Matter Research Articles

Structure of the Baryon Halo Around a Supermassive Primordial Black Hole

According to some theoretical models, primordial black holes with masses of more than 108 solar masses could be born in the early universe, and their possible observational manifestations have been investigated in a number of works. Dense dark matter and baryon halos could form around such primordial black holes even at the pre-galactic stage (in the cosmological Dark Ages epoch). In this paper, the distribution and physical state of the gas in the halo are calculated, taking into account the radiation transfer from the central accreting primordial black hole. This made it possible to find the ionization radius, outside of which there are regions of neutral hydrogen absorption in the 21 cm line. The detection of annular absorption regions at high redshifts in combination with a central bright source may provide evidence of the existence of supermassive primordial black holes. We also point out the fundamental possibility of observing absorption rings with strong gravitational lensing on galaxy clusters, which weakens the requirements for the angular resolution of radio telescopes.

Benchmarking simulation methods for understanding warm dense matter

Combining different simulations to achieve accurate theoretical predictions that are based on first principles

Pattern formations and their active manipulation in a Rydberg noisy-dressed Bose–Einstein condensate

We investigate the formation and manipulation of spatial patterns and their structural phase transitions by examining the effects of laser linewidth on the dynamics of Rydberg noise-dressed Bose–Einstein condensates (RnD BECs). We discover that the homogeneous matter wave can transition into various types of self-organized patterns, which are manipulated by tuning the laser linewidth, control field intensity, and atomic density. Remarkably, the system exhibits stable nonlocal matter-wave solitons, vortices, and soliton molecules under specific laser linewidths.

Electrical conductivity of warm dense hydrogen from Ohm’s law and time-dependent density functional theory

Abstract Understanding the electrical conductivity of warm dense hydrogen is critical for both fundamental physics and applications in planetary science and inertial confinement fusion. We demonstrate how to calculate the electrical conductivity using the continuum form of Ohm’s law, with the current density obtained from real-time time-dependent density functional theory. This approach simulates the dynamic response of hydrogen under warm dense matter conditions, with temperatures around 30,000 K and mass densities ranging from 0.02 to 0.98 g/cm³. We systematically address finite-size errors in real-time time-dependent density functional theory, demonstrating that our calculations are both numerically feasible and reliable. Our results show good agreement with other approaches, highlighting the effectiveness of this method for modeling electronic transport properties from ambient to extreme conditions.

Challenges and Prospects of DNA-Encoded Library Data Interpretation.

DNA-encoded library (DEL) technology is a powerful platform for the efficient identification of novel chemical matter in the early drug discovery process enabled by parallel screening of vast libraries of encoded small molecules through affinity selection and deep sequencing. While DEL selections provide rich data sets for computational drug discovery, the underlying technical factors influencing DEL data remain incompletely understood. This review systematically examines the key parameters affecting the chemical information in DEL data and their impact on hit triaging and machine learning integration. The need for rigorous data handling and interpretation is emphasized, with standardized methods being critical for the success of DEL-based approaches. Major challenges include the relationship between sequence counts and binding affinities, frequent hitters, and the influence of factors such as inhomogeneous library composition, DNA damage, and linkers on binding modes. Experimental artifacts, such as those caused by protein immobilization and screening matrix effects, further complicate data interpretation. Recent advancements in using machine learning to denoise DEL data and predict drug candidates are highlighted. This review offers practical guidance on adopting best practices for integrating robust methodologies, comprehensive data analysis, and computational tools to improve the accuracy and efficacy of DEL-driven hit discovery.

Dual symmetries of dense isotopically and chirally asymmetric QCD

In the present paper, the dual symmetries of dense quark matter phase diagram found in some massless three- and two-color NJL models in the mean field approximation have been shown to exist at a more fundamental level as dual transformations of fields and chemical potentials leaving the Lagrangian invariant. As a result, the corresponding dual symmetries of the full phase diagram can be shown without any approximation. And it has been shown not only in the NJL models, but also in framework of two- and three-color massless QCD itself. This is quite interesting, since one might say that it is not very common to show something completely non-perturbatively in QCD.

