Multipole Index Research Articles

Many-body multipole index and bulk-boundary correspondence

Many-body multipole index and bulk-boundary correspondence

Long‐range precipitation forecast based on multipole and preceding fluctuations of sea surface temperature

AbstractLong‐range precipitation forecasting is crucial for flooding control and water resources management. However, making precise forecasting is rather difficult due to the complex climatic factors and large uncertainties arising from long lead times. Sea surface temperature anomaly (SSTA) is one of the strongest signals that influence regional precipitation, often used for the development of precipitation forecasts. Traditional models using SSTA for precipitation forecasting usually screen SSTA over fixed oceanic zones and neglect its preceding temporal fluctuation information. In this study, we introduce a multipole SSTA index and the preceding fluctuation modes of SSTA to develop a monthly precipitation forecasting model, which is applied to the upper Yangtze River basin in China where monthly precipitation during May–October for the period of 1961–2020 are forecasted. Results show that more significant SSTA poles correlated with precipitation are found for September than for the other months. The new approach is able to forecast monthly precipitation for May–October in the basin, particularly for September. It outperforms traditional statistical and dynamical models and has much more skill in forecasting precipitation for June–September when heavy precipitation is more likely to occur than for May or October. Our approach enriches the knowledge of the relationship between precipitation and SSTA, which is conducive to the improvement of long‐range precipitation forecasting.

Zonal harmonics of solar magnetic field for solar cycle forecast

According to the scheme of action of the solar dynamo, the poloidal magnetic field can be considered a source of production of the toroidal magnetic field by the solar differential rotation. From the polar magnetic field proxies, it is natural to expect that solar Cycle 25 will be weak as recorded in sunspot data. We suggest that there are parameters of the zonal harmonics of the solar surface magnetic field, such as the magnitude of the l=3 harmonic or the effective multipole index, that can be used as a reasonable addition to the polar magnetic field proxies. We discuss also some specific features of solar activity indices in Cycles 23 and 24.

A complete FFT-based decomposition formalism for the redshift-space bispectrum

To fully extract cosmological information from nonlinear galaxy distribution in redshift space, it is essential to include higher-order statistics beyond the two-point correlation function. In this paper, we propose a new decomposition formalism for computing the anisotropic bispectrum in redshift space and for measuring it from galaxy samples. Our formalism uses tri-polar spherical harmonic decomposition with zero total angular momentum to compress the 3D modes distribution in the redshift-space bispectrum. This approach preserves three fundamental properties of the Universe: statistical homogeneity, isotropy, and parity-symmetry, allowing us to efficiently separate the anisotropic signal induced by redshift-space distortions (RSDs) and the Alcock-Paczy\'{n}ski (AP) effect from the isotropic bispectrum. The relevant expansion coefficients in terms of the anisotropic signal are reduced to one multipole index $L$, and the $L> 0$ modes are induced only by the RSD or AP effects. Our formalism has two advantages: (1) we can make use of Fast Fourier Transforms (FFTs) to measure the bispectrum; (2) it gives a simple expression to correct for the survey geometry, i.e., the survey window function. As a demonstration, we measure the decomposed bispectrum from the Baryon Oscillation Spectroscopic Survey (BOSS) Data Release 12, and, for the first time, present a $14\sigma$ detection of the anisotropic bispectrum in the $L=2$ mode.

Scalar fields in black hole spacetimes

The time-evolution of matter fields in black hole exterior spacetimes is a well-studied subject, spanning several decades of research. However, the behavior of fields in the black hole interior spacetime, has only relatively recently begun receiving some attention from the research community. In this paper, we numerically study the late-time evolution of scalar fields in both Schwarzschild and Kerr spacetimes, including the black hole interior. We recover the expected late-time power-law "tails" on the exterior (null infinity, time-like infinity and the horizon). In the interior region, we find an interesting oscillatory behavior that is characterized by the multipole index $\ell$ of the scalar field. In addition, we also study the extremal Kerr case and find strong indications of an instability developing at the horizon.

Energy of coronal mass ejections and large-scale structure of solar magnetic fields

The relationship between variations of the energy and linear velocity of coronal mass ejections (CME) and the typical dimensions of structural elements of the large-scale solar magnetic field structure (LSMFS) is investigated for the period of 1996–2014. It is shown that the maximum linear velocity and maximum energy of CME correspond to the values of the effective solar multipole index n ~ 4.0–4.4. These values determine the maximum size of the complexes of active regions, which, together with the observed maximum values of magnetic field intensity in the complexes, limit the possible maximum CME energy.

