Killing Tensor and Carter Constant for Painlevé–Gullstrand Form of Lense–Thirring Spacetime

Recently, the authors have formulated and explored a novel Painlevé–Gullstrand variant of the Lense–Thirring spacetime, which has some particularly elegant features, including unit-lapse, intrinsically flat spatial 3-slices, and some particularly simple geodesics—the “rain” geodesics. At the linear level in the rotation parameter, this spacetime is indistinguishable from the usual slow-rotation expansion of Kerr. Herein, we shall show that this spacetime possesses a nontrivial Killing tensor, implying separability of the Hamilton–Jacobi equation. Furthermore, we shall show that the Klein–Gordon equation is also separable on this spacetime. However, while the Killing tensor has a 2-form square root, we shall see that this 2-form square root of the Killing tensor is not a Killing–Yano tensor. Finally, the Killing-tensor-induced Carter constant is easily extracted, and now, with a fourth constant of motion, the geodesics become (in principle) explicitly integrable.

The evolutions of the innermost stable circular orbits in dynamical spacetimes

In this paper, we studied the evolutions of the innermost stable circular orbits (ISCOs) in dynamical spacetimes. At first, we reviewed the method to obtain the ISCO in Schwarzschild spacetime by varying its conserved orbital angular momentum. Then, we demonstrated this method is equivalent to the effective potential method in general static and stationary spacetimes. Unlike the effective potential method, which depends on the presence of the conserved orbital energy, this method requires the existence of conserved orbital angular momentum in spacetime. So it can be easily generalized to the dynamical spacetimes where there exists conserved orbital angular momentum. From this generalization, we studied the evolutions of the ISCOs in Vaidya spacetime, Vaidya-AdS spacetime and the slow rotation limit of Kerr–Vaidya spacetime. The results given by these examples are all reasonable and can be compared with the evolutions of the photon spheres in dynamical spacetimes.

A broadband radio study of PSR J0250+5854: the slowest-spinning radio pulsar known

We present radio observations of the most slowly rotating known radio pulsar PSR J0250+5854. With a 23.5 s period, it is close, or even beyond, the P-$\dot{P}$ diagram region thought to be occupied by active pulsars. The simultaneous observations with FAST, the Chilbolton and Effelsberg LOFAR international stations, and NenuFAR represent a five-fold increase in the spectral coverage of this object, with the detections at 1250 MHz (FAST) and 57 MHz (NenuFAR) being the highest- and lowest-frequency published respectively to date. We measure a flux density of 4 ± 2 μJy at 1250 MHz and an exceptionally steep spectral index of $-3.5^{+0.2}_{-1.5}$, with a turnover below ∼95 MHz. In conjunction with observations of this pulsar with the GBT and the LOFAR Core, we show that the intrinsic profile width increases drastically towards higher frequencies, contrary to the predictions of conventional radius-to-frequency mapping. We examine polarimetric data from FAST and the LOFAR Core and conclude that its polar cap radio emission is produced at an absolute height of several hundreds of kilometres around 1.5 GHz, similar to other rotation-powered pulsars across the population. Its beam is significantly underfilled at lower frequencies, or it narrows because of the disappearance of conal outriders. Finally, the results for PSR J0250+5854 and other slowly spinning rotation-powered pulsars are contrasted with the radio-detected magnetars. We conclude that magnetars have intrinsically wider radio beams than the slow rotation-powered pulsars, and that consequently the latter’s lower beaming fraction is what makes objects such as PSR J0250+5854 so scarce.

Slowly rotating neutron stars in scalar torsion theory

In this present paper, a slowly rotating stat is investigated in shift symmetric scalar torsion theory framework using a nondiagonal tetrad that gives an axially symmetric spacetime. We present the general equations for a general Lagrangian in a spherical symmetric space time and then in an axially symmetric spacetime. The obtained equations will allow us to study the behaviour of a specific model at the center of the star and at large distance. We find that this particular model affects the behaviour at the center but it is not case for large value of the radial coordinate r. The integration of the equations of motion, for different realistic equations of state (EoS), confirms that the mass, the radius as well as the moment of inertia are effected by varying the parameters of the model. Finally, we examine the universal relation of normalized moment of inertia and the stellar compactness of neutron star in slow rotation approximation. We showed that for all values of parameters present in the model leads to a deviation from GR for all EoS with a relative deviation below $$10\%$$ 10 % .

Radiative and Dynamic Controls on Atmospheric Heat Transport over Different Planetary Rotation Rates

Atmospheric heat transport is an important piece of our climate system, yet we lack a complete theory for its magnitude or changes. Atmospheric dynamics and radiation play different roles in controlling the total atmospheric heat transport (AHT) and its partitioning into components associated with eddies and mean meridional circulations. This work focuses on two specific controls: a radiative one, namely atmospheric radiative temperature tendencies, and a dynamic one, the planetary rotation rate. We use an idealized gray radiation model to employ a novel framework to lock the radiative temperature tendency and total AHT to climatological values, even while the rotation rate is varied. This setup allows for a systematic study of the effects of radiative tendency and rotation rate on AHT. We find that rotation rate controls the latitudinal extent of the Hadley cell and the heat transport efficiency of eddies. Both the rotation rate and radiative tendency influence the strength of the Hadley cell and the strength of equator–pole energy differences that are important for AHT by eddies. These two controls do not always operate independently and can reinforce or dampen each other. In addition, we examine how individual AHT components, which vary with latitude, sum to a total AHT that varies smoothly with latitude. At slow rotation rates the mean meridional circulation is most important in ensuring total AHT varies smoothly with latitude, while eddies are most important at rotation rates similar to, and faster than, those of Earth.

