The Landau level-superfluid modified factor and the overal soft X/γ-ray efficiency coefficient of a magnetar

Gao, Zhi; Peng, Qiu‐He; Wang, Na; Chou, Chih-Kang; Huo, Wensheng

doi:10.1007/s10509-011-0791-x

Cited by 23 publications

(13 citation statements)

References 56 publications

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“…Dong et al (2014)) found that both “outliers” of BH XRBs and bright AGNs follow a steeper fundamental plane of black hole activity. Coriat et al (2011) argued that the two fundamental planes are regulated by radiatively inefficient (e.g., ADAF) and radiatively efficient accretion processes (e.g., SSD + corona), respectively, if we assume the jet launching and radio radiation behave identically (see also, Deng et al 2020; Gao et al 2011a; Fu et al 2020; Li et al 2016; Zhu et al 2016; Wang et al 2020).…”

Section: Introductionmentioning

confidence: 99%

The fundamental plane of black hole activity for quiescent sources

Dong

Liu

et al. 2021

Astron Nachr

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In this work, we construct a sample of black hole X-ray binaries (BH XRBs), low-luminosity active galactic nuclei (LLAGNs), and FR Is with wider distribution of Eddington ratios and re-explore their fundamental plane of BH activities, that is, log L R = X log L X + M log L M BH + c 0. We find that the quiescent BH sources follow a similar fundamental plane (ξ X ∼ 0.6) with sub-Eddington BH sources very well, while the strong radio sources (e.g., FR Is) follow a steeper fundamental plane (ξ X ∼ 1.30). We also find that the radio-X-ray correlation of quiescent BH sources are still on the extension of sub-Eddington BH sources and the strong radio sources follow a steeper correlation (ξ X ∼ 1.30). The results are consistent with recent observations in BH XRBs. It is predicted that the X-ray emissions of both sub-Eddington BH sources and quiescent BH sources originate from radiatively inefficient accretion mode, while the X-ray emissions of strong radio sources dominantly originate from the jet.

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Section: Introductionmentioning

confidence: 99%

The fundamental plane of black hole activity for quiescent sources

Dong

Liu

et al. 2021

Astron Nachr

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“…However there is a serious mistake in their calculation. They use the following method to calculate the statistical weight (degeneracy) of the Landau level n. The possible microscopic state number density in the interval of momentum p z → p z + dp z along the magnetic field direction for the electron gas is given by (10) In their calculation. The result of the microscopic state number for the level (n +1) in the plane perpendicular to magnetic field is essentially equal to the area of the torus between (See Fig.2).…”

Section: A Misleading Approach Regarding the Fermi Energy Of The Elecmentioning

confidence: 99%

“…Following is how they calculate the number of microscopic states: the number density of microscopic states is , (11) by using Eq. (10). According to the Pauli Exclusion Principle, the number density of microscopic states is equal to electrons number density in a complete degenerate electron gas, , where Y e and ρ are electron fraction (5-8%) and mass density.…”

Section: A Misleading Approach Regarding the Fermi Energy Of The Elecmentioning

confidence: 99%

“…We have calculated in detail the x-ray luminosity of magnetars in terms of the electron capture process [10] , and making comparison with the observations for magnetars. We note that up to now, there are no other known theoretical models that can fully delineate the observed high x-ray luminosity of the magnetars.…”

Section: A Physical Mechanism Of High X-ray Luminosity For Magnetarsmentioning

confidence: 99%

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The Physics of Magnetars II - The Electron Fermi Energy of and the Origin of High X-ray Luminosity of Magnetars

Peng¹,

Zhang²,

Chou³

et al. 2016

ujpa

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In this paper we discuss in detail the quantization of Landau energy levels of a strongly magnetized and completely degenerate relativistic electron gas in neutron stars. In particular, we focus on the Fermi energy dependence of the magnetic field for a relativistic electron gas in the superstrong magnetic field of magnetars. We would like to point out that some of the results concerning the microscopic number density of states of a strongly magnetized electron gas given by well-known statistical physics text books are incorrect. The repeated use of these results in the last five decades probably seriously affects the physics of neutron stars and magnetars. The quantization of Landau energy levels is accurately delineated in terms of the Dirac -δ function. Relatively simple calculation shows that the Fermi energy of a relativistic electron gas in magnetars with superstrong magnetic fields B . On the basis of this simple but important new result we are leading naturally to propose a new mechanism for the production of high X-ray luminosity from magnetars.

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“…The Fermi energy of relativistic electrons E F (e) is one of most important and indispensable physical parameters in the EoS, and varies with matter density ρ. The electron Fermi energy influences directly weak-interaction processes including modified URCA reactions 4 , electron capture 5,6,7,8,9 and so on, in the circumstance of a NS. These influences will change intrinsic EoS, interior structure and heat evolution, and even affect the whole properties of the star.…”

Section: Introductionmentioning

confidence: 99%

Numerically fitting the electron Fermi energy and the electron fraction in a neutron star

Gao

et al. 2016

Int. J. Mod. Phys. D

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Based on the basic definition of the Fermi energy of degenerate and relativistic electrons, we obtain a special solution to the electron Fermi energy, [Formula: see text], and express [Formula: see text] as a function of the electron fraction, [Formula: see text], and matter density, [Formula: see text]. We obtain several useful analytical formula for [Formula: see text] and [Formula: see text] within classical models and the work of Dutra et al. (2014) (Type-2) in relativistic mean-field theory are obtained using numerically fitting. When describing the mean-field Lagrangian, density, we adopt the TMA parameter set, which is remarkably consistent with the updated astrophysical observations of neutron stars (NSs). Due to the importance of the density dependence of the symmetry energy, [Formula: see text], in nuclear astrophysics, a brief discussion on [Formula: see text] and its slop is presented. Combining these fitting formula with boundary conditions for different density regions, we can evaluate the value of [Formula: see text] in any given matter density, and obtain a schematic diagram of [Formula: see text] as a continuous function of [Formula: see text]. Compared with previous studies on the electron Fermi energy in other studies models, our methods of calculating [Formula: see text] are more simple and convenient, and can be universally suitable for the relativistic electron regions in the circumstances of common neutron stars. We have deduced a general expression of [Formula: see text] and [Formula: see text], which could be used to indirectly test whether one equation of state of a NS is correct in our future studies on neutron star matter properties. Since URCA reactions are expected in the center of a massive star due to high-value electron Fermi energy and electron fraction, this study could be useful in the future studies on the NS thermal evolution.

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The Landau level-superfluid modified factor and the overal soft X/γ-ray efficiency coefficient of a magnetar

Cited by 23 publications

References 56 publications

The fundamental plane of black hole activity for quiescent sources

The fundamental plane of black hole activity for quiescent sources

The Physics of Magnetars II - The Electron Fermi Energy of and the Origin of High X-ray Luminosity of Magnetars

Numerically fitting the electron Fermi energy and the electron fraction in a neutron star

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