-1 2 ) /sr/cm Brightness (W/cm

Calibration of CMB instruments

• One of the most difficult steps in the measurement of CMB spectrum, anisotropy and polarization, is the calibration of the instrument.

• 20% errors (in temperature units) are still normal for these experiments. A 5% measurement is considered high accuracy.

• The problem is due to

– The lack of suitable laboratory standards: the best available source producing known brightness at mm-waves is a

cryogenic blackbody – a source diffucilt to operate and to use.

– The lack of well known Galactic sources as celestial standards.

Planets are small and can have atmospheric features; AGNs are variable; HII regions are contaminated by surrounding diffuse emission.

Calibration of CMB instruments

• Let’s pose the problem in rigorous terms:

• We call B(α,δ) the brightness of the sky in W/m²/sr (we will deal with spectral dependance later; here we consider the signal integrated over the instrument spectral bandwidth)

• A generic photometer observing the direction α_ο,δ_ο, will detect a signal

• For a point source located in α,δ , the flux

F

• The responsivity (gain) (V/W) must be calibrated, and the angular response R(θ) as well. This is the response of the system to off-axis radiation as a function of the off-axis angle θ, normalized to the on- axis response to the same source.

• The calibration can be performed observing a source with known brightness or known flux.

[ ] ^Ω

ℜ

= ^A ∫ ^{B R d}

V

π

α δ ϑ α δ α δ

δ

α , )

( , ) ( , , , ) (

ℜ

[ ^{( , , , )} ]

) ,

( α

δ

A F R ϑ α

δ

α δ

V = ℜ

The CMB dipole as a calibrator

• The dipole anisotropy of the CMB is the best responsivity (gain) calibration source, for several reasons:

A. Its amplitude is well known, and derived from astrometric, non- photometric data.

B. Its spectrum is exactly the same as the spectrum of the CMB anisotropy. No color correction needed.

C. It is unpolarized.

D. Its signal is only about 10 times larger than the signal of CMB anisotropy: detector non linearities are avoided.

E. The Dipole brightness is present everywhere in the sky

• The disadvantage is that the dipole is a large-scale signal.

Significant sky coverage is needed to detect it with an

accuracy sufficient for instrument calibration. Moreover,

foreground contamination and 1/f noise effects increase as

larger sky areas are explored.

Derivation of the CMB dipole

• We are moving with a velocity v with respect to the CMB Last Scattering Surface.

• The CMB is isotropic in the reference frame O’ of the LSS, but is not isotropic in the restframe O of the

observer, which is in motion.

• The distribution function f of particles with momentum p is a Lorentz invariant: In fact

where dN is a scalar, so is invariant, and the phase

space volume dx

dp

can also be shown to be a Lorentz invariant. So

i

i

dp

dx f (p ) = dN

) ( )

( p f p

f ′ ′ =

Derivation of the CMB dipole

• The Lorentz transformation for the momentum p is

• Applying this eq. to the Planck distribution function for photons we get

• This formula was first derived by Mosengheil (1907), and rederived by Peebles and Wilkinson (1968), Heer and Kohl (1968), Forman (1970).

• For small β :

p c c

p

c r

r r

r ′

×

−

= −

/c n v

1

/ v

1 ^{2 2}

T c T

T p T

T p ′

−

= −

× ′

−

= −

′ ⇒

= ′

) cos(

1

1 /c

n v

1

/ v

1 ^{2 2 2}

θ β

r

β

r

⎥⎦

⎢ ⎤

⎣

⎡ + +

≅ cos( 2 )

) 2 cos(

1 )

(

2 θ

θ β β

θ T_o T

kinematic term

light aberration term

O’

p p n r = r /

vr O

pr

• The motion of the Earth with respect to the CMB is the β

combination of

– The motion of the Earth around the Sun (well known) – The motion of the Sun in the Galaxy (well known)

– The motion of the Galaxy in the Local Group (known)

– The bulk motion of the Local Group (not well known) due to the gravitational acceleration generated by all other large masses present in the Universe

• The annual revolution of the Earth around the Sun is known extremely well ( v ~ 30 km/s), and produces an annual

modulation in the CMB dipole. This is the main signal used in COBE and WMAP for the Dipole calibration, since it is known from astrometric measurements much better

than the total motion of the earth.

• This effect produces a modulation of the order of β T

, i.e.

about 300μK, on a total dipole of the order of 3.5 mK.

