[Paper Review] Relativistic Binary Pulsar B1913+16: Thirty Years of Observations and Analysis

J. M. Weisberg, J. H. Taylor|arXiv (Cornell University)|Jul 7, 2004

Pulsars and Gravitational Waves ResearchPhysics and Astronomy108 citations

TL;DR

This paper presents 30 years of timing and polarization data from the relativistic binary pulsar PSR B1913+16, demonstrating precise agreement (within 0.2%) between observed orbital decay and general relativity’s prediction of gravitational wave emission. It further reveals geodetic precession causing measurable changes in pulse shape, enabling a detailed model of the pulsar’s hourglass-shaped emission beam, which is elongated in latitude and pinched in longitude near its center.

ABSTRACT

We describe results derived from thirty years of observations of PSR B1913+16. Together with the Keplerian orbital parameters, measurements of the relativistic periastron advance and a combination of gravitational redshift and time dilation yield the stellar masses with high accuracy. The measured rate of change of orbital period agrees with that expected from the emission of gravitational radiation, according to general relativity, to within about 0.2 percent. Systematic effects depending on the pulsar distance and on poorly known galactic constants now dominate the error budget, so tighter bounds will be difficult to obtain. Geodetic precession of the pulsar spin axis leads to secular changes in pulse shape as the pulsar-observer geometry changes. This effect makes it possible to model the two-dimensional structure of the beam. We find that the beam is elongated in the latitude direction and appears to be pinched in longitude near its center.

Motivation & Objective

• To test general relativity through long-term timing measurements of the relativistic binary pulsar PSR B1913+16.
• To determine the masses of the pulsar and its companion with high accuracy using relativistic orbital parameters.
• To investigate the effects of geodetic precession on pulse shape and use them to model the three-dimensional structure of the pulsar's emission beam.
• To constrain the beam geometry and assess the impact of systematic uncertainties, particularly from galactic constants and pulsar distance.

Proposed method

• Time-of-arrival measurements of radio pulses from PSR B1913+16 were collected using the Arecibo Observatory with WAPP backends, achieving 13 μs timing precision in four 100 MHz bands.
• The TEMPO timing software was used to fit a relativistic timing model with 18 parameters, including orbital, astrometric, and spin parameters, based on the Damour & Deruelle (1985, 1986) formalism.
• The rate of change of orbital period ($\dot{P}_b$) was measured and corrected for galactic acceleration effects using the solar system’s motion relative to the pulsar system.
• Theoretical $\dot{P}_b$ under general relativity was computed using the Peters & Matthews (1963) formula, incorporating measured orbital elements and derived masses.
• Pulse shape evolution over time was analyzed using coherent de-dispersion and profile decomposition into even and odd components about the profile center.
• A noncircular, hourglass-shaped conal beam model was fitted to the even components of the 1400 MHz profiles, with beam elongation and longitudinal pinching as key features.

Experimental results

Research questions

• RQ1 To what extent does the observed orbital decay of PSR B1913+16 match the general relativistic prediction of energy loss via gravitational wave emission?
• RQ2 How do secular changes in pulse shape over 30 years reflect the geodetic precession of the pulsar’s spin axis?
• RQ3 What is the three-dimensional structure of the pulsar’s radio emission beam, and how does it deviate from a simple conical or circular beam?
• RQ4 What are the dominant systematic uncertainties limiting the precision of gravitational wave tests in this system?
• RQ5 How does the presence and evolution of a core component at lower frequencies (430 MHz) inform the beam geometry and line-of-sight motion?

Key findings

• The measured rate of change of orbital period ($\dot{P}_b = -2.4184 \pm 0.0009 \times 10^{-12}$ s/s) agrees with the general relativistic prediction ($\dot{P}_{b,GR} = -2.40242 \pm 0.00002 \times 10^{-12}$ s/s) to within 0.2%, after correcting for galactic acceleration.
• The corrected ratio $\dot{P}_{b,\text{corrected}} / \dot{P}_{b,GR} = 1.0013 \pm 0.0021$ implies consistency with general relativity at the $(0.13 \pm 0.21)$% level.
• The pulsar and companion masses were determined as $m_p = 1.4414 \pm 0.0002$ and $m_c = 1.3867 \pm 0.0002$ solar masses, respectively, with uncertainties dominated by $G$.
• Geodetic precession causes the line of sight to drift across the beam, resulting in measurable pulse shape changes over 30 years, with the separation between main pulse components shrinking since the mid-1990s.
• The emission beam is best modeled as an hourglass-shaped, noncircular cone, elongated in the latitude direction and pinched in longitude near its center, with a misalignment of ~20° between spin and orbital angular momentum.
• At 430 MHz, the core component of the pulse profile faded significantly from 1980 to 2003, supporting the model in which the line of sight is precessing away from a centered core beam.