Calibration of CMB instruments
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 αο,δο, will detect a
signal
• 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
4π
– 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.
[
V (α o , δ o ) = ℜ A F R ϑ (α o , δ o , α , δ )
The dipole anisotropy of the CMB is the best responsivity
(gain) calibration source, for several reasons:
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
r
v
O
• The Lorentz transformation for the momentum p is
r
1 − v2 / c 2 r
r r
cp =
cp′
r r
n = p/ p
1 − v × n /c
• Applying this eq. to the Planck distribution function for photons
we get
1− β 2
p
1− v 2 / c2
T =
T′ ⇒ T =
T′=
T′
r r
p′
1 − v × n /c
1 − β cos( θ )
• This formula was first derived by Mosengheil (1907), and
rederived by Peebles and Wilkinson (1968), Heer and Kohl
(1968), Forman (1970).
• For small β :
2


β
cos( 2θ ) 
T (θ ) ≅ T o 1 + β cos( θ ) +
2


kinematic
term
light aberration
term
]
Derivation of the CMB dipole
A. Its amplitude is well known, and derived from astrometric, nonphotometric 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 responsivity (gain) ℜ (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 onaxis response to the same source.
• The calibration can be performed observing a source with known
brightness or known flux.
The CMB dipole as a calibrator
•
[
V (α o , δ o ) = ℜ A ∫ B (α , δ ) R ϑ (α o , δ o , α , δ ) dΩ
• For a point source located in α,δ , the flux F (W/m2) produces a signal
O’
r
p
• 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
dN
f (p ) =
dx i dp i
where dN is a scalar, so is invariant, and the phase
space volume dxidpi can also be shown to be a Lorentz
invariant. So
f ′(p′ ) = f (p )
β
• The motion of the Earth with respect to the CMB is the
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 βTo , i.e.
about 300µK, on a total dipole of the order of 3.5 mK.
1
CMB dipole signal
xe
B(TCMB ,ν ) ∆T
ex −1
; x=
hν
kTCMB
300 GHz
-1
30 GHz
10
-14
10
-15
10
-16
2
∆I =
x
3 GHz
Brightness (W/cm /sr/cm )
• 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.
0.1
1
10
-1
wavenumbers (cm )
10 cm
I (θ ) = I o{1 + (3 − α ) β cos(θ ) + ...}
• This is very sensitive to steep features in the spectrum
(α large) which can compensate the smallness of β .
• The signal produced by the CMB dipole temperature
fluctuation is ∆ V DIP = ℜ A ∫ ∆ I DIP R [ϑ ]d Ω ⇒
∆ V DIP (α o , δ o ) = ℜ AK ∫ ∆ T DIP (α , δ ) R [ϑ (α o , δ o , α , δ )]d Ω
xe x
B (T CMB ,ν ) E (ν ) dν
x
TCMB
−1
• Since the dipole signal is almost constant within the beam
of the instrument
K =
1
∫e
∆VDIP (α o , δ o ) ≅ ℜAK ∆TDIP (α o , δ o ) ∫ R[ϑ ] dΩ
• So from a scatter plot of the measured signal vs. the
expected CMB Dipole the slope a can be estimated:
∆VDIP (α o , δ o ) = a ∆TDIP (α o , δ o ) + b
a = ℜAK ∫ R[ϑ ] dΩ
CMB dipole signal
[
where
∆T (α , δ )
(α o ,δ o )
=
∫∆
[
]
(α o ,δ o )
]
T (α , δ ) R ϑ (α o , δ o ,α ,δ ) dΩ
R[ϑ ]d Ω
∫ units to
• The conversion constant from voltage
Temperature units is the same we have obtained from the
Dipole calibration:
uncalibrated
calibrated
T map:
∆T (α, δ )
