Dust and Gravitational Waves

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Dust and Gravitational Waves

• Nathan Miller
• RPC Talk
• 12/5/06

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Outline

• Introduction to CMB Foregrounds
• Introduction to BICEP
• Why 220 GHz?
• Foreground Removal Techniques
• Optimization of Number of 220 GHz Pixels
• Future Plans

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380 Kyr
13.7 Gyr
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Inflation

• Alan Guth, 1981
• Early exponential expansion of the universe
• Solves many cosmological problems
• Horizon, Flatness, Magnetic Monopole
• Production of primordial gravitational waves
• Only early universe scenario that produces these
  gravitational waves
• Creates CMB B-modes
• Detection of B-mode would rule out other
  scenarios, such as Ekpyrotic
• Amount of B-modes gives info about energy scale
  of inflation

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CMB

• Universe was much smaller, hotter
• Photons in equilibrium with the proton/electron
  plasma
• As universe expanded, wavelength expanded,
  eventually energy smaller than required to keep
  equilibrium in proton/electron plasma
• Photons free-streamed to us today
• Density perturbations before recombination give
  rise to photon anisotropies

Boomerang 03 Flight
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CMB Polarization

• Quadrupole temperature anisotropy of photons
  gives rise to polarization

Graphics borrowed from Wayne Hus CMB introduction
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Types of Polarization

• Polarization can be broken up into 2 types
• E (grad) type polarization
• Produced by both density perturbations
  gravitational waves
• Like electric field, looks like gradient of a
  scalar field
• B (curl) type polarization
• Density perturbations do NOT produce this type of
  polarization
• Like magnetic field, curl of a vector

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BB vs. EE
Just EE modes
Just BB modes, r0.1
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From Map to Power Spectra
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Current WMAP Measurements
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Problems with Measurements

• FOREGROUNDS!!!
• Radiation at CMB wavelengths that is NOT the CMB
• Can overwhelm the CMB signal

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Galactic Foregrounds

• Dust
• Vibrating Dust Grains
• Rotating Dust Grains
• Thermal reradiation of absorbed stellar light
• Synchrotron
• Acceleration of ultrarelativstic electrons
  through magnetic fields
• Free-free emission (Bremsstrahlung)
• Acceleration when deflected by another charged
  particle

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Modeling Foregrounds

• Intensity of foregrounds depends on frequency
• Dust (1-Component Model)
• Synchrotron
• Free-Free

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Multi-Component Dust Models
fkfraction of power absorbed and re-emitted by
component k qkopacity
Dont have enough independent measurements to do
anything more than 1-component models
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Fit Results for Temperature
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Finkbeiner, Davis, Schlegel Dust Map
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Polarized FG

• Polarized FG Power spectra can be constrained
  from observations of Temperature anisotropy, but
  only so well.
• Sign (/-) of FG spectral indices are even in
  doubt for polarization can be positive or
  negative for example.
• WMAP SNR and EM freq. are too low to apply
  directly. WMAP results are consistent with
  Tegmark et al Foregrounds and Forecasts for the
  CMB from 2000.
• Spectral Indices can vary on the sky depending on
  galactic physics and galactic latitude.

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Temp vs. Pol FGs
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WMAP Temperature Map (23 94 GHz)
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WMAP Polarization Map (23 94 GHz)
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BICEP

• Ground-based millimeter wave bolometric array
• Housed at the South Pole
• Already taken 1 year of data
• Measurements taken at 100 and 150 GHz
• In the future, 220 GHz

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Bicep Cross Section
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Feed Cross Section
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Bicep Focal Plane
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Bicep looks in a small region of the sky near the
South Pole
Region of Low Dust
South Celestial Pole
Galaxy
20o spacings
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Creating Theoretical Dust Spectra

• Foregrounds behave as power laws in multipole
  (Tegmark 2000)
• Dust used proportional to FDS Model 2
  (one-component dust model with emissitivity
  a1.7)
• Similar to Tegmark's middle-of-road model
• Amplitude gotten from comparison of FDS Dust in
  Bicep region and WMAP region
• Sky coverage is uniform (not realistic, but
  useful as 1st approximation)

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Dust Power Spectra
EE Mode
BB Mode, r0.1
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CMB E/B Mixing

• When looking at partial sky, a transfer of power
  from E to B and B to E occurs
• Spherical harmonics not a complete set
• B is sub-dominant, so leakage from E alters them
  significantly
• Result depends on size and shape of region

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Why are we adding 220 GHz?

