Esempio di uso delle mappe• Supponiamo ci interessi realizzare lo spettro della galassia NGC253 alle frequenze di Planck.

Esempio di uso delle mappe

• Supponiamo ci interessi realizzare lo spettro della galassia NGC253 alle frequenze di Planck.

• La prima cosa da fare è andare sul sito skyview– http://skyview.gsfc.nasa.gov

• Qui si può scegliere l’interfaccia per astronomi, che offre un grande numero di surveys del cielo a tutte le lunghezze d’onda (compreso Planck) e un grande numero di opzioni di visualizzazione e salvataggio dei dati.  

143 GHz 217 GHz100 GHz

353 GHz 545 GHz 857 GHz

Planck views of NGC253

Per ricavare i flussi• Per una analisi quantitativa meglio affidarsi alle mappe originali, scaricabili dal 

Planck Legacy Archive.

• Si deve capire che informazioni sono contenute nei files delle mappe.• Il file FITS contiene un header di testo dove sono codificate in modo standardizzato 

tutte le informazioni  necessarie.

File = “HFI_SkyMap_857_2048_R2.00_full.fits“READ_FITS_MAP , File, T_sky, Hdr, Exthdr Print, Exthdr

XTENSION= 'BINTABLE' /Written by IDL: Fri Nov 28 17:04:26 2014 BITPIX = 8 / NAXIS = 2 /Binary tableNAXIS1 = 12 /Number of bytes per row NAXIS2 = 50331648 /Number of rows PCOUNT = 0 /Random parameter count GCOUNT = 1 /Group countTFIELDS = 3 /Number of columns COMMENT COMMENT *** End of mandatory fields *** COMMENT EXTVER = 1 /Extension versionDATE = '2014-11-28' /Creation date COMMENT COMMENT *** Column names *** COMMENT TTYPE1 = 'I_STOKES' / TTYPE2 = 'HITS ' / TTYPE3 = 'II_COV ' / COMMENT COMMENT *** Column formats *** COMMENT TFORM1 = 'E ' / TFORM2 = 'J ' / TFORM3 = 'E ' / COMMENT COMMENT *** Column units *** COMMENT TUNIT1 = 'MJy/sr ' / TUNIT2 = ' ' / TUNIT3 = '(MJy/sr)^2' /

COMMENT COMMENT *** Planck params *** COMMENT EXTNAME = 'FREQ-MAP' / Extension name PIXTYPE = 'HEALPIX ' / COORDSYS= 'GALACTIC' / Coordinate system ORDERING= 'NESTED ' / Healpix ordering NSIDE = 2048 / Healpix Nside FIRSTPIX= 0 / First pixel # (0 based) LASTPIX = 50331647 / Last pixel # (0 based) FILENAME= 'HFI_SkyMap_857_2048_R2.00_full.fits' / FITS filename BAD_DATA= -1.63750E+30 / bad pixel value FREQ = '857 ' / reference frequency PROCVER = 'DX11d ' / Product version COMMENT COMMENT ------------------------------------------------------------------------COMMENT Full channel sky map: full mission COMMENT ------------------------------------------------------------------------COMMENT For further details see Planck Explanatory Supplement at: COMMENT http://www.sciops.esa.int/wikiSI/planckpla COMMENT ------------------------------------------------------------------------COMMENT HFI-DMC objects: COMMENT in-group: MAP_DX11d_noZodi_2048_GALACTIC_0240_27005/ COMMENT Creation date - object name COMMENT hfi_dx11d_857_full_nozodi_bplcorrected_dust_ground.fits -> hfi_dx11d_857COMMENT 14-08-06 23:20 - 857GHz_W_TauDeconv_planet_H COMMENT 14-08-06 23:20 - 857GHz_W_TauDeconv_planet_II COMMENT ------------------------------------------------------------------------END

Per ricavare i flussi• Si devono impostare le coordinate galattichedelle linee di vista delle quali ci interessano i flussi. 

• ra=(0.0d00+47.6d00/60.d00) ; right ascension of NGC253 (hours)• dec=-(25.0d00+17.0d00/60.d00) ; declination of NGC253 (deg)• GLACTC, ra, dec, 2000, elled, bid, 1• elle=elled*!pi/180.d00• bi=bid*!pi/180.d00• phi=elle• theta=!pi/2.0d00-bi

• Ad esempio le linee di vista per il centro della galassia e quattro linee di vista di riferimento: 1,2,3,4 nella figura seguente.

