Nonradial Frequencies Research Articles

Impacts of symmetry energy slope on the oscillation frequencies of neutron stars with short-range correlation and admixed dark matter

Oscillation modes of compact stars, in general, can serve as a fingerprint in determining the equation of state (EOS) of dense matter. In this study, we examine the impact of symmetry energy slope (L) on the oscillation frequencies of neutron stars (NSs) with nucleon–nucleon short range correlation (SRC) and admixed dark matter (DM) for the first time within the relativistic mean-field theory. By adjusting the L, we revise the EOS and coupling parameters in light of the SRC and DM effects, and construct the new sets. The results reveal that NSs containing SRC and DM inside are more likely to satisfy the observational constraints, and we find that smaller L exhibits larger fundamental non-radial and radial frequencies, and that the effect on large separation is also mainly concentrated in the low-mass region. Moreover, we update the linear relationship between the non-radial frequency and mean density, and we further give empirical relations between non-radial and radial frequencies and tidal deformability at different L for 1.4 and 2. These findings will enable us to more effectively confine the NS EOSs, in turn, also provide a strategy to place constraints on the L.

Short-range correlation effects in neutron star's radial and non-radial oscillations * *Supported by the National Key Research and Development Program of China (2017YFA0402600, 2016YFE0129300), the National SKA Program of China (2020SKA0120300) and the National Natural Science Foundation of China (11833003, 11947211, 119051)

In this study, we determine the influence of the nucleon-nucleon short range correlation (SRC) on static spherically symmetric neutron stars (NSs) from the perspectives of radial and nonradial oscillations for the first time. We revise the equation of state and coupling parameters in the relativistic mean field theory after considering the SRC effect, and select the hyperon coupling parameters as the SU(3) model. For the non-radial oscillations, the SRC effect decreases the -mode frequency by kHz. For the radial oscillations, it decreases the fundamental radial frequency by 0.75 ~ 0.85 kHz. Additionally, we refit the linear relationship between the average density and -mode frequency for SRC. Combining the characteristics of the radial and non-radial frequencies, we provide a view of inferring the maximum mass of NSs. Owing to the characteristics of the SRC influence on the radial frequency, we expect that the SRC can be tested by future observation and can also be used as a probe for the structure inside NSs.

Radial frequency patterns describe a small and perceptually distinct subset of all possible planar shapes

The visual system is exposed to a vast number of shapes and objects. Yet, human object recognition is effortless, fast and largely independent of naturally occurring transformations such as position and scale. The precise mechanisms of shape encoding are still largely unknown. Radial frequency (RF) patterns are a special class of closed contours defined by modulation of a circle’s radius. These patterns have been frequently and successfully used as stimuli in vision science to investigate aspects of shape processing. Given their mathematical properties, RF patterns can not represent any arbitrary shape, but the ability to generate more complex, biologically relevant, shapes depicting the outlines of objects such as fruits or human heads raises the possibility that RF patterns span a representative subset of possible shapes. However, this assumption has not been tested before. Here we show that only a small fraction of all possible shapes can be represented by RF patterns and that this small fraction is perceptually distinct from the general class of all possible shapes. Specifically, we derive a general measure for the distance of a given shape’s outline from the set of RF patterns, allowing us to scan large numbers of object outlines automatically. We find that only between 1% and 6% of naturally smooth outlines can be exactly represented by RF patterns. We present results from a visual search experiment, which revealed that searching an RF pattern among non-radial frequency patterns is efficient, whereas searching an RF pattern among other RF patterns is inefficient (and vice versa). These results suggest that RF patterns represent only a restricted subset of possible planar shapes and that results obtained with this special class of stimuli can not simply be expected to generalise to any arbitrary planar shape.

Nothing more than a pair of curvatures: A common mechanism for the detection of both radial and non-radial frequency patterns

Radial frequency (RF) patterns, which are sinusoidal modulations of a radius in polar coordinates, are commonly used to study shape perception. Previous studies have argued that the detection of RF patterns is either achieved globally by a specialized global shape mechanism, or locally using as cue the maximum tangent orientation difference between the RF pattern and the circle. Here we challenge both ideas and suggest instead a model that accounts not only for the detection of RF patterns but also for line frequency patterns (LF), i.e. contours sinusoidally modulated around a straight line. The model has two features. The first is that the detection of both RF and LF patterns is based on curvature differences along the contour. The second is that this curvature metric is subject to what we term the Curve Frequency Sensitivity Function, or CFSF, which is characterized by a flat followed by declining response to curvature as a function of modulation frequency, analogous to the modulation transfer function of the eye. The evidence that curvature forms the basis for detection is that at very low modulation frequencies (1–3 cycles for the RF pattern) there is a dramatic difference in thresholds between the RF and LF patterns, a difference however that disappears at medium and high modulation frequencies. The CFSF feature on the other hand explains why thresholds, rather than continuously declining with modulation frequency, asymptote at medium and high modulation frequencies. In summary, our analysis suggests that the detection of shape modulations is processed by a common curvature-sensitive mechanism that is subject to a shape-frequency-dependent transfer function. This mechanism is independent of whether the modulation is applied to a circle or a straight line.