• Formally, it is impossible to constrain CMB
  SYNC DUST with only 2 frequencies.
• Dust, to date, not important for CMB anisotropy
  measurements but unknown for B modes.
• Dust physics interesting in its own right and
  useful to inform BICEP II.
• At 220 GHz only have 1 FG to confront DUST
• Two 220 GHz pixels already installed in BICEP

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BICEP Telescope Assumptions

• 49 total pixels
• Year 1 No 220 Ghz Data
• Year 2 25 100 GHz pixels, 22 150 GHz pixels, 2
  220 GHz pixels
• Year 3 some combination of 100, 150, and 220 GHz
  pixels
• Frequency Characteristics

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Study

• What are the improvements on our limit of r that
  come from adding 220 GHz channels?
• How many 220 GHz pixels do we need?

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Creating Maps

• Begin with theoretical Cl for both dust and CMB
  in all frequencies.
• CMB generated by CAMB
• Generate map using synfast (Nside256) for both
  dust and CMB at all frequencies and correct beam
  size
• Gaussian realization of dust
• Calculate uncertainty in measured value in map,
  assuming true NET/NEQ, fsky0.03, and observing
  time
• Map pixel size is based off of healpix pixel size
• Add maps of dust and CMB together in pixel space
  along with noise and then smooth to common beam
  resolution
• Note CMB and dust are random realizations but
  phase is preserved between maps made at different
  frequencies.

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Dust Realization
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Likelihood
Question Given a set of Cls, how well does it
fit the data? Answer Calculate the likelihood,
unnormalized probability density
Cl angular power spectrum recovered from
data Cl estimator for the measured angular power
spectrum fsky fraction of sky observed
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Dust vs. No Dust
If no removal, dust we are using is effectively
an additional CMB component with r0.1 when
calculating likelihood
No Dust
Would like to detect r0.1
Dust
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Many Types of Foreground Removal

• In Map Space
• Linear Combination of Maps
• Template Fitting
• MCMC Separation
• Maximum Entropy Method
• Independent Component Analysis
• In Frequency Space
• Minimize Power of alms

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Linear Combination

• Requires estimation of ratio of dust polarization
  amplitudes
• Estimated through Cls
• The higher the r, the worse the estimation
• If assumed same as temperature, wouldnt need to
  do actual removal technique
• Possible by looking at galaxy
• Find linear combination of all maps which cancels
  the dust, leaves CMB at unity, and minimizes noise

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Linear Combination Equations
Values in different frequencies
Separated component values
Shape Matrix
Covariance Matrix
Noise Matrix
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Linear Combination Likelihood

• 25 100s, 8 150s, 16 220s
• Both have max likelihood at same point

Approx Amps
True Amps
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Template Fitting

• Requires a template
• Derivative of 220 GHz Map
• Can use linear combination to find dust map
• Minimize
• Mpv measured value in pixel p, frequency ?
• Spv predicted foreground value, where foreground
  templates are used for spatial variations
• If template is bad, wont do anything

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Template Fitting

• True Dust Shape 1, 2.5, 7.7
• Calc Dust Shape 1.0, 3.2, 12.45
• No matter what, we should have a map that is
  completely free of CMB
• Min Chi2 Amps 0.0007, 0.053, 4.39
• Have gotten negative values
• Template is not that useful
• Too Much Noise
• Only look at this technique when S/N is gtgt 1

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Basic MCMC (Metropolis-Hastings)

• Explore Likelihood function
• Cant do it analytically, too complicated
• Given Xn choose Xn1 from any probability
  distribution
• usually uniform or gaussian distribution
• Accept Xn1 with probability
• If rejected, new point is old point
• Chain will converge to sample full likelihood
  distribution

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MCMC Component Separation

• 5 Variables
• CMB Q/U amplitudes
• Dust Q/U amplitudes
• Dust a
• Takes 10-60 seconds per MAP PIXEL
• Not useful for optimization
• Complicated noise
• Overall took 30 hours to run on low resolution
  data (Nside32) on my PC
• High resolution data has 64 times as many pixels