Excitation of surface and volume plasmons in a metal nanosphere by fast electrons

Collective multipole oscillations (surface and volume plasmons) excited in a metal nanosphere by moving electron and corresponding inelastic scattering spectra are studied based on the hydrodynamic approach. Along with the bulk (dielectric) losses traditionally taken into account, the surface and radiative ones are also considered as the physical mechanisms responsible for the plasmon damping. The second and third mechanisms are found to be essential for the surface plasmons (at small or large cluster radii, respectively) and depend very differently on the multipole mode order. The differential equations are obtained which describe the temporal evolution of every particular mode as that one of a linear oscillator excited by the given external force, and the electron energy loss spectra are calculated. The changes in spectrum shape with the impact parameter and with the electron passage time are analyzed; the first of them is found to be in good enough agreement with the data of scanning transmission electron microscopy experiments. It is shown that, in the general case, a pronounced contribution to the formation of the loss spectrum is given by the both surface and volume plasmons with low and high multipole indices. In particular, at long electron passage time, the integral (averaged over the impact parameter) loss spectrum which is calculated for the free-electron cluster model contains two main peaks: a broad peak from merging of many high-order multipole resonances of the surface plasmons and a narrower peak of nearly the same height from merged volume plasmons excited by the electrons that travel through the central region of the cluster. Comparatively complex dependences of the calculated excitation coefficients and damping constants of various plasmons on the order of the excited multipole result in wide diversity of possible types of the loss spectrum even for the same cluster material and should be taken into account in interpretation of corresponding electron energy loss spectroscopy experiments.

Quasinormal modes of generalized ABG black holes: scalar and gravitational perturbations

ABG black holes are charged regular black holes based on Einstein gravity and nonlinear electrodynamics, proposed by Ayon-Beato and Garcia. In 2005, they generalized the ABG black holes to a new class of regular black holes which have four characteristic parameters: the mass m, the electric charge q and the rest two parameters \(\alpha \) and \(\beta \) related with the dipole and quadrupole moment of the nonlinear electromagnetic field, respectively. In this paper, we study the quasinormal modes (QNMs) of these generalized ABG black holes for scalar and gravitational perturbations by the sixth-order WKB method. The numerical results show the generalized ABG black holes are stable and the relations between QNMs and the parameter of the perturbation fields and the parameters of the black holes are discussed. The real part and the imaginary part of the generalized ABG black holes increase as the charge increasing. Furthermore, the dependence of the QNMs on the other parameters is also illustrated and the analytical expression of the quasinormal frequency for the large multipole index is obtained.

Variations in the relationship between coronal mass ejections and corresponding X-ray flares during the 11-year solar activity cycle

The relationship between coronal mass ejections (CMEs) and corresponding X-ray flares was studied for the time interval covering cycle 23 and the beginning of cycle 24 (1996–2013). It is shown that the energy difference between CMEs and associated flares is larger at the decline of the solar cycle than in its rise phase. A similar relation is observed between the CME velocity (energy) and the effective solar multipole index, which characterizes the typical size of elements of the system of large-scale solar magnetic fields. This suggests that CMEs are mostly associated with individual active regions at the minimum and rise of the 11-year cycle, while the CME energy is mostly determined by active region complexes at the maximum and in the declining phase.

Relationship between cyclic variations in the velocity and occurrence frequency of coronal mass ejections and cyclic changes in the structure of the large-scale solar magnetic field

This paper investigates the relationship between cyclic variations in the velocity of coronal mass ejections and cyclic changes in the structure of the large-scale solar magnetic field (LSSMF) in solar cycle 23, using the effective solar multipole index as a parameter of the characteristic dimensions of LSSMF structural elements. Cyclic variations in the velocity and frequency of coronal mass ejections are found to resemble cyclic changes in the effective solar multipole index. It is suggested that cyclic changes in the maximum velocity of coronal mass ejections are associated with different conditions for the formation of complexes of active regions connected by coronal arch structures, the energy of which is the main source of energy (velocity) for coronal mass ejections. The study leads to some suggestions about the possible site of initiation of coronal mass ejections.

Object Picture of Quasinormal Modes for Stringy Black Holes

We study the quasinormal modes (QNMs) for stringyblack holes. By using numerical calculation, the relations betweenthe QNMs and the parameters of black holes are minutely shown. For(1+1)-dimensional stringy black hole, the real part of thequasinormal frequency increases and the imaginary part of thequasinormal frequency decreases as the mass of the black holeincreases. Furthermore, the dependence of the QNMs on the charge ofthe black hole and the flatness parameter is also illustrated. For(1+3)-dimensional stringy black hole, increasing either the eventhorizon or the multipole index, the real part of the quasinormalfrequency decreases. The imaginary part of the quasinormalfrequency increases no matter whether the event horizon is increased orthe multipole index is decreased.

