1. The Highest Time-Resolution Measurements in Radio Astronomy: The Crab Pulsar Giant Pulses Tim Hankins New Mexico Tech and NRAO, Socorro, NM Extreme Astrophysics in an Ever-Changing Universe 16-20 June, 2014

2. Acknowledgments Jim Cordes Jared Crossley Tracey Delaney Jean Eilek Glenn Jones Jeff Kern Mark McKinnon David Moffett Jim Sheckard Jim Weatherall Staffs of NRAO and NAIC Jim Cordes Jared Crossley Tracey Delaney Jean Eilek Glenn Jones Jeff Kern Mark McKinnon David Moffett Jim Sheckard Jim Weatherall Staffs of NRAO and NAIC Cornell University New Mexico Tech, NRAO New Mexico Tech, WV Wesleyan New Mexico Tech, NRAO Cal Tech, NRAO New Mexico Tech, NRAO New Mexico Tech, Furman University New Mexico Tech New Mexico Tech, FAA Cornell University New Mexico Tech, NRAO New Mexico Tech, WV Wesleyan New Mexico Tech, NRAO Cal Tech, NRAO New Mexico Tech, NRAO New Mexico Tech, Furman University New Mexico Tech New Mexico Tech, FAA

3. Science objectives What is the pulsar radio emission mechanism?What is the pulsar radio emission mechanism? How does a relativistic magnetized pair plasma radiate at equivalent brightness temperatures of 10 36  10 42 K?How does a relativistic magnetized pair plasma radiate at equivalent brightness temperatures of 10 36  10 42 K? Can we understand Crab Nebula pulsar?Can we understand Crab Nebula pulsar? Does the Crab fit the canonical pulsar model? Does the Crab fit the canonical pulsar model? Or is it unique? What is the pulsar radio emission mechanism?What is the pulsar radio emission mechanism? How does a relativistic magnetized pair plasma radiate at equivalent brightness temperatures of 10 36  10 42 K?How does a relativistic magnetized pair plasma radiate at equivalent brightness temperatures of 10 36  10 42 K? Can we understand Crab Nebula pulsar?Can we understand Crab Nebula pulsar? Does the Crab fit the canonical pulsar model? Does the Crab fit the canonical pulsar model? Or is it unique?

4. Summary Time resolution down to 0.2 nanoseconds achieved using a large-memory digital oscilloscope and coherent dedispersion

5. Scientific Method: Form Hypothesis: Emission is a form Shot noise: Cordes, 197 6 Make predictions: Shot noise cause: Collapsing solitons in turbulent plasma: Weatherall, 1998 Test by experiment: High-time resolution observations Form Hypothesis: Emission is a form Shot noise: Cordes, 197 6 Make predictions: Shot noise cause: Collapsing solitons in turbulent plasma: Weatherall, 1998 Test by experiment: High-time resolution observations

6. Collapsing soliton prediction I

7. Prediction II

8. How to get high time resolution: Coherent dedispersion required.  Sample receiver voltage at Nyquist rate.  Pass signal through a filter with the inverse dispersion characteristic of the Interstellar Medium.  Use square-law detectors to obtain intensity. (Polarization slightly more complex.) (Polarization slightly more complex.) Coherent dedispersion required.  Sample receiver voltage at Nyquist rate.  Pass signal through a filter with the inverse dispersion characteristic of the Interstellar Medium.  Use square-law detectors to obtain intensity. (Polarization slightly more complex.) (Polarization slightly more complex.)

