DIAGN ´ OSTICO SOBRE EL CONSUMO DE ENERG´IA EL´ ECTRICA EN

The are several other sources in the universe apart from the CMB which are emitting radiation on the same wavelengths as the CMB. In order to estimate the CMB power spectrum, one must either observe in areas of the sky without any of these foregrounds, or one must somehow remove them from the data. There are 5 main types of foregrounds which must be dealt with in order to study the CMB in contaminated areas of the sky. Galactic dust emission, free-free and synchrotron radiation are contaminants from our own galaxy. In addition there is the radiation from extra galactic point sources and the SZ effect from clusters of galaxies (the thermal AND kinetic) (see section (1.4.3)). Thanks to different spectral behavior of these foregrounds and the CMB, one can in principle sep- arate the CMB from the foreground contaminants. I will now discuss in detail some of these foregrounds. When no other reference is given, the information comes from (Bersanelli et al. 1996; Kogut et al. 1996; Bouchet and Gispert 1999; Hobson, Jones, Lasenby, and Bouchet 1998).

In interstellar space in our own galaxy there are dust grains (consisting of graphite and silicates) heated by the surrounding stars and thereby emitting elec- tromagnetic radiation. The spectrum of the dust emission from the galaxy was measured by the FIRAS instrument on the COBE satellite (see section (2.1.1)) with a 7◦ _{FWHM beam. Other balloon borne experiments have measured the}

galactic dust spectrum at higher resolution up to 30 arcminutes. At high galactic latitudes (away from the galactic plane) it has been found that the dust can be described well with a single dust component at 18K with an emissivity which goes as ν2 _{where ν is the frequency of radiation. In the direction of the galac-}

tic plane, there seems to be another component with a temperature of 21K and spectral dependencyν1.4_{. Maps of galactic dust have been made by DIRBE (an-}

other COBE instrument, see section (2.1.1)) at a resolution of 42 arc minutes and by theInfrared Astronomical SatelliteIRAS at 4 arcminutes. The high reso- lution images from IRAS has revealed an angular power spectrum of the dust of

2.2 The Analysis of CMB Data Sets 59

C` ∝`−3. At high galactic latitudes (outside of the galactic planeθ > 30◦, dust is

the dominating foregrounds component at frequencies above 100GHz. Recently there have been detection of emission from what appears to be spinning dust grains. This emission seems to be dominant at frequencies below 30GHz.

Another galactic foregrounds component operating at lower frequencies is the free-free emission from ionized hydrogenH2. The spectrum of the free-free emis- sion is well known to be ν−0.16_{, but good maps of interstellar H2 is lacking.}

Attempts to map the free-free emission directly was made using data from the COBE DMR instrument (Bennett et al. 1992; Bennett et al. 1994). Unfor- tunately the data was so noisy that only the quadrupole could be measured. Other attempts to mapH2 has been observation ofHα emission (Reynolds 1984;

Reynolds 1992) but these experiments suffered from undersampling and selection biases. For this reason, a correlation which is detected between free-free emission and dust emission is used. Dust is correlated with neutral hydrogen H1 which is again correlated with ionized hydrogen H2. The dust-free-free correlation has been detected in correlations of data between the DMR and DIRBE instruments and between data from the Saskatoon (Tegmark et al. 1997) experiment and DIRBE at smaller angular scales (Oliveira-Costa et al. 1997). For this reason, the same maps used to map dust (IRAS/DIRBE) are also used for free-free emis- sion. The angular power spectrum of free-free emission is assumed to be the same as for dust. Outside of the galactic plane, free-free emission is the domi- nant galactic foreground contaminant in the frequency range 5GHz to 100GHz.