CMB dipole signal

• The CMB temperature fluctuation corresponds to a CMB brightness fluctuation, which can be found by deriving the Planck formula with respect to T:

• This conversion from Temperature to Brightness is the same for the dipole and for any smaller scale temperature or polarization anisotropy. For this reason the Dipole

spectrum is the same as the spectrum of CMB

anisotropy. The maximum of this spectrum is at 271 GHz.

CMB x CMB

x

kT x h

T T

e B

I xe ν Δ = ν

= −

Δ ( , ) ;

1

0.1 1 10

10^-16 10^-15 10^-14

Brightness (W/cm2 /sr/cm-1 )

wavenumbers (cm^-1)

30 GHz 300 GHz

3 GHz

10 cm 1 cm 1 mm

Cosmic Dipoles

• If the isotropic source spectrum is not a BlackBody, the dipole formula is different.

• A typical example is the cosmic X-Ray background, whose specific brightness is basically a power law with slope

• In general the dipole anisotropy of the specific

brightness induced by our speed β with respect to the cosmic matter emitting the background can be derived as

• This is very sensitive to steep features in the spectrum (α large) which can compensate the smallness of β .

ν α ν

d dI I

v d

I

d =

= ln ln

...}

) cos(

) 3

( 1

{ )

( θ = I

+ − α β θ +

I

CMB dipole signal

• The signal produced by the CMB dipole temperature fluctuation is

• Since the dipole signal is almost constant within the beam of the instrument

• So from a scatter plot of the measured signal vs. the expected CMB Dipole the slope a can be estimated:

[ ]

∫

∫

= −

Ω Δ

ℜ

= Δ

ν ν

ν

δ α

δ α

ϑ δ

α δ

α

d E

T e B

xe K T

d R

T AK

V

x CMB x

CMB

o o

DIP o

o DIP

) ( ) , 1 (

1

) , ,

, (

) , ( )

, (

[ ] ^Ω

Δ ℜ

≅

Δ ^V

^{( α}

^{, δ}

^{) AK T}

^{( α}

^{, δ}

⁾ ∫ ^{R ϑ d}

[ ] ^Ω

ℜ

=

+ Δ

= Δ

∫ ^{R d}

AK a

b T

a

V

ϑ

δ α

δ

α , ) ( , )

(

calibration

constant (V/K)

[ ] ^{Ω ⇒}

Δ ℜ

=

Δ ^V

^A ∫ ^I

^{R ϑ d}

CMB dipole signal

• The CMB map obtained from the same instrument in voltage units (uncalibrated) is

where

• The conversion constant from voltage units to

Temperature units is the same we have obtained from the Dipole calibration:

[ ]

{ [ ] } ^{( , )}

) ,

(

) , ,

, (

) , ( )

, (

o o

T d

R AK

V

d R

T AK

V

o o

o o

o o

δ

δ

α ϑ

δ α

δ α

δ α

ϑ δ

α δ

α

Δ Ω

ℜ

= Δ

Ω Δ

ℜ

= Δ

∫

∫

a

T V

o o

) ,

) ( ,

(

δ δ α

α

= ^Δ Δ

[ ]

[ ]

Ω

= Δ

Δ

∫ ∫

d R

d R

T T ^{o o}

o

o ϑ

δ α δ α ϑ δ

δ α

α α δ

) , , , ( )

, ) (

,

( ( , )

calibrated T map:

uncalibrated V map:

calibration

constant (V/K)

CMB dipole signal

• Notice that

– since we have defined the calibrated temperature map as the intrinsic CMB map weighted with the angular response, and – since we have used the CMB dipole as a calibrator …

• the calibrated temperature map does not depend on the detailed angular response, and does not depend on the spectral response of the instrument:

• Where

a

T V

o o

) ,

) ( ,

(

δ δ α

α

= ^Δ Δ

[ ]

b T

a V

in d

R AK

a

o o

DIP o

o

DIP

= Δ +

Δ

Ω ℜ

= ∫

) ,

( )

,

( α δ α δ

ϑ

Sample CMB dipole signals:

• COBE map

Sample CMB dipole signals:

• COBE map

Gal. Eq.

apex of motion (WMAP)

l=(263.85+0.1)^o b=(48.25+0.04)^o

(close to the ecliptic…)

Amplitude (WMAP)

ΔT=(3.346+0.017)mK

Dipole signal in the B98 region (filtered in the same way as B98 data)

Detected signal at 150 GHz (detector B150A)

-1,0 -0,5 0,0 0,5 1,0 1,5 -0,008

-0,006 -0,004 -0,002 0,000 0,002 0,004

Preliminary Calibration BOOMERanG LDB 1998/99

55' pixels (1610)

Signal B150A (mV)

COBE dipole (mK)

Slope : a = (4.0+0.4) nV/μK

Point Sources

• A point source must be observed anyway to measure the Angular Response R( θ ). This is needed for estimates of the instrinsic power spectrum of the map.

