We investigate the structure and radial oscillations of anisotropic compact stars composed of dark energy, using the vanishing complexity factor formalism within general relativity. This novel approach establishes a direct link between the energy density and anisotropic factor, providing a robust framework for studying these exotic stellar objects. Employing an Extended Chaplygin Gas equation of state, we numerically compute interior solutions for both isotropic and anisotropic stars, revealing distinct differences in their properties. Additionally, we examine the oscillation modes and frequencies of these stars, highlighting the impact of anisotropy on their pulsational behaviour. Our results reveal distinct differences in the stellar properties, such as the metric potentials, pressure, speed of sound, and relativistic adiabatic index, between the two cases. Furthermore, we calculate the large frequency separation for the fundamental and first excited modes, offering insights relevant for future asteroseismology studies. Our findings shed light on the complex interplay of gravity, matter, and anisotropy in compact stars, providing a new perspective on dark energy's role in their structure and dynamics.

Chile

Grigoris Panotopoulos

Spain

Ángel Rincón

Portugal

Ilídio Lopes

Anisotropic dark energy stars within vanishing complexity factor formalism: Hydrostatic equilibrium, radial oscillations, and observational implications

We investigate the peculiar nature of strange stars through an analysis of different quark models, i.e. vBag model and CFL model equation of states at different parameter sets, and focus on understanding the equation of state governing the intriguing central compact object (CCO) within the supernova remnant HESS J1731-347, with a mass and radius of  $$M = 0.77^{+0.20}_{-0.17} M_{\odot }$$  <math> <mrow> <mi>M</mi> <mo>=</mo> <mn>0</mn> <mo>.</mo> <msubsup> <mn>77</mn> <mrow> <mo>-</mo> <mn>0.17</mn> </mrow> <mrow> <mo>+</mo> <mn>0.20</mn> </mrow> </msubsup> <msub> <mi>M</mi> <mo>⊙</mo> </msub> </mrow> </math>   and  $$R = 10.4^{+0.86}_{-0.78}$$  <math> <mrow> <mi>R</mi> <mo>=</mo> <mn>10</mn> <mo>.</mo> <msubsup> <mn>4</mn> <mrow> <mo>-</mo> <mn>0.78</mn> </mrow> <mrow> <mo>+</mo> <mn>0.86</mn> </mrow> </msubsup> </mrow> </math>   km, respectively. Additionally, we compare the radial oscillations of two models to determine the frequency of the HESS J1731-347 compact object at its maximum mass. The frequencies of radial oscillations are computed for each of the four EoSs considered. In total, the 10 lowest radial frequencies for each of those EoSs have been computed. By delving into these aspects, we aim at deepening our understanding of strange stars and their connection to the observed HESS J1731-347 mass-radius relationship.

Ishfaq Rather

Quark models and radial oscillations: decoding the HESS J1731-347 compact object’s equation of state

We investigate the effects of a nonstandard interaction (NSI) extension of the standard model of particle physics on solar neutrino flavor oscillations. This NSI model introduces a <math><mrow><msub><mrow><mi>U</mi></mrow><mrow><msup><mrow><mi>Z</mi></mrow><mrow><mo>′</mo></mrow></msup></mrow></msub><mo>(</mo><mn>1</mn><mo>)</mo></mrow></math> gauge symmetry through a <math><msup><mi>Z</mi><mo>′</mo></msup></math> boson that mixes with the photon, creating a neutral current between active neutrinos and matter fields via a unique coupling to up and down quarks. The interaction is defined by a single parameter, <math><msub><mi>ζ</mi><mi>o</mi></msub></math>, which is related to the <math><mrow><msup><mrow><mi>Z</mi></mrow><mrow><mo>′</mo></mrow></msup></mrow></math> boson’s mass <math><msub><mi>m</mi><msup><mi>Z</mi><mo>′</mo></msup></msub></math> and coupling constant <math><msub><mi>g</mi><msup><mi>Z</mi><mo>′</mo></msup></msub></math>. Notably, this model relaxes the bounds on coherent elastic neutrino-nucleus scattering experiments and fits the experimental values of the anomalous magnetic dipole moment of the muon. In this study, we use solar neutrino measurements and an up-to-date standard solar model to evaluate the neutrino flavor oscillations and assess the constraints on <math><msub><mi>ζ</mi><mi>o</mi></msub></math>. Our study indicates that the NSI model aligns with the current solar neutrino data when <math><msub><mi>ζ</mi><mi>o</mi></msub></math> is between <math><mo>−</mo><mn>0.7</mn></math> and 0.002. These models have <math><msubsup><mi>χ</mi><mi>ν</mi><mn>2</mn></msubsup></math> values equal to or better than the standard neutrino flavor oscillation model, which stands at a <math><msubsup><mi>χ</mi><mi>ν</mi><mn>2</mn></msubsup></math> of 3.12. The best NSI model comes with a <math><msub><mi>ζ</mi><mi>o</mi></msub></math> value of <math><mrow><mo>−</mo><mn>0.2</mn></mrow></math> and a <math><msubsup><mi>χ</mi><mi>ν</mi><mn>2</mn></msubsup></math> of 2.96. Including extra data from the Darwin experiment in our analysis refines the range of <math><msub><mi>ζ</mi><mi>o</mi></msub></math> values from <math><mo>−</mo><mn>0.7</mn></math> to 0.002, down to <math><mo>−</mo><mn>0.5</mn></math> to <math><mo>−</mo><mn>0.002</mn></math>. These results hint at the possible existence of novel interactions, given that NSI models achieve a comparable or superior fit to the solar neutrino data when contrasted with the prevailing standard model of neutrino flavor oscillation.