The third galactic source of microwave radiation is synchrotron emission re- sulting from the acceleration of cosmic ray electrons in the galactic magnetic field. Due to the varying magnetic field strength in the galaxy, the spectral index of synchrotron emission is varying. Observations at 408GHz show that the spectrum of synchrotron emission goes as νβ _{where β is between −2.7 and−3.1. Observa-}

tions at higher frequencies indicate an index ofβ =₋0.9 for the frequency range of interest for CMB experiments. For synchrotron emission, the maps used are the 408MHz map by (Haslam et al. 1981) and the 1420MHz map by (Reich and Reich 1988). For CMB experiments, the data of synchrotron emission in these maps are extrapolated to the higher frequencies. These maps have an angular resolution of 0.85◦ _{and 0.6}◦ _{FWHM respectively. There is no data available at}

higher resolution. As these maps seem to indicate that the power spectrum falls of as C` ∝ `−3, this is the assumption usually adopted. This is the same power

spectrum observed for dust at small scales. Apparently synchrotron emission is the galactic contaminant for which one has the least information. Synchrotron radiation is together with free-free important at frequencies below 100GHz and is dominant below 5GHz.

2.2 The Analysis of CMB Data Sets 60

These can be AGNs (Active galactic nuclear), radio galaxies, quasars or BL Lac objects in the radio domain of the spectrum. In the Far-IR (Far-Infrared) do- main, the dust emission from dust dominated infrared galaxies is present. The spectrum of these objects is dependent on redshift. Unfortunately the spectrum and the evolution of these objects are not well known. In (Toffolatti et al. 1998), a last update on the observations and evolutionary models is found. They con- clude that on Planck resolution, the radio sources is the dominating point source contaminant on frequencies ν < 100GHz, the Far-IR sources are dominating at ν >200GHz and in the intermediate range both types are comparable. They do however point out, that even in the most pessimistic models, the amplitude of fluctuations due to point sources is well below the amplitude of the CMB at the frequencies 100₋200GHz. In (Hobson et al. 1999), it is shown how these models can be adopted to remove point sources in CMB data.

Another source of extra galactic point sources is the SZ-effect from clusters of galaxies. The change of the CMB spectrum due to the thermal motion of electrons in the clusters (thermal SZ effect) and the bulk motion of the cluster (kinematic SZ effect) is also contaminating the underlying CMB. Fortunately, the SZ effect has a certain spectral signature that makes it easy to identify. According to (Zeldovich and Sunyaev 1969), the relative temperature change of the CMB due to the SZ effect is given by

∆T T =y xcothx 2 −4 , (2.14)

wherex=hν/kT, his Planck’s constant, k is Boltzmann’s constant and yis the Compton y parameter measuring the line of sight density of electrons given as

y=

Z s

0

kTe

mc2ds, (2.15)

whereTeis the electron temperature,m is the electron mass and s is the Thomp-

son optical depth s=RσTρedl. Here σT is the Thompson cross section and ρe is

the electron density. Figure (2.6) shows the spectral signature.

For the kinetic SZ effect, the spectrum is constant (Sunyaev and Zeldovich 1980)

∆T

T =

vr

c s, (2.16)

wherevr is the radial velocity of the cluster. The kinematic effect is typically an

2.2 The Analysis of CMB Data Sets 61

Figure 2.6: The spectral change in the CMB due to the thermal SZ effect.

Finally I will review some of the standard method of separating the different components of the CMB. One can define a functionf(ˆn, ν) which is the intensity in the direction nˆ at frequency ν. This intensity consists of contributions from different components like the CMB, galactic emission or the SZ effect. Assuming that the different components can be factorised into a spatial part x(ˆn) and a spectral part s(ν) one can write the intensity as

f(ˆn, ν) =

np

X

j=1

sj(ν)xj(ˆn), (2.17)

where the sum goes over thenp different components. For an experiment withnc

frequency channels one can assign the observation in the ith channel to the ith element of a vector ygiven as

y(ˆn) =Px(ˆn) +n(ˆn). (2.18)

Here x(ˆn) is an np element vector, the elements being the xj(ˆn) above for each

channel,n(ˆn) is an np element vector containing the noise in each channel andP