9. Coherent dedispersion Emitted signal: s(t)  S(  )Emitted signal: s(t)  S(  ) Dispersive ISM: H(  ) = exp[ik(  )z]  h(t)Dispersive ISM: H(  ) = exp[ik(  )z]  h(t) Received signal: s(t)*h(t)  S(  ) H(  )Received signal: s(t)*h(t)  S(  ) H(  ) Dedispersion processing: S(  )H(  )H(  ) –1  s(t)Dedispersion processing: S(  )H(  )H(  ) –1  s(t) »and 10,000 lines of code  : Fourier Transform  : Fourier Transform * : Convolution * : Convolution Emitted signal: s(t)  S(  )Emitted signal: s(t)  S(  ) Dispersive ISM: H(  ) = exp[ik(  )z]  h(t)Dispersive ISM: H(  ) = exp[ik(  )z]  h(t) Received signal: s(t)*h(t)  S(  ) H(  )Received signal: s(t)*h(t)  S(  ) H(  ) Dedispersion processing: S(  )H(  )H(  ) –1  s(t)Dedispersion processing: S(  )H(  )H(  ) –1  s(t) »and 10,000 lines of code  : Fourier Transform  : Fourier Transform * : Convolution * : Convolution

10. What Can You Do With It? Diagnostic for emission mechanism studies: Found nanostructure predicted by Weatherall Propagation studies : Precision DM determination Discoveries: Echoes of Crab “giant” pulses Crab Interpulse spectral bands Diagnostic for emission mechanism studies: Found nanostructure predicted by Weatherall Propagation studies : Precision DM determination Discoveries: Echoes of Crab “giant” pulses Crab Interpulse spectral bands

11. Crab “Megapulse” at 9.25 GHz 0.4 ns 2.2 Mega-Jansky pulse Duration: 0.4 nanoseconds

12. Not all pulses are so short Typical Main Pulse, 9 GHz 0 1 2 3 4 5 6 Time (Microseconds)

13. Giant Pulse Widths

14. Dispersion Measure Determination Methods: Time delay between two frequencies Must account for pulse shape change & Scattering broadening Split receiver passband Cross-correlate micro-, nanostructure Adjust dispersion removal filter to Maximize pulse intensity variance Minimize equivalent width Time delay between two frequencies Must account for pulse shape change & Scattering broadening Split receiver passband Cross-correlate micro-, nanostructure Adjust dispersion removal filter to Maximize pulse intensity variance Minimize equivalent width

15. Two-frequency Cross-correlation

16. Split-band Cross-correlation

17. Adjust Dispersion Measure DM = 56.739780

18. Adjust Dispersion Measure DM = 56.735001

19. Modulation Spectra Main PulsesInterpulses 10 -3

20. Unexpected Discoveries Giant Pulse Echoes Dynamic Spectra: Interpulse Bands Main pulse DM ≠ Interpulse DM

21. Giant pulse Echoes 1435.1 MHz Echo 1435.1 MHz 4885.1 MHz Echo

22. Dynamic Spectra

23. Intensity and spectrum of a Main pulse

24. Intensity and spectrum of an Interpulse

25. Main pulse: Wideband Interpulse: Banded

26. Some definitions: Band Separation Band Width

27. Interpulse band bandwidths

28. Interpulse Band Frequencies At 30 GHz: Q ≈ Band Separation = 1.8 GHz = 36 Band Width 0.05 GHz Band Separation Sky Freq = 0.058 Least-squares fit slope =

29. Band Center Frequency Memory

30. Main pulse/Interpulse Dispersion

31. Main pulse Interpulse

32. Main Pulse InterpulseDispersioncorrected

33. DM vs. Flux Interpulses Main pulses

34. DM vs. Time  Interpulses Main pulses −Jodrell Bank DM

35. SummarySummary Fast sampling: versatility in processing allows detailed emission studies. “The more you look, the more you see.” The Crab pulsar: Continues to “amaze and mystify”

36. FutureFuture Dedispersion Processing: My old, 8-core Mac: 5 GHz data bandwidth: 4000x real time. (2 ms data in 8 seconds) [with lots of diagnostic overhead] Add n GPUs (Graphics Processor Units): Processing time reasonable. Moore’s Law:

37. Coherent Dedispersion History: Bandwidth vs. Date

38. Giant Main Pulses are Wideband From Glenn Jones at the GAVRT Telescope Time (Microseconds) 5 10 15 20 25 30 5 15 25 3 4 5 6 7 8 9 10 Frequency (GHz)

39. The End

40. Giant pulse Echoes 20 40 60 Time (microseconds) 100 120 140 1435.1 MHz Echo