• The point source will inevitably have a spectrum different from the spectrum of the CMB.

• The signal from the source will be:

• where F( ν ) is the specific flux of the source (W/m

/Hz).

• If the source flux is known, and the instrument makes a map of the region surrounding the source, the observation can be used to estimate the calibration constant a as

follows:

[ ] _∫

ℜ

= ϑ α δ α δ ν ν ν

δ

α A R F E d

V (

,

) (

,

, , ) ( ) ( )

Point Sources

• So the calibration constant a , needed to convert the uncalibrated map into a calibrated CMB map , can be estimated from:

– The uncalibrated map of the source V(α,δ⁾ – The flux of the source F(ν)

– The relative spectral response of the instrument E(ν⁾

[ ] [ ]

∫

∫ ∫

∫

∫ ∫ ∫

Ω −

=

= Ω

ℜ

=

⇒ Ω

ℜ Ω =

ν ν

ν

ν ν

δ ν α

ϑ ν ϑ ν

ν

δ α

d E

F T

d E

T e B

xe d

V

d R

K A a

d RA

d A E

F

d V

CMB x CMB

x

o o

o o

) ( ) (

) ( ) , 1 (

) ,

(

) ( ) (

) ,

(

Point Sources

• CMB anisotropy/polarization experiment have a typical resolution of a few arcmin.

• Known sources much smaller than this typical size can be considered point-sources and can be used to measure the angular response and the gain.

• Several kinds can be used:

– Planets

– Compact HII regions – AGNs

• All kinds have their own peculiarities.

Gaseous Planets :

•The size is in the sub-arcmin range.

•Atmospheric features can be important.

• Has a tenuous atmosphere, and no sub-mm features. Its Mars

emitting surface is basically a blackbody at 180 K.

• The typical size is 6” (check the ephemeres for the time of the observation).

• The typical signal expected from Mars is equivalent to a CMB temperature fluctuation. This can be found as

follows:

{ [ ] } { [ ]

}

= Ω Δ

⇒

⎪⎩ ⇒

⎪⎨

⎧

Δ Ω ℜ

= Δ

Ω ℜ

= Δ

∫ ∫

∫ ∫

d R

K

d E

T T B

T d

R AK

V

d E

T B A

V

Mars Mars

Mars

Mars Mars

Mars Mars

Mars

ϑ

ν ν

ν ϑ

ν ν

ν

) ( ) , (

) ( ) , (

) , ,

( )

( ) , 1 (

) ( ) , (

c CMB Mars

Beam Mars CMB

x CMB x

Mars Beam

Mars CMB

Mars

T f T T

d E

T e B

xe

d E

T T B

T ν

ν ν

ν

ν ν

ν

Ω

= Ω

− Ω

= Ω Δ

∫

∫

10 100

10 100 1000

ΔT (mK CMB)

frequency (GHz)

Signal from Mars (6”) in CMB units in a 5’ FWHM beam : About 1000 times the rms CMB anisotropy in the same beam.

More than enough to measure the angular response.

But what about linearity ? Is there a saturation risk ?

Beam Mars

TMars

Ω Ω

Degree-scale anisotropy as a calibrator

• Many experiments focus on a small sky patch, in order to obtain maximum S/N per pixel, to study CMB

anisotropy/polarization at intermediate and small scales.

• Large scale signals are not measured and are filtered out to remove the effect of 1/f noise and detector instability.

• The Dipole is not a suitable calibrator for these experiments.

• A possibility is to use the WMAP data in the selected region. WMAP has detected CMB anisotropy with S/N~1 for 15’ pixels, and 0.5% calibration accuracy.

