1. Characterizing Millimeter Wavelength Atmospheric Fluctuations at the South Pole William L. Holzapfel (UCB) In collaboration with: R. Shane Bussmann (UCB) Chao-Lin Kuo (JPL) ACBAR team

2. Atmosphere Characterization: Why do we care? Atmospheric noise limits the sensitivity of ground-based mm-wavelength imaging experiments Atmospheric noise limits the sensitivity of ground-based mm-wavelength imaging experiments By characterizing the atmosphere, we have a quantitative method to compare observation sites around the world and predict effect of atmospheric fluctuations on new generation of experiments By characterizing the atmosphere, we have a quantitative method to compare observation sites around the world and predict effect of atmospheric fluctuations on new generation of experiments

3. Atmospheric Transmission Water Vapor Emission Dotted = 0.5mm pwv Solid = 0.1mm pwv Frequency (GHz) Total Atmosphere Transmission Brown = 0.5mm pwv Black = 0.0mm pwv Frequency (GHz)

4. Why Water Vapor? Atmosphere is described by a uniform sky brightness with small spatial fluctuations due to water vapor Atmosphere is described by a uniform sky brightness with small spatial fluctuations due to water vapor Dry components of atmosphere (e.g. N 2 and O 2 ) are well-mixed and produce only a constant signal which is removed by differential imaging Dry components of atmosphere (e.g. N 2 and O 2 ) are well-mixed and produce only a constant signal which is removed by differential imaging Water vapor is nearly uniformly distributed, but also fluctuates in its mass fraction, producing brightness temperature fluctuations which can not be removed by differential imaging Water vapor is nearly uniformly distributed, but also fluctuates in its mass fraction, producing brightness temperature fluctuations which can not be removed by differential imaging

5. Model: Spatial Component Kolmogorov power law: derived from conservation of kinetic energy Kolmogorov power law: derived from conservation of kinetic energy Independent of turbulence mechanism Independent of turbulence mechanism k (wavenumber) Power k -11/3 viscosity kicks in input scale A large vortex generates smaller ones, and so on..

6. Model: Temporal Evolution Taylor (1938): Frozen Turbulence Hypothesis (FTH) Taylor (1938): Frozen Turbulence Hypothesis (FTH) w Small scale turbulence velocity is much smaller than either global advection flow (w) or chopper speed Small scale turbulence velocity is much smaller than either global advection flow (w) or chopper speed

7. Analysis Convert 3D power spectrum of turbulence, P 3D (k x,k y,k z ), to 2D angular power spectrum P( α ) = B sky 2 (  ) ( α x 2 + α y 2 ) -b/2 Convert 3D power spectrum of turbulence, P 3D (k x,k y,k z ), to 2D angular power spectrum P( α ) = B sky 2 (  ) ( α x 2 + α y 2 ) -b/2 Assume values of wind velocity to convert 2D angular power spectrum to 1D correlation function, C( θ) Assume values of wind velocity to convert 2D angular power spectrum to 1D correlation function, C( θ) Compare the observed correlations between array elements in ACBAR data with the model. Compare the observed correlations between array elements in ACBAR data with the model. Fit four free parameters of the model : power law index, b; amplitude, B sky 2 (  ); wind vector components, w Φ and w ε Fit four free parameters of the model : power law index, b; amplitude, B sky 2 (  ); wind vector components, w Φ and w ε

8. Example Correlation Matrices 150 GHz data – May 30, 2002 Note difference with chop direction Model (L)Model (R) Data (L) Data (R) Pair A  :-16’  :0’ Pair D  :0’  :-16’ Pair E  :-16’  :-16’ Pair F  :+16’  :-16’

9. Measured Spectral Index We expect to be in the 3D regime of Kolmogorov model  b=11/3 We expect to be in the 3D regime of Kolmogorov model  b=11/3 Plot of model-fitted spectral index as a function of day b = 4.1+/-0.6 close to 11/3 b = 4.1+/-0.6 close to 11/3

10. Cumulative Distribution Functions for Amplitude Python: Austral Summer ACBAR: Austral Winter 40 GHz The ACBAR data show no noise floor Median 150 GHz winter amplitude is 20 mK 2 rad -5/3 Median summer amplitude scaled to 150 GHz ~ 130 mK 2 rad -5/3 Winter atmosphere is more stable than summer From Lay & Halverson, 2000 219 GHz 274 GHz 150 GHz

