cosmic microwave background, foregrounds and component separation what are foregrounds and how to...

Cosmic Microwave Cosmic Microwave Background, Foregrounds Background, Foregrounds

and Component Separationand Component Separation

What are foregrounds and What are foregrounds and how to deal with them in CMB data analysishow to deal with them in CMB data analysis

Carlo Baccigalupi, SISSACarlo Baccigalupi, SISSAAstrophysics School ``Francesco Lucchin”, Astrophysics School ``Francesco Lucchin”,

Bertinoro, May 24-29, 2009Bertinoro, May 24-29, 2009

Outline Outline

Foreground fundamentalsForeground fundamentals The GalaxyThe Galaxy Other galaxiesOther galaxies Contamination to the CMBContamination to the CMB Why is it important to control foregrounds?Why is it important to control foregrounds? Component separationComponent separation

Foregrounds fundamentalsForegrounds fundamentals

Foreground fundamentals: the Galaxy, Foreground fundamentals: the Galaxy, the other galaxies, and their clustersthe other galaxies, and their clusters

Foreground fundamentals: Foreground fundamentals: differences with respect to the CMBdifferences with respect to the CMB Together with instrumental systematics, foregrounds are the ultimate Together with instrumental systematics, foregrounds are the ultimate

limitation of CMB observationslimitation of CMB observations Unlike CMB, the foreground knowledge is mainly empirical, we know Unlike CMB, the foreground knowledge is mainly empirical, we know

the main physical processes activating them, but their emission is the main physical processes activating them, but their emission is calibrated mainly through observationscalibrated mainly through observations

Unlike CMB, the Galactic emission is strongly inhomogeneous, Unlike CMB, the Galactic emission is strongly inhomogeneous, concentrated on the Galactic planeconcentrated on the Galactic plane

Unlike CMB, foregrounds are distributed non-linearly in the skyUnlike CMB, foregrounds are distributed non-linearly in the sky Unlike CMB the extra-Galactic emission is point-like, with the exception Unlike CMB the extra-Galactic emission is point-like, with the exception

of a few, closeby galaxy clustersof a few, closeby galaxy clusters Unlike CMB, the foregrounds do not possess a black body frequency Unlike CMB, the foregrounds do not possess a black body frequency

spectrumspectrum Unlike CMB, the foregrounds do possess a space varying frequency Unlike CMB, the foregrounds do possess a space varying frequency

dependencedependence Unlike CMB, the diffuse foreground emission is markedly non-GaussianUnlike CMB, the diffuse foreground emission is markedly non-Gaussian Unlike CMB, the foregrounds are expected to have equal power in the E Unlike CMB, the foregrounds are expected to have equal power in the E

and B modes of polarizationand B modes of polarization

Foreground fundamentals: Foreground fundamentals: antenna temperatureantenna temperature

You can use your favorite units for describing foreground You can use your favorite units for describing foreground emission, in total intensity as well as polarizationemission, in total intensity as well as polarization

In the community, a popular choice is represented by the In the community, a popular choice is represented by the antenna temperature TA, simply defined as the antenna temperature TA, simply defined as the temperature that a black body would have in the temperature that a black body would have in the Raileigh-Jeans region of the spectrum, corresponding to Raileigh-Jeans region of the spectrum, corresponding to a given flux densitya given flux density

In formulas, TIn formulas, TAA=c=c22 × flux density / (2 Boltzmann constant × flux density / (2 Boltzmann constant frequency)frequency)22

For a black body, the antenna temperature fluctuations For a black body, the antenna temperature fluctuations are related to the thermodynamic ones by are related to the thermodynamic ones by δδ T TAA= = δδ T × x T × x22 × exp(x) / (exp(x)-1)× exp(x) / (exp(x)-1)22, where x=Planck constant × , where x=Planck constant × frequency / (Boltzmann constant × CMB temperature) frequency / (Boltzmann constant × CMB temperature)

Foreground fundamentalsForeground fundamentals

Bennett et al. 2003, Page et al. 2007

The GalaxyThe Galaxy

Milky wayMilky way At microwaves, the main emission At microwaves, the main emission

does not come from stars, but does not come from stars, but from the diffuse gas, either from the diffuse gas, either primordial and unprocessed, or primordial and unprocessed, or ejected from stars through ejected from stars through explosionsexplosions

