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Measuring Dispersion in Signals from the Crab Pulsar Jared Crossley National Radio Astronomy Observatory Tim Hankins & Jean Eilek New Mexico Tech FORS Team, 8.2 m VLT, ESO FORS Team, 8.2 m VLT, ESO 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) 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-timeresolution single pulses Dispersion • Dispersion = velocity of light depends on frequency • Radio wave propagation through ionized charges undergoes dispersion • For cold plasma, lower frequencies propagate slower QuickTime™ and a decompressor are needed to see this picture. QuickTime™ and a decompressor are needed to see this picture. • Measured using the time of arrival difference between pulses at two frequencies 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. Observations Observed 9 days using Very Large Array,1993 and 1999 Observed 20 days using Arecibo Radio Telescope, 2002 - 2007 QuickTime™ and a decompressor are needed to see this picture. QuickTime™ and a decompressor are needed to see this picture. •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 Measuring Dispersion 1. Remove dispersion using avg-profile DM 2. Cross-correlate pulses 3. Measure the CCFpeak offset from zerolag 4. Offset true <DM Offset ==> typically 1 µs Bright-pulse DM follows the same long-time-scale trend as average profile DM •Main pulse DM is closer to the avg-profile DM •Interpulse DM is larger and more scattered Suggests interpulse has additional, variable dispersion Main pulse Interpulse •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 Location: The pulsar magnetosphere - the region very close to the star - is the only place where variations occur this rapidly! Main pulse Interpulse Interpulse DM has a weak tendency to increase with frequency ==> suggests non-cold-plasma dispersion 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. 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. Compare with Magnetosphere Model #2 •Strong magnetic field ==> change in particle motion ==> change dispersion law •Index of refraction (Lyutikov & Parikh, 2000) ==> DMmag •Result: DMmag < 0 for all radio frequencies •My data shows the opposite: DMmag = DMIP > 0 This dispersion model does not apply to my data. Dispersion Conclusions Main Pulse Interpulse Less variable; consistent with DM larger and more variable average profile DM 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 The Big Picture 1 Time scale info shows •Variability in microbursts •Small delay echoes •Unexpected dispersion variability Frequency info shows •IP dispersion increases with frequency (new dispersion law!) •Microburst have finite bandwidth, < 4 GHz 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 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