12

34

NGC253 – PLANCK 857 GHz Comparison positions:Distance from center (‘)

1 - 8.52 - 14.43 - 8.54 - 14.3

• Poi si deve cercare il numero healpix dei pixel corrispondenti a queste 5 linee di vista

• nside=[1024,2048,2048,2048,2048,2048,2048]• freq=[70,100,143,217,353,545,857]• file=strarr(7)• file[0]="c:\LFI_SkyMap_070_1024_R2.01_full.fits"• file[1]="c:\HFI_SkyMap_100_2048_R2.00_full.fits"• file[2]="c:\HFI_SkyMap_143_2048_R2.00_full.fits"• file[3]="c:\HFI_SkyMap_217_2048_R2.00_full.fits"• file[4]="c:\HFI_SkyMap_353_2048_R2.00_nominal.fits"• file[5]="c:\HFI_SkyMap_545_2048_R2.00_full.fits"• file[6]="c:\HFI_SkyMap_857_2048_R2.00_full.fits«• units=['K_cmb','K_cmb','K_cmb','K_cmb','K_cmb','MJy/sr','MJy/sr']• ordering='NESTED'• temp=fltarr(7)• temp1=fltarr(7)• temp2=fltarr(7)• temp3=fltarr(7)• temp4=fltarr(7)

• for i=0,6 do begin• READ_FITS_MAP , File(i), T_sky, Hdr, Exthdr• ang2pix_nest, nside(i), theta, phi, ipnest• Temp(i)=T_sky(ipnest,0)• print,freq(i),temp(i),' ',units(i)• t_sky=0• endfor

• ; conversion Kcmb to brightness in MJy/sr• Tcmb=2.725 ; K• sigm=freq/29.979 ; cm-1• x=1.4388*sigm/Tcmb• CMB=1.2e-12*sigm^3/(exp(x)-1.) ; W/cm2/sr/cm-1• fff(i) = CMB[i]*x[i]*exp(x[i])/(exp(x[i])1.)/Tcmb*1.e4/2.9979e10/1.e-20;MJy/sr

HzsrmWsrMJy

TT

exeTBBB x

x

22010/1

1),(

GHz center pluses 1 asterisks 2 diamonds 3 triangles 4 squares

70 0.0471458 0.0146702 0.0303175 0.00107269 0.000184984100 0.123439 0.0494964 0.0279401 0.00403761 -0.0144365143 0.256772 0.0480003 0.0543403 0.0125795 -0.00171171217 1.67140 0.0593637 0.103898 0.0350521 0.0318471353 6.72921 0.195811 0.249595 0.189013 0.189880545 27.5415 0.549157 0.552807 0.547431 0.421523857 118.595 1.39218 1.07878 1.25566 0.977533

MJy

/sr

Beam issues• La brillanza riportata nelle mappe 

per ciascun pixel è la brillanza misurata quando l’asse ottico del telescopio di Planck puntava verso quel pixel. 

• Ma il beam dello strumento è più grande di un pixel, quindi il risultato della misura dipende dalla brillanza del pixel puntato, ma anche da quella dei pixel circostanti, se la riposta angolare del telescopio li comprende.

• Beams di Planck: http://wiki.cosmos.esa.int/planckpla/index.php/Beamshttp://arxiv.org/pdf/1303.5068.pdf

• Pixel size: Nside = 2048 ‐> 1.7’

Pixel size: Nside = 2048 ‐> 1.7’

100 GHzbeam

857 GHzbeam

Il beam di «riferimento» a 100 GHz contiene emissione della galassia.Quello a 857 GHz molto meno. 