(α o , δ o )
calibration
constant (V/K)
CMB dipole signal
• The CMB map obtained from the same instrument in
voltage units (uncalibrated) is
∆V (α o , δ o ) = ℜAK ∫ ∆T (α , δ ) R ϑ (α o , δ o , α , δ ) dΩ
{∫ R[ϑ ]dΩ} ∆T (α ,δ )
1 mm
CMB dipole signal
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
d ln I v dI
α=
=
d lnν I dν
• 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
∆V (α o , δ o ) = ℜAK
1 cm
∆V (αo , δo ) V map:
=
calibration
a
• 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:
∆T (α , δ )
• Where
(α o ,δ o )
=
∆V (α o , δ o )
a
a = ℜAK ∫ R[ϑ ] dΩ
in
∆VDIP (α o , δ o ) = a ∆TDIP (α o , δ o ) + b
constant (V/K)
2
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…)
Dipole signal in the B98 region (filtered in the same way as B98 data)
Amplitude
(WMAP)
∆T=(3.346+0.017)mK
Detected signal at 150 GHz (detector B150A)
Point Sources
0,004
Signal B150A (mV)
0,002
Preliminary Calibration
BOOMERanG LDB
1998/99
• 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:
0,000
-0,002
Slope : a = (4.0+0.4) nV/µK
-0,004
-0,006
-0,008
-1,0
55' pixels (1610)
-0,5
0,0
0,5
COBE dipole (mK)
1,0
1,5
[
]
V (α o , δ o ) = ℜA R ϑ (α o , δ o , α , δ ) ∫ F (ν ) E (ν )dν
• where F(ν) is the specific flux of the source (W/m2/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:
3
∫ V (α o , δ o )dΩ
Point Sources
= ℜ A ∫ RA [ϑ ]dΩ
∫ F (ν ) E (ν ) dν
a = ℜA K ∫ R [ϑ ]dΩ
= ∫ V (α o , δ o ) dΩ
⇒
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:
=
xe x
B (TCMB ,ν ) E (ν )dν
x
−1
TCMB ∫ F (ν ) E (ν ) dν
∫e
– Planets
– Compact HII regions
– AGNs
• So the calibration constant a , needed to convert the
uncalibrated map into a calibrated CMB map , can be
estimated from:
• All kinds have their own peculiarities.
– 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)
Mars
Gaseous Planets :
• Has a tenuous atmosphere, and no sub-mm features. Its
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:  ∆ V
= ℜ AΩ
B (T
, ν ) E (ν ) d ν



Mars
Mars
∆ V Mars = ℜ AK
⇒ ∆ T Mars =
•The size is in the sub-arcmin range.
•Atmospheric features can be important.
∆TMars = TCMB
∆T (mK CMB)
1000
TMarsΩ
ΩBeam
Mars
10
10
100
frequency (GHz)
∫ B(T
Mars
∫ B (T ,ν ) E (ν ) d ν
K {∫ R [ϑ ]d Ω }
Mars
,ν )E(ν )dν
Mars
x
⇒
Mars
xe
∫ ex −1B(TCMB,ν )E(ν )dν
= TCMB
ΩMars
f (T , T ,ν )
ΩBeam Mars CMB c
Degree-scale anisotropy as a calibrator
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 ?
100
ΩMars
ΩBeam
Ω Mars
∫
{∫ R [ϑ ]d Ω }∆ T
• 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.
4
CMB rms
100
frequency (GHz)
200
−2 .55
e
e
b (d )
b (d )
g
g
WMAP 1st yr
g
g
e
e
b (d )
b (d )
BOOMERanG 98
e
e
b (d )
g
e
e
b (d )
94GHz l (deg)
b (d )
60GHz l (deg)
WMAP 1st yr
e
b (d )
g
g
g
90GHz l (deg)
150GHz l (deg)
BOOMERanG 98
g
b (d )
e
 F / Ω20' 
ν


 = 430

CMB 
 100GHz
 µK

150GHz l (deg)
90GHz l (deg)
• There are additional AGNs lost
in the confusion of the CMB
fluctuations.
WOMBAT catalog
• The WOMBAT catalogue and
tools predict quite well the flux
100
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
10
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.