Exploring nonstandard quark interactions through solar neutrino studies

Within Einstein’s General Relativity we study exotic stars made of dark energy assuming an extended Chaplygin gas equation-of-state. Taking into account the presence of anisotropies, we employ the formalism based on the complexity factor to solve the structure equations numerically, obtaining thus interior solutions describing hydrostatic equilibrium. Making use of well-established criteria we demonstrate that the solutions are well behaved and realistic. A comparison with another, more conventional approach, is made as well.

Anisotropic stars made of exotic matter within the complexity factor formalism

LOPES, the LOFAR prototype station, was an antenna array for cosmic-ray air showers operating from 2003 to 2013 within the KASCADE-Grande experiment. Meanwhile, the analysis is finished and the data of air-shower events measured by LOPES are available with open access in the KASCADE Cosmic Ray Data Center (KCDC). This article intends to provide a summary of the achievements, results, and lessons learned from LOPES. By digital, interferometric beamforming the detection of air showers became possible in the radio-loud environment of the Karlsruhe Institute of Technology (KIT). As a prototype experiment, LOPES tested several antenna types, array configurations and calibration techniques, and pioneered analysis methods for the reconstruction of the most important shower parameters, i.e., the arrival direction, the energy, and mass-dependent observables such as the position of the shower maximum. In addition to a review and update of previously published results, we also present new results based on end-to-end simulations including all known instrumental properties. For this, we applied the detector response to radio signals simulated with the CoREAS extension of CORSIKA, and analyzed them in the same way as measured data. Thus, we were able to study the detector performance more accurately than before, including some previously inaccessible features such as the impact of noise on the interferometric cross-correlation beam. These results led to several improvements, which are documented in this paper and can provide useful input for the design of future cosmic-ray experiments based on the digital radio-detection technique.

Germany

W. Apel

Mexico

J. Arteaga-Velázquez

Netherlands

L. Bähren

K. Bekk

Italy

M. Bertaina

P. Biermann

J. Blümer

H. Bozdog

E. Cantoni

A. Chiavassa

K. Daumiller

Brazil

V. Souza

F. Di Pierro

P. Doll

R. Engel

H. Falcke

B. Fuchs

H. Gemmeke

C. Grupen

A. Haungs

D. Heck

J. Hörandel

A. Horneffer

D. Huber

T. Huege

Romania

P. Isar

K.H. Kampert

D. Kang

O. Krömer

J. Kuijpers

K. Link

Poland

P. Łuczak

M. Ludwig

H. Mathes

M. Melissas

C. Morello

S. Nehls

J. Oehlschläger

N. Palmieri

T. Pierog

J. Rautenberg

H. Rebel

M. Roth

C. Rühle

A. Saftoiu

H. Schieler

A. Schmidt

S. Schoo

United States

F.G. Schröder

O. Sima

G. Toma

G. Trinchero

A. Weindl

J. Wochele

J. Zabierowski

J. Zensus

Final results of the LOPES radio interferometer for cosmic-ray air showers

We obtain well behaved interior solutions describing hydrostatic equilibrium of anisotropic relativistic stars in scale-dependent gravity, where Newton’s constant is allowed to vary with the radial coordinate throughout the star. Assuming (1) a linear equation-of-state in the MIT bag model for quark matter, and (2) a certain profile for the energy density, we integrate numerically the generalized structure equations, and we compute the basic properties of the strange quark stars, such as mass, radius and compactness. Finally, we demonstrate that stability criteria as well as the energy conditions are fulfilled. Our results show that a decreasing Newton’s constant throughout the objects leads to slightly more massive and more compact stars.