GHz center pluses 1 asterisks 2 diamonds 3 triangles 4 squares

70 0.0471458 0.0146702 0.0303175 0.00107269 0.000184984100 0.123439 0.0494964 0.0279401 0.00403761 -0.0144365143 0.256772 0.0480003 0.0543403 0.0125795 -0.00171171217 1.67140 0.0593637 0.103898 0.0350521 0.0318471353 6.72921 0.195811 0.249595 0.189013 0.189880545 27.5415 0.549157 0.552807 0.547431 0.421523857 118.595 1.39218 1.07878 1.25566 0.977533

MJy

/sr

Esercizio• Ripetere questa procedura per Andromeda

Polarizzazione del fondo cosmico di microonde

• L’ universo si è raffreddato espandendosi. • C’è stata un’epoca nel passato in cui l’universo era talmente 

caldo da essere ionizzato. • Questa fase  è detta di “Primeval Fireball” e dura per i primi 

400000 anni dal Big Bang.• In questa fase lo spessore ottico per scattering Thomson era 

estremamente alto, ed i fotoni percorrevano un “random walk” da elettrone ad elettrone.

• Quando l’ universo si è raffreddato abbastanza da permettere la ricombinazione degli elettroni e protoni in atomi di idrogeno, la sezione d’ urto è diminuita drasticamente, e l’ universo è diventato trasparente.

LSS• I fotoni che erano in equilibrio con la materia (corpo nero) si propagano fino a noi, raffreddandosi con l’ ulteriore espansione dell’ universo, ma mantenendo la forma di corpo nero. Radiazione cosmica di fondo, CMB.

• I fotoni della CMB subiscono il loro ultimo scattering Thomson quando l’ universo si raffredda a 3000K, ad un redshift zLSS~1100.

• Quindi i fotoni di CMB provengono da una “superficie di ultimo scattering” (last scattering surface) posta a z~1100.

• Questa superficie ha un certo spessore, perchè l’ universo impiega tempo a diventare trasparente.

zLSS

zLSS

H neutro (trasparente)

H ionizzato (opaco)

LSS (semitrasparente)

zLSS

zLSS

H neutro

H ionizzato

LSS

Random walk

Ultimo scattering

Propagazione libera

• I fotoni che erano in equilibrio con la materia (corpo nero) si propagano fino a noi, raffreddandosi con l’ ulteriore espansione dell’ universo, ma mantenendo la forma di corpo nero. Radiazione cosmica di fondo, CMB.

• I fotoni della CMB subiscono il loro ultimo scattering Thomson quando l’ universo si raffredda a 3000K, ad un redshift zLSS~1100.

• Quindi i fotoni di CMB provengono da una “superficie di ultimo scattering” (last scattering surface) posta a z~1100.

• Questa superficie ha un certo spessore, perchè l’ universo impiega tempo a diventare trasparente.

LSS• Lo spessore della superficie di ultimo scattering si può calcolare vedendo quanto è profonda la transizione da spessore ottico basso a spessore ottico maggiore di 1.

• In formule

• Dove x(z) è la frazione di idrogeno ionizzata.• La soluzione richiede l’ integrazione dell’ equazione di Saha per la frazione ionizzata.

• Il risultato è un grafico del tipo seguente: 

)()1()(

1)1()())(()(

3

02

)(

0

zxznzn

zzHcdzzndznz

oe

z

oTe

z

Te

0 1000

(z)

z0

1

0.5

zLSS

zLSS

2

1.5

)()()( ze ezn

dzzdN

Densitàdi diffusorial redshift z

Attenuazione

Numero difotoni cheprovengono da un redshift z

Oggi si conosce (WMAP, Planck)zLSS con grande precisione:zLSS=1089+1zLSS=185+2   (FWHM)Bennet et al. 2003

Polarization of the Cosmic Microwave Background

• CMB photons are last scattered at recombination• This is a Thomson scattering. If and ’ are the wave versors of the scattereddirection and of the incoming direction, respectively, the differential cross‐section is given by

• The scattered photons are polarized if and only if the incoming photons have a quadrupole anisotropy. This can be demonstrated as follows:

• In general the incoming intensity distribution can be written

where =cos(). • Integrating over all the possible incoming directions one gets

where is the optical depth for Thomson scattering. For a detailed calculation, see e.g. http://ned.ipac.caltech.edu/level5/Kosowsky/Kosowsky1.html

3

2

311 nno PcbaII

monopole quadrupole higher multipoles

dipole

2

//

// 1.0 bIIIIp

22 cos

83ˆ'ˆ

83 TT

dd

'̂̂

e

-

-

+

-

+ x

y

--

+

-

+

x

y

-x

y

-10ppm +10ppm

= e- at last scattering

• The pattern of polarization depends on the pattern of quadrupole anisotropy at recombination