The diffuse gas is composed by The diffuse gas is composed by free electrons, ions, a variety of free electrons, ions, a variety of large molecules, also known as large molecules, also known as grains, such as silicates, …grains, such as silicates, …

The galaxy is a hot system, 20 K The galaxy is a hot system, 20 K or so, not isolated because heated or so, not isolated because heated back by starlightback by starlight

The galaxy possesses a magnetic The galaxy possesses a magnetic field of order few µG, with a large field of order few µG, with a large scale component orthogonal to the scale component orthogonal to the plane and elongated along arms, plane and elongated along arms, and a largely unknown small scale and a largely unknown small scale component , largely generated by component , largely generated by supernova remnantssupernova remnants

Foregrounds from the radio band: Foregrounds from the radio band: Galactic synchrotronGalactic synchrotron

What it is: cosmic ray What it is: cosmic ray electrons spiraling around electrons spiraling around the lines of the Galactic the lines of the Galactic magnetic field, generated magnetic field, generated in particular by supernova in particular by supernova remnantsremnants

In frequency, it behaves In frequency, it behaves as a decaying power law, as a decaying power law, because the electron because the electron number is a decreasing number is a decreasing power law of their energy, power law of their energy, N(E)N(E)∝E ∝E -|p|-|p|, with the flux , with the flux density density F(f)F(f)∝f ∝f -|b|-|b|, , related by b=-(|p|-1)/2related by b=-(|p|-1)/2


The electron density varies The electron density varies substantially across the sky, substantially across the sky, making the frequency making the frequency dependence depending on the dependence depending on the direction of observationdirection of observation

The spectrum tends to be The spectrum tends to be steeper at high latitudes, steeper at high latitudes, spectral index -3 or less in spectral index -3 or less in antenna temperature, flatter antenna temperature, flatter at intermediate and low at intermediate and low latitudes, -2.5 or solatitudes, -2.5 or so

Existing information on all Existing information on all sky, in total intensity, taken sky, in total intensity, taken in the radio band (Haslam et in the radio band (Haslam et al. 1986, Reich et al. 1998) al. 1986, Reich et al. 1998) and at microwaves by WMAP and at microwaves by WMAP (Bennett et al. 2003)(Bennett et al. 2003)


The Galactic synchrotron is The Galactic synchrotron is strongly polarized, up to 75% strongly polarized, up to 75% for the pure emission for the pure emission mechanism, which is actually mechanism, which is actually never reached because of never reached because of depolarization effectsdepolarization effects

In the radio band, the main In the radio band, the main depolarization effect is given depolarization effect is given by Faraday rotation of the by Faraday rotation of the polarization angle, due to the polarization angle, due to the two circular polarization modes two circular polarization modes composing linear polarization composing linear polarization traveling with different traveling with different velocities: rotation ~ 420 velocities: rotation ~ 420 degrees / kpc / frequencydegrees / kpc / frequency22, , with frequency expressed in with frequency expressed in GHz, for a Galactic magnetic GHz, for a Galactic magnetic field of order 1 µGfield of order 1 µG


At microwave frequencies, At microwave frequencies, Faraday depolarization Faraday depolarization disappears, but still, line of sight disappears, but still, line of sight effects lead to a measured effects lead to a measured polarized intensity of order 10% of polarized intensity of order 10% of the total onethe total one

The frequency scaling is close to The frequency scaling is close to the one of total intensity, varying the one of total intensity, varying in the skyin the sky

All sky polarization observations in All sky polarization observations in the radio band exist (La Porta et the radio band exist (La Porta et al. 2006), affected by Faraday al. 2006), affected by Faraday depolarizationdepolarization

The main observations in the The main observations in the microwave bands are from WMAP microwave bands are from WMAP (Kogut et al. 2007, Page et al. (Kogut et al. 2007, Page et al. 2007), at 22 GHz where it is 2007), at 22 GHz where it is mostly dominating over CMBmostly dominating over CMB

Foregrounds from the radio band: Foregrounds from the radio band: Galactic free-freeGalactic free-free

What it is: Bremstraahlung radiation What it is: Bremstraahlung radiation from free electrons hitting ionsfrom free electrons hitting ions

