Follow up

Follow up

Tomi Ylinen KTH/HIK

KTH 5A5461

Experimental Techniques in

Particle Astrophysics

Question 1

• Compare heterodyne and incoherent detection.

2/9

• HEMT

– Phase-conserving  limited by quantum noise – Higher system temperature

– More suitable for lower frequncies

• Bolometer

– No phase conserving amplification  no quantum noise  limited by photon noise instead

– Very low system temperature

– More suitable for higher frequencies

• For single optimized polarization bolometers and HEMTs, sensitivity is essentially the same for CMB measurements up to about 60 GHz. Transition region is at frequencies approaching the peak of the black-body, where the photon occupation number falls below unity.

P. L. Richards, ”Bolometric Detectors for Measurements of the Cosmic Microwave Background”, J. of Supercond. , Vol. 17, No. 5, (2004) 545-550

Question 2

• Explain cosmic variance and the analogy with the Frenchman.

3/9

Universe

Observable Universe

Earth Scale of

physical process

• Initial state of Universe is random, but in a clearly specified way, where the

amplitude of the inhomogenities are 10^-5

• Theory gives expectation value, i.e. what you would get after you average over an ensemble of Universes

• Data is one realization from one Universe

• Inherent uncertainty when sample size is small, which it is on large scales 

Cosmic variance

Question 2

• The model:

The population of the world consists of 1% French, 30% American and 69% Other

• The Frenchman:

If the observable Universe of the

Frenchman consists of his own backyard, it will be difficult for him to test the above model, since he only has one person in his sample, himself.

In the same way, its hard to test statistical properties of the Universe on large scales, since the sample size is so small.

Universe

Observable Universe

Frenchman

• Explain cosmic variance and the analogy with the Frenchman.

Question 3

• How is polarization produced in the CMB and why ~5%?

5/9

• Thomson scattering cross-section is polarization dependent

where ε (ε’) are the incident (scattered) polarization directions

• The incident light sets up oscillations of the target electron in the direction of the electric field

vector E, i.e. the polarization direction  The scattered radiation intensity peaks in

direction normal to, with polarization parallel to, the incident polarization

ˆ

ˆ 

 _  _{ } d 

d

polarization direction

scattering

W. Hu & M. White, ”A CMB Polarization Primer”, New Astronomy, 2, (1997) 323-344

Question 3

• How is polarization produced in the CMB and why ~5%?

6/9

• Isotropic incoming radiation field  orthogonal polarization states from incident directions separated by 90° cancel each other  outgoing radiation unpolarized

• Quadrupolar variation in incoming radiation field (with intensity peaks at 90°)  Linear polarization in scattered radiation

+ =

net polarization (anisotropies)

Question 3

• How is polarization produced in the CMB and why ~5%?

7/9

• Calculation done by Basko & Polnarev (1980). They integrate the Boltzmann equation for the photon distribution and show that polarization anisotropy (E

) to temperature anisotropy ratio (T

) is

where is the optical depth.

• Calculating the optical depth using ”ordinary” atomic physics and the thermal history of the Universe (Peebles 1968, Zeldovich et al. 1969)

 E

/T

~ 5%

   

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   

 ^{e e}  ^{z d z}

z d z e

e T

E

z z

z z

rms rms

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L. Page et al., ”Three-year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Polarization Analysis”, ApJ. Suppl. Ser., 170, (2007) 335-376

Question 4

• Provide further information about the residual plot shown for the COBE blackbody plot. In particular, why are the non-blackbody fits to the data rejected?

8/9

• Proper way of interpreting the plot is probably that these other models can’t be completely ruled out. The fits show the highest ”divergence” from a black-body which is allowed by data. The

influence of the non-black-body components as given by the homepage seem very small.

Body with reflectivity 100 ppm instead of 0

Hot electron adding excess of 60 ppm of energy

1000 years after Big Bang

Question 4

• Provide further information about the residual plot shown for the COBE blackbody plot. In particular, why are the non-blackbody fits to the data rejected?

9/9

J. C. Mather et al., ”Measurement of the Cosmic Microwave Background Spectrum by the COBE FIRAS Instrument”, ApJ., 420, (1994) 439-444

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