ds k hat is )? For small angles the vector q=k-k in is in the plane of the aperture and q=k. he diffracted component with wavevector k is the sum of the contributions from all the elements ds of the aperture, each with its own phase: u q S u iqr oe a uq uoe 0 0 ds iqrcos rddr a z k in Bessel functions q r ds a u o 0 J ( aq) Jo( qr) rdr uo aq k q hat is )? he intensity is di J ( ak ) I o d ak Eample: a m diameter mirror used at cm and at mm s a=m = cm = mm off-ais angle (deg) 0. 6

7 0//07 hat is )? he intensity is di J ( ak ) I o d ak s a = m = cm = mm off-ais angle (deg) hat is )? he intensity is di J ( ak ) I o d ak he first zero is for 0. a a = m = cm = mm off-ais angle (deg) hat is )? he intensity is di J ( ak ) I o d ak he first zero is for 0. a he FHM is similar FHM a = m = cm = mm off-ais angle (deg) hat is )? he intensity is ( ak ) di J I o d ak he envelope of the off-ais response scales as - approimately starting from 0. at the FHM a = m = cm = mm ) off-ais angle (deg) eercise For the of a circular aperture, compare the power in the to the power in the s Hint: J ( ak ) P A B sind s ak 0.6 / a s P A 0.6 / a J ( ak ) ak But use approimated formulas 0 B sind Low diffraction design Real-world s are worse than the one studied here. Sharp edges are in general important sources of diffraction, and must be avoided in low s design. Use smoothed edges. A trumpet has a slow transition to free space at the aperture to avoid diffraction of sound waves. he spider supporting the secondary mirror in a Cassegrain telescope is an important source of diffraction. Penzias and ilson used an under-illuminated offais paraboloid, to get low s 7

8 0//07 0dB = a factor 0 in power Other eample of low s design: Planck SRAY LIGH Main Beam Response Main Beam 0 7 Far Sides Sub Spillover Main Spillover ear Sides Main Spillover F. Villa, LFI Angle from F. Villa, LFI Another low s design: BOOMERanG Even more stringent nequirements due near earth operation 8

9 0//07 Sun Shield. m Angle of sunshield R S Cold Lyot Stop + baffles P Ground Shield 9