It never dominates the emission: at It never dominates the emission: at any frequency, synchrotron or CMB any frequency, synchrotron or CMB or other foregrounds are brighteror other foregrounds are brighter

It is measured through indirect HIt is measured through indirect Hαα emission line (hydrogen 3 to 2 level emission line (hydrogen 3 to 2 level transition), except in areas with transition), except in areas with high optical depthhigh optical depth

Analytic treatments exist for Analytic treatments exist for converting emission from converting emission from HHαα to to free-free microwave intensity, free-free microwave intensity, depending on several parameters, depending on several parameters, like electron effective temperature, like electron effective temperature, densities of electrons and ions, etc., densities of electrons and ions, etc., making predictions particularly making predictions particularly difficult and model dependent, difficult and model dependent, requiring an empirical calibration of requiring an empirical calibration of the emissionthe emission

Foregrounds from the radio band: Foregrounds from the radio band: Galactic free-freeGalactic free-free

Its emission decays in Its emission decays in frequency, less fast than frequency, less fast than synchrotron, with spectral synchrotron, with spectral index about -2.15 in antenna index about -2.15 in antenna temperaturetemperature

An HAn Hαα full sky map has been full sky map has been assembled (Finkbeiner 2003)assembled (Finkbeiner 2003)

WMAP free-free data are WMAP free-free data are based on the assumed based on the assumed correlation with Hcorrelation with Hαα (Bennett et (Bennett et al. 2003)al. 2003)

Foreground from the infrared band: Foreground from the infrared band: Galactic dustGalactic dust

What it is: molecules or dust What it is: molecules or dust grains form a thermal grains form a thermal component, temperature of component, temperature of about 20 K, heated back by about 20 K, heated back by starlight starlight

The emission is described as a The emission is described as a modified (grey) black body, modified (grey) black body, raising with frequency in the raising with frequency in the microwave bandmicrowave band

Detailed physical content Detailed physical content largely unknown; current best largely unknown; current best fit assumes two almost thermal fit assumes two almost thermal species, with temperatures of species, with temperatures of about 9 and 16 K, dominating about 9 and 16 K, dominating at frequency smaller or larger at frequency smaller or larger than a few hundreds GHz, than a few hundreds GHz, respectively (Finkbeiner et al. respectively (Finkbeiner et al. 1999)1999)


The dust temperature(s) vary The dust temperature(s) vary across the sky, at the level of 10%, across the sky, at the level of 10%, at least on angular scales of a few at least on angular scales of a few degrees or more, as it is evident degrees or more, as it is evident correlating data at 100 and 240 µm, correlating data at 100 and 240 µm, making the dust spectral index making the dust spectral index varying in the sky comparablyvarying in the sky comparably

WMAP data (Bennett et al. 2003) WMAP data (Bennett et al. 2003) are consistent with the are consistent with the extrapolation from IRAS data (data extrapolation from IRAS data (data available, 6 arcminutes resolution, available, 6 arcminutes resolution, Finkbeiner et al. 1999), mostly at Finkbeiner et al. 1999), mostly at low Galactic latitudes, and in the W low Galactic latitudes, and in the W bandband

A dust correlated component, A dust correlated component, suggested initially by Draine and suggested initially by Draine and Lazarian (1998) component may be Lazarian (1998) component may be present in the 20-40 GHz band present in the 20-40 GHz band (Gold et al. 2008, Miville-(Gold et al. 2008, Miville-Deschenes et al. 2008, Bonaldi et Deschenes et al. 2008, Bonaldi et al. 2007)al. 2007)


The grains are magnetized, and The grains are magnetized, and get aligned locally with the get aligned locally with the direction of the Galactic magnetic direction of the Galactic magnetic field, making the overall emission field, making the overall emission polarizedpolarized

The intensity of the Galactic The intensity of the Galactic magnetic field is likely to align magnetic field is likely to align grains with high efficiency (Jones, grains with high efficiency (Jones, 1995)1995)

Polarization properties may vary Polarization properties may vary with frequency and sky direction; with frequency and sky direction; the dominance of different grain the dominance of different grain population at different frequencies population at different frequencies may induce a loss of polarization may induce a loss of polarization efficiency for frequencies larger efficiency for frequencies larger than a few hundreds of GHz than a few hundreds of GHz (Vaillancourt et al. 2008)(Vaillancourt et al. 2008)


