Vortex axisymmetrization, inviscid damping, and vorticity depletion in the linearized 2D Euler equations

Coherent vortices are often observed to persist for long times in turbulent 2D flows even at very high Reynolds numbers and are observed in experiments and computer simulations to potentially be asymptotically stable in a weak sense for the 2D Euler equations. We consider the incompressible 2D Euler equations linearized around a radially symmetric, strictly monotone decreasing vorticity distribution. For sufficiently regular data, we prove the inviscid damping of the θ-dependent radial and angular velocity fields with the optimal rates ∥ur(t)∥≲⟨t⟩−1 and ∥∥uθ(t)∥∥≲⟨t⟩−2 in the appropriate radially weighted L2 spaces. We moreover prove that the vorticity weakly converges back to radial symmetry as t→∞, a phenomenon known as vortex axisymmetrization in the physics literature, and characterize the dynamics in higher Sobolev spaces. Furthermore, we prove that the θ-dependent angular Fourier modes in the vorticity are ejected from the origin as t→∞, resulting in faster inviscid damping rates than those possible with passive scalar evolution. This non-local effect is called vorticity depletion. Our work appears to be the first to find vorticity depletion relevant for the dynamics of vortices

Stationary Structures Near the Kolmogorov and Poiseuille Flows in the 2d Euler Equations

We study the behavior of solutions to the incompressible 2d Euler equations near two canonical shear flows with critical points, the Kolmogorov and Poiseuille flows, with consequences for the associated Navier–Stokes problems. We exhibit a large family of new, non-trivial stationary states that are arbitrarily close to the Kolmogorov flow on the square torus $$\mathbb {T}^2$$ in analytic regularity. This situation contrasts strongly with the setting of some monotone shear flows, such as the Couette flow: there the linearized problem exhibits an “inviscid damping” mechanism that leads to relaxation of perturbations of the base flows back to nearby shear flows. Our results show that such a simple description of the long-time behavior is not possible for solutions near the Kolmogorov flow on $$\mathbb {T}^2$$. Our construction of the new stationary states builds on a degeneracy in the global structure of the Kolmogorov flow on $$\mathbb {T}^2$$, and we also show a lack of correspondence between the linearized description of the set of steady states and its true nonlinear structure. Both the Kolmogorov flow on a rectangular torus and the Poiseuille flow in a channel are very different. We show that the only stationary states near them must indeed be shears, even in relatively low regularity. In addition, we show that this behavior is mirrored closely in the related Navier–Stokes settings: the linearized problems near the Poiseuille and Kolmogorov flows both exhibit an enhanced rate of dissipation. Previous work by us and others shows that this effect survives in the full, nonlinear problem near the Poiseuille flow and near the Kolmogorov flow on rectangular tori, provided that the perturbations lie below a certain threshold. However, we show here that the corresponding result cannot hold near the Kolmogorov flow on $${\mathbb T}^2$$

Different twins in the millisecond pulsar recycling scenario: optical polarimetry of PSR J1023+0038 and XSS J12270-4859

We present the first optical polarimetric study of the two transitional pulsars PSR J1023+0038 and XSS J12270-4859. This work is focused on the search for intrinsical linear polarisation (LP) in the optical emission from the two systems. We carried out multiband optical and NIR photo-polarimetry of the two systems using the ESO NTT at La Silla (Chile), equipped with the EFOSC2 and the SOFI instruments. XSS J12270-4859 was observed during its radio-pulsar state; we did not detect LP in all bands, with 3 sigma upper limits of, e.g., 1.4% in the R-band. We built the NIR-optical averaged spectral energy distribution (SED) of the system, that could be well described by an irradiated black body with radius $R_{*} = 0.33\pm0.03\,R_{\odot}$ and albedo $\eta=0.32\pm0.05$, without the need of further components (thus excluding the visible presence of an extended accretion disc and/or of relativistic jets). The case was different for PSR J1023+0038, that was in its accretion phase during our campaign. We measured a LP of $1.09\pm0.27\%$ and $0.90\pm 0.17\%$ in the V and R bands, respectively. The phase-resolved polarimetric curve of the source in the R-band reveals a hint of a sinusoidal modulation at the source 4.75 hr orbital period, peaked at the same orbital phase as the light curve. The measured LP of PSR J1023+0038 could in principle be interpreted as scattering with free electrons (that can be found in the accretion disc of the system or even in the hot corona that surrounds the disc itself) or to synchrotron emission from a relativistic particles jet or outflow. However, the NIR-optical SED of the system built starting from our dataset did not suggest the presence of a jet. We conclude that the optical LP observed for PSR J1023+0038 is possibly due to Thomson scattering with electrons in the disc, as also suggested from the possible modulation of the R-band LP at the system orbital period.Comment: 10 pages, 8 figures, 4 tables. Accepted for publication in Sec. 7. Stellar structure and evolution of Astronomy and Astrophysic

