Lecture 2: CMB data Larissa Santos University of Science and Technology of China, USTC 05/06/2015
Outline • The Interactive Data Languague • Hierarchical Equal Area isoLatitude Pixelation • Planck maps • Foregrounds • Masks • Code for Anisotropies in the Microwave Background • Simulations
Very short CMB timeline COBE WMAP Planck BOOMERANG SPT
IDL • The Interactive Data Language (IDL) is a proprietary system distributed bu Exelis Visual Information Solution, inc • It can be downloaded from http://www.exelisvis.com/ProductsServices/IDL.aspx • IDL is currently available in LINUX, Windows and Macintosh versions • Programming language usually used for CMB data analysis
Screenshot
Gorski et al. (2005) • HEALPix: Hierarchical Equal Area isoLatitude Pixelation • Produces a subdivision of a spherical surface in which each pixel covers the same surface area as every other pixel • The lowest resolution partition is comprised of 12 base pixels • The resolution increases by 3 steps from the base level
Definitions • Nside � • Expresses the resolution of the grid • Npix � • Denotes the total number of pixels. Npix=12*Nside*Nside the ~N scaling for the non-iso-latitude sampling distributions In the figure, the sphere is • partitioned, respectively, into 12, 48, 192 and 768 pixels (Nside = 1, 2, 4 and 8)
Pixel numbering schemes: • RING : counting the pixels • moving down from the north to the south pole along each iso- latitude ring. � NESTED: arranging the pixel • indices in twelve tree structures, corresponding to base-resolution pixels
Visualization (IDL)
Planck satellite • The Planck satellite was launched on May14 th of 2009 • The low frequency instrument (LFI) covers 3 frequency bands • 30, 44 and 70GHz • The high frequency instrument (HFI) detectors cover 6 frequency bands • 100, 143, 217, 353, 545 and 857GHz
Planck maps • Nside: 2048 • Npix= 5.03316e+07!!! • Ordering: NESTED • Format: fits file • FITS (Flexible Image Transport System) is the data format most widely used within astronomy for transporting, analyzing and archiving scientific data files • They can be downloaded from http://pla.esac.esa.int/pla/
Useful HEALPix subroutines • MAPS: read_fits_map, read_fits_s, read_tqu, write_fits_map, write_tqu • Down-grading and NESTED/RING pixel reordering: ud_grade • Example: � � � map = ‘/Users/larissasantos/Documents/Dados_Planck/' � map_ilc= "COM_CompMap_CMB-smica_2048_R1.20.fits" � � � read_fits_map, map+map_ilc, smica � ud_grade, smica, a1, nside_out=8, order_in='nested', order_out='ring'
Planck frequency maps
Example of a degraded CMB map
Examples of CMB visualization
Foregrounds • Light coming from foreground sources in our galaxy or other galaxies must be measured accurately, so as to separate out this light from the CMB signal
Foreground overview 30 44 70 100 143 217 353 545 857 Synchrotron radiation: • Sum fg t s Rms brightness temperature ( µ K RJ ) u d l a m emission of relativistic r e 2 h T 10 electrons gyrating in a C M B magnetic field 1 10 Free-free Free-Free: emission of • 0 10 Spinning dust CO 1-0 electrons when deflected S y n c h r by massive ions o -1 t r 10 o n 10 30 100 300 1000 Frequency (GHz)
• Thermal dust: emission from interstellar dust grains mostly made of graphites, silicates and polycyclic aromatic hydrocarbons (PAHs) • Spinning dust: the most plausible candidate is tiny PAH particles spinning with dipole moment • CO molecular clouds: Rotational transitions of carbon monoxide
• Extragalactic point sources: some point sources can emit in the radio-millimetric domain
The microwave sky as seen by Planck Galatic dust Anisotropies of the CMB and of Free-free (Gum nebula) the cosmic infrared background
Planck HFI maps- CMB removed 100 GHz 143 GHz 217 GHz 353 GHz 545 GHz 857 GHz Planck collaboration, arXiv: 1101.2048
Synchrotron emission at 23 GHz Thermal dust emission map at estimated in the WMAP 9-year 353 GHz estimated by Planck analysis experiment Free-free (Dickinson et al., 2003; Finkbeiner, 2003) α
Estimate map for spinning dust in the WMAP K band First estimate map for CO line emission by Planck
Noise power spectra in the HFI sky maps Noise Power Spectra in the HFI Sky Maps • Noise power spectra on the full sky (solid line) and after masking the Galactic plane (dotted line) • The biggest difference is seen for high frequency maps as expected since the Galactic signal is larger
• Diffuse foregrounds consist of several distinct emission processes which dominate on large angular scales • It is important to understand the foreground emission in order to achieve the most precise CMB maps and cosmological information • They are os astrophysical interest and consideres foregrounds only for CMB studies!!!
