James M Anderson. in collaboration with Jan Noordam and Oleg Smirnov. MPIfR, Bonn, 2006 Dec 07

Transcription

1 Ionospheric Calibration for Long-Baseline, Low-Frequency Interferometry in collaboration with Jan Noordam and Oleg Smirnov Page 1/36

2 Outline The challenge for radioastronomy Introduction to the ionosphere Mathematics Existing techniques Wedge model MIM idea 2D MIM 3D MIM Other thoughts Page 2/36

3 Interferometry Basics Plus Ionosphere Page 3/36

4 Ionospheric Distortions in Wide-Field Imaging 320 MHz observations using the VLBA Fringe fitting removed ionospheric delay at field center Coherence for other detected sources minimal --- selfcalibration needed Wide-field/ ionospheric calibration with E. Lenc Page 4/36

5 LOFAR Isoplanatic Patch Size Model Patch size for modest daytime observations Overpredicts VLA 74 MHz isoplanatic patch size by factor ~2 Small scale structure will reduce this size Page 5/36

6 Ionospheric Effects on Observations Radio sources selected from a deep VLA 74 MHz image. The individual 30-second maps were compiled as animations of the nine hour measurement, running from nighttime through two hours past sunrise. The variations in position, peak intensity, and sidelobe structure show the effects of differential ionospheric effects across the field. Movie and text from J. Lazio Page 6/36

7 Calibration Strategy Strong Sources Self-calibration Multi-frequency analysis Weak Sources Phase Referencing Modeling At low frequencies modeling the ionosphere is essential to enable imaging of weak objects Page 7/36

8 The Ionosphere Basics I Solar radiation ionizes atmospheric particles during daytime Recombination reduces the electron density during the nighttime Number density of neutral particles many orders of magnitude higher Peak density around 300 km, but extends well above and From R.M. Campbell presentation: authorship unknown below this height Page 8/36

9 The Ionosphere Basics II Picture from R.M. Campbell Electrons constrained by magnetic field lines Magnetic equator shifted toward Europe Northern Europe located at magnetic mid-latitudes Page 9/36

10 Vertical Total Electron Content Behavior 1 TECU = 1016 m-2 1 TECU = about 4/3 turn of phase at 1 GHz LOFAR needs differential ionosphere to TECU Ionization fraction lags Solar noon Electrons raised in equatorial fountain fall along flux lines to either side of equator Page 10/36

11 Buoyancy Waves Vertical structure important Waves occur throughout atmosphere, but often seen in ionosphere around 100 km Vertical streaks from meteors Page 11/36

12 Airglow Above Arecibo Left: optical emission showing buoyancy waves Right: simple model of two interfering waves Typical wavelength: 30 km ( km) Page 12/36

13 Some Ionospheric Phase Delay Math Page 13/36

14 Some More Math Page 14/36

15 Existing Ionospheric Correction Techniques for Radioastronomy: TECOR TECOR uses IONEX format files standard IONEX files sampled at 2 hour intervals grid spacing 5 by 2.5 (lon x lat) effectively 2-D model ignoring height information Page 15/36

16 Existing Ionospheric Correction Techniques for Radioastronomy: GPS Observations I Only a handful of GPS satellites visible at one time GPS satellites typically very far from astronomical source on sky Large area of northern sky unsampled Plot from R.M. Campbell Page 16/36

17 Existing Ionospheric Correction Techniques for Radioastronomy: GPS Observations II Plot from R.M. Campbell Westerbork GPS measurements Tracks for one 24 hour period shown (day number 298 of year 1995) Large gap toward the northern part of sky always present Page 17/36

18 Existing Ionospheric Correction Techniques for Radioastronomy: Realtime MHD Modeling Model made by FusinNumerics Example of current computational modeling incorporating GPS data 2 by 2 grid 3-D model includes height effects for slant paths Improvement over TECOR, but still not high enough resolution Page 18/36

19 Ionospheric Wedge Model Assume differential delay related to ionospheric density GRADIENT, so ϕ = (x1 x2) * K Depends on BASELINE length, not station or ionosphere POSITION Page 19/36

20 Gradient Model Breaks Down for Long Baselines For stations at great distances, large-scale ionospheric structure and ionospheric waves cause gradient approach to fail Gradient approach also fails for large angular separations on sky Page 20/36

21 Minimum Ionospheric Model (MIM) as Expressed by Noordam Minimum number of parameters (few bright sources available, sometimes none) Only deal with observables (not interested in internal structure of ionosphere) Assume large-scale (>100 km) structure and go progressively smaller, until. Page 21/36

22 Ionospheric Blanket With Many Piercing Points Page 22/36

23 Example 2D MIM Form: Polynomials VTEC(x,y,t) = Σi=0 to mσj=0 to n ci,j(t) xi yj ci,j(t) = Σk=0 to p ak tk Scale vertical electron content VTEC by elevation angle term to get slant TEC x,y could be Latitude,Longitude or RA,Dec and so on Page 23/36

24 2D MIM --- Lat,Lon Page 24/36

25 2D Absolute Residuals Comparison against full 3D integrated density (static ionosphere) Fit to random directions on sky above specified elevation limit Stations within 1 km Works well for small areas of the sky Page 25/36

26 2D Residuals: Poor for Long Baselines 50 km Maximum Baseline 1000 km Page 26/36

27 Ionosphere Varies with Latitude, Longitude, and HEIGHT Page 27/36

28 3D MIM --- Lat,Lon,Height Page 28/36

29 3D MIM --- Height Page 29/36

30 3D Absolute Residuals Residuals reduced more than an order of magnitude Works well with baselines out to at least 400 km More improvement possible Relative residuals (interferometry) are even smaller Page 30/36

31 Ionospheric Waves MeqTree simulation by O. Smirnov Simulated VLA observation with sinusoidal ionospheric wave Large position motions replicated Beam shape changes replicated 2 sinusoidal waves in different directions reproduce the complex behavior of actual observations Page 31/36

32 MIM Conclusions Need parameters to model static ionosphere for entire Dutch LOFAR array Ionospheric waves require 6 8 parameters each Probably need extra parameters Need 20 to 60 total parameters Dutch LOFAR should have stations * several beams, so should have sufficient measurements Extended LOFAR calibration requires more study Page 32/36

33 Thoughts on Faraday Rotation Working with M Walker Plot shows rotation measure for random directions on sky for afternoon above Westerbork RM values almost follow path delay times magnetic field at 300 km Need accuracy of 0.01 SRM on this scale Page 33/36

34 Thoughts on Refraction Refraction will be a significant problem at very low frequencies Changes ray path through disturbing medium Plot for 1000 km baseline, for 20 degrees elevation (red) and 30 degrees (blue) Page 34/36

35 Additional Thoughts Multiple beam directions really help constrain the ionosphere It is good to have several telescopes within 50 km to provide different lines of sight through the ionosphere for modeling Refraction as a function of frequency for LOFAR important, and expensive Higher order terms in index of refraction (n) are ~10% at 20 MHz, so extrapolation of 20 MHz delay from 50 MHz observations not straightforward Page 35/36

36 The End Page 36/36