The Current State of Biotransformation Science - Industry Survey of In Vitro and In Vivo Practices, Clinical Translation, and Future Trends.

Embedded within the field of drug metabolism and pharmacokinetics (DMPK), biotransformation is a discipline that studies the origins, disposition, and structural identity of metabolites to provide a comprehensive safety assessment, including the assessment of exposure coverage in toxicological species. Spanning discovery and development, metabolite identification (metID) scientists employ various strategies and tools to address stage-specific questions aimed at guiding the maturation of early chemical matter into drug candidates. During this process, the identity of major (and minor) circulating human metabolites is ascertained to comply with the regulatory requirements such as the Metabolites in Safety Testing (MIST) guidance. Through the International Consortium for Innovation and Quality in Pharmaceutical Development (IQ), the "Translatability of MetID In Vitro Systems Working Group" was created within the Translational and ADME Sciences Leadership Group. The remit of this group was to objectively determine how accurate commonly employed in vitro systems have been with respect to prediction of circulating human metabolites, both qualitatively and quantitatively. A survey composed of 34 questions was conducted across 26 pharmaceutical companies to obtain a foundational understanding of current metID practices, preclinically and clinically, as well as to provide perspective on how successful these practices have been at predicting circulating human metabolites.The results of this survey are presented as an initial snapshot of current industry-based metID practices, including our perspective on how a harmonized framework for the conduct of in vitro metID studies could be established. Future perspectives from current practices to emerging advances with greater translational capability are also provided.

The properties of axion with three different sets of parameters in two flavor Nambu-Jona-Lasinio model

Abstract While the properties of axions have been studied primarily through high-energy physics and cosmology, there are some potential connections between the research results and the aerospace field. We study the properties of axions in hot and dense matter with three different sets of parameters in the Nambu-Jona-Lasinio model, including axion mass and self-coupling. We discussed axion mass and self-coupling, noting that axion properties are very sensitive to chiral phase transitions for three sets of parameters. The axion mass and self-coupling rapidly decrease in the chiral crossover region. The value of self-coupling becomes very sharp, appearing as a kinklike feature in the chiral phase transition.

Relaxation and rheology in beam-vibrated granular system

The yielding transition in dense granular matter under vibrated beams, despite its significance for animal and robotic locomotion on granular surfaces and underground structural engineering, remains underexplored. In this study, we systematically modulate the frequency and amplitude of beam vibrations through experiments and simulations to investigate the granular relaxation dynamics. We uncover dual yielding behaviors: gradual, ductile transitions in the time domain, where the system smoothly stabilizes, and abrupt, brittle transitions in the frequency domain, characterized by sharp shifts between metastable states and pronounced hysteresis, highlighting the dynamic consistency between the behavior of the beam and the granular materials. Through detailed analysis of the mesostructural evolution, encompassing particle motion, and mechanical stability, we unveil the root of the hysteresis as stemming from anomalous diffusion driven by memory effects, where the system's response is influenced by its stress history. These findings lead to the development of a nonmonotonic constitutive law that captures the unique frequency-dependent coupling between the beam and granular material. Our findings pave the way for advanced theoretical models in this domain, offering profound insights into the nuanced behaviors of vibrated granular systems.

Theoretical study on [formula omitted] and [formula omitted] correlation functions

We examine the Λ-4He (α) and Ξα momentum correlation in high-energy collisions to further elucidate the properties of the hyperon–nucleon interactions. For the Λα system, we compare Λα potential models with different strengths at short range. We find that the difference among the models is visible in the momentum correlation from a small-size source. This indicates that the Λα momentum correlation can constrain the property of the ΛN interaction at short range, which plays an essential role in dense nuclear matter. For the Ξα system, we employ the folding Ξα potential based on the lattice QCD ΞN interactions. The Ξα potential supports a Coulomb assisted bound state of Ξ5H in the Ξ−α channel, while the Ξ0α channel is unbound. To examine the sensitivity of the correlation function to the nature of the Ξα potential, we vary the potential strength simulating stronger and weaker interactions. The result of the correlation function clearly reflects the bound state nature in the Ξ−α correlation.

