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What Goes into a Pulsar Timing Model? David Nice Physics Department, Princeton University Pulsar Timing Array: A Nanohertz Gravitational Wave Telescope Center for Gravitational Wave Physics Penn State University 21 July 2005

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Propagation of gravitational wave Basic idea: 1.Pulses travel from pulsar to telescope. 2.The passage of a gravitational wave perturbs the time-of-flight of the pulse. The perturbation is complicated! (GW period

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Page 1: What Goes into a Pulsar Timing Model? David Nice Physics Department, Princeton University Pulsar Timing Array: A Nanohertz Gravitational Wave Telescope

What Goes into a Pulsar Timing Model?

David NicePhysics Department, Princeton University

Pulsar Timing Array: A Nanohertz Gravitational Wave TelescopeCenter for Gravitational Wave PhysicsPenn State University21 July 2005

Page 2: What Goes into a Pulsar Timing Model? David Nice Physics Department, Princeton University Pulsar Timing Array: A Nanohertz Gravitational Wave Telescope

Observing The Pulsar Signal

Page 3: What Goes into a Pulsar Timing Model? David Nice Physics Department, Princeton University Pulsar Timing Array: A Nanohertz Gravitational Wave Telescope

Observing The Pulsar Signal

Propagation of gravitational wave

Basic idea:1. Pulses travel from pulsar to telescope. 2. The passage of a gravitational wave perturbs the time-of-flight of the pulse.

The perturbation is complicated! (GW period << pulse travel time)3. Search for patterns in pulse ‘arrival times’ indicative of gravitational waves.4. Many other phenomena affect measured arrival times. Analyzing all these

phenomena is called ‘pulse timing’ and is the subject of this talk.

Page 4: What Goes into a Pulsar Timing Model? David Nice Physics Department, Princeton University Pulsar Timing Array: A Nanohertz Gravitational Wave Telescope

Observing The Pulsar Signal

PSR J1713+0747Splaver et al. 2005ApJ 620: 405astro-ph/0410488

Page 5: What Goes into a Pulsar Timing Model? David Nice Physics Department, Princeton University Pulsar Timing Array: A Nanohertz Gravitational Wave Telescope

A long-wavelength gravitational wave might continuously increase the proper distance traveled by a pulsar over the entire observation program. The plot shows an increase in travel time of 2 s over 6 years, a distance of only 600 m (compared to pulsar distance of 1.1 kpc, for l/l=610-16).Exactly the same thing would be observed if the pulsar rotation period were slightly longer, 4.57013652508278 ms instead of 4.57013652508274 ms (1 part in 1014). The period is known only from timing data always need to fit out a linear term in timing measurements to find pulse period a perturbation due to gravitational waves which is linear in time cannot be detected

Page 6: What Goes into a Pulsar Timing Model? David Nice Physics Department, Princeton University Pulsar Timing Array: A Nanohertz Gravitational Wave Telescope

Pulsar rotation slows down over time due to magnetic dipole rotation. The ‘spin-down’ rate is not known a priori.The plot shows what the residuals of J1713+0747 look like if we forget to include spin-down. As the pulsar slows down, pulses are delayed by an amount quadratic in time.The spin-down rate is known only from timing data always need to fit out a quadratic term in timing measurements to find pulse period a perturbation due to gravitational waves which is quadratic in time cannot be detected

Page 7: What Goes into a Pulsar Timing Model? David Nice Physics Department, Princeton University Pulsar Timing Array: A Nanohertz Gravitational Wave Telescope

rotation periodrotation period derivative

Page 8: What Goes into a Pulsar Timing Model? David Nice Physics Department, Princeton University Pulsar Timing Array: A Nanohertz Gravitational Wave Telescope

sun

Page 9: What Goes into a Pulsar Timing Model? David Nice Physics Department, Princeton University Pulsar Timing Array: A Nanohertz Gravitational Wave Telescope

sun

Delays of ~500 s due to time-of-flight across the Earth’s orbit.The amplitude and phase of this delay depend on the pulsar position.Position known only from timing data always need to fit annual terms out of timing solution a perturbation due to gravitational waves with ~1 yr period cannot be detected

Page 10: What Goes into a Pulsar Timing Model? David Nice Physics Department, Princeton University Pulsar Timing Array: A Nanohertz Gravitational Wave Telescope

sun

Other astrometric phenomena:

Proper Motion

Page 11: What Goes into a Pulsar Timing Model? David Nice Physics Department, Princeton University Pulsar Timing Array: A Nanohertz Gravitational Wave Telescope

sun

Other astrometric phenomena:

Proper Motion

Parallax

Curved wavefronts

Page 12: What Goes into a Pulsar Timing Model? David Nice Physics Department, Princeton University Pulsar Timing Array: A Nanohertz Gravitational Wave Telescope

Measurement of a pulse time of arrival at the observatory is a relativistic event.It must be transformed to an inertial frame: that of the solar system barycenter.