Painlevé–Gullstrand form of the Lense–Thirring Spacetime

The standard Lense–Thirring metric is a century-old slow-rotation large-distance approximation to the gravitational field outside a rotating massive body, depending only on the total mass and angular momentum of the source. Although it is not an exact solution to the vacuum Einstein equations, asymptotically the Lense–Thirring metric approaches the Kerr metric at large distances. Herein we shall discuss a specific variant of the standard Lense–Thirring metric, carefully chosen for simplicity, clarity, and various forms of improved mathematical and physical behaviour, (to be more carefully defined in the body of the article). We shall see that this Lense–Thirring variant can be viewed as arising from the linearization of a suitably chosen tetrad representing the Kerr spacetime. In particular, we shall construct an explicit unit-lapse Painlevé–Gullstrand variant of the Lense–Thirring spacetime, one that has flat spatial slices, a very simple and physically intuitive tetrad, and extremely simple curvature tensors. We shall verify that this variant of the Lense–Thirring spacetime is Petrov type I, (so it is not algebraically special), but nevertheless possesses some very straightforward timelike geodesics, (the “rain” geodesics). We shall also discuss on-axis and equatorial geodesics, ISCOs (innermost stable circular orbits) and circular photon orbits. Finally, we wrap up by discussing some astrophysically relevant estimates, and analyze what happens if we extrapolate down to small values of r; verifying that for sufficiently slow rotation we explicitly recover slowly rotating Schwarzschild geometry. This Lense–Thirring variant can be viewed, in its own right, as a “black hole mimic”, of direct interest to the observational astronomy community.

The effects of surface fossil magnetic fields on massive star evolution: III. The case of τ Sco

τ Sco, a well-studied magnetic B-type star in the Uτer Sco association, has a number of surprising characteristics. It rotates very slowly and shows nitrogen excess. Its surface magnetic field is much more complex than a purely dipolar configuration which is unusual for a magnetic massive star. We employ the cmfgen radiative transfer code to determine the fundamental parameters and surface CNO and helium abundances. Then, we employ mesa and genec stellar evolution models accounting for the effects of surface magnetic fields. To reconcile τ Sco’s properties with single-star models, an increase is necessary in the efficiency of rotational mixing by a factor of 3 to 10 and in the efficiency of magnetic braking by a factor of 10. The spin down could be explained by assuming a magnetic field decay scenario. However, the simultaneous chemical enrichment challenges the single-star scenario. Previous works indeed suggested a stellar merger origin for τ Sco. However, the merger scenario also faces similar challenges as our magnetic single-star models to explain τ Sco’s simultaneous slow rotation and nitrogen excess. In conclusion, the single-star channel seems less likely and versatile to explain these discrepancies, while the merger scenario and other potential binary-evolution channels still require further assessment as to whether they may self-consistently explain the observables of τ Sco.

Planetary and atmospheric properties leading to strong super-rotation in terrestrial atmospheres studied with a semi-grey GCM

<div> <div>Super-rotation is a phenomenon in atmospheric dynamics where the specific axial angular momentum of the wind (at some location) in an atmosphere exceeds that of the underlying planet at the equator. Hide's theorem states that in order for an atmosphere to super-rotate, non-axisymmetric disturbances (eddies) are required to induce transport of angular momentum up its local gradient. This raises a question as to the origin and nature of the disturbances that operate in super-rotating atmospheres to induce the required angular momentum transport.</div> <br><div>The primary technique employed to investigate this question has involved numerically modelling super-rotating atmospheres, and diagnosing the processes that give rise to super-rotation in the simulations. These modelling efforts can be separated into one of two approaches. The first approach utilises 'realistic', tailor-made models of Solar System atmospheres where super-rotation is present (e.g., Venus and Titan) to investigate the specific processes responsible for generating super-rotation on each planet. The second approach takes simple, 'Earth-like' models, typically dry dynamical cores with radiative transfer represented using a Newtonian cooling approach, and explores the effect of varying a single (or occasionally multiple) planetary parameters (e.g., the planetary radius or rotation rate) on the atmospheric dynamics. Notably, studies of this flavour have shown that super-rotation may emerge 'spontaneously' on planets with slow rotation rate or small radius (relative to the Earth's; Venus and Titan have these characteristics). However, the strength of super-rotation obtained in simulations of this type is far weaker than that observed in Venus' or Titan's atmospheres, or in tailored numerical models of either planet.</div> <br><div>In this work, our aim is to bridge the gap between these two modelling approaches. We will present results from a suite of simulations using an idealised general circulation model with a semi-grey representation of radiative transfer. Our experiments explore the effects of varying planetary size and rotation rate, atmospheric mass, and atmospheric absorption of shortwave radiation on the acceleration of super-rotation. A novel aspect of this work is that we vary multiple planetary properties away from their Earth-like 'defaults' in conjunction. This allows us to investigate how properties characteristic of the atmospheres of planets such as Venus and Titan combine to yield the strong super-rotation observed in their atmospheres (and realistic numerical models). We are also able to illustrate how features such as increased atmospheric mass and absorption of shortwave radiation modify the weakly super-rotating state obtained in simple, Earth-like models towards one more characteristic of Titan or Venus.</div> </div>