11. Angular Wind Vector, Plots Altitude of emission: reasonable consistency with radiosonde derived water vapor pressure profiles adds to confidence in model Model fit emission elevation Radiosonde water vapor profile

12. Preliminary Conclusions: Correlation analysis with ACBAR data probes to the lowest atmosphere amplitudes (no obvious instrument noise floor as in L&H, 2000) Correlation analysis with ACBAR data probes to the lowest atmosphere amplitudes (no obvious instrument noise floor as in L&H, 2000) Kolmogorov-Taylor model provides a good fit to the atmospheric fluctuations seen by ACBAR. Kolmogorov-Taylor model provides a good fit to the atmospheric fluctuations seen by ACBAR. Median amplitude at the South Pole in winter is 20 mK 2 rad -5/3, compared to 130 mK 2 rad -5/3 during summer at South Pole and 8000 mK 2 rad -5/3 at the Atacama desert in Chile (L&H2000). (Uses WV emissivity to scale to 150 GHz) Median amplitude at the South Pole in winter is 20 mK 2 rad -5/3, compared to 130 mK 2 rad -5/3 during summer at South Pole and 8000 mK 2 rad -5/3 at the Atacama desert in Chile (L&H2000). (Uses WV emissivity to scale to 150 GHz)

13. The 2D angular power spectrum, P( α ), can be obtained by integrating the third spatial dimension of the 3D power spectrum: The 2D angular power spectrum, P( α ), can be obtained by integrating the third spatial dimension of the 3D power spectrum: This can be re-written as: P( α ) = B sky 2 (  ) ( α x 2 + α y 2 ) -b/2 This can be re-written as: P( α ) = B sky 2 (  ) ( α x 2 + α y 2 ) -b/2 B sky 2 (  ), b are two of the four free parameters of model B sky 2 (  ), b are two of the four free parameters of model 3D  2D Angular Power Spectrum “b/2” α = angular wave number

14. Amplitude Analysis: Scaling Between Frequencies AT (Atmospheric Transmission) code used to understand scaling of amplitudes between frequencies. AT (Atmospheric Transmission) code used to understand scaling of amplitudes between frequencies. Frequency 40 GHz 150 GHz 219 GHz 274 GHz  T CMB 2 0.67 mK 2 rad -5/3 20. mK 2 rad -5/3 160 mK 2 rad -5/3 860 mK 2 rad -5/3  T RJ 2 0.62 mK 2 rad -5/3 6.7 mK 2 rad -5/3 17. mK 2 rad -5/3 31. mK 2 rad -5/3  2 (normalized to 40GHz) 10.050.0220.02 Results here still somewhat tentative Need better understanding of AT code, numbers above calculated under conditions of Mauna Kea

15. Methodology Fit four free parameters: power law index, b; amplitude, B sky 2 (  ); wind vector components, w Φ and w ε Fit four free parameters: power law index, b; amplitude, B sky 2 (  ); wind vector components, w Φ and w ε Minimize difference between observed data and the theoretical correlation matrix generated from model by varying parameters of model Minimize difference between observed data and the theoretical correlation matrix generated from model by varying parameters of model

16. Instrument Background Data acquired using ACBAR, the Arcminute Cosmology Bolometric Array Receiver (Runyan et. al, 2002) Data acquired using ACBAR, the Arcminute Cosmology Bolometric Array Receiver (Runyan et. al, 2002) Primary science goal is precise measurement of high- l CMB power spectrum at 150 GHz (Kuo et. al 2002) Primary science goal is precise measurement of high- l CMB power spectrum at 150 GHz (Kuo et. al 2002)

17. Cooled to 240mK He3/He3/He4 Fridge Arcminute Cosmology Bolometer Array Receiver 4K 350mK 240mK FET 120K Spider web Bolometers 16-element array Corrugated feed horns

18. Geometrical Situation A sheet of atmospheric turbulence is observed at height h, thickness Δh, and is in the presence of a wind vector w A sheet of atmospheric turbulence is observed at height h, thickness Δh, and is in the presence of a wind vector w From Lay & Halverson, 2000 Blobs of water vapor within that sheet whose spatial spectrum can be described by a Kolmogorov power law Blobs of water vapor within that sheet whose spatial spectrum can be described by a Kolmogorov power law Small scale of turbulence fluctuations compared to Δh means we observe the 3-D regime of Kolmogorov power law: b=11/3 Small scale of turbulence fluctuations compared to Δh means we observe the 3-D regime of Kolmogorov power law: b=11/3

