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Register a new userMeasuring the mass of solar system planets using pulsar timing
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High-precision pulsar timing relies on a solar-system ephemeris in order to convert times of arrival (TOAs) of pulses measured at an observatory to the solar system barycenter. Any error in the conversion to the barycentric TOAs leads to a systematic variation in the observed timing residuals; specifically, an incorrect planetary mass leads to a predominantly sinusoidal variation having a period and phase associated with the planets orbital motion about the Sun. By using an array of pulsars (PSRs J0437-4715, J1744-1134, J1857+0943, J1909-3744), the masses of the planetary systems from Mercury to Saturn have been determined. These masses are consistent with the best-known masses determined by spacecraft observations, with the mass of the Jovian system, 9.547921(2)E-4 Msun, being significantly more accurate than the mass determined from the Pioneer and Voyager spacecraft, and consistent with but less accurate than the value from the Galileo spacecraft. While spacecraft are likely to produce the most accurate measurements for individual solar system bodies, the pulsar technique is sensitive to planetary system masses and has the potential to provide the most accurate values of these masses for some planets.
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Pulsar timing arrays (PTAs) can be used to study the Solar-system ephemeris (SSE), the errors of which can lead to correlated timing residuals and significantly contribute to the PTA noise budget. Most Solar-system studies with PTAs assume the dominance of the term from the shift of the Solar-system barycentre (SSB). However, it is unclear to which extent this approximation can be valid, since the perturbations on the planetary orbits may become important as data precision keeps increasing. To better understand the effects of SSE uncertainties on pulsar timing, we develop the LINIMOSS dynamical model of the Solar system, based on the SSE of Guangyu Li. Using the same input parameters as DE435, the calculated planetary positions by LINIMOSS are compatible with DE435 at centimetre level over a 20-year timespan, which is sufficiently precise for pulsar-timing applications. We utilize LINIMOSS to investigate the effects of SSE errors on pulsar timing in a fully dynamical way, by perturbing one SSE parameter per trial and examining the induced timing residuals. For the outer planets, the timing residuals are dominated by the SSB shift, as assumed in previous work. For the inner planets, the variations in the orbit of the Earth are more prominent, making previously adopted assumptions insufficient. The power spectra of the timing residuals have complex structures, which may introduce false signals in the search of gravitational waves. We also study how to infer the SSE parameters using PTAs, and calculate the accuracy of parameter estimation.
Pulsar-timing analyses are sensitive to errors in the solar-system ephemerides (SSEs) that timing models utilise to estimate the location of the solar-system barycentre, the quasi-inertial reference frame to which all recorded pulse times-of-arrival are referred. Any error in the SSE will affect all pulsars, therefore pulsar timing arrays (PTAs) are a suitable tool to search for such errors and impose independent constraints on relevant physical parameters. We employ the first data release of the International Pulsar Timing Array to constrain the masses of the planet-moons systems and to search for possible unmodelled objects (UMOs) in the solar system. We employ ten SSEs from two independent research groups, derive and compare mass constraints of planetary systems, and derive the first PTA mass constraints on asteroid-belt objects. Constraints on planetary-system masses have been improved by factors of up to 20 from the previous relevant study using the same assumptions, with the mass of the Jovian system measured at 9.5479189(3)$times10^{-4}$ $M_{odot}$. The mass of the dwarf planet Ceres is measured at 4.7(4)$times10^{-10}$ $M_{odot}$. We also present the first sensitivity curves using real data that place generic limits on the masses of UMOs, which can also be used as upper limits on the mass of putative exotic objects. For example, upper limits on dark-matter clumps are comparable to published limits using independent methods. While the constraints on planetary masses derived with all employed SSEs are consistent, we note and discuss differences in the associated timing residuals and UMO sensitivity curves.
In this paper, we investigate the statistical signal-processing algorithm to measure the instant local clock jump from the timing data of multiple pulsars. Our algorithm is based on the framework of Bayesian statistics. In order to make the Bayesian algorithm applicable with limited computational resources, we dedicated our efforts to the analytic marginalization of irrelevant parameters. We found that the widely used parameter for pulsar timing systematics, the `Efac parameter, can be analytically marginalized. This reduces the Gaussian likelihood to a function very similar to the Students $t$-distribution. Our iterative method to solve the maximum likelihood estimator is also explained in the paper. Using pulsar timing data from the Yunnan Kunming 40m radio telescope, we demonstrate the application of the method, where 80-ns level precision for the clock jump can be achieved. Such a precision is comparable to that of current commercial time transferring service using satellites. We expect that the current method could help developing the autonomous pulsar time scale.
The error in the Solar system ephemeris will lead to dipolar correlations in the residuals of pulsar timing array for widely separated pulsars. In this paper, we utilize such correlated signals, and construct a Bayesian data-analysis framework to detect the unknown mass in the Solar system and to measure the orbital parameters. The algorithm is designed to calculate the waveform of the induced pulsar-timing residuals due to the unmodelled objects following the Keplerian orbits in the Solar system. The algorithm incorporates a Bayesian-analysis suit used to simultaneously analyse the pulsar-timing data of multiple pulsars to search for coherent waveforms, evaluate the detection significance of unknown objects, and to measure their parameters. When the object is not detectable, our algorithm can be used to place upper limits on the mass. The algorithm is verified using simulated data sets, and cross-checked with analytical calculations. We also investigate the capability of future pulsar-timing-array experiments in detecting the unknown objects. We expect that the future pulsar timing data can limit the unknown massive objects in the Solar system to be lighter than $10^{-11}$ to $10^{-12}$ $M_{odot}$, or measure the mass of Jovian system to fractional precision of $10^{-8}$ to $10^{-9}$.
Exoplanet surveys have confirmed one of humanitys (and all teenagers) worst fears: we are weird. If our Solar System were observed with present-day Earth technology -- to put our system and exoplanets on the same footing -- Jupiter is the only planet that would be detectable. The statistics of exo-Jupiters indicate that the Solar System is unusual at the ~1% level among Sun-like stars (or ~0.1% among all stars). But why are we different? Successful formation models for both the Solar System and exoplanet systems rely on two key processes: orbital migration and dynamical instability. Systems of close-in super-Earths or sub-Neptunes require substantial radial inward motion of solids either as drifting mm- to cm-sized pebbles or migrating Earth-mass or larger planetary embryos. We argue that, regardless of their formation mode, the late evolution of super-Earth systems involves migration into chains of mean motion resonances, generally followed by instability when the disk dissipates. This pattern is likely also ubiquitous in giant planet systems. We present three models for inner Solar System formation -- the low-mass asteroid belt, Grand Tack, and Early Instability models -- each invoking a combination of migration and instability. We identify bifurcation points in planetary system formation. We present a series of events to explain why our Solar System is so weird. Jupiters core must have formed fast enough to quench the growth of Earths building blocks by blocking the flux of inward-drifting pebbles. The large Jupiter/Saturn mass ratio is rare among giant exoplanets but may be required to maintain Jupiters wide orbit. The giant planets instability must have been gentle, with no close encounters between Jupiter and Saturn, also unusual in the larger (exoplanet) context. Our Solar System system is thus the outcome of multiple unusual, but not unheard of, events.
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