A NICER View of PSR J1231−1411: A Complex Case

Abstract Recent constraints on neutron star mass and radius have advanced our understanding of the equation of state (EOS) of cold dense matter. Some of them have been obtained by modeling the pulses of three millisecond X-ray pulsars observed by the Neutron Star Interior Composition Explorer (NICER). Here, we present a Bayesian parameter inference for a fourth pulsar, PSR J1231−1411, using the same technique with NICER and XMM-Newton data. When applying a broad mass-inclination prior from radio timing measurements and the emission region geometry model that can best explain the data, we find likely converged results only when using a limited radius prior. If limiting the radius to be consistent with the previous observational constraints and EOS analyses, we infer the radius to be 12.6 ± 0.3 km and the mass to be 1.04 − 0.03 + 0.05 M ⊙, each reported as the posterior credible interval bounded by the 16% and 84% quantiles. If using an uninformative prior but limited between 10 and 14 km, we find otherwise similar results, but R eq = 13.5 − 0.5 + 0.3 km for the radius. In both cases, we find a nonantipodal hot region geometry where one emitting spot is at the equator or slightly above, surrounded by a large colder region, and where a noncircular hot region lies close to southern rotational pole. If using a wider radius prior, we only find solutions that fit the data significantly worse. We discuss the challenges in finding the better fitting solutions, possibly related to the weak interpulse feature in the pulse profile.

Mimetic Weyl geometric gravity

We consider a mimetic type extension of the Weyl geometric gravity theory, by assuming that the metric of the space–time manifold can be parameterized in terms of a scalar field, called the mimetic field. The action of the model is obtained by starting from a conformally invariant gravitational action, constructed, in Weyl geometry, from the square of the Weyl scalar, the strength of the Weyl vector, and an effective matter term, respectively. After linearizing the action in the Weyl scalar by introducing an auxiliary scalar field, we include the mimetic field, constructed from the same auxiliary scalar field used to linearize the action, via a Lagrange multiplier. The conformal invariance of the action is maintained by imposing the trace condition on the effective matter energy–momentum tensor, built up from the ordinary matter Lagrangian, and some specific functions of the Weyl vector, and the scalar field, respectively, thus making the matter sector of the action conformally invariant. The field equations are derived by varying the action with respect to the metric tensor, the Weyl vector field, and the scalar field, respectively. We investigate the cosmological implications of the Mimetic Weyl geometric gravity by considering the dynamics of an isotropic and homogeneous Friedmann–Lemaitre–Robertson–Walker FLRW Universe. The generalized Friedmann equations of the model are derived, and their solutions are obtained numerically for a dust filled Universe. Moreover, we perform a detailed comparison of the predictions of the considered model with a set of observational data for the Hubble function, and with the results of the ΛCDM standard paradigm. Our results indicate that the present model give a good description of the observational data, and they reproduce almost exactly the predictions of the ΛCDM scenario. Hence, Mimetic Weyl geometric gravity can be considered a viable alternative to the standard approaches to cosmology, and to the gravitational phenomena.

Unravelling the Asphericities in the Explosion and Multifaceted Circumstellar Matter of SN 2023ixf