Characteristics of the structure in the Galactic polarized radio background at 350 MHz

Angular power spectra and structure functions of the Stokes parameters Q and U and polarized intensity P are derived from three sets of radio polarimetric observations. Two of the observed fields have been studied at multiple frequencies, allowing determination of power spectra and structure functions of rotation measure RM as well. The third field extends over a large part of the northern sky, so that the variation of the power spectra over Galactic latitude and longitude can be studied. The power spectra of Q and U are steeper than those of P, probably because a foreground Faraday screen creates extra structure in Q and U, but not in P. The extra structure in Q and U occurs on large scales, and therefore causes a steeper spectrum. The derived slope of the power spectrum of P is the multipole spectral index , and is consistent with earlier estimates. The multipole spectral index decreases with Galactic latitude (i.e. the spectrum becomes flatter), but is consistent with a constant value over Galactic longitude. Power spectra of the rotation measure RM show a spectral index , while the structure function of RM is approximately flat. The structure function is flatter than earlier estimates from polarized extragalactic sources, which could be due to the fact that extragalactic source RM probes the complete line of sight through the Galaxy, whereas as a result of depolarization diffuse radio polarization only probes the nearby ISM.

Object picture of quasinormal ringing on the background of small Schwarzschild anti–de Sitter black holes

We investigate the evolution of a scalar field propagating in small Schwarzschild anti--de Sitter black holes. The imaginary part of the quasinormal frequency decreases with the horizon size and the real part of the quasinormal frequency keeps nearly as a constant. The object picture clarifies the question about the quasinormal modes for small anti--de Sitter black holes. The dependence of the quasinormal modes on spacetime dimensions and the multipole index for small anti--de Sitter black holes is also illustrated.

Evolution of a massless scalar field in Reissner-Nordström anti–de Sitter spacetimes

We investigate the evolution of a scalar field propagating in Reissner-Nordstr\"om anti--de Sitter spacetime. Because of the characteristic of spacetime geometry, the radiative tails associated with a massless scalar field propagation have an oscillatory exponential decay. The object picture of the quasinormal ringing has also been obtained. For small charges, the approach to thermal equilibrium is faster for larger charges. However, after the black-hole charge reaches a critical value, we get the opposite behavior for the imaginary frequencies of the quasinormal modes. Some possible explanations concerning the wiggle of the imaginary frequencies have been given. The picture of the quasinormal modes depending on the multipole index has also been illustrated.

Quasinormal modes of maximally charged black holes.

A new algorithm for computing the accurate values of quasinormal frequencies of extremal Reissner-Nordstr\"{o}m black holes is presented. The numerically computed values are consistent with the values earlier obtained by Leaver and those obtained through the WKB method. Our results are more precise than other results known to date. We also find a curious fact that the resonant frequencies of gravitational waves with multi-pole index $l$ coincide with those of electromagnetic waves with multi-pole index $l-1$ in the extremal limit.

Frozen‐flux upper limits to the magnitudes of geomagnetic Gauss coefficients, based on MAGSAT observations

If the earth's core is regarded as a perfect conductor and the surrounding mantle as an insulator, then the unsigned magnetic flux, Po, crossing the core‐mantle boundary remains constant in time. In practice this constancy is limited by the core's finite conductivity, but it is expected to hold for at least millenia. For such time spans an upper limit Gnm or Hnm may be derived for the magnitude of any geomagnetic Gauss coefficient gnm or hnm, by assuming that the entire value of Po is attributed to that coefficient alone. Such upper limits are evaluated here for n = 1 ‐ 4, using a value of Po derived from Magsat data.The ratio |gnm/Gnm|, |hnm/Hnm| between the observed magnitude of a coefficient and its upper limit defines a "relative multipole index" for the present value of that coefficient. Using the Magsat model MGST 6/80 it is found that for the dipole term this ratio is about 0.72, suggesting that |g10| is presently only about 28% lower than the maximum value during the past few millenia. Also, the largest of the other multipole indices calculated (|g3¹/G3¹| ≃ 0.23) is a factor of over 3 smaller, so presumably a dramatic change in field configuration outside the core is required before the next polarity reversal is completed.