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1-D Marginalized Likelihood Plots (CMB,Linear),
Pixel 9651

• Red True Values
• Dashed Lines 1-s errors bars for 100 GHz map
• Greenish-yellow Max Marginalized Likelihoods
• Dark Blue Mean Values
• Light Blue Overall Max Likelihood Point

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1-D Marginalized Likelihood Plots (Dust,Linear),
Pixel 9651

• Red True Values
• Dashed Lines 1-s errors bars for 100 GHz map
• Greenish-yellow Max Marginalized Likelihoods
• Dark Blue Mean Values
• Light Blue Overall Max Likelihood Point

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1-D Marginalized Likelihood Plots (Non-Linear),
Pixel 9651
Red True Values, Greenish-yellow Max
Marginalized Likelihoods Dark Blue Mean Values,
Light Blue Overall Max Likelihood Point
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Optimization

• 100, 150, and 220 GHz feeds
• Find optimal number of 220 GHz feeds
• Need Fast foreground removal technique
• Linear Combination
• Template Fitting

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Fisher Matrix

• Curvature of the likelihood function
• How fast the function curves corresponds to how
  good we can measure it
• Function of Cl derivatives and uncertainty in Cl
  measurements

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Linear Combination Optimization

• 220 Measures dust, 100 has little dust
• Color measures ?r for r0.0
• Minimum ?r is 0.14, level spacing is 0.01
• Assumes perfect foreground removal
• What it would be if used temperature a (and it is
  correct)
• Optimal is 32,0,17

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Template Removal Optimization

• Color measures ?r for r0.0
• Minimum ?r is 0.10
• Levels are separated by values of 0.007
• Assumes perfect foreground removal

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Optimization II

• Run through actual foreground removal technique
  and look at results
• Noise Map is scaled by pixel uncertainty value
• See if dust is actually removed
• Using different ways of calculating a might help
  this
• Find combination of feeds that removes dust
  adequately and has the lowest noise

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Map Space Optimization

• Currently working on this
• Have run a loop over different combinations
• Found some bugs which I have corrected
• Best for most cases (of what I tested) was 25
  100s, 8 150s, and 16 220s

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Findings

• Without 220 GHz, dust will limit minimum r
• Cant probe below the dust level
• Looked for min r using only 150 and 220 pixels
• Dependence of min r on of 220 GHz pixels is
  weak, but 6-10 is close to optimal.
• 6 is decently close to 16
• Getting dust even to 50 reduction in maps leads
  to factor of 4 improvement in C_L

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Plans for Future

• Different Foreground Removal Techniques
• FastICA
• CMB Lensing and Neutrinos
• How well can a Polarbear type experiment
  constrain the neutrino mass through its lensing
  measurements?
• Predictions have been done for other experiments
• Study of TE anticorrelation as probe of
  primordial gravitational waves

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FastICA

• Assumes all but one component (CMB) is
  non-Gaussian
• Would require non-gaussian realization for dust
  map
• More sophisticated than LC
• Maximizes non-gaussianity as a measure of
  statistical independence
• A variable that is a mixture of independent
  variables is more Gaussian than the original
  ones
• Special case of blind source separation
• Might be more sophisticated way of doing LC

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Cosmology and Neutrinos

• Small-scale matter power spectrum changed by 8fv
  percent by neutrinos
• 4 times larger than effect on CMB
• Study weak lensing
• Map through statistical analysis of CMB temp and
  pol maps

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Lensing

• Deflection angle is gradient of lensing potential
• Estimator for d is calculated from a pair (a,b)
  of observed temperature or polarization modes
• 5 different combinations
• W is dependent on pair used

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Current Predictions
Lesgourgues et. al 2006
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Current Predictions
No prediction for PolarBear, BICEP II projects
that we are involved in at UCSD Previously
started doing this, but got sidetracked by
foreground removal
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(Anti) Correlation
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(Anti) Correlation
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TE anticorrelation

• Density perturbations produce a correlation at
  low l
• Gravitational waves produce an anti-correlation
• Baskaran, Grishchuk, Polnarev 2006