• Two sources of quadrupole anisotropy, with different symmetry properties:– Scalar fluctuations (density)– Tensor fluctuations (gravitational waves)

• Both generated by inflation.• See density fluctuations first:

Convergingflux

Same flux as seen in the

electronrest frameDiverging

flux

Quadrupole anisotropydue to Doppler effect

redshift

blueshift

blueshift

redshift

+ +

+

+

- -

-

-

resultingCMB polarizationfield (E-modes)

Velocity fieldsat recombination

Expect E- modes and a T-E correlation

Hot, densespot

Cold, less dense spot

• E‐modes are irrotational

• E modes are related to velocities, while T is related mainly to density

• We expect a power spectrum of the E‐modes, <EE>, with maxima and mimina in quadrature with the anisotropy power spectrum <TT>. 

CMB polarization (B)• CMB photons are last scattered at recombination. • It’s a Thomson scattering, and any quadrupole anisotropy in the incoming photons produces a degree of linear polarization in the scattered photons.

• Tensor perturbations (gravitational waves) produce a small degree of linear polarization with curl properties (B‐modes)

• Also, lensing of E‐modes does the same at smaller scales

E‐modes and B‐modesfor a plane‐wave

E‐modes and B‐modesaround a density extreme

If inflation really happened…

• It stretched geometry of space to nearly Euclidean

• It produced a nearly scale invariant spectrum of density fluctuations

• It produced a stochastic background of gravitational waves.

?

OK

OK

observer

• If inflation really happened: It stretched geometry of space to

nearly Euclidean It produced a nearly scale invariant

spectrum of gaussian density fluctuations

It produced a stochastic background of gravitational waves: Primordial G.W.The background is so faint that even LISA will not be able to measure it.

• Tensor perturbations also produce quadrupole anisotropy. They generate irrotational (E-modes) and rotational (B-modes) components in the CMB polarization field.

• Since B-modes are not produced by scalar fluctuations, they represent a signature of inflation.

Quadrupole from P.G.W.

E-modes

B-modes

• The amplitude of this effect is very small, but depends on the Energy scale of inflation. In fact the amplitude of tensor modes normalized to the scalar ones is:

• and

• There are theoretical arguments to expect that the energy scale of inflation is close to the scale of GUT i.e. around 1016 GeV.

• The current upper limit on anisotropy at large scales gives T/S<0.12 (at 2) 

• A competing effect is lensing of E‐modes, which is important at large multipoles.

• See Muchanov’s  http://arxiv.org/pdf/1303.3925.pdf  for a robustlower bound on r, r > 0.01, with  of the order of 1.

GeV107.3 16

4/14/1

2

24/1

V

CC

ST

Scalar

GW Inflation potential

B-modes from P.G.W.

GeV102

1.02

)1(16

4/1

maxVKcB

E-modes & B-modes

• From the measurements of the Stokes Parameters Qand U of the linear polarization field we can recover both irrotational and rotational alm by means of modified Legendre transforms:

nYiaaniUQ mm

Bm

Em

2

,)(

nYniUQnYniUQnWdi

a

nYniUQnYniUQnWda

mmBm

mmEm

22

22

)()(21

)()(21

E-modes produced by scalar and tensor perturbations

B-modes produced only by tensor perturbations

Spin-2 quantity Spin-2 basis

The signal is extremely weak• Nobody really knows how to detect this.

–Pathfinder experiments are needed• Whatever smart, ambitious experiment we

design to detect the B-modes:– It needs to be extremely sensitive– It needs an extremely careful control of

systematic effects– It needs careful control of foregrounds– It will need independent experiments

with orthogonal systematics.• There is still a long way to go: …

34

The observable - 2• Our second observable is the angular power spectrum

of CMB polarization, and in particular the component produced by tensor fluctuations (B-modes).

• In particular, LSPE measures the angular power spectrum at large angular scales, i.e. at multipoles (l=2-200), because this is where B-modes from inflation produce maximum signal, while competing effects are weaker.

• This requires an angular resolution around 2° i.e. an aperture diameter of 50 cm for a 20-modes detector at 2mm (140 GHz)

• The frequency range must cover the peak of CMB brightness (140 GHz) and extend to lower and higher frequencies to monitor local contaminating emission (interstellar dust, synchrotron).

