Characterization Analysis for the Canadian Hydrogen Intensity Mapping Experiment

Transcription

1 Characterization Analysis for the Canadian Hydrogen Intensity Mapping Experiment by Ze Scales A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF Bachelor of Science in THE FACULTY OF SCIENCE (Physics and Astronomy) The University Of British Columbia (Vancouver) April 2013 c Ze Scales, 2013

2 Abstract The goal of the Canadian Hydrogen Intensity Mapping Experiment (CHIME) is to map the distribution of neutral hydrogen over redshifts in the range 0.8 < z < 2.5. This will further our understanding of dark energy by giving a better picture of the recent expansion history of the universe. The CHIME telescope is presently under construction at the Dominion Radio Astronomical Observatory (DRAO) in Penticton, B.C. We have analyzed results from a prototype two-dish interferometer, also located at DRAO. We determined the gain of the system by assuming that gain variations are due to the effects of temperature variations on the components of the system. We were able to achieve better results once we separated the temperature into a high-frequency component and a low-frequency component and fitted these components independently. We also compared results from two different correlators installed at the prototype telescope. We found that both produce results which are essentially the same for common scenarios. ii

3 Table of Contents Abstract ii Table of Contents iii List of Figures v Glossary vii Acknowledgments viii 1 Introduction and Background Expansion Baryon Acoustic Oscillations The CHIME System Prototype Two-Dish System Thermal Gain Model Gain Modelling Gain Refining the Model Shortcomings Correlator Comparison Correlators iii

4 3.2 Comparing the Correlators Outlook Summary Bibliography iv

5 List of Figures Figure 1.1 Figure 1.2 The final Canadian Hydrogen Intensity Mapping Experiment (CHIME) telescope. Each cylindrical dish is 20 m wide by 100 m long. Feeds are located at the focus of each dish, along the centerline of the cylinder Photograph of the two-dish prototype system at Dominion Radio Astronomical Observatory (DRAO) Figure 2.1 Least squares fit of equation (2.2) to data at 487 MHz Figure 2.2 Measured temperature inside the electronics hut Figure 2.3 Fast Fourier transform of the temperature inside the electronics hut. Green denotes frequencies lower than 1 cycle per 20 minutes while blue indicates higher frequencies. The blue spike has a period of 5 minutes and is due to the heating, ventillation, and air conditioning (HVAC) system Figure 2.4 Least squares fit of equation (2.3) to data at 487 MHz. The results more closely match the data compared to Figure v

6 Figure 3.1 Figure 3.2 The left-hand panel shows sky data as processed by the UBC correlator and the right-hand panel shows McGill s correlator. These data both come from the prototype telescope s West dish. The feed was split and the sky signal was processed by both correlators simultaneously. Hence, we expect both datasets to look essentially the same. The large daily spikes correspond to the radio-bright supernova remnant Cassiopeia A. 15 This plot shows data from the McGill correlator plotted against data from the UBC correlator. The top panel also shows a linear fit of the McGill data to the UBC data. The bottom panel shows the error in this fit vi

7 Glossary ADC BAO analog-digital converter baryon acoustic oscillations CHIME Canadian Hydrogen Intensity Mapping Experiment CMB DRAO FFT FPGA GPU HVAC IFT LNA RFI cosmic microwave background Dominion Radio Astronomical Observatory fast Fourier transform field programmable gate array graphics processing unit heating, ventillation, and air conditioning inverse Fourier transform low noise amplifier radio-frequency interference ROACH reconfigurable open architecture computing hardware vii

8 Acknowledgments Thanks to Gary Hinshaw and Mark Halpern for their invaluable help. I am also grateful for the kind assistance of others in my lab, particularly Mandana Amiri, Greg Davis, Meiling, and Don Wiebe. viii

9 Chapter 1 Introduction and Background The Canadian Hydrogen Intensity Mapping Experiment (CHIME) project aims to construct a radio interferometer to study dark energy and the expansion history of the universe. CHIME will accomplish this by measuring 21 cm emission from the hyperfine transition in neutral hydrogen. CHIME will observe the 21 cm line in the redshift range 0.8 < z < 2.5, corresponding to radio emission in the range of approximately 400 MHz to 800 MHz. Ultimately, CHIME will carry out an all-sky survey of hydrogen intensity. 1.1 Expansion It has been known since 1929 that the universe is expanding [5] thanks to the measurements of red-shifted stars that Edwin Hubble made. He found a linear relationship between the velocity with which galaxies are moving away and their distance from Earth. That this expansion is actually accelerating is a fact which has only become known more recently. It is believed that this accelerating expansion is due to a hypothetical form of energy called dark energy, which exerts a negative pressure [7, 8]. 1

