What Goes into a Pulsar Timing Model? David Nice Physics Department, Princeton University Pulsar...

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

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.

Observing The Pulsar Signal

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

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

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

rotation periodrotation period derivative

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

Other astrometric phenomena:

Proper Motion

Other astrometric phenomena:

Proper Motion

Parallax

Curved wavefronts

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

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.

positionproper motionparallax

Precession

Shapiro Delay

Gravitational Radiation

023 sinsin1ln2 imcGt

5 mmmm

Grav Redshift/Time Dilationr

)(2 21

2 mm+2mmP

e )(2m

PSR J1713+0747 Shapiro Delay

Apparent inverse correlation between orbital period and pulsar mass.

(Nice et al., ApJ, submitted)

Keplerian orbital elements relativistic orbital elements

kinematic perturbations of orbital elements (secular and annual phenomena)

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

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

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

dispersion measuredispersion meas. variations

solar electron density

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.

The z timing noise statistic applied to J1713+0747

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

Timing noise in several young pulsars.

Single

BinaryHigh EccentricityLow Eccentricity

Single

RebirthSpin-up

Single

Smaller MeasurementUncertainty

Single

Smaller MeasurementUncertainty

dispersion measuredispersion meas. variations

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.

What Goes into a Pulsar Timing Model? David Nice Physics Department, Princeton University Pulsar...

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