Interstellar Medium Mitigation
Techniques in Pulsar Timing Arrays
Lina Levin Preston
West Virginia University
LISA symposium – 21 May 2014
•!Dispersion
•! Characteristics
•! Correction Methods
•! ISM models
•!Scattering
•! Characteristics
•! Magnitudes
•! Correction Methods
•!Summary
Overview
LISA symposium – 21 May 2014
Efforts in all areas of ISM and
DM mitigation are underway in EPTA, PPTA and NANOGrav
Examples in this talk are from
NANOGrav data
Pulsar radio emission interacts with the ISM
mainly in two ways:
- Dispersion
From the overall integrated column density of free electrons
- Scattering
Due to spatial inhomogeneities in the ISM
The Interstellar Medium
LISA symposium – 21 May 2014
Pulsar radio emission interacts with the ISM
mainly in two ways:
- Dispersion
From the overall integrated column density of free electrons
- Scattering
Due to spatial inhomogeneities in the ISM
The Interstellar Medium
LISA symposium – 21 May 2014
Dispersion Measure
LISA symposium – 21 May 2014
The broad band radio emission from a pulsar
interacts with the ISM plasma
Group velocity
Plasma frequency
The electron density in the Galactic plane
Dispersion Measure definition
Time delay of the wave due to the DM
Dispersion Measure
LISA symposium – 21 May 2014
Lorimer & Kramer (2005)
Dispersion Measure
LISA symposium – 21 May 2014
Pulsar distance can be inferred from its DM
Higher DM does not necessarily mean larger distance
Models of the free electrons in the Galaxy are used to predict distance, most
comprehensive model to date is the NE2001-model (Cordes & Lazio 2002)
Scattering
LISA symposium – 21 May 2014
-! Mainly directly observed in high
DM pulsars
!! not included in PTAs
-! Indirectly through dynamic
spectra
- Scattering proportional to v-4
Lorimer & Kramer (2005)
Pulsar spectrum
LISA symposium – 21 May 2014
Maron et al. (2000)
Typical ordinary pulsar spectrum
Average pulsar spectral index: -1.4
Scattering proportional to v-4
=> PTA pulsars are chosen to be
observed at frequencies where they
are bright, but not too scattered
To accurately determine the DM, PTAs observe pulsars in the array
at multiple frequency bands, at a maximum of a few days apart
LISA symposium – 21 May 2014
GASP
64 MHz
GUPPI
800 MHz
GUPPI
200 MHz
GASP
64 MHz
Dispersion Measure Correction
LISA symposium – 21 May 2014
The pulsar, the interstellar plasma and the earth
all have different velocities => DM value
measured for a pulsar varies with time
Demorest et al. in prep
J1600-3053
Pulsar radio emission interacts with the ISM
mainly in two ways:
- Dispersion
From the overall integrated column density of free electrons
- Scattering
Due to spatial inhomogeneities in the ISM
The Interstellar Medium
LISA symposium – 21 May 2014
The Thin Screen Model
Lorimer & Kramer 2005
!
"#d$
1
2%&d
!
"d#D$
d
2
2c
!
"td #c
2$%Veff
D
2c& d
Pulse broadening time Scintillation bandwidth Scintillation timescale
Veff
LISA symposium – 21 May 2014
Scattering
LISA symposium – 21 May 2014
Multi-path propagation effects are produced due to
spatial inhomogeneities in the ISM
Most important manifestations for pulsars:
- Refractive Scintillation
- Diffractive Scintillation
- Pulse Broadening
Multi-path scattering
LISA symposium – 21 May 2014
Refractive scintillation
Diffractive scintillation
Dispersion
Measure
Cordes & Shannon 2010
LISA symposium – 21 May 2014
Refractive scintillation
Diffractive scintillation
Dispersion
Measure
!
"tPBF
!
"t#PBF
Multipath broadening of pulses from diffraction, from interstellar
density structure of scale size ~106 – 108 cm,
changes slowly with time, on time scales of weeks to months
Diffractive fluctuations of the PBF,
associated with the finite number of scintles in an observation
which is statistically independent between epochs
Diffractive Scintillation
Diffractive Scintillation
LISA symposium – 21 May 2014
- Scale size ~106 - 108 cm
- Measured through scintles in
dynamic spectra
- Limited in time because interference
pattern at observer has a characteristic length scale which becomes a characteristic
time scale due to the relative motion of the
system.
- Limited in frequency because coherent rays have extra scattering delays of ~
which gives rise to a diffractive bandwidth
!
"#d$
1
2%&d
!
"d
LISA symposium – 21 May 2014
Refractive scintillation
Diffractive scintillation
Dispersion
Measure
!
"tAOA
!
"tAOA ,SSBC
Geometrical delay from angle of arrival fluctuations,
Inhomogeneities at refractive scales (1010 – 1012 cm) cause flux
density variations and image distortions.
Associated with transforming measured TOAs to the Solar
System Barycenter. AOA fluctuations changes the effective
position of the source, which introduces an error that would have
a period of 1 year, if it was not time dependent on its own.
!
"t#PBF ,RISSRefractive modulations of the PBF, observationally hard to
distinguish from the PBF error, but conceptually different.
Connected with the expansion and contraction of the ray bundle
by refractive scintillation
LISA symposium – 21 May 2014
Refractive scintillation
Diffractive scintillation
Dispersion
Measure
!
"tDM ,#
Frequency dependent variations of the dispersion measure,
Multi-path scattering causes the volume of the ISM used to
determine the DM to be frequency dependent, and gives rise to
a timing delay proportional to v -23/6.
Multi-path scattering
LISA symposium – 21 May 2014
Refractive scintillation
Diffractive scintillation
Dispersion
Measure
Cordes & Shannon 2010
Scattering delay measurements
•! Dynamic spectra analysis of wideband G/PUPPI data - Intensity of the on-pulse over frequency band and observing time
•! Create 2D Autocorrelation function and fit
with Gaussians - !"d = half-width at half-maximum
- !td = half-width at 1/e
•! Convert !"d into scattering delays
LISA symposium – 21 May 2014
!
"#d$
1
2%&d
LISA symposium – 21 May 2014
Scattering Delay Variations
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Levn et al. in prep
LISA symposium – 21 May 2014 Levin et al. in prep
Scattering Delay Variations
LISA symposium – 21 May 2014
-! For most pulsars the scattering delay variations
are << TOA uncertainty
-! PTA pulsars are chosen to have small values of
scattering (through small DM)
Summary
•! Time-variable Dispersion Measure can be exactly corrected for in
the timing procedure
•! Interstellar density fluctuations cause delays in the pulse time of
arrival, but for most PTA pulsars, scattering delays are much smaller
than median TOA error at L-band
•! While scattering is not a limiting factor for most MSPs today, ability
to correct for scattering delays may become increasingly important
with new wide-band receivers and higher timing accuracy. In
addition, it may allow adding more distant pulsars to the array in the
future.
LISA symposium – 21 May 2014