10 1.2 Baryon Acoustic Oscillations Baryon acoustic oscillations (BAO) are acoustic waves which propagated in the primordial soup of the early universe. This primordial soup was a hot, dense plasma comprising photons, protons, and electrons. It was so hot and dense that light was actually coupled to matter through Compton scattering of photons by the charged plasma. In a matter-dense region of the plasma, one would expect an inward pressure due to gravity. However, because of the coupling between light and matter, this inward gravity pressure was balanced by an outward radiation pressure. The interplay between gravity and radiation pressure caused spherical oscillations in the plasma centered on the overdense regions [2]. These acoustic oscillations are the BAO. When the universe cooled below around 3000 K, light and matter decoupled and the BAO were effectively frozen in matter while the photons escaped. These photons are the cosmic microwave background (CMB). The wavelength of the BAO propagating in the primordial plasma is precisely known[6] as 147 Mpc which makes it possible to use BAO as a standard ruler. By measuring the angular size of the BAO over a range of redshifts, it is possible to determine the expansion history of the universe. BAO manifest themselves in the matter density of the universe. Because the BAO were frozen after years, matter can be found preferentially separated by the BAO wavelength, called the sound horizon. This can be analyzed quantitatively by studying the two-point autocorrelation function, hereafter referred to as the correlation function (as is common in astrophysics). The correlation function is a function of one variable (distance) which gives the probability of finding matter separated by that distance. This means that in principle, one can see BAO in any survey of matter distribution. For instance, BAO have been observed in the distribution of galaxies[3], where galaxies are found to be preferentially separated by the BAO wavelength. 2

11 1.3 The CHIME System CHIME will survey the expansion history of the universe by studying the distribution of neutral hydrogen via observations of emission from the 21 cm line over a range of redshifts from z 0.8 to z 2.5. This range was chosen for practical reasons 21 cm radiation at z = 0.8 corresponds to about 800 MHz, just below cell phone frequencies. The telescope itself will comprise five cylindrical dishes, each measuring 20 m by 100 m (see Figure 1.1). These dishes will operate as an interferometer, scanning half the sky each day. Each dish has an array of feeds distributed along the focus, at the center of the cylinder. In total, CHIME will have 2560 feeds. This enables the use of digital beamforming to achieve high angular resolution. Digital beamforming is a technique where the feeds are used as a phased array to steer the beam to a specific area of the sky. CHIME will use a hybrid design where the beam is scanned in the North-South direction using beamforming while the Earth s rotation effectively scans the beam in the East-West direction. Each feed will be connected to a microwave low noise amplifier (LNA) before digitization and correlation. CHIME will use custom-built LNA boards which have been designed to operate at room temperature. After amplification, the signals pass into a system of analog-digital converter (ADC) and correlator boards which will be constructed using field programmable gate arrays (FPGAS) and graphics processing units (GPUS). With any telescope, understanding the characteristics of the system is of vital importance. To help characterize the feeds and amplifiers to be used in CHIME, a prototype interferometer system consisting of two 8 m circular parabolic dishes separated by 19 m has been constructed. Basic modelling of the amplifier gain has already been carried out, but many unknown phenomena remain. The goal of the proposed analysis is to resolve these uncertainties. Additionally, the CHIME telescope picks up many signals that are due to radiofrequency interference (RFI). These RFI signals must be eliminated to the greatest 3

12 Figure 1.1: The final CHIME telescope. Each cylindrical dish is 20 m wide by 100 m long. Feeds are located at the focus of each dish, along the centerline of the cylinder. degree possible to improve resolution. Therefore, it is important to try to identify the origin of the RFI. Some RFI inevitably results from hardware problems which can often be resolved. On the other hand, sometimes RFI originates from external sources which are completely outside the experimenter s control Prototype Two-Dish System A two-dish interferometer has been constructed at the location chosen for the final CHIME telescope at DRAO. This prototype is meant to characterize the site and serve as a testbed for CHIME components. The telescope is equipped with the same feeds and LNAS that the final CHIME telescope will use. It also uses the same second-stage amplifier, ADC, and correlator. All of the data used in this work come from the prototype system. 4

13 Figure 1.2: Photograph of the two-dish prototype system at DRAO. 5

14 Chapter 2 Thermal Gain Model 2.1 Gain Gain is a property of amplifiers and microwave systems which quantifies the ratio of output signal to input signal. It is defined as ( ) Pout G = 10log 10 P in (2.1) where P out and P in are the output power and input power, respectively. Gain is measured in units of db. In any scientific system, precise knowledge of of a system s gain is critical. Without knowing the gain, it is impossible to relate measured signals to physical quantities. Many elements of the system contribute to the overall gain. These include the coupling between different components, LNA gain, digitization gain, correlation gain, and losses due to coaxial transmission lines. While there are numerous things which can cause the gain to vary over time, one of the most significant effects is due to environmental temperature variations. Many of the components which contribute to the overall gain of the system are affected by temperature. The most susceptible are the LNAS, which are mounted above the 6

15 dish at the feeds, and the ADC and correlator which are located inside a shielded electronics hut. It is possible to reduce some of the gain variation by controlling the temperature of sensitive components. For instance, the temperature inside the hut can be maintained at a relatively stable level. On the other hand, there is no way to effectively control the temperature of the LNAS which are located outside. It is a fact that the LNAS will experience significant temperature variation over a 24 hour cycle. CHIME aims to undertake an all-sky survey, lasting for at least two years, which will generate an astronomical amount of data. Therefore, it is relatively important to be able to correct for gain variations in real time. One way to accomplish this, or to better understand temperature variation with an eye to accomplish this, is to produce an effective model which describes the variations in gain as a function of temperature. 2.2 Modelling Gain First, we assume that the measured power is given by P = (g 0 + g 1 T hut + g 2 T dish )(P sky + n 0 ), (2.2) where T hut is the temperature inside the electronics hut, T dish is the temperature at the antenna focus, P sky is the received power from the sky, and n 0 is a noise term. g i are gain coefficients which will be determined by making least-squares fits to the data. We assume that all temperature effects are linear. This is approximately valid for temperature fluctuations which are either sufficiently small or sufficiently slow. The gain, then, comprises the terms which multiply P sky. For this analysis, P sky was provided by the Haslam map [4], a popular radio map of the sky originally made at the frequency of 408 MHz. In this analysis, we scaled the map to match whatever frequency was required and convolved it with 7

16 Figure 2.1: Least squares fit of equation (2.2) to data at 487 MHz. a Gaussian beam. A least squares fit of Equation (2.2) using the Haslam map can be seen in Figure Refining the Model The model fit shown in Figure 2.1 agrees fairly well with the data, but sometimes overshoots and sometimes undershoots. One factor which could cause this behavior is a difference in dependence on fast temperature variations as compared to slow temperature variations. For instance, some components might respond differently to daily temperature cycles than to more rapid changes. Figure 2.2 shows 8

17 (a) Two days of temperature data. The daily variation in temperature can be seen. (b) Detail of the hut temperature showing fluctuations of about 3 K with a period of around 5 minutes. These are caused by the cycling of the HVAC system. Figure 2.2: Measured temperature inside the electronics hut. 9

18 Figure 2.3: Fast Fourier transform of the temperature inside the electronics hut. Green denotes frequencies lower than 1 cycle per 20 minutes while blue indicates higher frequencies. The blue spike has a period of 5 minutes and is due to the HVAC system. that there are temperature variations with a variety of frequencies. We can quantify this by analyzing the power spectrum of the temperature. The power spectrum tells how the power carried by a signal is distributed over frequencies and can be estimated from a discrete signal using the fast Fourier transform (FFT). The FFT of the hut temperature is shown in Figure 2.3. We can account for the different effects induced by fast or slow temperature variations by separating the two components and treating them independently in the fit. We accomplish this by dividing the FFT of the temperature at some cut- 10

19 Figure 2.4: Least squares fit of equation (2.3) to data at 487 MHz. The results more closely match the data compared to Figure 2.1. off frequency. We then apply the inverse Fourier transform (IFT) to the highfrequency and low-frequency components separately to obtain high-frequency and low-frequency temperature signals. Replacing T hut in Equation (2.2) with T hut,slow and T hut,fast, we have P = (g 0 + g 1 T hut,slow + g 2 T hut,fast + g 3 T dish )(P sky + n 0 ). (2.3) A fit of this model to data is shown in Figure 2.4. It turns out that the rapid temperature changes come from the HVAC system in the electronics hut. The hut is equipped with both an air conditioning (AC) unit 11

20 and heater which are both running at all times. Figure 2.2b shows what happens as both try to adjust the temperature to their set point. Here we have shown results for only one frequency bin, for illustrative purposes. In general, all other things being equal, the model applies equally well to other bins. In practice, some bins have more radio-frequency interference (RFI) than other bins and so the model does not fit as well in these bins. 2.4 Shortcomings While the thermal gain model describes the data fairly well, it does have some fallbacks. The thermal gain model cannot account for RFI in the signal, since this results from sources other than the sky. The deviations of the fit from the data in Figure 2.4 are likely due to RFI effects. To some extent, this can be addressed by adding one or more terms to Equation (2.3) which include the RFI. It can sometimes be difficult, however, to sufficiently isolate the RFI. 12

21 Chapter 3 Correlator Comparison 3.1 Correlators One important aspect of the CHIME system is the correlator. In an interferometer, the correlator is responsible for combining the signals from all of the dishes by computing cross-correlations between them [1]. The cross-correlation of two signals is defined as f g = f (τ)g(t + τ)dτ, (3.1) where f indicates the complex conjugate of f. This is similar to a convolution and in fact the cross-correlation obeys the same identity for the Fourier transform of cross-correlations: F [ f g] = (F [ f ]) F [g], (3.2) where F [ ] denotes the Fourier transform. Hence, a correlator is implemented using Fourier transforms. Instead of computing convolution integrals, a correlator can use fast, numerical Fourier transform methods. CHIME will ultimately use a correlator based on FPGAS and GPUS which is currently being developed by a team at McGill. Until recently, the CHIME prototype system has been using a reconfigurable open architecture computing hard- 13

22 ware (ROACH) based correlator. ROACH 1 is an FPGA based board developed at Berkeley. The McGill correlator is designed to be constructed relatively inexpensively from off-the-shelf components. Since an N element interferometer requires computing N 2 cross-correlations, many correlator units are required to achieve good processing speed. Until October 2012, the prototype CHIME telescope used the ROACH based correlator exclusively. From October 2012 to January 2013, both the ROACH correlator and the McGill correlator were installed simultaneously. After January, the ROACH correlator was disconnected and only the McGill correlator has been operational since. 3.2 Comparing the Correlators In principle, the output of both the McGill correlator (FPGA and GPU based) and the UBC correlator (ROACH based) should be identical. In practice, since the devices use different hardware, there will be some differences. For instance, the gain might have different characteristics. The prototype system has been operational for around two years and the CHIME project has amassed a large amount of invaluable characterization data. In order to compare these data (which were processed through the UBC correlator) with the data being taken now using the McGill correlator, it is important to understand how the two correlators differ. We can get an understanding of how the two correlators behave relative to each other by feeding the same signal into both correlators and comparing the output. This is simple enough to do at the prototype telescope. All that is required is to split the signal coming from one of the telescope feeds and connect the cable to both correlators. Figure 3.1 shows an example of simultaneous data from both correlators. By looking at the data side-by-side, it seems like both data sets are pretty similar. To get a more quantitative idea of the agreement, we can simply make a plot with the UBC data as the abscissa and McGill data as the ordinate

23 Figure 3.1: The left-hand panel shows sky data as processed by the UBC correlator and the right-hand panel shows McGill s correlator. These data both come from the prototype telescope s West dish. The feed was split and the sky signal was processed by both correlators simultaneously. Hence, we expect both datasets to look essentially the same. The large daily spikes correspond to the radio-bright supernova remnant Cassiopeia A. 15

24 Figure 3.2: This plot shows data from the McGill correlator plotted against data from the UBC correlator. The top panel also shows a linear fit of the McGill data to the UBC data. The bottom panel shows the error in this fit. Then, if both correlators measure the same value (up to scaling and an offset) at the same point in time, we should see a linear trend. The line of best fit then essentially gives us a conversion between McGill data and UBC data. This can be seen in Figure 3.2. We observed that this linear relationship held across all of the frequency bins. 16

25 Chapter 4 Outlook The CHIME project recently received full funding to construct the complete CHIME telescope at DRAO. Construction began in January of 2013 and is expected to be complete before Commissioning and testing will follow once the telescope is built and are expected to take another year. The final CHIME survey will then take four years to produce an all-sky map of neutral hydrogen intensity. In the short term, while construction of the CHIME telescope is continuing at DRAO, equipment development is underway at UBC and at McGill. A prototype of the McGill GPU correlator is installed at the prototype telescope. The feeds are being designed and tested at UBC. Future work on this project will be largely in the same vein. There still remains much analysis to be carried out. Some forms of RFI have proved particularly difficult to understand and isolate. 17

26 Chapter 5 Summary The goal of this project was to perform analysis which furthers the characterization of the CHIME system. Understanding gained at this stage of the project development is invaluable in informing the future development of components for the telescope. Developing characterization methods at this stage makes future characterization much easier. This will be important later because the full telescope costs a significantly greater amount of money to operate than the prototype (because of the greatly increased computational resources required to process the data). It saves money and time in the long run to work on characterization now. In this analysis, we examined a method to calibrate the system gain using a thermal gain model. This model assumes that all gain variations are due to temperature effects. We achieved fairly good results with this model; however, we were able to refine it by distinguishing between temperature variations which had a fast timescale versus temperature variations which had a slower timescale. We found that these affected the gain of the system differently. We also compared the results obtained from the original UBC correlator to those obtained with the prototype McGill correlator. We found that for most common scenarios, the two produced very similar results which were effectively in one-to-one correspondence. 18

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