• A scatter plot of experiment data vs. WMAP can provide the gain calibration. Point sources (AGN) should be

removed first, since their effect is strongly frequency

dependent.

b (deg) b (deg) b (deg)b (deg)

l (deg) 90GHz

l (deg)

b (deg)

220GHz

WMAP 1st yrBOOMERanG 98

b (deg)

l (deg) 150GHz

41GHz _{l (deg)} 60GHz _{l (deg)} 94GHz _{l (deg)}

b (deg) b (deg) b (deg)b (deg)

l (deg) 90GHz

l (deg)

b (deg)

220GHz

b (deg)

l (deg) 150GHz

41GHz _{l (deg)} 60GHz _{l (deg)} 94GHz _{l (deg)} PKS0537-441

BOOMERanG 98WMAP 1st yr

b (deg) b (deg) b (deg)b (deg)

l (deg) 90GHz

l (deg)

b (deg)

220GHz

b (deg)

l (deg) 150GHz

41GHz _{l (deg)} 60GHz _{l (deg)} 94GHz _{l (deg)} PMNJ0519-4546

BOOMERanG 98WMAP 1st yr

b (deg) b (deg) b (deg)b (deg)

l (deg) 90GHz

l (deg)

b (deg)

220GHz

b (deg)

l (deg) 150GHz

41GHz _{l (deg)} 60GHz _{l (deg)} 94GHz _{l (deg)} PKS0454-46

WMAP 1st yrBOOMERanG 98

10 100 100 1000 10000

30 200

CMB rms

PKS0537-441 PMNJ0519-4546 PKS0454-46

μ K

in a 20' beam

frequency (GHz)

55 . 2 '

20

430 100

/ ⁻

⎟⎠

⎜ ⎞

⎝

= ⎛

⎟⎟⎠

⎜⎜ ⎞

⎝

⎛ Ω

GHz K

F

CMB

ν μ

• There are additional AGNs lost in the confusion of the CMB

fluctuations.

• The WOMBAT catalogue and tools predict quite well the flux observed for the 3 detected

AGN, and can be used to estimate the contamination due to unresolved AGNs.

• In the 3% of the sky mapped by B98 the contamination of the PS at 150 GHz is less than 0.3% at l=200, and less than 8% at l=600.

• This is reduced by 50% if the resolved sources (at 150 GHz) are removed, and by 80% if are removed those resolved at 41 GHz.

0.0 0.5 1.0 1.5 2.0 2.5 3.0 1

10 100

Flux (Jy) @ 150 GHz

counts

WOMBAT catalog

http://astron.berkeley.edu/wombat/foregrounds/radio.html

0 200 400 600 800 1000 1200 1400 0

1000 2000 3000 4000 5000

6000 _CMB

all sources

resolved @150GHz removed resolved @40GHz removed

l(l+1)c l/2

π

μ

multipole l

150GHz

b (deg) b (deg) b (deg)b (deg)

l (deg) 90GHz

l (deg)

b (deg)

220GHz

WMAP 1st yrBOOMERanG 98

b (deg)

l (deg) 150GHz

41GHz _{l (deg)} 60GHz _{l (deg)} 94GHz _{l (deg)}

Scatter Plot

• Once point sources have been removed, one can

scatter-plot the experiment data (in V) vs. the WMAP data (in K

), and obtain the calibration constant (in V/K) from the slope of the best fit line.

• Problems of this approach:

a) The experiment beam is different from the WMAP beam (see next slide).

b) The experiment response to large scales can be different from the WMAP response

c) The noise level of the two experiments is different: this biases the best fit slope.

• A solution for a) is to re-bin the maps in pixels larger than the beams.

• Problem b)&c) can be corrected carrying out detailed

simulations to estimate the bias.

B98-150GHz

WMAP 94GHz

B98 150 GHz

WMAP 94GHz

11

’G au ss ian

13’G

au ss ian 13’G

auss ian

11’G

auss ian

a)

b)

b)

b) • Experiment data = y

; WMAP data = x

• In the case of BOOMERanG 98 and WMAP, in 7’

pixels, σ(y

) ~30μK, σ(x

) ~80μK .

• Best slope estimate :

1) Remove averages from data sets y_i and x_i , so that y=ax 2) Find the value of a which minimizes χ² :

3) Make simulations of best fit lines for correlated data with

different levels of noise for x_i and y_i. To understand if - for the noises of the experiment and of WMAP - there is a bias.