The polarized intensity was The polarized intensity was found to be about 5% of the found to be about 5% of the total one along the Galactic total one along the Galactic plane by Archeops (Benoit et plane by Archeops (Benoit et al. 2005) and WMAP (Page et al. 2005) and WMAP (Page et al. 2007), confirming the dust al. 2007), confirming the dust to be one of the major CMB to be one of the major CMB contaminant at high frequencycontaminant at high frequency

At intermediate and high At intermediate and high Galactic latitudes, the Galactic latitudes, the polarized intensity can be polarized intensity can be larger, reaching 10% or more, larger, reaching 10% or more, because of the absence of line because of the absence of line of sight cancelation effectsof sight cancelation effects

Other galaxiesOther galaxies

Other galaxiesOther galaxies To imagine the emission from other galaxies, you may simply To imagine the emission from other galaxies, you may simply

think to the one from the Milky Way put at distance from us, think to the one from the Milky Way put at distance from us, emitting synchrotron emission in the radio, dust in the infrared emitting synchrotron emission in the radio, dust in the infrared bandband

Being point-like, their signal behaves similarly to instrumental Being point-like, their signal behaves similarly to instrumental noise, having a flat power in the angular power spectrum, noise, having a flat power in the angular power spectrum, apart from clustering effectsapart from clustering effects

In clusters of galaxies, the central hot gas of electrons give In clusters of galaxies, the central hot gas of electrons give kicks to the CMB photons, which migrate from low kicks to the CMB photons, which migrate from low frequencies to high frequencies, distorting their spectrum frequencies to high frequencies, distorting their spectrum through the Sunyaev Zel’dovich effect, yielding a signal which through the Sunyaev Zel’dovich effect, yielding a signal which is interesting for single object detection, but fainter than point is interesting for single object detection, but fainter than point sources as a diffuse CMB contaminantsources as a diffuse CMB contaminant

Polarization angle is randomly distributed in the sky, Polarization angle is randomly distributed in the sky, therefore, a key quantity for the forecasted polarization therefore, a key quantity for the forecasted polarization emission is given by the average polarization fraction emission is given by the average polarization fraction

Other galaxiesOther galaxies

Wright et al. 2008, see also Massardi et al. 2009

Other galaxiesOther galaxies The contamination to the CMB The contamination to the CMB

polarization from point sources is polarization from point sources is currently unknowncurrently unknown

Large surveys in the high Large surveys in the high frequency radio band exist frequency radio band exist (Massardi et al. 2008), indicating (Massardi et al. 2008), indicating polarization fractions up to 10%polarization fractions up to 10%

Similar information in the infrared Similar information in the infrared band is missing, current data on band is missing, current data on single objects indicate percentage single objects indicate percentage polarization fraction or lesspolarization fraction or less

If these levels are confirmed, If these levels are confirmed, polarized point sources may be polarized point sources may be thought to induce an effective noise thought to induce an effective noise component comparable to the CMB component comparable to the CMB lensing signal in B modeslensing signal in B modes

Contamination to the CMBContamination to the CMB

Masking the Galaxy: total intensityMasking the Galaxy: total intensity

The sky emission is dominated The sky emission is dominated by the Galaxy at all frequenciesby the Galaxy at all frequencies

The contamination is always The contamination is always evaluated after removing its evaluated after removing its brightest part, together with the brightest part, together with the main known point sourcesmain known point sources

In total intensity, the removal of In total intensity, the removal of the brightest part of the sky the brightest part of the sky leaves the sky substantially leaves the sky substantially dominated by the CMB at dominated by the CMB at microwave frequenciesmicrowave frequencies

The quantification of the The quantification of the contamination is usually done by contamination is usually done by means of the angular power means of the angular power spectrum of the masked skyspectrum of the masked sky

Bennett et al. 2006see also Gold et al. 2008

Masking the Galaxy: polarizationMasking the Galaxy: polarization

The sky emission is dominated The sky emission is dominated by the Galaxy at all frequenciesby the Galaxy at all frequencies

The contamination is always The contamination is always evaluated after removing its evaluated after removing its brightest part, together with the brightest part, together with the main known point sourcesmain known point sources