Simultaneous Multi-band Radio & X-ray Observations of the Galactic Center Magnetar SGR 1745−-2900

We report on multi-frequency, wideband radio observations of the Galactic Center magnetar (SGR 1745$-$2900) with the Green Bank Telescope for $\sim$100 days immediately following its initial X-ray outburst in April 2013. We made multiple simultaneous observations at 1.5, 2.0, and 8.9 GHz, allowing us to examine the magnetar's flux evolution, radio spectrum, and interstellar medium parameters (such as the dispersion measure (DM), the scattering timescale and its index). During two epochs, we have simultaneous observations from the Chandra X-ray Observatory, which permitted the absolute alignment of the radio and X-ray profiles. As with the two other radio magnetars with published alignments, the radio profile lies within the broad peak of the X-ray profile, preceding the X-ray profile maximum by $\sim$0.2 rotations. We also find that the radio spectral index $\gamma$ is significantly negative between $\sim$2 and 9 GHz; during the final $\sim$30 days of our observations $\gamma \sim -1.4$, which is typical of canonical pulsars. The radio flux has not decreased during this outburst, whereas the long-term trends in the other radio magnetars show concomitant fading of the radio and X-ray fluxes. Finally, our wideband measurements of the DMs taken in adjacent frequency bands in tandem are stochastically inconsistent with one another. Based on recent theoretical predictions, we consider the possibility that the dispersion measure is frequency-dependent. Despite having several properties in common with the other radio magnetars, such as $L_{\textrm{X,qui}}/L_{\textrm{rot}} \lesssim 1$, an increase in the radio flux during the X-ray flux decay has not been observed thus far in other systems.Comment: 15 pages, 9 figures, 3 tables; accepted to Ap

The discovery, monitoring and environment of SGR J1935+2154

We report on the discovery of a new member of the magnetar class, SGR J1935+2154, and on its timing and spectral properties measured by an extensive observational campaign carried out between July 2014 and March 2015 with Chandra and XMM-Newton (11 pointings). We discovered the spin period of SGR J1935+2154 through the detection of coherent pulsations at a period of about 3.24s. The magnetar is slowing-down at a rate of 1.43(1)x10^{-11} s/s and with a decreasing trend due to a negative second period derivative of -3.5(7)x10^{-19} s/s^2. This implies a surface dipolar magnetic field strength of about 2.2x10^{14} G, a characteristic age of about 3.6kyr and, a spin-down luminosity L_{sd} of about 1.7x10^{34} erg/s. The source spectrum is well modelled by a blackbody with temperature of about 500eV plus a power-law component with photon index of about 2. The source showed a moderate long-term variability, with a flux decay of about 25\% during the first four months since its discovery, and a re-brightening of the same amount during the second four months. The X-ray data were also used to study the source environment. In particular, we discovered a diffuse emission extending on spatial scales from about 1" up to at least 1' around SGR J1935+2154 both in Chandra and XMM-Newton data. This component is constant in flux (at least within uncertainties) and its spectrum is well modelled by a power-law spectrum steeper than that of the pulsar. Though a scattering halo origin seems to be more probable we cannot exclude that part, or all, of the diffuse emission is due to a pulsar wind nebula.Comment: To appear in MNRAS; 10 pages, 3 color figures, 4 table