Simulation Pipeline for Velocity Field Measurements using ... · Simulation Pipeline for Velocity Field Measurements using the Kinetic Sunyaev-Zel’dovich Eﬀect Yubo Su1 Mentor:

Simulation Pipeline for Velocity Field Measurementsusing the Kinetic Sunyaev-Zel’dovich Effect

Yubo Su1

Mentor: Sunil R. Golwala1

1California Institute of Technology

August 20, 2015

Yubo Su (Caltech) SURF 2015 Final Presentation August 20, 2015 1 / 27

IntroductionThe kSZ effect

Cosmic Microwave Background(CMB) is thermal radiation leftover from the Big Bang.Variations are one part in 104,highly homogeneous.

SZ effects blueshift CMB due toscattering off energeticelectrons.

http://astro.uchicago.edu/sza/primer.html


IntroductionThe kSZ effect

Three kinds of SZ effects:thermal (tSZ), kinetic (kSZ),relativistic (rSZ).kSZ gives peculiar velocitymeasurements.Independent of redshift; onlydepends on electron velocity,optical depth, localcharacteristics.Different systematics.

Velocity fields are important tomeasure precisely to identifycosmological models (e.g. darkenergy vs. modifications togravity).kSZ recently measured peculiarvelocities in a single clustera.Next generation of detectors willhave improved sensitivity, largersurveys.

aSayers et. al. 2013


IntroductionCharacterizing Detectors

Need simulation to understand how known sources of error affect nextgeneration of detectors.Generate mock data containing CMB, fake sources, SZ effects.Include instrumental effects.Feed through data processing pipeline.

Subtract foreground sources.Examine kSZ effect.

Understand how kSZ detection depends on various factors.


IntroductionCharacterizing Detectors

Need simulation to understand how known sources of error affect nextgeneration of detectors.Generate mock data containing CMB, fake sources, SZ effects.Include instrumental effects.Feed through data processing pipeline.

Subtract foreground sources.Examine kSZ effect.

Understand how kSZ detection depends on various factors.


MethodsSetup

Multiple detectors survey same area in different frequencies.Correlate data across frequencies to identify point sources to subtract.

Data is represented as an image in multiple frequencies, noise + signal

vν(x, y) = nν(x, y) +∑i

Aisν(x, y)

Sources are all point sources, same profile sν .Confusion noise.


MethodsApproach

Source subtraction as a fitting procedure.Goodness of fit is described by χ2

χ2 =

∣∣∣observed− fit(ξ)∣∣∣2

(expected deviation)2 =∑ν

∣∣∣∣vν(kx, ky)−∑iAisν(kx, ky; ξ)

∣∣∣∣2Jν(kx, ky)

Noise has point-wise correlations1, so have to work in angularfrequency space. J is the power spectral density of the noise.Progressively build up to full model, start with single source, singlefrequency → multiple source, multiple frequency.

1Thermal noise is approximately white but atmospheric noise is angularfrequency-dependent (Sayers et. al. 2009).


MethodsSingle frequency, single source

Turn this into this.



Sources are characterized solely by their position x0 and brightness A.χ2 is then

χ2 =

∣∣∣v(kx, ky)− As(kx, ky; x0)∣∣∣2

J(kx, ky)

Minimize χ2 to find A brightness estimatorTo find x0, want to convolve v(x, y) with source profile s(x, y),“maximum overlap.”

Instead convolve with “optimal filter” s(x, y)J

.



Optimal Filter



Convolving only identifies to nearest pixel!Since s(x, y) is known (Gaussian), shape of convolution is known, canfit near peak to extract inter-pixel maximum.



How do we verify our subtraction is optimal?

Using the general result σ2ξ =

[12

d2χ2

dξ2

]−1

, can compute expected

variance of A, x0, agrees with simulations.




MethodsSingle frequency, multiple source

Turn this into this.



Found that iterative subtraction mis-estimates brightness due tomixing.Problem is linear in brightnesses, can be formulated in matricies andvectors, de-couples.



Mean still not correct, and variance is high. Why?Blends


MethodsSingle frequency, multiple source (blends)



Thankfully, if blend is identified, iterative subtraction converges.Must identify which sources are blends and which are not.Intuitively: mean?





Problems with mean:Images are generally mean-subtracted; mean is meaningless.No clear criterion for what mean is sufficiently “close to zero.”

F-test of additional parameter.Ran into peculiar problems /Test suggested whether another beam is required depends on size ofimage, unreasonable.

Blends are not too big of a problem in general, bright-bright is rareand bright-dim inevitable.


MethodsMultiple frequency



Multiple frequencies is just setting χ2 =∑i

χ2i and applying previous

formalism.Few catches because beam profile is function of frequency:

Source width increases linearly with wavelength.Source amplitude follows grey body spectrum — power lawapproximation.

Aν ∝ν3+β

ehν

kTdust − 1−−−−−−→Tdust→∞

∝ ν2+β

Let’s first assume a known power law dependence, for simplicity.



Recall in one frequency, fit for inter-pixel location.No longer holds with multiple frequencies! x0 is not the same in everyfrequency.Solution: weighted average works.


MethodsMoving forward

Recall Aν ∝ν3+β

ehν

kTdust − 1−−−−−−→Tdust→∞

∝ ν2+β

β, Tdust are independent for each source.Power law approximation

β is non-linear parameter like x0, but nothing like convolution to do.Gradient search on χ with respect to β.Preliminary results are in line with expectations but not ready forpresentation.

Full grey body calculationGradient search over β, Tdust.Preliminary results require more characterization but are encouraging.


Where next?

Characterize the effect of confusion noise on subtraction with realisticsource distribution.Examine subtraction threshold in presence of confusion noise.

Devise pipeline for kSZ detection.


Acknowledgements

Prof. Sunil R. Golwala — Thank you for your infinite patience andconsistently illuminating discussions.Caltech SFP/SURF program — Thank you for funding this piece ofresearch.


References


Sayers, J., S. R. Golwala, P. A. R. Ade, J. E. Aguirre, J. J. Bock, S. F.Edgington, J. Glenn, A. Goldin, D. Haig, A. E. Lange, G. T. Laurent, P. D.Mauskopf, H. T. Nguyen, and P. Rossinot. ”Studies of Atmospheric Noiseon Mauna Kea at 143 GHz with Bolocam.” Millimeter and SubmillimeterDetectors and Instrumentation for Astronomy IV (2008): n. pag. Web.

Sayers, J., T. Mroczkowski, M. Zemcov, P. M. Korngut, J. Bock, E. Bulbul,N. G. Czakon, E. Egami, S. R. Golwala, P. M. Koch, K.-Y. Lin, A. Mantz, S.M. Molnar, L. Moustakas, E. Pierpaoli, T. D. Rawle, E. D. Reese, M. Rex,J. A. Shitanishi, S. Siegel, and K. Umetsu. ”A Measurement Of The KineticSunyaev-Zel’dovich Signal Toward Macs J0717.5 3745.” ApJ TheAstrophysical Journal 778.1 (2013): 52. Web.



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Simulation Pipeline for Velocity Field Measurements using ... · Simulation Pipeline for Velocity Field Measurements using the Kinetic Sunyaev-Zel’dovich Eﬀect Yubo Su1 Mentor: