Development of a solar imaging array of Very Small Radio Telescopes

Transcription

1 Development of a solar imaging array of Very Small Radio Telescopes Ted Tsiligaridis University of Washington, Seattle Mentor: Alan E.E. Rogers MIT Haystack Observatory Summer 27

2 Outline 1. Solar Physics 2. Hardware 3. Concepts 4. Software Developed 5. Results & Discussion

3 -- 1. Solar Physics -- Higher frequency rays penetrate more deeply than lower ones. Our observing frequency is 12 GHz (λ=2.5cm); we mostly have a uniform effective temperature as we range across the distance from the center of the disk. As the frequency increases, the size of the radio disk decreases down to the optical disk size.

4 -- 2. Hardware -- Local oscillator generates a signal which is beat against the signal of interest to mix it to a different frequency. LNB takes a wide block of relatively high frequencies, amplifies them, and converts them to similar signals carried at much lower frequencies (IF), which can travel through cables with much less attenuation (fixed on the dish).

5 -- 2. Hardware -- Picture on left shows the azimuth and elevation motors. Picture in middle shows the triple feed LNB; pointing is correct (image of Sun centered at third feed). Picture on right shows a VSRT dish tracking the Sun. Half-power point beam width: 3.9 Dish diameter: 45 cm (~18 ) Rough cost estimate: ~$6

6 -- 3. Concepts -- a) Visibility By visibility, we represent the amplitude of the observed lobe pattern; the fringe amplitude. The complex visibility function is the Fourier Transform of the source brightness distribution. We represent the visibility of the solar disk as a 2D integral: V ( z) R 2π = B( r, ϑ) e jrz( ϑ) rdrdϑ We normalize the visibility by dividing by: R 2π B( r, ϑ) rdrdϑ

7 -- 3. Concepts -- It is convenient to approximate this calculation using the superposition of several 1D integrals, instead of using a heavily oversampled DFT. For a uniform disk, we compute the normalized visibility as follows: V uniform ( z) = R R 2 r 2 πr 4 cos( rz) dr 2 = 2J 1 ( Rz) Rz

8 -- 3. Concepts -- Advanced limb brightening was implemented to add many outer rings: 1.4 Limb Brightening profile, F = 3.5% 1.2 offset 1.1 X:.275 Y: X:.265 Y: 1 offset 2 Normalized Visibility.8.6 Uniform Sun Limb Brightened.2.4 Outer portion X:.295 Y:.1 Solar Radius (degrees)

9 -- 3. Concepts -- b) Closure Phase (Self-Calibration) Suppose we have a 3-element interferometer set up like below. Let the complex visibility of the fringe associated with baseline b jk be denoted by V jk. V jk = V jk e source jk jφ φ = φ + ε ε + δ jk jk j k jk where ε j, ε k are atmosphere turbulence-induced phase errors at the j th, k th apertures, and δ jk indicates measurement noise. φ = ( φ c = φ source 12 source 12 + ε ε + δ ) + ( φ + φ 1 2 source 23 + φ 12 source 31 source 23 + ( δ 12 + ε ε + δ ) + ( φ + δ δ 31 ) 23 source 31 + ε ε + δ ) It s called the method of self-calibration because phase errors are eliminated.

10 -- 4. Software Developed -- Data was taken using a real-time Java console data acquisition program, which allowed us to record the visibility amplitudes and the closure phase in RAD files. Programs in MATLAB and Python were developed to read the data collected and compare them with the model. Programs parameterized to superimpose the following on top of the uniform Sun: Sunspot Amplitude (intensity) Angle (around solar disk) Distance away from center of solar disk Size Limb Brightening Use one outer ring or many Fraction of the Sun s radio output in the enhanced brightness of the limb Linear Brightness Gradient (to simulate dish mispointing) Gradient fraction Least-squares analysis programs were also developed to compute the sum of squares for a certain closure phase fit, or for various fits (construction of surface for ranges of parameters).

11 -- 5. Results & Discussion -- Although solar activity during observation led to a scarcity of interesting data, around July 8 th, some significant sunspot activity took place. It is of interest to see how well we can detect these changes in the sun s surface using the 3 baseline VSRT interferometer. To do this, we use the closure phase concept because it s independent of the station atmosphere and local oscillator phases. It s largely free from instrumental errors and can be used to model source structure and remove the ambiguity in structure modeled with the visibility amplitudes alone.

12 Here are the results of a simulation run: Results & Discussion --.5 Baseline 2 (Intermediate) Vis. Amplitude Baseline 1 (Long) Vis. Amplitude.5 Vis. Amplitude Baseline (Short).6.4 gradient: % brightening: 3.5%.2 brightening + gradient + sunspot: angle = 18, rad =.2R, size =.1R, amp = Closure Phase (deg) Closure Phase UT Time (hr)

13 -- 5. Results & Discussion -- Here is the sum-of-squares surface for July 8 th (day 189): Day = 189, Number of tiles = 4, Exclude data = 1, Gradient = -5% x x Sum of Squares Sum of Squares X: 2.2 Y:.275 Z: 2.338e Angular Angular Radius Sunspot Amplitude Sunspot Amplitude We pick the optimum parameters by finding the minimum of this surface.

14 Nobeyama Sun during July 7

15 -- 5. Results & Discussion -- After taking the same approach for the next three days, we were able to fit the model curves to the actual closure phase data collected: 2 Closure Phase 2 Closure Phase Data: rad Gradient: -5% Limb brightening: 3.5% Sunspot: angle = 18, rad =.2R, size =.1R, amp = 2.2 R =.275 o Day 189 Amp.= Data: rad Gradient: -5% Limb brightening: 3.5% Sunspot: angle = 18, rad =.2R, size =.1R, amp = 1.5 R =.275 o Day 19 Amp.=1.5 Closure Phase (deg) Closure Phase (deg) UT Time (hr) UT Time (hr) 2 Closure Phase 2 Closure Phase Data: rad Gradient: -1% Limb brightening: 3.5% Sunspot: angle = 18, rad =.2R, size =.1R, amp = 1.36 R =.2752 o Day 191 Amp.= Data: rad Gradient: % Limb brightening: 3.5% Sunspot: angle = 18, rad =.2R, size =.1R, amp = 1.25 R =.275 o Day 192 Amp.=1.25 Closure Phase (deg) Closure Phase (deg) UT Time (hr) UT Time (hr)

16 -- 5. Results & Discussion -- Data wasn t taken on day 193, but the data for day 194 showed that the sunspot intensity trend continued: 2 Closure Phase 15 Data: rad Gradient: 5% Limb brightening: 3.5% Sunspot: angle = 18, rad =.2R, size =.1R, amp = 1.2 R =.275 o Day 194 Amp.= Closure Phase (deg) UT Time (hr)

17 -- 5. Results & Discussion -- Below is a 2D point of view of the sum-of-squares as the sunspot intensity is varying (1.2 to 2.2), when the solar radius is set to.275 (99 arcsec). x 1 6 Day = 189, Number of tiles = 1, Exclude data = 1, Gradient = -5% x 1 6 Day = 19, Number of tiles = 1, Exclude data = 1, Gradient = -5% Day Day 19 Sum of Squares Sum of Squares Sunspot Intensity Sunspot Amplitude x 1 6 Day = 191, Number of tiles = 1, Exclude data = 1, Gradient = -1% Day 191 The optical disk radius at mid-july is 944 =.262. Sum of Squares The Nobeyama disk radius is ~956 = Sunspot Amplitude

18 -- 5. Results & Discussion -- In summary, the sunspot intensity trend over the period of six days looks like this (derived form the closure phase fitting): Sunspot Intensity Trend Sunspot Amplitude D Days

19 Acknowledgments Special thanks to: My mentor, Alan Rogers, for cooperation and encouragement Bill Rideout, for programming help Preethi Pratap, for support and guidance Divya Oberoi, for providing references and suggestions John Gilling, for the fruitful office conversations Richard Crowley, for providing needed software Mike Albu, for computer help Madeline Needles, for providing the books And to all of you for coming!

20 Questions?