Nothing more than a curve: a common mechanism for the detection of radial and non-radial frequency patterns?

Nothing more than a curve: a common mechanism for the detection of radial and non-radial frequency patterns?

44 Tau: Discrimination between MS and post-MS models

Inhalt (u.a.): M. BREGER: Delta Scuti stars: Observational aspects; M.S. Cunha: Theory of rapidly oscillating Ap stars; M. SACHKOV et al.: Vertical structure of pulsations in roAp stars; G. HOUDEK: Theoretical asteroseismology of solar-like oscillations; B.L. POPIELSKI: Core modes as a seismic probe of mixing beyond the convective core; M. GODART: Temperature gradients in the core overshooting region; W.A. DZIEMBOWSKI – J. DASZYŃSKA-DASZKIEWICZ – A.A. PAMYATNYKH: Interpretation of the Be star HD 163868 oscillation spectrum based on the MOST observations; D. KILKENNY: Pulsating Hot Subdwarfs – An Observational Review; M.H. MONTGOMERY: Mapping Convection using Pulsating White Dwarf Stars; M. ROTH: The Network Activities in HELAS; I. KUDZEJ et al.: A New Slovak Observatory 500 km from Vienna; W.W. WEISS: Microsatellites; G. KOPACKI – S. FRANDSEN: RR Lyrae stars in M4

Pulsational properties of V2109 Cyg

AbstractIn this study V2109 Cyg (a pulsating δ Scuti star) has been modelled. In treating the oscillation equations perturbation in gravitational potential energy has been taken into account. Both radial and nonradial oscillations are treated with adiabatic approximation. The so called radial fundamental frequency (5.3745 c/d) and the nonradial frequency (5.8332 c/d) were obtained within a satisfactory precision. It was found that the Cowling approximation introduced more error as one went from low overtones to high overtones in radial oscillations. A similar trend was observed in nonradial case with low values of l. By keeping the effective temperatures almost the same as with V2109 Cyg two more models with different masses have also been calculated to see the effect of inclusion of perturbation in gravitational potential energy on oscillation frequencies in different masses. Conclusion arrived is that one must be careful to employ the Cowling approximation especially for high nonradial oscillation frequencies. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

An oscillating model suggestion for 63 Her

AbstractAn attempt has been made towards explaining the observed frequencies in 63 Her. The evolution of rotating stars of 1.96, 1.98, 2.00, 2.05 and 2.10 M⊙ have been studied up to a point where stellar parameters match the observed luminosity and effective temperature of 63 Her. Radial and nonradial adiabatic oscillation frequencies were obtained in low harmonic degrees ( l = 0,1,2,3 ). One radial and three nonradial frequency values that match with the observed values were found for the model of mass 2.00 M⊙.

Radial and Nonradial Oscillations of 44 Tauri

Evolutionary stellar models of 44 Tauri, a multiperiodic δ Scuti star, have been developed theoretically and compared with earlier observational reports. The models depict 44 Tau at the hydrogen-shell–burning stage, when it is in radiative equilibrium with a very thin surface convective layer. Using the models, we performed calculations to obtain radial and nonradial adiabatic oscillation frequencies, and the equations were treated linearly. The results showed that the radial fundamental (6.899 cycles day-1) and first-overtone (8.961 cycles day-1) frequencies and the five nonradial modes of low harmonic degree that had been determined theoretically were in agreement with the observed values of previous authors to an accuracy of a few parts in 103. However, a difference emerged in the nonradial frequencies, which we classified as g-modes of low harmonic degree, whereas the observational reports had classified them as p-modes. In addition, even though 44 Tau has a rotation v sin i = 6.8 km s-1 (according to Solano and Fernley), which we considered negligible, we analyzed the effect of rotation. Our findings revealed that rotation modulated the oscillation frequencies of the nonrotating model on the order of 10-2.

Evidence for a small, high-Z, iron-like solar core

The high-Z core (HZC) model of the Sun, supported in Rouse (1985) by superior agreements of nonradial g-mode periods of oscillation with long period observations, is used to calculate frequencies of oscillation in the five-minute band (5MB). Allowing for the fact that the present HZC model profile does not include an upper photosphere and self-consistent chromosphere, the HZC model of the Sun is also supported by the very good agreements of the 5MB nonradial frequencies of oscillation with observations for HZC l degrees 0 to 19 and orders n ≲ 20, and the good agreement of the HZC purely radial frequencies of oscillation with about the same n-orders with observations previously identified as l = 0 oscillations. Two important aspects of these agreements are (1) the nonradial frequencies were calculated with the equations that neglect the gravitational perturbation (the Cowling approximation), and (2) the radial frequencies were calculated with the equation that includes the gravitational perturbation. The present agreements suggest that for solar-type stars, the gravitational perturbation may not affect the nonradial p-modes of oscillation as much as it affects the radial modes and the nonradial g-modes. More research will be performed.