We present a detailed investigation of photometric, spectroscopic, and polarimetric observations of the Type II SN 2023ixf. Earlier studies have provided compelling evidence for a delayed shock breakout from a confined dense circumstellar matter (CSM) enveloping the progenitor star. The temporal evolution of polarization in the SN 2023ixf phase revealed three distinct peaks in polarization evolution at 1.4 days, 6.4 days, and 79.2 days, indicating an asymmetric dense CSM, an aspherical shock front and clumpiness in the low-density extended CSM, and an aspherical inner ejecta/He-core. SN 2023ixf displayed two dominant axes, one along the CSM-outer ejecta and the other along the inner ejecta/He-core, showcasing the independent origin of asymmetry in the early and late evolution. The argument for an aspherical shock front is further strengthened by the presence of a high-velocity broad absorption feature in the blue wing of the Balmer features in addition to the P-Cygni absorption post-16 days. Hydrodynamical light-curve modeling indicated a progenitor mass of 10 M ⊙ with a radius of 470 R ⊙ and explosion energy of 2 × 1051 erg, along with 0.06 M ⊙ of 56 Ni, though these properties are not unique due to modeling degeneracies. The modeling also indicated a two-zone CSM: a confined dense CSM extending up to 5 × 1014 cm with a mass-loss rate of 10−2 M ⊙ yr−1 and an extended CSM spanning from 5 × 1014 to at least 1016 cm with a mass-loss rate of 10−4 M ⊙ yr−1, both assuming a wind-velocity of 10 km s−1. The early-nebular phase observations display an axisymmetric line profile of [O i], redward attenuation of the emission of Hα post 125 days, and flattening in the Ks-band, marking the onset of dust formation.

Searching for Dark Matter Based on Gravitational Lensing

Gravitational lensing is a powerful astronomical tool in which scholars can accurately predict the distribution of dark matter in massive objects by observing the bending effects of light in the gravitational fields of huge objects (e.g., galaxies or galaxy clusters). Since dark matter does not emit directly, or is strongly interacts with ordinary matter, gravitational lensing gives us a unique view of observing and measuring dark matter. This study introduces some principles of gravitational lensing effect to provide favorable evidence in the study of dark matter and other celestial bodies (including an engineering study in the focal region of solar gravitational lensing (SGL) and other experiments). This research will see how the properties of the clear and focused gravitational lens are applied to celestial observations, and how they are captured by the detector. Strong gravitational lensing can better show distant galaxies (including high redshift) around the dark matter distribution, and through the several basic quantities in gravitational lens analytical and numerical calculation and analysis, to simulate the center of the supermassive black hole, and gravitational lensing image and model of dark matter mass can be detected and dark matter has the key evidences of the interaction. It reveals the intrinsic and distribution of dark matter, thus driving the understanding of the universe’s evolution and its fundamental components. Therefore, gravitational lensing has an irreplaceable value and a far-reaching influence in exploring the unsolved mystery of dark matter.

The glow of axion quark nugget dark matter

Context. The existence of axion quark nuggets is a potential consequence of the axion field, which provides a possible solution to the charge-conjugation parity violation in quantum chromodynamics. In addition to explaining the cosmological discrepancy of matter-antimatter asymmetry and a visible-to-dark-matter ratio of Ωdark/Ωvisible ≃ 5, these composite compact objects are expected to represent a potentially ubiquitous electromagnetic background radiation by interacting with ordinary baryonic matter. We conducted an in-depth analysis of axion quark nugget-baryonic matter interactions in the environment of the intracluster medium in the constrained cosmological Simulation of the LOcal Web (SLOW). Aims. Here, we aim to provide upper limit predictions on electromagnetic counterparts of axion quark nuggets in the environment of galaxy clusters by inferring their thermal and non-thermal emission spectrum originating from axion quark nugget-cluster gas interactions. Methods. We analyzed the emission of axion quark nuggets in a large sample of 161 simulated galaxy clusters using the SLOW simulation. These clusters are divided into a sub-sample of 150 galaxy clusters, ordered in five mass bins ranging from 0.8 to 31.7 × 1014 M⊙, along with 11 cross-identified galaxy clusters from observations. We investigated dark matter-baryonic matter interactions in galaxy clusters in their present stage at the redshift of z = 0 by assuming all dark matter consists of axion quark nuggets. The resulting electromagnetic signatures were compared to thermal Bremsstrahlung and non-thermal cosmic ray (CR) synchrotron emission in each galaxy cluster. We further investigated individual frequency bands imitating the observable range of the WMAP, Planck, Euclid, and XRISM telescopes for the most promising cross-identified galaxy clusters hosting detectable signatures of axion quark nugget emission. Results. We observed a positive excess in the low- and high-energy frequency windows, where thermal and non-thermal axion quark nugget emission can significantly contribute to (or even outshine) the emission of the intracluster medium (ICM) in frequencies up to νT ≲ 3842.19 GHz and νT ϵ [3.97, 10.99] × 1010GHz, respectively. Emission signatures of axion quark nuggets are found to be observable if CR synchrotron emission of individual clusters is sufficiently low. The degeneracy in the parameters contributing to an emission excess makes it challenging to offer predictions with respect to pinpointing specific regions of a positive axion quark nugget excess; however, a general increase in the total galaxy cluster emission is expected based on this dark matter model. Axion quark nuggets constitute an increment of 4.80% of the total galaxy cluster emission in the low-energy regime of νT ≲ 3842.19 GHz for a selection of cross-identified galaxy clusters. We propose that the Fornax and Virgo clusters represent the most promising candidates in the search for axion quark nugget emission signatures. Conclusions. The results from our simulations point towards the possibility of detecting an axion quark nugget excess in galaxy clusters in observations if their signatures can be sufficiently disentangled from the ICM radiation. While this model proposes a promising explanation for the composition of dark matter, with the potential to have this outcome verified by observations, we propose further changes that are aimed at refining our methods. Our ultimate goal is to identify the extracted electromagnetic counterparts of axion quark nuggets with even greater precision in the near future.

