Universal scaling of the 3:2 twin-peak quasi-periodic oscillation frequencies with black hole mass and spin revisited

We discuss further observational support of an idea formulated a decade ago by Abramowicz, Klu{\'z}niak, McClintock and Remillard. They demonstrated that the 3:2 pairs of frequencies of the twin-peak black hole (BH) high-frequency quasi-periodic oscillations (QPOs) scale inversely with the BH masses and that the scaling covers the entire range from stellar to supermassive BHs. For this reason, they believed that the QPOs may be used for accurate measurements of masses and spins of BHs.Comment: ApJL, 798, L5 (2015

Relativistic Fe Kα\alpha Line Revealed in the Composite X-ray Spectrum of Narrow Line Seyfert 1 Galaxies --- do their black holes have averagely low or intermediate spins?

While a broad profile of the Fe K$\alpha$ emission line is frequently found in the X-ray spectra of typical Seyfert galaxies, the situation is unclear in the case of Narrow Line Seyfert 1 galaxies (NLS1s)---an extreme subset which are generally thought to harbor less massive black holes with higher accretion rates. In this paper, the ensemble property of the Fe K$\alpha$ line in NLS1s is investigated by stacking the X-ray spectra of a large sample of 51 NLS1s observed with {\it XMM-Newton}. The composite X-ray spectrum reveals a prominent, broad emission feature over 4--7 keV, characteristic of the broad Fe K$\alpha$ line. In addition, there is an indication for a possible superimposing narrow (unresolved) line, either emission or absorption, corresponding to Fe XXVI or Fe XXV, respectively. The profile of the broad emission feature can well be fitted with relativistic broad-line models, with the line energy consistent either with 6.4 keV (i.e., neutral Fe) or with 6.67 keV (i.e., highly ionized Fe), in the case of the narrow line being emission and absorption, respectively. Interestingly, there are tentative indications for low or intermediate values of the average spins of the black holes ($a<0.84$), as inferred from the profile of the composite broad line. If the observed feature is indeed a broad line rather than resulting from partial covering absorption, our results suggest that a relativistic Fe line may in fact be common in NLS1s; and there are tentative indications that black holes in NLS1s may not spin very fast in general.Comment: accepted for publication in MNRA

Some Developments of the Casimir Effect in pp-Cavity of (D+1)(D+1)-Dimensional Spacetime

The Casimir effect for rectangular boxes has been studied for several decades. But there are still some points unclear. Recently, there are new developments related to this topic, including the demonstration of the equivalence of the regularization methods and the clarification of the ambiguity in the regularization of the temperature-dependent free energy. Also, the interesting quantum spring was raised stemming from the topological Casimir effect of the helix boundary conditions. We review these developments together with the general derivation of the Casimir energy of the $p$-dimensional cavity in ($D+1$)-dimensional spacetime, paying special attention to the sign of the Casimir force in a cavity with unequal edges. In addition, we also review the Casimir piston, which is a configuration related to rectangular cavity.Comment: 49 pages, review articl

Solar system tests for realistic f(T)f(T) models with nonminimal torsion-matter coupling

In the previous paper, we have constructed two $f(T)$ models with nonminimal torsion-matter coupling extension, which are successful in describing the evolution history of the Universe including the radiation-dominated era, the matter-dominated era, and the present accelerating expansion. Meantime, the significant advantage of these models is that they could avoid the cosmological constant problem of $\Lambda$CDM. However, the nonminimal coupling between matter and torsion will affect the tests of Solar system. In this paper, we study the effects of Solar system in these models, including the gravitation redshift, geodetic effect and perihelion preccesion. We find that Model I can pass all three of the Solar system tests. For Model II, the parameter is constrained by the measure of the perihelion precession of Mercury.Comment: 10 page

Towards realistic f(T)f(T) models with nonminimal torsion-matter coupling extension

Using the observation data of SNeIa, CMB and BAO, we establish two concrete $f(T)$ models with nonminimal torsion-matter coupling extension. We study in detail the cosmological implication of our models and find they are successful in describing the observation of the Universe, its large scale structure and evolution. In other words, these models do not change the successful aspects of $\Lambda$CDM scenario under the error band of fitting values as describing the evolution history of the Universe including radiation-dominated era, matter-dominated era and the present accelerating expansion. Meanwhile, the significant advantage of these models is that they could avoid the cosmological constant problem of $\Lambda$CDM. A joint analysis is performed by using the data of CMB+BAO+JLA, which leads to $\Omega_{m0}=0.255\pm 0.010, \Omega_{b0}h^2=0.0221\pm 0.0003$ and $H_0=68.54\pm 1.27$ for model I and $\Omega_{m0}=0.306\pm 0.010, \Omega_{b0}h^2=0.0225\pm 0.0003$ and $H_0=60.97\pm 0.44$ for model II at 1$\sigma$ confidence level. The evolution of the decelaration parameter $q(a)$ and the effective equation of state $w_{DE}(a)$ are displayed. Furthermore, The resulted age of the Universe from our models is consistent with the ages of the oldest globular clusters. As for the fate of the Universe, model I results in a de Sitter accelerating phase while model II appears a power-law one, even though $w_{DE0}< -1$ makes model I look like a phantom at present time.Comment: 12 pages, 5 figure