19. Dataset Description Data were collected during the austral winter of 2002 Data were collected during the austral winter of 2002 Approximately 200 files over that period, each constituting roughly six hours of continuous observation ~100 GB data Approximately 200 files over that period, each constituting roughly six hours of continuous observation ~100 GB data

20. Comparison to Previous Studies Similar atmosphere characterization done by Lay and Halverson (2000), but… Similar atmosphere characterization done by Lay and Halverson (2000), but… Their dataset spanned the austral summer. It is expected that the colder temperatures of the winter will produce lower fluctuation amplitudes compared to the summer Their dataset spanned the austral summer. It is expected that the colder temperatures of the winter will produce lower fluctuation amplitudes compared to the summer The correlation analysis capitalizes on the large number of array elements and sensitivity of ACBAR and allows us to probe the fluctuation amplitude well below the detector noise, even during the best weather The correlation analysis capitalizes on the large number of array elements and sensitivity of ACBAR and allows us to probe the fluctuation amplitude well below the detector noise, even during the best weather

21. Amplitude Measurements Log plot of 150 GHz amplitude as a function of time Log plot of 150 GHz amplitude as a function of time Triangles represent observations where Kolmogorov model fails (~15% of data) Triangles represent observations where Kolmogorov model fails (~15% of data)

22. Angular Wind Vector Measurements Need to use high signal-to-noise observations because angular wind-speed determination is poor for low amplitude fits Need to use high signal-to-noise observations because angular wind-speed determination is poor for low amplitude fits Half the data survive the SNR cut Half the data survive the SNR cut Current limiting factor in angular wind vector measurements is component perpendicular to motion of chopper Current limiting factor in angular wind vector measurements is component perpendicular to motion of chopper

23. Application to SPT Tom Crawford (U. Chicago) is running observing strategy simulations for design of South Pole Telescope Tom Crawford (U. Chicago) is running observing strategy simulations for design of South Pole Telescope The median fluctuation amplitude and scale height of the water vapor during winter observations are critical numbers in these simulations The median fluctuation amplitude and scale height of the water vapor during winter observations are critical numbers in these simulations

24. Minimize  2 Schematic representation of data processing Schematic representation of data processing IDL AMOEBA routine used to adjust free input parameters of model to minimize  2 IDL AMOEBA routine used to adjust free input parameters of model to minimize  2 Data vectors x i, x j B sky 2 (  ), b, w , w  Calculate the averaged correlation C[  ( , w ,w  ), B sky 2 (  ), b] Mode removal matrix:  Compare 22 Model P P t

25. Validity of Model For 85% of the observations, the Kolmogorov-Taylor model fits the data very well For 85% of the observations, the Kolmogorov-Taylor model fits the data very well For the other 15%, the data exhibit anomalously high amplitude fluctuations that do not fit the KT model. These observations are identified via a  2 cut For the other 15%, the data exhibit anomalously high amplitude fluctuations that do not fit the KT model. These observations are identified via a  2 cut

26. Angular Wind Vector (cont.) Both wind direction and speed are fairly constant as function of altitude (based on radiosonde data) Both wind direction and speed are fairly constant as function of altitude (based on radiosonde data) We can compare ACBAR angular wind- speed to radiosponde linear wind-speed to obtain a rough estimation of the scale height of the emission We can compare ACBAR angular wind- speed to radiosponde linear wind-speed to obtain a rough estimation of the scale height of the emission Accuracy is limited by determination of chopper-perpendicular angular wind-speed Accuracy is limited by determination of chopper-perpendicular angular wind-speed

27. Data Processing, Part 3 Perform mode removal: project out a second order polynomial to remove large scale power Perform mode removal: project out a second order polynomial to remove large scale power Resultant correlation matrix is ready for comparison to model Resultant correlation matrix is ready for comparison to model

28. Angular Offset Values pair ΔΔΔΔΔεPairΔΦΔεPairΔΦΔε A-16’0’E-16’-16’I+32’-16’ B-32’0’F-32’-16’J+48’-16’ C-48’0’G-48’-16’ D0’-16’H+16’-16’

29. Theoretical Correlation Matrix How do we compare observed correlation matrix, to theoretical correlation function, C( θ )? How do we compare observed correlation matrix, to theoretical correlation function, C( θ )? Assuming stationary noise, construct a theoretical correlation matrix, C T ij, from C( θ ) Assuming stationary noise, construct a theoretical correlation matrix, C T ij, from C( θ ) Apply identical mode removal to C T ij Apply identical mode removal to C T ij Resulting theoretical correlation matrix can be directly compared to Resulting theoretical correlation matrix can be directly compared to