1
• This is reduced by 50% if the
0.0 0.5 1.0 1.5 2.0 2.5 3.0
resolved sources (at 150 GHz)
Flux (Jy) @ 150 GHz
are removed, and by 80% if
are removed those resolved at
41 GHz.
http://astron.berkeley.edu/wombat/foregrounds/radio.html
counts
µKCMB in a 20' beam
1000
30
b (d )
220GHz l (deg)
PKS0537-441
PMNJ0519-4546
PKS0454-46
10
b (d )
g
90GHz l (deg)
94GHz l (deg)
e
BOOMERanG 98
41GHz l (deg)
10000
100
PKS0454-46
g
WMAP 1st yr
e
g
e
b (d )
g
e
b (d )
150GHz l (deg)
60GHz l (deg)
b (d )
e
b (d )
BOOMERanG 98
e
b (d )
g
e
b (d )
e
b (d )
220GHz l (deg)
220GHz l (deg)
94GHz l (deg)
e
60GHz l (deg)
b (d )
41GHz l (deg)
90GHz l (deg)
g
e
b (d )
g
PMNJ0519-4546
WMAP 1st yr
e
b (d )
g
e
150GHz l (deg)
g
220GHz l (deg)
41GHz l (deg)
94GHz l (deg)
b (d )
60GHz l (deg)
g
g
e
b (d )
g
g
g
e
b (d )
g
41GHz l (deg)
PKS0537-441
5
e
b (d )
g
g
e
b (d )
g
g
g
e
b (d )
g
6000
WMAP 1st yr
CMB
all sources
2
l(l+1)c l/2π (µK )
resolved @150GHz removed
resolved @40GHz removed
4000
150GHz
3000
41GHz l (deg)
60GHz l (deg)
e
e
e
b (d )
b (d )
94GHz l (deg)
b (d )
2000
BOOMERanG 98
5000
1000
0
0
200
400
600
800 1000 1200 1400
multipole l
220GHz l (deg)
Scatter Plot
•
150GHz l (deg)
a)
Once point sources have been removed, one can
scatter-plot the experiment data (in V) vs. the WMAP
data (in KCMB), and obtain the calibration constant (in
V/K) from the slope of the best fit line.
Problems of this approach:
•
90GHz l (deg)
B98-150GHz
WMAP 94GHz
G’ a u s
13
G1 a1 u’ s s i a
sian
WMAP 94GHz
B98
150
GHz
n
s ia n
s s ia
aus
Gau
13’ G
11’
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.
n
•
•
b)
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.
b)
6
l (o)
•
•
i ; WMAP data = x i
In the case of BOOMERanG 98 and WMAP, in 7’
pixels, σ(yi) ~30µK, σ(xi) ~80µK .
Best slope estimate :
1) Remove averages from data sets yi and xi , so that y=ax
2) Find the value of a which minimizes χ2 :
( y − axi )2
χ 2 (a ) = ∑ 2 i
2 2
i σ ( yi ) + a σ ( xi )
3) Make simulations of best fit lines for correlated data with
different levels of noise for xi and yi. To understand if - for the
noises of the experiment and of WMAP - there is a bias.
A variant of this correlation method is
based on the cross-power spectrum:
– Compute the Angular Power Spectrum of the
uncalibrated experiment, XX(ll ), and the Cross Power
Spectrum between the uncalibrated experiment and
WMAP, XW(ll ):
1/a(ll )[V/K]=
XW(ll)/XX(ll)
– 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(ll)[V/K]= [XW(ll )/(BX(ll )BW(ll))]/[XX(ll )/BX2 (ll)]
where B2 are the spherical harmonic transforms of
the beams/responses (Hivon E. et al. 2003, Polenta
et al. 2004).
WMAP/B98 (gain recalibration)
Raw maps on 1.8% of the sky
(Netterfield et al. cut)
Channel
Pixel based
C(l) based
B150A
0.95 +/ - 0.03
0.96 +/ - 0.02
B150A1
0.89 +/ - 0.03
0.85 +/ - 0.02
B150A2
0.97 +/ - 0.03
0.95 +/ - 0.02
B150B2
0.96 +/ - 0.03
0.97 +/ - 0.03
Sum
0.95 +/ -0.03
0.95 +/ - 0.01
Destriped maps on 1.8% of the sky
(Netterfield et al. cut)
Channel
Pixel based
C(l) based
B150A
0.95 +/ - 0.03
0.96 +/ - 0.02
B150A1
0.91 +/ - 0.03
0.92 +/ - 0.03
B150A2
0.98 +/ - 0.03
0.98 +/ - 0.02
B150B2
0.95 +/ - 0.03
0.95 +/ - 0.02
Sum
0.95 +/ -0.03
0.95 +/ - 0.01
• 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
b(o) N
R
a min
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
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
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
260.0 270.0 -60.0 -50.0 3847.