Foreground-cleaned temperature maps
• The Planck team used four methods to separate CMB from diffuse foreground emission • The methods can be dived in two types • Foreground are removed by combining the multifrequency data to minimize the variance of the CMB component • A parameterized model of the CMB an foreground is constructed and the CMB component is obtained by sampling from the posterior distribution of parameters
Multipole expansion: do you remember? [ ] θ ∈ 0, π Δ T m = l l max ∑ ∑ ( ) = ( ) θ , φ Y lm θ , φ a lm [ ) φ ∈ 0,2 π T l = 2 m = − l ( ) ! l − m 2 l + 1 ( ) = ( ) λ lm x ) ! P lm x ( 0 4 π l + m ⩾ m ( ) = λ lm (cos θ ) e im φ Y lm θ , φ m<0 m λ l m ( ) = − 1 ( ) λ lm x m=0 ( ) = 0 λ lm x
Decomposing the CMB map: quadrupole � m=0 L=2 = + m=1,-1 m=2,-2 +
Octopole L=3 m=0 = + m=1,-1 m=2,-2 m=3,-3 + +
HEALPix program: Anafast This program performs • harmonic analysis of the HEALPix maps up to a specified maximum spherical harmonic order lmax Anafast reads a file containing • the map and produces a file containing the temperature power spectrum and, if requested, also the polarization power spectra The a lm coefficients computed • during the execution also can be written to a file if requested
HEALPix routine: Synfast • This program can be used to create HEALPix maps • Temperature only • Temperature and polarization • The map resolution, Gaussian beam and random seed for the simulation can be selected by the user
Masks • Even the multifrequency CMB maps are not completely free of foregrounds • Remove possible contaminated pixels from CMB maps • Planck released 3 main temperature masks with different sky cuts and 1 polarization mask
fsky = 74.83 fsky = 83.65 fsky = 78.67
Masked CMB temperature map
CAMB Lewis Challinor and Lasenby (2000) • Code for Anisotropies in the Microwave Background • CAMB Web interface: http:// lambda.gsfc.nasa.go v/toolbox/ tb_camb_form.cfm
INPUT h , h 2 Ω b , h 2 Ω c , h 2 Ω µ , Ω k , w • Cosmological parameters: and so on OUTPUT C TT , C EE , C BB , C TE • CMB power spectra: � • Matter power spectrum � • Matter transfer functions
CMB simulations TRUE � Known only by UNIV. Mother Nature Statistically realized What we want!! OBSERVABLE h h 2 Ω µ UNIV. h 2 Ω b h 2 Ω c Measurements Ω k Cosmological Measured Our � data Univ. model Analysis Interpretation
From the cosmological parameters • that we extract from the data we do NOT have a unique realization of the universe! Based on our cosmological model • we can generate infinitely realizations Each one of them generated with • the best fit parameters that we found For a statistical analysis compare • the realizations from your model with the measured data.
“The map of what we call reality is an ever-shifting mosaic of ideas.” –Marcelo Gleiser
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