Time transfer: Observatory clock GPS UT TDBPosition transfer: For Earth and Sun positions, use a solar system ephemeris, e.g., JPL ‘DE405’ For earth orientation (UT1, etc.), use IERS bulletin B

sun

Page 13: What Goes into a Pulsar Timing Model? David Nice Physics Department, Princeton University Pulsar Timing Array: A Nanohertz Gravitational Wave Telescope

PSR J1713+0747 analyzed using DE 405 solar system ephemeris

PSR J1713+0747 analyzed using previous-generation DE 200 solar system ephemeris.

~1s timing errors 300 m errors in Earth position.

Page 14: What Goes into a Pulsar Timing Model? David Nice Physics Department, Princeton University Pulsar Timing Array: A Nanohertz Gravitational Wave Telescope

sun

rotation periodrotation period derivative

positionproper motionparallax

Page 15: What Goes into a Pulsar Timing Model? David Nice Physics Department, Princeton University Pulsar Timing Array: A Nanohertz Gravitational Wave Telescope
Page 16: What Goes into a Pulsar Timing Model? David Nice Physics Department, Princeton University Pulsar Timing Array: A Nanohertz Gravitational Wave Telescope

Precession

Shapiro Delay

Gravitational Radiation

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)(11

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cGP b

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Grav Redshift/Time Dilationr

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2 mm+2mmP

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Page 17: What Goes into a Pulsar Timing Model? David Nice Physics Department, Princeton University Pulsar Timing Array: A Nanohertz Gravitational Wave Telescope

PSR J1713+0747 Shapiro Delay

Page 18: What Goes into a Pulsar Timing Model? David Nice Physics Department, Princeton University Pulsar Timing Array: A Nanohertz Gravitational Wave Telescope

Apparent inverse correlation between orbital period and pulsar mass.

(Nice et al., ApJ, submitted)

Page 19: What Goes into a Pulsar Timing Model? David Nice Physics Department, Princeton University Pulsar Timing Array: A Nanohertz Gravitational Wave Telescope

sun

rotation periodrotation period derivative

Keplerian orbital elements relativistic orbital elements

kinematic perturbations of orbital elements (secular and annual phenomena)

positionproper motionparallax

Page 20: What Goes into a Pulsar Timing Model? David Nice Physics Department, Princeton University Pulsar Timing Array: A Nanohertz Gravitational Wave Telescope

Interstellar Dispersion

431 MHz

430 MHz

column density of electrons: DM = ne(l) dl excess propagation time: t (sec) = DM / 2.4110–4 [f(MHz)]2

Page 21: What Goes into a Pulsar Timing Model? David Nice Physics Department, Princeton University Pulsar Timing Array: A Nanohertz Gravitational Wave Telescope

DM Variations in PSR J0621+1002 timing (Splaver et al., ApJ 581: 509, astro-ph/0208281)

Page 22: What Goes into a Pulsar Timing Model? David Nice Physics Department, Princeton University Pulsar Timing Array: A Nanohertz Gravitational Wave Telescope

Figure 1. Polar plots of solar wind speed as a function of latitude for Ulysses' first two orbits. Sunspot number (bottom panel) shows that the first orbit occurred through the solar cycle declining phase and minimum while the second orbit spanned solar maximum. Both are plotted over solar images characteristic of solar minimum (8/17/96) and maximum (12/07/00); from the center out, these images are from the Solar and Heliospheric Observatory (SOHO) Extreme ultraviolet Imaging Telescope (Fe XII at 195 Å), the Mauna Loa K-coronameter (700950 nm), and the SOHO C2 Large Angle Spectrometric Coronagraph (white light)

Figure 2. Twelve-hour running averaged solar wind proton speed, scaled density and temperature, and alpha particle to proton ratio as a function of latitude for the most recent part of the Ulysses orbit (black line) and the equivalent portion from Ulysses' first orbit (red line).