( ) ( )

( ) ( )

∑ ₊ ⁻

=

i i i

i i

x a

y

ax

a

y

2 2

σ

χ σ

230.0 240.0 -20.0 -10.0 1380. 0.116 7.700 240.0 250.0 -20.0 -10.0 7332. 0.296 2.900 250.0 260.0 -20.0 -10.0 7353. 0.381 2.300 260.0 270.0 -20.0 -10.0 7289. 0.246 2.400 270.0 280.0 -20.0 -10.0 885. 0.221 2.900 230.0 240.0 -30.0 -20.0 3940. 0.305 3.200 240.0 250.0 -30.0 -20.0 6954. 0.305 2.500 250.0 260.0 -30.0 -20.0 6954. 0.285 2.700 260.0 270.0 -30.0 -20.0 6869. 0.279 2.500 270.0 280.0 -30.0 -20.0 143. 0.154 7.100 230.0 240.0 -40.0 -30.0 5518. 0.178 4.600 240.0 250.0 -40.0 -30.0 6213. 0.270 2.800 250.0 260.0 -40.0 -30.0 6213. 0.337 3.000 260.0 270.0 -40.0 -30.0 6158. 0.288 2.200 270.0 280.0 -40.0 -30.0 520. 0.227 2.600 230.0 240.0 -50.0 -40.0 5117. 0.188 4.200 240.0 250.0 -50.0 -40.0 5416. 0.285 3.100 250.0 260.0 -50.0 -40.0 5417. 0.291 2.900 260.0 270.0 -50.0 -40.0 5200. 0.245 3.000 270.0 280.0 -50.0 -40.0 1196. 0.243 2.500 230.0 240.0 -60.0 -50.0 230. 0.262 3.200 240.0 250.0 -60.0 -50.0 3415. 0.171 3.600 250.0 260.0 -60.0 -50.0 2583. 0.164 3.800

l(^o) b(^o) N R a_min

• Results for several regions:

• First 4 columns define the region, in Galactic

coordinates; 5th column is the number of pixels

observed by both

experiments; 6th column is Pearson’s correlation

coefficient; 7th column is the best fit calibration

constant.

• Resulting average calibration:

(3.5+0.3)ADU/μK

A variant of this correlation method is based on the cross-power spectrum:

– Compute the Angular Power Spectrum of the

uncalibrated experiment, XX(l), and the Cross Power Spectrum between the uncalibrated experiment and WMAP, XW(l):

1/

a( l)[V/K]= XW(l)/XX(l)

– Using the same region, cosmic variance is not effective

– The method is computationally more costly

– Beam and low multipoles response differences can be taken into account easily:

– 1/a(l)[V/K]= [XW(l)/(BX(l)BW(l))]/[XX(l)/BX2 (l)]

where B² are the spherical harmonic transforms of the beams/responses (Hivon E. et al. 2003, Polenta et al. 2004).

100 200 300 400 500 600 0.7

0.8 0.9 1.0 1.1 1.2 1.3

B98 - 150 GHz A+A1+A2+B1 raw

c l[WMAPxB98]/c l[B98*B98]

multipole

No obvious trend vs multipole: beam calibration OK Gain calibration: to be multiplied by 0.95 + 0.01

Hivon E. et al. 2003 All c_l

corrected for beam and

finite sky coverage

WMAP/B98 (gain recalibration)

0.95 +/- 0.01 0.95 +/-0.03

Sum

0.97 +/- 0.03 0.96 +/- 0.03

B150B2

0.95 +/- 0.02 0.97 +/- 0.03

B150A2

0.85 +/- 0.02 0.89 +/- 0.03

B150A1

0.96 +/- 0.02 0.95 +/- 0.03

B150A

C(l) based Pixel based

Channel

Raw maps on 1.8% of the sky (Netterfield et al. cut)

0.95 +/- 0.01 0.95 +/-0.03

Sum

0.95 +/- 0.02 0.95 +/- 0.03

B150B2

0.98 +/- 0.02 0.98 +/- 0.03

B150A2

0.92 +/- 0.03 0.91 +/- 0.03

B150A1

0.96 +/- 0.02 0.95 +/- 0.03

B150A

C(l) based Pixel based

Channel

Destriped maps on 1.8% of the sky (Netterfield et al. cut)

Hivon E. et al. 2003

• The nominal

calibration of the 150 GHz map was off by 5% (well

within the published 10% error)

• The new calibration is accurate to 1%, which is very good news for the

calibration of B2K

Beam pattern calibration

• We have seen before why beam calibration is so important.

• For example it affects directly the estimates of the angular power spectrum at high multipoles:

• Where B is the spherical harmonics transform of the beam, a steeply decreasing function at high multipoles

!

2 ,

l l

l

B

c = c

B98-150GHz

WMAP 94GHz

B98 150 GHz

WMAP 94GHz

11

’G au ss ian

13’G

au ss ian 13’G

auss ian

11’G

auss ian

R( θ )

B _l ²

BOOM98: 150 GHz window function

Combination of:

Pixelization (14’ healpix) Effective beam (including

estimated 2’ rms pointing jitter)

Freq. FWHM 90GHz 18’+2’

150GHz 10’+1’

240GHz 14’+1’

410GHz 13’+1’

Pointing jitter

• As an example of how important can be the estimate of the instrument beam and of systematic errors, let’s consider what happened for the first release of the BOOMERanG data (B98 Nature paper).