How can we measure it ?• «layman» polarimeter

– Examples: BOOMERanG‐03 (Masi et al. 2006, A&A, 458 , 687); Planck‐HFI (Lamarre et al. A&A, 2010, 520, A9); BICEP2 (Ade et al., ApJ 792, 62 (2014)); CLASS (astro‐ph/1408.4789)… 

• Stokes polarimeter– Examples: SPIDER (astro‐ph/1106.2158), 

EBEX (astro‐ph/0501111), LSPE (astro‐ph/1208.0282), PILOT (astro‐ph/1410.5760)

• Correlation polarimeter– Examples: DASI (Leitch et al. Nature 420 

(2002) 763‐771), QUIET (Reeves, JLTP 167 929 (2012)), 

RotatingHWP

lens

Tran

smitted

FocalPlane

Reflected Focal Plane

Difficult to scale in a large array 

Polarization‐sensitive bolometer (Jones et al. astro‐ph/0209132)

No subtraction: each detector measures I, Q and U

Pol = Ia‐Ib

Stokes PolarimeterSRHRPDW HVHV )()(,,

i

i

i

i

VUQI

S

The power reaching each power detector is :

where :  S is the Stokes parameters vector of the radiation being analyzed, in the reference frame of the instrument   i ; R is the rotation matrix, and g is the rotation angle of the principal axis of the HWP; H is the Mueller matrix of a vertical HWP; PH is the Mueller matrix of a horizontal polarizer while PV is the Mueller matrix of a horizontal polarizer (these apply to the reflected and transmitted focal planes, respectively); D is the vector representing the power detector.

0001D

10000)()(00)()(00001

)(22

22

cssc

R

)2cos()(2 c

)2sin()(2 s

1000010000100001

H

0000000000110011

21

HP

0000000000110011

21

VP

iiiVV UsQcISHPDW 4421)( iiHH UsQcISHPDW 442

1)(

HWP lens

Tran

smitted

FocalPlane

Reflected Focal Plane

Stokes PolarimeterSRHRPDW HVHV )()(,, The power reaching each power detector is :

By matrix multiplication one gets (for the two focal planes):

iiiVV UsQcISHPDW 4421)(

iiiHH UsQcISHPDW 4421)(

The Stokes parameters in the reference frame of the sky Ss are related to the Stokes parameters in the reference frame of the instrument Si by a rotation. If the vertical axis of the instrument is rotated by an angle  with respect to the meridian, we have:

s

ss

ss

s

s

s

s

s

s

i

i

i

i

i

VUcQs

UsQcI

VUQI

cssc

SR

VUQI

S)()(

)()(

10000)()(00)()(00001

22

22

22

22

Substituting, we get

)24sin()24cos(21 sssH UQIW

)24sin()24cos(21 sssV UQIW

HWP lens

Tran

smitted

FocalPlane

Reflected Focal Plane

38CMB Polarization (detected since 2002 … ): E-modes 3 K

39

primordialB-modes( r = 0.1 )

CMB Polarization (detected since 2002 … ): E-modes 3 K

40

primordialB-modes.

Chi

ang

et a

l. 20

10

GeV102

1.02

)1(16

4/1

maxVKcB

B-modes depend on the energy-scale of inflationMaximum signal at large angular scales.

41

Large Number of Detectors for Sensitivity : TES bolometers with phased-array antennas(Caltech + JPL) for BICEP2

BICEP2 CMBquakeMarch 2014

42

BICEP2/KECK (south pole)

3 dark winters of integrationIn the best sky spot(<1000 sq. deg)

BICEP2 : single frequency 150 GHz

43

BICEP2 @ south pole :• 3 dark winters of integration with hundreds of polarization-sensitive bolometers • Extremely deep map (87 nK deg) of the lowest foreground intensity patch in the sky• Single frequency (150 GHz)

see astro-ph/1403-3985 and astro-ph/1403-4302

44

45

46

Cosmic variance limit

current claim (BICEP2)

IF the detected B-modes are generated by cosmic inflation:– What has been measured is the

result of pre-inflationary quantum fluctuations in the spacetime metric

– The energy-scale of inflation is 2x1016 GeV (quite precise !)