D J McComas et al 2003. Geophys Res Lett 30, 1517

Page 23: What Goes into a Pulsar Timing Model? David Nice Physics Department, Princeton University Pulsar Timing Array: A Nanohertz Gravitational Wave Telescope

sun

rotation periodrotation period derivative

Keplerian orbital elements relativistic orbital elements

kinematic perturbations of orbital elements (secular and annual phenomena)

dispersion measuredispersion meas. variations

positionproper motionparallax

solar electron density

Page 24: What Goes into a Pulsar Timing Model? David Nice Physics Department, Princeton University Pulsar Timing Array: A Nanohertz Gravitational Wave Telescope

The examples so far are from 6 years of 1713+0747 data.If all the phenomena discussed so far are removed from those pulse arrival times, the remaining residuals look nearly flat.

But: incorporating two years of additional data (taken several years earlier), shows that the residuals are not flat over longer time scales.

This is a common feature of pulsar timing data, called `timing noise.’ Timing noise is probably indicative of irregularities in pulsar rotation; its physical origin remains unclear.

Page 25: What Goes into a Pulsar Timing Model? David Nice Physics Department, Princeton University Pulsar Timing Array: A Nanohertz Gravitational Wave Telescope

The z timing noise statistic applied to J1713+0747

Page 26: What Goes into a Pulsar Timing Model? David Nice Physics Department, Princeton University Pulsar Timing Array: A Nanohertz Gravitational Wave Telescope

Timing noise and DM variations of the original millisecond pulsar, B1937+21

Page 27: What Goes into a Pulsar Timing Model? David Nice Physics Department, Princeton University Pulsar Timing Array: A Nanohertz Gravitational Wave Telescope

Timing noise in several young pulsars.

Page 28: What Goes into a Pulsar Timing Model? David Nice Physics Department, Princeton University Pulsar Timing Array: A Nanohertz Gravitational Wave Telescope

Single

BinaryHigh EccentricityLow Eccentricity

Page 29: What Goes into a Pulsar Timing Model? David Nice Physics Department, Princeton University Pulsar Timing Array: A Nanohertz Gravitational Wave Telescope

Birth

Single

BinaryHigh EccentricityLow Eccentricity

Page 30: What Goes into a Pulsar Timing Model? David Nice Physics Department, Princeton University Pulsar Timing Array: A Nanohertz Gravitational Wave Telescope

Birth

Death

Single

BinaryHigh EccentricityLow Eccentricity

Page 31: What Goes into a Pulsar Timing Model? David Nice Physics Department, Princeton University Pulsar Timing Array: A Nanohertz Gravitational Wave Telescope

Birth

Death

RebirthSpin-up

Single

BinaryHigh EccentricityLow Eccentricity

Page 32: What Goes into a Pulsar Timing Model? David Nice Physics Department, Princeton University Pulsar Timing Array: A Nanohertz Gravitational Wave Telescope

Single

BinaryHigh EccentricityLow Eccentricity

Page 33: What Goes into a Pulsar Timing Model? David Nice Physics Department, Princeton University Pulsar Timing Array: A Nanohertz Gravitational Wave Telescope

Single

BinaryHigh EccentricityLow Eccentricity

Smaller MeasurementUncertainty

Page 34: What Goes into a Pulsar Timing Model? David Nice Physics Department, Princeton University Pulsar Timing Array: A Nanohertz Gravitational Wave Telescope

Single

BinaryHigh EccentricityLow Eccentricity

Smaller MeasurementUncertainty

Less

Tim

ing

Noi

se

Page 35: What Goes into a Pulsar Timing Model? David Nice Physics Department, Princeton University Pulsar Timing Array: A Nanohertz Gravitational Wave Telescope

sun

rotation periodrotation period derivative

Keplerian orbital elements relativistic orbital elements

kinematic perturbations of orbital elements (secular and annual phenomena)

dispersion measuredispersion meas. variations

positionproper motionparallax

solar electron density

Fit for all of these simultaneously to find the best pulsar timing solution (‘tempo’), then examine the residuals for signs of gravitational waves.


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