Interior solutions of relativistic stars with anisotropic matter in scale-dependent gravity

We compute the lowest frequency radial oscillation modes of boson stars. It is assumed that the object is made of pseudo-Goldstone bosons subjected to a scalar potential that leads to a repulsive self-interaction force, and which is characterized by two unknown mass scales m (mass of the particle) and F (decay constant). First we integrate the Tolman-Oppenheimer-Volkoff equations for the hydrostatic equilibrium of the star, and then we solve the Sturm-Liouville boundary value problem for the perturbations using the shooting method. The effective potential that enters into the Schrödinger-like equation as well as several associated eigenfunctions are shown as well. Moreover, we found that the large frequency separation, i.e. the difference between consecutive modes, is proportional to the square root of the mass of the star and the cube of the mass scale defined by <math><mi>Λ</mi><mo>≡</mo><msqrt><mrow><mi>m</mi><mi>F</mi></mrow></msqrt></math>.

Radial oscillations of boson stars made of ultralight repulsive dark matter

The next generation of solar neutrino detectors will provide a precision measure of the <math><mrow><mmultiscripts><mrow><mi>B</mi></mrow><mprescripts></mprescripts><none></none><mrow><mn>8</mn></mrow></mmultiscripts></mrow></math> electron-neutrino spectrum in the energy range from 1–15 MeV. Although the neutrino spectrum emitted by <math><mrow><mmultiscripts><mrow><mi>B</mi></mrow><mprescripts></mprescripts><none></none><mrow><mn>8</mn></mrow></mmultiscripts></mrow></math> <math><mi>β</mi></math>-decay reactions in the Sun’s core is identical to the neutrino spectrum measured in the laboratory, due to vacuum and matter flavor oscillations, this spectrum will be very different from that measured on Earth by the different solar neutrino experiments. We study how the presence of dark matter (DM) in the Sun’s core changes the shape of the <math><mrow><mmultiscripts><mrow><mi>B</mi></mrow><mprescripts></mprescripts><none></none><mrow><mn>8</mn></mrow></mmultiscripts></mrow></math> electron-neutrino spectrum. These modifications are caused by local variations of the electronic density and the <math><mrow><mmultiscripts><mrow><mi>B</mi></mrow><mprescripts></mprescripts><none></none><mrow><mn>8</mn></mrow></mmultiscripts></mrow></math> neutrino source, induced by local changes of the temperature, density and chemical composition. Particularly relevant are the shape changes at low and medium energy range (<math><msub><mi>E</mi><mi>ν</mi></msub><mo>≤</mo><mn>10</mn><mtext> </mtext><mtext> </mtext><mi>MeV</mi></math>), for which the experimental noise level is expected to be quite small. If such a distortion in the <math><mrow><mmultiscripts><mrow><mi>B</mi></mrow><mprescripts></mprescripts><none></none><mrow><mn>8</mn></mrow></mmultiscripts><msub><mrow><mi>ν</mi></mrow><mrow><mi>e</mi></mrow></msub></mrow></math> spectrum were to be observed, this would strongly hint in favor of the existence of DM in the Sun’s core. The <math><mrow><mmultiscripts><mrow><mi>B</mi></mrow><mprescripts></mprescripts><none></none><mrow><mn>8</mn></mrow></mmultiscripts></mrow></math> electron-neutrino spectrum provides a complementary method to helioseismology and total neutrino fluxes for constraining the DM properties. In particular, we study the impact of light asymmetric DM on solar neutrino spectra. Accurate neutrino spectra measurements could help to determine whether light asymmetric DM exists in the Sun’s core, since it has been recently advocated that this type of DM might resolve the solar abundance problem.

France

United Kingdom

Joseph Silk

Dark matter imprint on <math><mrow><mmultiscripts><mrow><mi>B</mi></mrow><mprescripts></mprescripts><none></none><mrow><mn>8</mn></mrow></mmultiscripts></mrow></math> neutrino spectrum