In polarization, the removal of the In polarization, the removal of the brightest part of the sky leaves brightest part of the sky leaves the sky substantially dominated the sky substantially dominated by the CMB at microwave by the CMB at microwave frequenciesfrequencies

The quantification of the The quantification of the contamination is usually done by contamination is usually done by means of the angular power means of the angular power spectrum of the masked skyspectrum of the masked sky

Page et al. 2006See also Gold et al. 2008

CMB contamination: total intensityCMB contamination: total intensity

Bennett et al. 2003

CMB contamination: polarizationCMB contamination: polarization

Page et al. 2006

A comparison between WMAP data A comparison between WMAP data and the Planck expectationsand the Planck expectations

Page et al. 2006 Planck reference sky, 2004

Do we have any hope to see B modes? Do we have any hope to see B modes?

WMAP has no detection in WMAP has no detection in large sky areas in polarizationlarge sky areas in polarization

Very naive estimates may be Very naive estimates may be attempted in those areas, attempted in those areas, indicating that the foreground indicating that the foreground level might be comparable to level might be comparable to the cosmological B mode at all the cosmological B mode at all frequencies, in all sky regionsfrequencies, in all sky regions

We need to rely on multi-We need to rely on multi-frequency observations as well frequency observations as well as robust data analysis as robust data analysis techniques which are able to techniques which are able to remove at most the foreground remove at most the foreground emission from polarization emission from polarization CMB dataCMB data

Page et al. 2006

Are there foreground clean regions Are there foreground clean regions at all in polarization? at all in polarization?

WMAP has no detection in WMAP has no detection in large sky areas in polarizationlarge sky areas in polarization

Very naive estimates may be Very naive estimates may be attempted in those areas, attempted in those areas, indicating that the foreground indicating that the foreground level might be comparable to level might be comparable to the cosmological B mode at all the cosmological B mode at all frequencies, in all sky regionsfrequencies, in all sky regions

We need to rely on multi-We need to rely on multi-frequency observations as well frequency observations as well as robust data analysis as robust data analysis techniques which are able to techniques which are able to remove at most the foreground remove at most the foreground emission from polarization emission from polarization CMB dataCMB data

Page et al. 2006

EBEX proposal to NASA, 2007

Contamination from point sourcesContamination from point sources

Toffolatti et al. 1998, 1999

Why is it important Why is it important to control foregrounds? to control foregrounds?

Why is it important to control Why is it important to control foregrounds?foregrounds?

Is the low quadrupole a problem? Unclear, it was Is the low quadrupole a problem? Unclear, it was demonstrated to depend on the foreground demonstrated to depend on the foreground subtraction method (Bonaldi et al. 2007) subtraction method (Bonaldi et al. 2007)

Small scale CMB power, excess? Small scale CMB power, excess? North-south asymmetry?North-south asymmetry? Primordial non-Gaussianity? WMAP data are Primordial non-Gaussianity? WMAP data are

non-Gaussian as some inflationary models non-Gaussian as some inflationary models predict (or a bit more, Yadav and Wandelt 2007), predict (or a bit more, Yadav and Wandelt 2007), a debate is ongoing if this is an effect of a debate is ongoing if this is an effect of unresolved foregrounds or notunresolved foregrounds or not

CMB anisotropiesCMB anisotropies

T(ň), Q(ň), U(ň), V(ň)

aTlm, aE

lm, aBlm

Cl=Σm (almT,E,B)(alm

T,E,B)*/2(l+1)

spherical harmonics

informationcompression

Cosmic asymmetry?Cosmic asymmetry?

Evidence for north Evidence for north south asymmetry south asymmetry (Hansen et al. 2005, (Hansen et al. 2005, Hoftuft et al. 2009)Hoftuft et al. 2009)

Confirmed by several Confirmed by several foreground subtraction foreground subtraction methods (Maino et al. methods (Maino et al. 2007)2007)

Consistency with Consistency with Bianchi cosmological Bianchi cosmological models (Jaffe et al. models (Jaffe et al. 2006)2006)

Suggested readingSuggested reading

Baccigalupi 2003 for a pre-WMAP review on Baccigalupi 2003 for a pre-WMAP review on foregrounds, foreground B mode dangerforegrounds, foreground B mode danger

Bennett et al. 2003, for the WMAP results in total Bennett et al. 2003, for the WMAP results in total intensityintensity

