Tracking Hidden Magnetospheric Fluctuations in Accretion-powered Pulsars With a Kalman Filter

Melatos, A.; Meyers, P. M.; O'Leary, Jared

doi:10.3847/1538-4357/acab5a

Cited by 5 publications

(41 citation statements)

References 85 publications

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“…The spatial structure in the simulations, e.g., the geometry of the magnetic field near the disk-magnetosphere boundary, cannot be inferred uniquely from the observables ( ) P t and ( ) L t . In this paper, therefore, we choose to describe accretion in terms of the canonical, spatially averaged, magnetocentrifugal model (Ghosh & Lamb 1979), motivated by the promising results presented in Melatos et al (2023). The reader is directed to the latter reference for a full account of the model, its physical justification, and its implementation in the form of a Kalman filter; we do not repeat here the in-depth discussion in Melatos et al (2023).…”

Section: Measuring the Magnetic Momentmentioning

confidence: 99%

“…In this paper, therefore, we choose to describe accretion in terms of the canonical, spatially averaged, magnetocentrifugal model (Ghosh & Lamb 1979), motivated by the promising results presented in Melatos et al (2023). The reader is directed to the latter reference for a full account of the model, its physical justification, and its implementation in the form of a Kalman filter; we do not repeat here the in-depth discussion in Melatos et al (2023). Instead, in this section, we introduce briefly the variables, definitions, and dynamical equations needed to implement the Kalman filter, so that the interested reader is equipped to reproduce the key results of this paper, namely the independent measurements of μ and the radiative efficiency for SXP 18.3.…”

Section: Measuring the Magnetic Momentmentioning

confidence: 99%

“…In Section 2.1, we relate the observables ( ) P t and ( ) L t via nonlinear measurement equations to four time-dependent state variables, three of which are hidden. In Section 2.2, we discuss (i) the canonical magnetocentrifugal torque law; (ii) the degeneracy that exists between μ and the radiative efficiency for systems near magnetocentrifugal equilibrium; and (iii) a phenomenological, idealized model of the stochastic forces associated with instabilities at the disk-magnetosphere boundary, which drive the system away from equilibrium, first introduced in Section 2.4 in Melatos et al (2023). The nonlinear measurement equations in Section 2.1 and equations of motion in Section 2.2 are linearized about the state of magnetocentrifugal equilibrium in Section 2.3, producing a state-space formulation of the problem which is suitable for Kalman filter analysis.…”

Section: Measuring the Magnetic Momentmentioning

confidence: 99%

“…In this paper, we generalize previous magnetocentrifugal estimates of μ for accretion-powered pulsars by exploiting the additional information available in the fluctuations of L(t) and P(t) around their time-averaged values, breaking the degeneracy between μ and the radiative efficiency. To do so, we apply the signal-processing framework developed by Melatos et al (2023), which (i) utilizes a Kalman filter to track fluctuations in three hidden state variables associated with magnetocentrifugal accretion (the mass accretion rate, the Maxwell stress at the disk-magnetosphere boundary, and the radiative efficiency), and (ii) maximizes the Kalman filter likelihood to estimate the underlying, static physical parameters, including μ. As this is the first time the method has been applied to astronomical data, we focus in this paper on demonstrating its feasibility using a single, regularly monitored object with sufficient samples of L(t) and P(t), namely the X-ray transient SXP 18.3 in the Small Magellanic Cloud (SMC; Corbet et al 2003).…”

Section: Introductionmentioning

confidence: 99%

“…We briefly describe its properties and the Rossi X-ray Timing Explorer (RXTE) observations used throughout the analysis. We choose to focus our analysis on SXP 18.3 for two practical reasons: (i) the rotational state of the star has been classified by Yang et al (2017) as being approximately in equilibrium; and (ii) the RXTE Proportional Counter Array (PCA) sensor collected 854 observations over a period of ∼16 yr, comparable in volume to the representative test case involving synthetic data presented in Melatos et al (2023). New estimates of the magnetic dipole moment μ and radiative efficiency η 0 associated with SXP 18.3 are presented in Section 4.…”

Section: Introductionmentioning

confidence: 99%

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Measuring the Magnetic Dipole Moment and Magnetospheric Fluctuations of SXP 18.3 with a Kalman Filter

