1. The Crab Nebula Pulsar: Its Giant Pulses
Tim Hankins
New Mexico Tech, NRAO, NAIC
Arecibo Observatory, February 15, 2007

2. Acknowledgments Jeff Kern Jean Eilek Jim Weatherall Jared Crossley
Jim Cordes
David Moffett
Tracey Delaney
Staffs of NRAO and NAIC
New Mexico Tech
FAA, New Mexico Tech
Cornell University
Furman University
Univ of Minnesota

3. Science objectives What is the pulsar radio emission mechanism?
How does a relativistic magnetized pair plasma radiate at equivalent brightness temperatures of 1036  1042 K?
Can we understand Crab Nebula pulsar?
Pulsars discovered 40 years ago. Still no firm consensus on radio emission mechanism.
Exraordinary brightness temperature.
Crab Nebula pulsar continues to present new mysteries. What’s going on?

4. Summary History Crab pulsar phenomenology Dispersion removal
Emission mechanisms
Observations
Future directions

5. History 0: Crab supernova 1054 AD
VLT photo of the Crab Nebula.
Showed this once at an interview: Guy I replaced promptly fell asleep.

6. History I
Discovery of the Crab pulsar: by its dispersed “giant” pulses (Staelin and Reifenstein, 1968 Science, 162, 148)

7. Crab discovery by “giant” pulses

8. Crab pulsar phenomenology
Frequency dependence
Pulse components
Giant pulse polarization
Giant pulse amplitude distribution
Giant pulse bandwidth

9. Crab pulsar profiles, radio through X-ray
Pre-
cursor
Main
Pulse
Interpulse
Crab pulsar profiles, radio through X-ray
High Frequency
Components (HFCs)
Dotted lines: MP and IP except GHz: IP early.
Infra-red
Visible
Ultra-violet
X-ray

10. Crab pulsar profiles 0.3-8.4 GHz
High-freq Comp 1
High-freq Comp 2
Crab pulsar profiles GHz
Low-freq
Comp 1
8.4 GHz
Note: MP to IP not 180 deg.
Inter-
Main
pulse
Pulse
0.3 GHz

11. Soglosnov, et al., 2004, personal corresp.
Crab giant pulse at 23 MHz
Soglosnov, et al., 2004, personal corresp.

12. Crab giant pulse at 15 GHz

13. Component positions
HFCs pulse phase linearly dependent on frequency

14. Giant pulse occur-rence
Black:
averaged
intensity
Red:
peak
histogram
Black: Averaged intensity
Red: Location of each period’s peak. Note: no peaks at HFCs.

15. MP-IP frequency dependence
Main Pulse
2.85 GHz
8.65 GHz
Interpulse
Low freq IP is gone at 2.85 GHz
MP nearly gone at high freqs
WAPP data by Cordes, et al.
Pulse Phase

16. 5-GHz average pulse polarization
Linear Polarization
Circular Polarization
Total Intensity (Jy)
MP: unpolarized?
IP and HFCs100% linearly polarized.

17. Giant main pulse polarization
1425 MHz,VLA
Position angle makes no sense.Total polarization small.

18. Amplitude distribution
0.43 GHz
8.8 GHz
Main pulse
Interpulse
Low freqs: Mostly MPs
High freqs: Mostly Ips, but when MP is there, it can be very large.
Main pulse
Interpulse

19. Giant pulse bandwidth? VLA to Green BankGB
VLA

20. Crab (1996, VLA to Green Bank)
Systematic delay VLA to GB not known exactly. Scatter about mean is shown.

21. Crab giant pulse, 1435 to 4885 MHz
1435 MHz
4885 MHz

22. Dispersed giant pulse, 9250 MHz
RCP
2.2 GHz bandwidth.
LCP

23. Summary so far: Multiple, frequency dependent components Polarization:
Main pulse: Weak or random
Interpulse: 100% linear at high frequencies
Amplitude: More interpulses at 9 GHz
Bandwidth: Wide

24. “We know why they pulse, but why do they shine?” --Sandra Faber

25. Standard pulsar model
Rotation produces the pulsing, and if the rotational and magnetic axes are orthogonal, you can get two pulses per period.