We predict the sterile neutrino spectrum of some of the key solar nuclear reactions and discuss the possibility of these being observed by the next generation of solar neutrino experiments. By using an up-to-date standard solar model with good agreement with current helioseismology and solar neutrino flux data sets, we found that from solar neutrino fluxes arriving on Earth only 3–4% correspond to the sterile neutrino. The most intense solar sources of sterile neutrinos are the pp and $$^7Be$$ <math><mrow><msup><mrow></mrow><mn>7</mn></msup><mi>B</mi><mi>e</mi></mrow></math>  nuclear reactions with a total flux of $$2.2\times 10^{9}$$ <math><mrow><mn>2.2</mn><mo>×</mo><msup><mn>10</mn><mn>9</mn></msup></mrow></math>  and $$1.8\times 10^{8}\;{{\mathrm{cm}}^2 {\mathrm{s}}^{-1}}$$ <math><mrow><mn>1.8</mn><mo>×</mo><msup><mn>10</mn><mn>8</mn></msup><mspace width="0.277778em"></mspace><mrow><msup><mrow><mi>cm</mi></mrow><mn>2</mn></msup><msup><mrow><mi>s</mi></mrow><mrow><mo>-</mo><mn>1</mn></mrow></msup></mrow></mrow></math> , followed by the $$^{13}N$$ <math><mrow><msup><mrow></mrow><mn>13</mn></msup><mi>N</mi></mrow></math>  and $$^{15}O$$ <math><mrow><msup><mrow></mrow><mn>15</mn></msup><mi>O</mi></mrow></math>  nuclear reactions with a total flux of $$1.9\times 10^{7}$$ <math><mrow><mn>1.9</mn><mo>×</mo><msup><mn>10</mn><mn>7</mn></msup></mrow></math>  and $$1.7\times 10^{7}\;{\mathrm{cm}}^2\, {\mathrm{s}}^{-1}$$ <math><mrow><mn>1.7</mn><mo>×</mo><msup><mn>10</mn><mn>7</mn></msup><mspace width="0.277778em"></mspace><msup><mrow><mi>cm</mi></mrow><mn>2</mn></msup><mspace width="0.166667em"></mspace><msup><mrow><mi>s</mi></mrow><mrow><mo>-</mo><mn>1</mn></mrow></msup></mrow></math> . Moreover, we compute the sterile neutrino spectra of the nuclear proton–proton nuclear reactions – pp, hep and $$^8B$$ <math><mrow><msup><mrow></mrow><mn>8</mn></msup><mi>B</mi></mrow></math>  and the carbon–nitrogen–oxygen – $$^{13}N$$ <math><mrow><msup><mrow></mrow><mn>13</mn></msup><mi>N</mi></mrow></math> , $$^{15}O$$ <math><mrow><msup><mrow></mrow><mn>15</mn></msup><mi>O</mi></mrow></math>  and $$^{17}F$$ <math><mrow><msup><mrow></mrow><mn>17</mn></msup><mi>F</mi></mrow></math>  and the spectral lines of $$^7Be$$ <math><mrow><msup><mrow></mrow><mn>7</mn></msup><mi>B</mi><mi>e</mi></mrow></math> .

The spectroscopy of solar sterile neutrinos

The radio technique is a promising method for detection of cosmic-ray air showers of energies around <math><mn>100</mn><mspace width="0.2em"></mspace><mtext>PeV</mtext></math> and higher with an array of radio antennas. Since the amplitude of the radio signal can be measured absolutely and increases with the shower energy, radio measurements can be used to determine the air-shower energy on an absolute scale. We show that calibrated measurements of radio detectors operated in coincidence with host experiments measuring air showers based on other techniques can be used for comparing the energy scales of these host experiments. Using two approaches, first via direct amplitude measurements, and second via comparison of measurements with air shower simulations, we compare the energy scales of the air-shower experiments Tunka-133 and KASCADE-Grande, using their radio extensions, Tunka-Rex and LOPES, respectively. Due to the consistent amplitude calibration for Tunka-Rex and LOPES achieved by using the same reference source, this comparison reaches an accuracy of approximately <math><mn>10</mn><mtext>%</mtext></math> – limited by some shortcomings of LOPES, which was a prototype experiment for the digital radio technique for air showers. In particular we show that the energy scales of cosmic-ray measurements by the independently calibrated experiments KASCADE-Grande and Tunka-133 are consistent with each other on this level.

W.D. Apel

J.C. Arteaga-Velázquez

Russia

P.A. Bezyazeekov

P.L. Biermann

I.M. Brancus

N.M. Budnev

V. de Souza

O. Fedorov

O.A. Gress

R. Hiller

J.R. Hörandel

P.G. Isar

Y. Kazarina

M. Kleifges

E.E. Korosteleva

D. Kostunin

L.A. Kuzmichev

N. Lubsandorzhiev

H.J. Mathes

R.R. Mirgazov

R. Monkhoev

E.A. Osipova

A. Pakhorukov

L. Pankov

V.V. Prosin

G.I. Rubtsov

G.C. Trinchero

R. Wischnewski

A. Zagorodnikov

J.A. Zensus

A comparison of the cosmic-ray energy scales of Tunka-133 and KASCADE-Grande via their radio extensions Tunka-Rex and LOPES