O’Leary,

Melatos,

O’Neill

et al. 2024

ApJ

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The magnetic dipole moment μ of an accretion-powered pulsar in magnetocentrifugal equilibrium cannot be inferred uniquely from time-averaged pulse period and aperiodic X-ray flux data, because the radiative efficiency η 0 of the accretion is unknown, as are the mass, radius, and distance of the star. The degeneracy associated with the radiative efficiency is circumvented if fluctuations of the pulse period and aperiodic X-ray flux are tracked with a Kalman filter, whereupon μ can be measured uniquely up to the uncertainties in the mass, radius, and distance. Here, the Kalman filter analysis is demonstrated successfully in practice for the first time on Rossi X-ray Timing Explorer observations of the X-ray transient SXP 18.3 in the Small Magellanic Cloud (SMC), which is monitored regularly. The analysis yields μ = 8.0 − 1.2 + 1.3 × 10 30 G cm 3 and η 0 = 0.04 − 0.01 + 0.02 , compared to μ = 5.0 − 1.0 + 1.0 × 10 30 G cm 3 as inferred traditionally from time-averaged data assuming η 0 = 1. The analysis also yields time-resolved estimates of two hidden state variables, the mass accretion rate and the Maxwell stress at the disk–magnetosphere boundary. The success of the demonstration confirms that the Kalman filter analysis can be applied in the future to study the magnetic moments and disk–magnetosphere physics of accretion-powered pulsar populations in the SMC and elsewhere.

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Section: Measuring the Magnetic Momentmentioning

confidence: 99%

Section: Measuring the Magnetic Momentmentioning

confidence: 99%

Section: Measuring the Magnetic Momentmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Measuring the Magnetic Dipole Moment and Magnetospheric Fluctuations of SXP 18.3 with a Kalman Filter

O’Leary,

Melatos,

O’Neill

et al. 2024

ApJ

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Kalman tracking and parameter estimation of continuous gravitational waves with a pulsar timing array

Kimpson,

Melatos,

O’Leary

et al. 2024

Monthly Notices of the Royal Astronomical Society

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Continuous nanohertz gravitational waves from individual supermassive black hole binaries may be detectable with pulsar timing arrays. A novel search strategy is developed, wherein intrinsic achromatic spin wandering is tracked simultaneously with the modulation induced by a single gravitational wave source in the pulse times of arrival. A two-step inference procedure is applied within a state-space framework, such that the modulation is tracked with a Kalman filter, which then provides a likelihood for nested sampling. The procedure estimates the static parameters in the problem, such as the sky position of the source, without fitting for ensemble-averaged statistics such as the power spectral density of the timing noise, and therefore complements traditional parameter estimation methods. It also returns the Bayes factor relating a model with a single gravitational wave source to one without, complementing traditional detection methods. It is shown via astrophysically representative software injections in Gaussian measurement noise that the procedure distinguishes a gravitational wave from pure noise down to a characteristic wave strain of $h_0 \approx 2 \times 10^{-15}$. Full posterior distributions of model parameters are recovered and tested for accuracy. There is a bias of $\approx 0.3$ rad in the marginalized one-dimensional posterior for the orbital inclination $\iota$, introduced by dropping the so-called pulsar terms. Smaller biases $\lesssim 10~{{\ \rm per\ cent}}$ are also observed in other static parameters.

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State-space analysis of a continuous gravitational wave source with a pulsar timing array: inclusion of the pulsar terms

Kimpson,

Melatos,

O’Leary

et al. 2024

Monthly Notices of the Royal Astronomical Society

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Pulsar timing arrays can detect continuous nanohertz gravitational waves emitted by individual supermassive black hole binaries. The data analysis procedure can be formulated within a time-domain, state-space framework, in which the radio timing observations are related to a temporal sequence of latent states, namely the intrinsic pulsar spin frequency. The achromatic wandering of the pulsar spin frequency is tracked using a Kalman filter concurrently with the pulse frequency modulation induced by a gravitational wave from a single source. The modulation is the sum of terms proportional to the gravitational wave strain at the Earth and at every pulsar in the array. Here we generalize previous state-space formulations of the pulsar timing array problem to include the pulsar terms; that is, we copy the pulsar terms from traditional, non-state-space analyses over to the state-space framework. The performance of the generalized Kalman filter is tested using astrophysically representative software injections in Gaussian measurement noise. It is shown that including the pulsar terms corrects for previously identified biases in the parameter estimates (especially the sky position of the source) which also arise in traditional matched-filter analyses that exclude the pulsar terms. Additionally, including the pulsar terms decreases the minimum detectable strain by 14%. Overall, the study verifies that the pulsar terms do not raise any special extra impediments for the state-space framework, beyond those studied in traditional analyses. The inspiral-driven evolution of the wave frequency at the Earth and at the retarded time at every pulsar in the array is also investigated.

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Tracking Hidden Magnetospheric Fluctuations in Accretion-powered Pulsars With a Kalman Filter

Cited by 5 publications

References 85 publications

Measuring the Magnetic Dipole Moment and Magnetospheric Fluctuations of SXP 18.3 with a Kalman Filter

Measuring the Magnetic Dipole Moment and Magnetospheric Fluctuations of SXP 18.3 with a Kalman Filter

Kalman tracking and parameter estimation of continuous gravitational waves with a pulsar timing array

State-space analysis of a continuous gravitational wave source with a pulsar timing array: inclusion of the pulsar terms

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