26. Shot noise model for pulsar signals (Cordes, 1976)
Amplitude modulated noise s(t) = a(t) n(t)
Noise:
n(t) = ensemble of N shot pulses per time resolution interval, Dt.
Typical observations: N >> 1 (white Gaussian noise by Central Limit Theorem)
Objective: very small Dt,  N ~ 1
Never thought we would get to N=1

27. Emission mechanisms Emission Process Saturation Mechanism
Saturation Timescale (ms)
Coherent curvature
Beam trapping
0.01 – 1
Plasma turbulence
Soliton collapse
0.001
Maser
Quasilinear diffusion
0.1

28. Collapsing soliton prediction I
“a soliton is a self-reinforcing solitary wave caused by a delicate balance between nonlinear and dispersive effects in the medium.” Wikipedia

29. Prediction II

30. Predicted ACF of nanostructure
Now we have a reason to look for short time structure. Is it there?

31. History II Microstructure discovered by
Craft, Comella and Drake at Arecibo
(1968, Nature, 218, 1122)

32. First microstructure (Craft, 1968)
Note date: This was only 3.5 months after pulsars were announced

33. History III Coherent dedispersion: Original idea from Ken Bowles, UCSD
First application:
Hankins and Rickett, Dec 1970 at Arecibo
Bowles: Heard about pulsars at IEEE Meeting in March Said” Those clever radar guys at Arecibo will think of ‘coherent dedispersion’ real soon. We have to beat them to it.”

34. Micropulses coherently dedispersed (Arecibo, 1970)

35. Dedispersion principles

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

37. Crab Giant pulse at 430 MHz, Arecibo, (1973)

38. Giant pulses at 4.9 GHz, Arecibo, 2002
The abscissa of this plot is synchronous with the pulsar rotation rate. Note the jitter in arrival time.
Note pulse #3, the bushy one.

39. Crab giant pulse (pulse #3)

40. Nanostructure
Click to increase time resolution by factors of 10.

41. A Crab “Megapulse”, 9.25 GHz 0.4 ns 2.2 Mega-Jansky pulse
Duration: 0.4 nanoseconds
0.4 ns

42. Megapulse statistics Duration: 0.4 ns implies source size of 12 cm.
Peak power: 10% of total power from the Sun
Equivalent brightness temperature: 21041 K
Energy density: 61025 2 erg cm3,
(beam angle)

43. Mega pulse source size Soccer ball: 22 cm = 8 3/4 in.
Softball:
10 cm = 3 3/4 in

44. Dynamic spectra, dispersion removed

45. Intensity and spectrum of a main pulse

46. Intensity and spectrum of an interpulse

47. Main pulse Interpulse Refreshing your short-term memory:
These two pulses were recorded within 12 minutes of each other and processed exactly the same, except that the interpulse intensity was smoothed more than the main pulse.
First assumptionwas: the bands are equally spaced : Bracewell’s “shah” function. OK. Langmuir waves producing an impulse train?

48. Interpulse spectral band spacing proportional to frequency

49. Interpulse with dispersion corrected
Note that the intensity rise time is now considerably shorter and there is more significant detail in the pulse.

50. Crab dispersion measure vs. time
This is a whole colloquium in itself, but the thing I want to point out is that the IP DM > MP DM.

51. Comparison: Main pulse and interpulse
Temporal structure:
Nanoshots
Broad, smooth
Radio spectrum structure:
1/nanoshots
Proportionally spaced bands, 
Dispersion:
Similar to average profile
DMIP/DMMP 
Polarization:
Weak on microsecond scale
Strongly linearly polarized

52. Interpulse Simple Models, I
Complication: Proportional band spacing rules out temporal impulse train.
Resonant cyclotron emission -- like “zebra bands” in solar flares?
Problem: Requires high altitude emission to bring cyclotron emission down to radio band.

53. Interpulse Simple Models, II
Geometrical models: Interference fringes?
Requires:
Broadband radiation source, bandwidth > 5 GHz, i.e., wider than existing emission models predict.
Long-lived plasma structure. Only magnetic field can provide long-term (>1 s) stability.
Split path length difference of only a few cm.
Must allow pulse phase jitter.

54. Simple dipole magnetic field
Standard pulsar model
Simple dipole magnetic field

55. Effects of additional poles?
Here are two configurations of quadrupoles computed by my colleague Jean Eilek at New Mexico Tech. Just adding one additional set of poles complicates the geometry enormously.

56. To do:
Calibrated polarimetry -- to aid understanding of geometry and magnetic field configurations.
Record wider bandwidths. What is the full emission bandwidth? Critical for identifying emission physics.

57. Conclusions Crab main pulse and interpulse are radically different.
Main pulse produces the strongest pulses in the Universe from tiny radiating entities.
Interpulse proportional band spacing - interference ducted from emission source by odd magnetic field configuration? Multiple poles?
Weatherall’s plasma turbulence model: probably correct, with qualifications.

58. The End

59. Giant pulse intrinsic widths and scattering widths

60. Implications Smallest entities ever detected outside the solar system:
D=cDt = (3  108 cm/s) (2  10-9 s) = 60 cm
Brightest radio pulses in the Universe (equivalent brightness temperature=1037 K
Energy density of 2-ns  103-Jy pulse
= 2 x 1014 erg/cm3 (comparable to plasma energy density, implies nonlinear, collective emission process)

61. Next steps 2. Extragalactic pulsars?
See:
“The Brightest Pulses in the Universe”,
Cordes, et al., in press (2003)