The shape of dark matter halos: A new fundamental cosmological invariance

In this article, we focus on the complex relationship between the shape of dark matter (DM) halos and the cosmological models underlying their formation. We have used three realistic cosmological models from the DEUS numerical simulation project. These three models have very distinct cosmological parameters (Ωm, σ8, and w) but their cosmic matter fields beyond the scale of DM halos are quasi-indistinguishable, providing an exemplary framework to examine the cosmological dependence of DM halo morphology. First, we developed a robust method for measuring the halo shapes detected in numerical simulations. This method avoids numerical artifacts on DM halo shape measurements, induced by the presence of substructures depending on the numerical resolution or by any spherical prior that does not respect the triaxiality of DM halos. We then obtain a marked dependence of the halo’s shape both on their mass and the cosmological model underlying their formation. As it is well known, the more massive the DM halo, the less spherical it is and we find that the higher the σ8 of the cosmological model, the more spherical the DM halos. Then, by reexpressing the properties of the shape of the halos in terms of the nonlinear fluctuations of the total cosmic matter field or only of the cosmic matter field which is internal to the halos, we managed to make the cosmological dependence disappear completely. This new fundamental cosmological invariance is a direct consequence of the nonlinear dynamics of the cosmic matter field. As the universe evolves, the nonlinear fluctuations of the cosmic field increase, driving the dense matter halos toward sphericity. The deviation from sphericity, measured by the prolaticity, triaxiality, and ellipticity of the DM halos, is therefore entirely encapsulated in the nonlinear power spectrum of the cosmic field. From this fundamental invariant relation, we retrieve with remarkable accuracy the root-mean-square of the nonlinear fluctuations and, consequently, the power spectrum of the cosmic matter field in which the halos formed. We also recover the σ8 amplitude of the cosmological model that governs the cosmic matter field at the origin of the DM halos. Our results therefore highlight, not only the nuanced relationship between DM halo formation and the underlying cosmology but also the potential of DM halo shape analysis of being a powerful tool for probing the nonlinear dynamics of the cosmic matter field.

Minimally deformed regular Hayward black hole solutions in Rastall theory

Abstract We profit from the minimal geometric deformation technique of
gravitational decoupling and extend the regular Hayward black hole,
to derive new black hole solutions in the context of Rastall theory.
The field equations with an extended matter source are decoupled
into two subsystems. The first of these are specified by the metric
components of the regular Hayward black hole while the second set
which contains the effects of the added source is solved by
utilizing a constraint imposed via a linear equation of state. By a
linear combination of the solutions of these two subsystems, we
obtain two cases of the extended solutions. For specified values of
the Rastall and decoupling parameters, we investigate some
physical/thermodynamical properties of the obtained models. It turns
out that only the first model preserves asymptotic flatness. It is
found that the first and second models are described by exotic and
ordinary matter, respectively. Finally, we obtain an acceptable
behavior of the Hawking temperature and thermodynamic stability for
both models.