0.107
6.400
•
•
2.700
3.000
•
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
1.3
cl [WMAPxB98]/cl[B98*B98]
b)
• Experiment data = y
B98 - 150 GHz A+A1+A2+B1 raw
1.2
All cll
corrected
for beam
and
finite sky
coverage
1.1
1.0
0.9
0.8
0.7
100
200
300
400
multipole
500
600
No obvious trend vs multipole: beam calibration OK
Gain calibration: to be multiplied by 0.95 + 0.01
Hivon E. et al. 2003
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:
cl =
cl ,measured
Bl2
• Where B is the spherical harmonics transform of the
beam, a steeply decreasing function at high multipoles
!
Hivon E. et al. 2003
7
BOOM98: 150 GHz window function
Combination of:
B98-150GHz
WMAP 94GHz
G’ a u s
13
n
s ia n
s s ia
aus
Gau
13’ G
11’
B98
150
GHz
G1 a1 u’ s s i a
sian
WMAP 94GHz
Pixelization
(14’ healpix)
Effective beam
(including
estimated 2’ rms
pointing jitter)
n
Freq.
90GHz
150GHz
240GHz
410GHz
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
FWHM
18’+2’
10’+1’
14’+1’
13’+1’
Corresponding Effect on the PS
7000
Original data,
as published
in Nature,
with
published
random and
systematic
errors
Nature -1σ gain
3000
2000
1000
0
0
100
200
300
400
500
600
multipole
7000
6000
Nature -1σ gain
5000
Nature +1σ gain +1 σ beam
Nature -1σ gain -1σ beam
4000
3000
1000
0
0
100
200
300
multipole
400
500
600
• 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
original Nature data
jitter underestimate
and gain corrected
Nature +1σ gain
Nature -1 σ gain
6000
5000
l(l+1)cl/2 π (µK 2)
original Nature data
jitter underestimate corrected
Nature +1σ gain
2
l(l+1)cl/2π (µK )
Nature -1σ gain -1σ beam
4000
Also Calibration Correction
2000
Correction substantial
at l =600 (+35%, but
Nature +1σ gain +1 σ beam
5000
7000
Original data
and data corrected for
jitter underestimate
original Nature data
Nature +1σ gain
6000
•
2
R(θ)
SHT
l(l+1)cl /2π (µK )
Bl
2
Nature +1σ gain +1σ beam
Nature -1 σ gain -1σ beam
4000
3000
2000
1000
0
0
100
200
300
400
500
600
multipole
still within published
errors)
8
Effect of jitter underestimate
in preliminary results: 10’ –> 12.7’
Corrected data : the 2nd peak is not evident yet
2
4%
3000
2000
peak amplitude
5000
4000
208
location of peak
lp (multipole)
1%
2
B98 data corrected
6000
l(l+1)cl/2π (µ K )
•
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.
Old beam
204
New beam
200
196
192
5000
(l>320 average)/ lp(lp+1)clp/2π (µK )
(peak amplitude)
7000
•
4900
4800
4700
4600
4500
1000
4%
0
0
100
200
300
400
500
600
multipole
0.32
0.30
0.28
0.26
6
8
10
12
14
beam FWHM (arcmin)
Effects of jitter underestimate
and calibration correction on science
• Cosmological parameters extraction from the
corrected B98 together with the COBE-DMR PS
data:
• Ωo remains the same – (1% effect is negligible)
• Ωbh2 changes from 0.036+0.006 to 0.027+0.006
(same weak priors, l <625):
Telescope BEAM Calibration
At ground calibration with artificial
planet (tethered blackbody + CCD
monitor)
• (cfr. BBN: Ωbh2 = 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 : 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’
Compact HII region in an area
free from Galactic confusion
Acbar data at 1.4 mm = 2.5’ diam.
P.de Bernardis Oct.2000
9