Measuring Dispersion in Signals from the Crab Pulsar

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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
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FORS Team, 8.2 m VLT, ESO
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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
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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
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Dispersion

• Dispersion velocity of light depends on
  frequency
• Radio wave propagation through ionized charges
  undergoes dispersion
• For cold plasma, lower frequencies propagate
  slower

• Measured using the time of arrival difference
  between pulses at two frequencies

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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.

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Observations
Observed 20 days using Arecibo Radio Telescope,
2002 - 2007
Observed 9 days using Very Large Array,1993 and
1999

• 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

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Measuring Dispersion

1. Remove dispersion using avg-profile DM
2. Cross-correlate pulses
3. Measure the CCF-peak offset from zero-lag
4. Offset gt true DM

Offset typically lt 1 µs
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Single pulse and Avg. profile DM
Bright-pulse DM follows the same long-time-scale
trend as average profile DM
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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

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• 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!
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Interpulse DM Frequency Dependence
Main pulse
Interpulse
Interpulse DM has a weak tendency to increase
with frequency gt suggests non-cold-plasma
dispersion
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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.

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Compare with Magnetosphere Model 1

• A strong radio wave gt relativistic plasma
  motion gt 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.

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Compare with Magnetosphere Model 2

• Strong magnetic field gt change in particle
  motion gt change dispersion law
• Index of refraction (Lyutikov Parikh, 2000) gt
  DMmag
• Result DMmag lt 0 for all radio frequencies
• My data shows the opposite DMmag DMIP gt 0

This dispersion model does not apply to my data.
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Dispersion Conclusions
Main Pulse Interpulse
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

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The Big Picture 1
Time scale info shows Frequency info shows
Variability in microbursts Small delay echoes Unexpected dispersion variability IP dispersion increases with frequency (new dispersion law!) Microburst have finite bandwidth, lt 4 GHz
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The Big Picture 2

• Variability shows that something changes on short
  scales.
• This something cannot be in the interstellar
  medium gt something is changing in the star
• Differences between main pulse and interpulse gt
  variability does not affect all emission
• It may be localized within the magnetosphere

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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

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Example pulses, just for fun