Novel search for light dark photon in the forward experiments at the LHC

We propose a novel approach for discovering a light dark photon in the forward experiments at the LHC, including the SND@LHC and the FASER experiments. Assuming the dark photon is lighter than twice the electron mass and feebly interacts with ordinary matter, it is long-lived enough to pass through 100 m of rock in front of the forward experiments and also through the detector targets. However, some portion of them could be converted into an electron-positron pair inside the detector through their interaction with the detector target, leaving an isolated electromagnetic shower as a clear new physics signature of the dark photon. With copiously produced dark photons from neutral pion decays in the forward region of the LHC, we expect to observe sizable events inside the detector. Our estimation shows that more than 10 signal events of the dark photon could be observed in the range of kinetic mixing parameter, 6.2×10-5≲ϵ≲2×10-1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$6.2\ imes 10^{-5} \\lesssim \\epsilon \\lesssim 2\ imes 10^{-1}$$\\end{document} and 3×10-5≲ϵ≲2×10-1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$3\ imes 10^{-5} \\lesssim \\epsilon \\lesssim 2\ imes 10^{-1}$$\\end{document} for dark photon mass mA′≲\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$m_{A^\\prime } \\lesssim $$\\end{document} 1 MeV with integrated luminosities of 150 fb-1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$^{-1}$$\\end{document} and 3 ab-1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$^{-1}$$\\end{document}, respectively.

Structural design and test of superconducting magnet coil for the cooling storage ring external-target experiment

Abstract Heavy ion collision is an unique method for studying cold and dense nuclear matter in labs. The Cooling Storage Ring (CSR) External-target Experiment (CEE) at the Heavy Ion Research Facility in Lanzhou (HIRFL), China, is the first multi-purpose nuclear physics experimental device to operate in the GeV energy range. One of the key parts is a large acceptance dipole magnet, which is used to bend particles so that they can be detected by various detectors. A superconducting coil with the size of 3.1 m ×3.6 m × 2 m was designed to verify the rationality of the scheme. Although the coil-dominated superconducting magnet with NbTi has been used to reduce the weight and size of the magnet, large deformation and stress will occur in the cooldown and excitation stages owing to the large volume and weight. Therefore, it is crucial to design a reasonable structure to ensure the strength of the magnet and prevent the magnet from interfering with other components due to large deformation, and even the possibility of quenching. A truss supporter is proposed for the support of the superconducting coil. In this study, the structural design of the cold mass of a superconducting magnet is introduced, and its mechanical behaviors during cooldown and excitation are analyzed in detail. To verify the feasibility of the coil design and process route, a sub-size prototype was manufactured and tested at 4.2 K and reached the design current successfully.

Gravitational wave asteroseismology of charged strange stars in the Cowling approximation: the fluid pulsation modes

In this work we study, within the framework of Cowling approximation, the effect of the electric charge on the gravitational wave frequency of fluid oscillation modes of strange quark stars. For this purpose, the dense matter of the stellar fluid is described by the MIT bag model equation of state (EoS), while for the electric charge profile, we consider that the electric charge density is proportional to the energy density. We find that the gravitational wave frequencies change with the increment of electric charge; these effects are more noticeable at higher total mass values. We obtain that the f-mode is very sensitive to the change in the electric charge of the star. Furthermore, in the case of the p1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$p_1$$\\end{document} mode, the effect of the electric charge is not very significant. Our results reveal that the study of the fundamental pulsation mode of an electrically charged compact star is very important in distinguishing whether compact stars could contain electric charge. We also employ another electric charge distribution profile that follows a power law, and it is found that the f-mode change is more noticeable than the p1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$p_1$$\\end{document}-mode when the electric charge is incremented.