Kogut et al. 2007, Page et al. 2007 for the WMAP Kogut et al. 2007, Page et al. 2007 for the WMAP results in polarizationresults in polarization

Gold et al. 2008, Dunkley et al. 2008, for the update Gold et al. 2008, Dunkley et al. 2008, for the update on WMAP five yearson WMAP five years

Wright et al. 2008, Massardi et al. 2007, 2008 for Wright et al. 2008, Massardi et al. 2007, 2008 for point source observations and assessment of the point source observations and assessment of the CMB contamination from themCMB contamination from them

Component separationComponent separation

CMB data analysis: a fantastic CMB data analysis: a fantastic information compressioninformation compression

A typical CMB probe A typical CMB probe takes records of the sky takes records of the sky radiation tens of times per radiation tens of times per second per detector, from second per detector, from weeks to yearsweeks to years

Sky maps contain tens of Sky maps contain tens of millions of resolution millions of resolution elementselements

CCll are a few thousands are a few thousands Parameters representing Parameters representing

physical quantities are a physical quantities are a fewfew

CMB data analysis levelsCMB data analysis levels

Level 1, telemetry, timelines processing, Level 1, telemetry, timelines processing, calibrationcalibration

Level 2, map-makingLevel 2, map-making Level 3, point source extraction, Level 3, point source extraction,

component separation, CMB cleaning and component separation, CMB cleaning and power spectra estimation, cosmological power spectra estimation, cosmological parametersparameters

Dealing with foregroundsDealing with foregrounds

First step: detecting and masking point sourcesFirst step: detecting and masking point sources Off-band known sources are maskedOff-band known sources are masked Sky maps are convolved with beam-like filters Sky maps are convolved with beam-like filters

(Wavelets, see Herranz et al. 2009), and signals (Wavelets, see Herranz et al. 2009), and signals above a certain threshold are identified as above a certain threshold are identified as sources and removedsources and removed

The same operation, with the information of the The same operation, with the information of the SZ frequency scaling, is used to isolate and SZ frequency scaling, is used to isolate and mask galaxy clustersmask galaxy clusters

Second step: diffuse component separation…Second step: diffuse component separation…

ss

22

ss

11

xx1 1 = = aa11 11 xx2 2 = = aa21 21

+ a+ a12 12

+ a+ a22 22

+ n+ n11

+ n+ n22

11

22


ss

22

ss

11

xx1 1 = a= a11 11

ss1 1 xx2 2 = a= a21 21

ss11

+ a+ a12 12 ss22

+ a+ a22 22

ss2 2

+ n+ n11

+ n+ n22

11

22


ss

22

ss

11

xx = = As+nAs+n

11

22


Invert for s!

xx = = As+nAs+n

Component separation: Component separation: criteria to achieve separationcriteria to achieve separation

In typical applications, s is unknown in polarization, while somewhat known in total intensity from In typical applications, s is unknown in polarization, while somewhat known in total intensity from non-microwave data; A is known to 10% accuracy, and is known to vary in the skynon-microwave data; A is known to 10% accuracy, and is known to vary in the sky

Physical aspects in the data are exploited in order to stabilize the inversionPhysical aspects in the data are exploited in order to stabilize the inversion Statistics: CMB and foregrounds are statistically independent; by using the statistical distrubution Statistics: CMB and foregrounds are statistically independent; by using the statistical distrubution

provided by multi-frequency data, it is possible to recover each independent component (see e.g. provided by multi-frequency data, it is possible to recover each independent component (see e.g. the Independent Component Analysis, Maino et al., 2007, and references therein)the Independent Component Analysis, Maino et al., 2007, and references therein)

Parametrization: foregrounds are modeled through parameters, entering either in A or s; single-Parametrization: foregrounds are modeled through parameters, entering either in A or s; single-resolution element multi-frequency fitting (see e.g. Stompor et al. 2009) or spatial correlations resolution element multi-frequency fitting (see e.g. Stompor et al. 2009) or spatial correlations (see Bonaldi et al. 2006) may be used to estimate unknowns(see Bonaldi et al. 2006) may be used to estimate unknowns

Relevant literature from Brandt et al. 1994, to Leach et al. 2008, successful applications to Relevant literature from Brandt et al. 1994, to Leach et al. 2008, successful applications to COBE, BEAST, WMAPCOBE, BEAST, WMAP