– We can reject several classes of inflation models

– With new instruments and more precise measurements of B-modes we can constrain other parameters of inflation

– high-energy theory is to construct models of new physics near the Planck scale that include inflation.

– knowing the slope of the spectrum of tensor perturbations would provide a new observational constraint of physics in this energy range that CANNOT be probed by any other means

BICEP2 results: potentially a huge impact on Cosmology and

Fundamental Phsyics r=0.2

47

However …• Extraordinary discoveries require extraordinary evidence

• Is the BICEP2 B‐modes signal really in the sky ?My personal opinion is YES, despite of the tiny level, there is more than enough evidence for this in the papers. A systematics paper will be published soon, to fully convince. 

• Is the BICEP2 B‐modes signal really primordial ?My personal opinion is that these is NOT enough evidence for this in the papers.

48

Models for theforegorund signal (mainly interstellar dust)

From BICEP2 paper :

49

Interstellar dust polarization• Interstellar dust grains

are elongated and aligned in the magnetic field of our Galaxy

• Dust grains are heated by UVs from stars, and re-emit as grey-body sources in the FIR, with a temperature of 20-30K.

• Due to the alignement, the emission is polarized.

• The polarization fraction depends on the degree of alignment and on the coherence of the B-field along the line of sight

• In high-latitude regions the line of sight crosses only one or a few thin dust clouds, where the magnetic field is likely to be coherent. So lower dust intensity does not imply necessarily low dust polarization.

• Planck polarization data at 340 GHz are very sensitive to polarized dust. • Other data are very scarce and there are no data are available in the

region observed by BICEP2.

50100 GHzPlanck data in the BICEP2 region

51143 GHzPlanck data in the BICEP2 region

52217 GHzPlanck data in the BICEP2 region

53353 GHzPlanck data in the BICEP2 region

54545 GHzPlanck data in the BICEP2 region

55857 GHzPlanck data in the BICEP2 region

56

Interstellar dust polarization• Only information available from Planck at the the time of

BICEP2 results: two maps shown at a conference (ESLAB 2013, J.P.Bernard talk)

dustdustCIBdust

pI

UQIIUQ

p

2222

Apparently the BICEP2 team used p as it was from the map, so underestimated the level of polarized dust emission in their region.

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Planck intermediate results. XXX. The angular power spectrum of polarized dust emission at intermediate and high Galactic latitudes

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• This work was started well before 2013 as part of a group of papers on dust polarization physics; it was delayed due to the difficulty of the analysis, as it concerns the faintest dust emission.

• The work is based entirely on Planck data. - the bulk of the paper is about the characterization of polarized dust emission (both E and B modes) at intermediate and high galactic latitudes.

• It is not about primordial gravitational waves. However, it is of general interest to all B-mode experiments, in particular to find the regions which are cleanest with respect to interstellar dust.

• Only a small part of the paper is specifically related to Bicep2. The main result with regard to Bicep2 is that the amount of dust in the Bicep2 field is not negligible. It is in fact significantly higher than was assumed in the Bicep2 PRL paper.

• This fact does not affect the Bicep2 detection of B-modes at 150 GHz. Rather, it affects their interpretation of these signals as arising primarily from primordial gravitational waves. It is likely that the significance of the Bicep2 detection of primordial B-modes will be reduced, possibly significantly.

• How much the Bicep2 interpretation is affected - the key question - is not yet clear and will be the outcome of a detailed joint analysis of Bicep2 and Planck data being carried out by the two teams jointly.

• In this work, the contribution of B-modes due to polarized interstellar dust emission is being evaluated using the Planck 353 GHz data mainly.

• This analysis is ongoing and will result in a publication in the same timeframe as the 2014 release of Planck data and results.

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Planck intermediate results. XXX. The angular power spectrum of polarized dust emission at intermediate and high Galactic latitudes

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NGP SGP

B-modes from dust, as estimated from Planck 343 GHz dust polarizationPlanck PIP XXX 1409.5738

1010.10.01

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IN THE REGION OBSERVED BY BICEP2, dust polarization is significant :

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Forthcoming steps :- Planck polarization data (feb. 2015)- Joint analysis Planck-BICEP2 (feb. 2015)- BICEP3 95 GHz survey (on-going, 2015)