1. Measuring Dispersion in Signals from the Crab Pulsar Jared Crossley National Radio Astronomy Observatory Tim Hankins & Jean Eilek New Mexico Tech Jared Crossley National Radio Astronomy Observatory Tim Hankins & Jean Eilek New Mexico Tech FORS Team, 8.2 m VLT, ESO

3. Pulsar Basics Pulsars are magnetized neutron stars that rotate rapidly Magnetic field is a dipole (north and south pole) Light is emitted in a beam from the magnetic poles 1800+ pulsars have been found since 1968 Imagine the Universe! at NASA/GSFC Michael Kramer (University of Manchester)

4. The Crab Pulsar is Unique Only 6000 light years away Only 956 years old 2 pulses per rotation: “main pulse” and “interpulse” Occasional very bright pulses -- over 1 million times brighter than average Very Bright pulses We can observe high-time- resolution single pulses

5. Dispersion Measured using the time of arrival difference between pulses at two frequencies Dispersion = velocity of light depends on frequency Radio wave propagation through ionized charges undergoes dispersion For cold plasma, lower frequencies propagate slower

6. Dispersion Dispersion is important because: It must be properly removed to see pulse structure in its original form Tells us about the medium between pulsar and Earth Previous studies have measured dispersion for pulse ensembles, averaged over minutes to hours of observation. My research is a study of dispersion in single pulses, which occur on microsecond time scales. We can now see how dispersion changes over very short times.

7. Observations We record data using customized “back-end” instrumentation for high time resolution measurements Only the brightest pulses are recorded Recorded pulses at observing frequencies 1 to 10 GHz Observed 9 days using Very Large Array,1993 and 1999 Observed 20 days using Arecibo Radio Telescope, 2002 - 2007

8. Measuring Dispersion 1.Remove dispersion using avg-profile DM 2.Cross-correlate pulses 3.Measure the CCF- peak offset from zero- lag 4.Offset ==> true DM Offset typically < 1 µs

9. Single pulse and Avg. profile DM Bright-pulse DM follows the same long-time-scale trend as average profile DM

10. Close up of DM vs. Time Main pulse DM is closer to the avg-profile DM Interpulse DM is larger and more scattered Suggests interpulse has additional, variable dispersion

11. Main pulseInterpulse DM scatter is larger than single pulse uncertainty Interpulse DM scatter is larger than main pulse scatter No systematic variation with time or pulsar phase The pulsar magnetosphere - the region very close to the star - is the only place where variations occur this rapidly! Location:

12. Interpulse DM Frequency Dependence Interpulse DM has a weak tendency to increase with frequency ==> suggests non-cold-plasma dispersion Main pulse Interpulse

13. Measure Alternative Dispersion Law Two dispersion sources: Assume magnetosphere dispersion is power law: x = 2 for cold plasma Measure x using interpulse data: Scatter in single-pulse DM data produces wide range of x.

14. Compare with Magnetosphere Model #1 A strong radio wave ==> relativistic plasma motion ==> change in dispersion law Index of refraction (Wu & Chian, 1995) convert to DM: B depends on magnetospheric conditions My data shows no correlation between DM and flux Correlation may be hidden by DM variability from some other phenomena I measure an upper limit on B to constrain magnetospheric conditions.

15. Strong magnetic field ==> change in particle motion ==> change dispersion law Index of refraction (Lyutikov & Parikh, 2000) ==> DM mag Result: DM mag < 0 for all radio frequencies My data shows the opposite: DM mag = DM IP > 0 This dispersion model does not apply to my data. Compare with Magnetosphere Model #2

16. Dispersion Conclusions Main PulseInterpulse Less variable; consistent with average profile DM DM larger and more variable than main pulse No dependence on observing frequency DM increases slightly with increasing frequency Additional, variable interpulse dispersion, likely from magnetosphere Compare interpulse DM with mag-sphere dispersion models: –Strong radio waves: I find no correlation between DM and flux –Strong magnetic field: Predicts less DM, but I see more DM

17. The Big Picture 1 Time scale info showsFrequency info shows Variability in microbursts Small delay echoes Unexpected dispersion variability IP dispersion increases with frequency (new dispersion law!) Microburst have finite bandwidth, < 4 GHz

18. The Big Picture 2 Variability shows that something changes on short scales. This something cannot be in the interstellar medium ==> something is changing in the star Differences between main pulse and interpulse ==> variability does not affect all emission –It may be localized within the magnetosphere

19. Next Steps Additional observations –Good spectral coverage Further constrain microburst bandwidth Confirm or refute magnetospheric dispersion –Extend microburst study to interpulses –Better quantify the microburst flux-width upper limit Archival data may reveal additional pulse echo events New theory is needed to explain –New information from microburst study –Magnetospheric dispersion

20. Example pulses, just for fun