Independent Component Analysis (ICA)Independent Component Analysis (ICA)

Assume statistical independence between different Assume statistical independence between different astrophysical emissionsastrophysical emissions

The statistics of their superposition tends to be close to The statistics of their superposition tends to be close to GaussianityGaussianity

Reverse the process with linear combinations of the Reverse the process with linear combinations of the signals at different frequencies, extremizing the non-signals at different frequencies, extremizing the non-Gaussianity Gaussianity

The extrema correspond to the independent componentsThe extrema correspond to the independent components Achievements: successfully recovered CMB results for Achievements: successfully recovered CMB results for

COBE, BEAST, WMAPCOBE, BEAST, WMAP

See Maino et al. 2007, and references therein

Component separation: ICAComponent separation: ICA

Correlated component analysis Correlated component analysis (CCA)(CCA)

Parametrize unknowns in AParametrize unknowns in A Construct the data correlation function, Construct the data correlation function,

CCxx((δθδθ,,δφδφ)=<x()=<x(θθ,,φφ)x()x(θθ++δθδθ,,φφ++δφδφ)>)>

One has COne has Cxx=AC=ACssAATT+C+Cnn

Use enough data for estimating unknowns in A Use enough data for estimating unknowns in A and Cand Css

Perform a regularized inversion for sPerform a regularized inversion for s Achievements: successfully applied to WMAP Achievements: successfully applied to WMAP

datadata

See Bonaldi et al. 2007, and references therein

Pixel based parametric fittingPixel based parametric fitting

Parametrize unknowns in A,sParametrize unknowns in A,s Write a likelihood Write a likelihood ∝ exp[-(x-As)∝ exp[-(x-As)TTNN-1-1(x-As)](x-As)] Use multi-frequency data to fit for Use multi-frequency data to fit for

unknowns pixel by pixelunknowns pixel by pixel Achievements: not many so far, Achievements: not many so far,

successfully applied to WMAP large successfully applied to WMAP large scales, but promising in terms of error scales, but promising in terms of error propagationpropagation

See Stompor et al. 2009, and references therein

Where are we now with Where are we now with component separation?component separation?

In total intensity, a In total intensity, a comparison of different comparison of different methods applied to methods applied to simulated Planck data simulated Planck data exists (Leach et al. 2008)exists (Leach et al. 2008)

Preliminary results show Preliminary results show a substantial cleaning a substantial cleaning from diffuse foregrounds, from diffuse foregrounds, and a considerable and a considerable residual contamination residual contamination from unresolved point from unresolved point sourcessources

Where are we now with Where are we now with component separation?component separation?

In polarization, a similar, In polarization, a similar, unpublished analysis indicate a unpublished analysis indicate a possible recovery of the EE CMB possible recovery of the EE CMB power spectrum up to l=1000power spectrum up to l=1000

A separate, most important case A separate, most important case for component separation for component separation concerns sub-orbital probes, concerns sub-orbital probes, aiming at detecting B modes in aiming at detecting B modes in likely conditions of substantial likely conditions of substantial foreground contamination (see foreground contamination (see Stivoli et al., 2006, and the EBEX Stivoli et al., 2006, and the EBEX proposal to NASA, 2007)proposal to NASA, 2007)

Estimation of the minimum Estimation of the minimum detectable tensor power in detectable tensor power in presence of foreground cleaning is presence of foreground cleaning is in progressin progress

Suggested readingSuggested reading

The Planck blue book is available at The Planck blue book is available at http://www.rssd.esa.int/Planck

Oxley et al. 2005 for a description of EBEXOxley et al. 2005 for a description of EBEX Leach et al. 2008 for the present status of Leach et al. 2008 for the present status of

our capability of cleaning CMB from our capability of cleaning CMB from foregrounds with Planck, in total intensityforegrounds with Planck, in total intensity

Bonaldi et al. 2006, Stivoli et al. 2006, Bonaldi et al. 2006, Stivoli et al. 2006, Stompor et al. 2009 for the component Stompor et al. 2009 for the component separation techniques we plan to exploit in separation techniques we plan to exploit in the forthcoming yearsthe forthcoming years

cosmic microwave background, foregrounds and component separation what are foregrounds and how to...

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