30. Data Processing, Part 2 Statistical correlation depends only on the relative displacement of the channels: correlation matrices corresponding to pairs of array elements with identical relative displacements and operating at the same frequency are averaged together Statistical correlation depends only on the relative displacement of the channels: correlation matrices corresponding to pairs of array elements with identical relative displacements and operating at the same frequency are averaged together Very few observations demonstrate changes over the span of the 6 hour observation: average all correlation matrices in an observation together to improve SNR Very few observations demonstrate changes over the span of the 6 hour observation: average all correlation matrices in an observation together to improve SNR

31. Data Processing, Part 1 x i and x j are each 128 element data vectors (or sweeps) to be correlated x i and x j are each 128 element data vectors (or sweeps) to be correlated Subtract telescope offset (averaged over many sweeps) from each sweep Subtract telescope offset (averaged over many sweeps) from each sweep The 128x128 element correlation matrix calculated from the data vectors is defined as The 128x128 element correlation matrix calculated from the data vectors is defined as

32. Calculating, θ, the Angular Lag γ is set by observing strategy γ is set by observing strategy ΔΦ and Δε are fixed according to the angular separation of the array elements being correlated ΔΦ and Δε are fixed according to the angular separation of the array elements being correlated w Φ and w ε, the two components of the wind vector, are the final two free parameters in the model w Φ and w ε, the two components of the wind vector, are the final two free parameters in the model

33. 2D Angular PS  C( θ ) C( θ ) = Fourier Transform(P( α )) C( θ ) = Fourier Transform(P( α )) θ is measured in the reference frame of the fluctuations θ is measured in the reference frame of the fluctuations Given the temporal lag, τ, chopper angular speed, γ, and the wind angular speed (w Φ,w ε ) in the Φ (azimuth) and ε (elevation) directions, θ is given by Given the temporal lag, τ, chopper angular speed, γ, and the wind angular speed (w Φ,w ε ) in the Φ (azimuth) and ε (elevation) directions, θ is given by 2π2π

34. Goals of Research Verify accuracy of Kolmogorov model of atmospheric turbulence by comparing to data Verify accuracy of Kolmogorov model of atmospheric turbulence by comparing to data Characterize parameters of model for the entire 2002 austral winter Characterize parameters of model for the entire 2002 austral winter Check consistency of results with other data (e.g. radiosonde weather balloons, previous similar studies) Check consistency of results with other data (e.g. radiosonde weather balloons, previous similar studies)

35. Model: Spatial & Temporal We expect to see a frozen pattern of Gaussian noise with Kolmogorov spectrum blown through the telescope beams by wind or the chopper motion in a certain direction, similar to this: Python Experiment (From Lay & Halverson, 2000) Unfortunately, signal-to-noise is usually much lower than what is shown here. Blobs of water vapor

36. Calibration Voltage signal  CMB temperature units Voltage signal  CMB temperature units Use known flux of planets to get absolute conversion Use known flux of planets to get absolute conversion Mars, 2001: 5% error Venus, 2002: 8% error Mars, 2001: 5% error Venus, 2002: 8% error Skydips used to characterize transmission of atmosphere Skydips used to characterize transmission of atmosphere Total uncertainty of 10% for 2002 CMB observations Total uncertainty of 10% for 2002 CMB observations

37. Observation Strategy A chopping flat mirror sweeps the telescope beam over 3 o across the sky at a rate of 0.3 Hz and at constant elevation A chopping flat mirror sweeps the telescope beam over 3 o across the sky at a rate of 0.3 Hz and at constant elevation Each 3 o sweep is binned into a vector (x) of 128 temperature measurements for each of the 16 detectors Each 3 o sweep is binned into a vector (x) of 128 temperature measurements for each of the 16 detectors Data vectors from two array elements form the foundation of the correlation analysis Data vectors from two array elements form the foundation of the correlation analysis

38. Water Vapor Characteristics Radiosonde weather balloon data were taken once per day at the South Pole during the winter of 2002. Radiosonde weather balloon data were taken once per day at the South Pole during the winter of 2002. Data on pressure, temperature, relative humidity, and wind speed and direction as functions of altitude Data on pressure, temperature, relative humidity, and wind speed and direction as functions of altitude Most water vapor pressure exists below 2km. P wv = RH * P0 * exp(-To/T)