• The effective beam is the convolution of the telescope beam

[(9.2+0.5)’FWHM @ 150 GHz] with the telescope pointing jitter.

• The results in Nature were based on a jitter estimate of (2+1)’rms

from a few scans of RCW38 done in CMB mode. This is, however, on the edge of the area surveyed for CMB measurements. We understand now that this result is not representative of all the data in CMB mode.

• With the improved pointing solution it is possible to infer the effective beam (and the jitter) from many more measurements of 3 AGN in the center of the CMB area. We see that the old pointing solution had a jitter of (4+2)’ rms -> Nature results should be corrected: the effective beam was (12.7+1.4)’FWHM instead of the assumed (10+1)’FWHM.

• The new pointing solution has a jitter of (2.5+2.0)’ rms. The effective beam for the new data with new pointing solution is

(10.9+1.4)’FWHM.

Corresponding Effect on the PS

• Original data, as published in Nature, with

published random and systematic errors

0 100 200 300 400 500 600

0 1000 2000 3000 4000 5000 6000 7000

original Nature data Nature +1σ gain Nature -1σ gain

Nature +1σ gain +1σ beam Nature -1σ gain -1σ beam

l(l+1)c l/2π (μK2 )

multipole

Corresponding Effect on the PS

Original data

and data corrected for jitter underestimate

Correction substantial at l=600 (+35%, but still within published

errors)

0 100 200 300 400 500 600

0 1000 2000 3000 4000 5000 6000 7000

original Nature data

jitter underestimate corrected Nature +1σ gain

Nature -1σ gain

Nature +1σ gain +1σ beam Nature -1σ gain -1σ beam

l(l+1)c l/2π (μK2 )

multipole

Also Calibration Correction

• We also found a better treatment of the effect of high pass filters in the Dipole calibration

• 10% (1σ)

decrease of gain i.e. additional 20% coherent increase of the PS values

0 100 200 300 400 500 600

0 1000 2000 3000 4000 5000 6000 7000

original Nature data jitter underestimate and gain corrected

Nature +1σ gain Nature -1σ gain

Nature +1σ gain +1σ beam Nature -1σ gain -1σ beam

l(l+1)c l/2π (μK2 )

multipole

0 100 200 300 400 500 600 0

1000 2000 3000 4000 5000 6000 7000

B98 data corrected

l(l+1)c l/2π (μK2 )

multipole

Corrected data : the 2nd peak is not evident yet

• After the

correction, there is a hint of a 2nd peak, but it is not statistically

significant.

• the data (from a single bolometer) are still not

sensitive enough.

192 196 200 204 208

location of peak lp (multipole)

4500 4600 4700 4800 4900 5000

peak amplitude lp(lp+1)c lp/2π (μK2 )

6 8 10 12 14

0.26 0.28 0.30 0.32

beam FWHM (arcmin) (l>320 average)/ (peak amplitude)

Effect of jitter underestimate

in preliminary results: 10’ –> 12.7’

1%

4%

4%

Old beam New beam

Effects of jitter underestimate

and calibration correction on science

• Cosmological parameters extraction from the

corrected B98 together with the COBE-DMR PS data:

• Ω

remains the same – (1% effect is negligible)

• Ω

h

changes from 0.036+0.006 to 0.027+0.006 (same weak priors, l<625):

• (cfr. BBN: Ω

h

= 0.020+0.002)

• We are comparing the density of baryons 3 minutes after the big-bang (assuming it is the same as at z=3) to the density of baryons 300000 yrs after the Big Bang.

• Different physics (nuclear reactions vs acoustic waves in a plasma), different experimental methods and systematic effects!

Artificial Planet

Diam = 20, 40 cm Dist. 2 km

(4, 8 arcmin)

Telescope BEAM Calibration

At ground calibration with artificial planet (tethered blackbody + CCD monitor)

Telescope Beam Calibration : scans on RCW38

For BOOMERanG this is a point source, very useful to get our beam size. We have hundreds

of scans for each detector, so we can obtain both the telescope beam and the pointing jitter

2.5’

P.de Bernardis Oct.2000

Compact HII region in an area free from Galactic confusion

Acbar data at 1.4 mm = 2.5’ diam.