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We have performed a parametrized post-Newtonian (PPN) test of a black hole spacetime using observational data of the star S0-2/S2 orbiting the massive black hole at our galactic center Sgr A*. After introducing our PPN model of black hole spacetime, we report the result of $\chi^2$ fitting of the PPN model with the observational data. A new finding through our PPN model is a detectability of the gravitational lens effect on the null geodesics connecting S0-2 and observer under the present observational uncertainties, if a PPN parameter is about one order larger than the value for general relativity case. On the other hand, the effect of black hole spin on the S0-2's motion is not detectable. Thus our present PPN test is performed with spherically symmetric vacuum black hole spacetime. The resultant value of the PPN parameter, which corresponds to the minimum $\chi^2$, implies that the gravitational field of Sgr A* is not of Schwarzschild metric or that there exists a sufficient amount of dark matters around Sgr A* to be detected by present telescopes. However, the difference between the minimum $\chi^2$ and the $\chi^2$ of Schwarzschild case is not large enough to ensure a statistical significance of non-Schwarzschild result. A more precise statistical analysis than $\chi^2$ statistics is necessary to extract a statistically significant information of the gravitational field of Sgr A* from present observational data. We will report a result by a Bayesian analysis in next paper., Comment: 43 pages, 4 figures, Accepted for Publication in Prog.Theor.Exp.Phys / Typos are corrected

We study magnetic field strengths along the jet in NGC~315. First, we estimated the angular velocity of rotation in the jet magnetosphere by comparing the measured velocity profile of NGC~315 with the magneto-hydrodynamic jet model of proposed by Tomimatsu and Takahashi. Similar to the case of M87, we find that the model can reproduce the logarithmic feature of the velocity profile and suggest a slowly rotating black hole magnetosphere for NGC~315. By substituting the estimated $\Omega_{F}$ into the jet power predicted by the Blandford-Znajek mechanism, we estimate the magnetic field strength near the event horizon of the central black hole as $5\times 10^{3}~{\rm G}\lesssim B_{H}\lesssim 2\times 10^{4}~{\rm G}$. We then estimate magnetic-field strengths along the jet by comparing the spectral index distribution obtained from VLBI observations with a synchrotron-emitting jet model. Then we constrain the magnetic field strength at a de-projected distance $z$ from the black hole to be in the range $0.06~{\rm G}\lesssim B(z)\lesssim 0.9~{\rm G}$ for $5.2 \times 10^{3}~r_{g}\lesssim z \lesssim 4.9 \times 10^{4}~r_{g}$, where $r_{g}$ represents the gravitational radius. By combining the obtained field strengths at the event horizon and the downstream section of the jet, we find that the accretion flow at the jet base is consistent with a magnetically arrested disk (MAD). We discuss a comparison of the jet power and the magnetic flux anchored to the event horizon in NGC~315 and M87., Comment: Accepted for publication in The Astrophysical Journal

The tremendous tidal force that is linked to the supermassive black hole (SMBH) at the center of our galaxy is expected to strongly subdue star formation in its vicinity. Stars within 1" from the SMBH thus likely formed further from the SMBH and migrated to their current positions. In this study, spectroscopic observations of the star S0-6/S10, one of the closest (projected distance from the SMBH of about 0.3") late-type stars were conducted. Using metal absorption lines in the spectra of S0-6, the radial velocity of S0-6 from 2014 to 2021 was measured, and a marginal acceleration was detected, which indicated that S0-6 is close to the SMBH. The S0-6 spectra were employed to determine its stellar parameters including temperature, chemical abundances ([M/H], [Fe/H], [alpha/Fe], [Ca/Fe], [Mg/Fe], [Ti/Fe]), and age. As suggested by the results of this study, S0-6 is very old (> ~10 Gyr) and has an origin different from that of stars born in the central pc region., Comment: 15 pages, 6 figures, 10 tables, accepted for publication in Proceedings of the Japan Academy, Ser. B, Physical and Biological Sciences

A linear analysis based on two-fluid equations in the approximation of a cold plasma, wherein the plasma temperature is assumed to be zero, demonstrates that a two-stream instability occurs in all cases. However, if this were true, the drift motion of electrons in an electric current over a wire would become unstable, inducing an oscillation in an electric circuit with ions bounded around specific positions. To avoid this peculiar outcome, we must assume a warm plasma with a finite temperature when discussing the criterion of instability. The two-stream instability in warm plasmas has typically been analyzed using kinetic theory to provide a general formula for the instability criterion from the distribution function of the plasma. However, the criteria based on kinetic theory do not have an easily applicable form. Here, we provide an easily applicable criterion for the instability based on the two-fluid model at finite temperatures, extensionally in the framework of special relativity. This criterion is relevant for analyzing two-stream instabilities in low-density plasmas in the universe and in Earth-based experimental devices., Comment: 18pages, 4 figures, accepted for pubblication on PoP

Motivated by the measured velocity profile of the M87 jet using the KVN and VERA Array (KaVA) by Park et al. indicating that the starting position of the jet acceleration is farther from the central engine of the jet than predicted in general relativistic magnetohydrodynamic simulations, we explore how to mitigate the apparent discrepancy between the simulations and the KaVA observation. We use a semi-analytic jet model proposed by Tomimatsu and Takahashi. consistently solving the trans-magnetic field structure but neglecting any dissipation effects. By comparing the jet model with the observed M87 jet velocity profile, we find that the model can reproduce the logarithmic feature of the velocity profile, and can fit the observed data when choosing $c/(100r_{g}) \lesssim \Omega_{F} \lesssim c/(70r_{g})$ where $r_{g}$ is the gravitational radius. While a total specific energy (${\cal E}$) of the jet changes the terminal bulk Lorentz factor of the jet, a slower angular velocity of the black hole magnetosphere (funnel region) ($\Omega_{F}$) makes a light-cylinder radius ($r_{\rm lc}$) larger and it consequently pushes out a location of a starting point of the jet acceleration. Using the estimated $\Omega_{F}$ we further estimate the magnetic field strength on the event horizon scale in M87 by assuming Blandford-Znajek (BZ) process is in action. The corresponding magnetic flux threading the event horizon of M87 is in good agreement with a magnetically arrested disc (MAD) regime., Comment: 27 pages, 10 figures; accepted for publication in ApJ

We explore superradiance for Alfv\'en waves (Alfv\'enic superradiance) in an axisymmetric rotating magnetosphere of a Kerr black hole within the force-free approximation. On the equatorial plane of the Kerr spacetime, the Alfv\'en wave equation is reduced to a one-dimensional Schr\"{o}dinger-type equation by separating variables of the wave function and introducing a tortoise coordinate mapping the inner and outer light surfaces to $-\infty$ and $+\infty$, respectively, and we investigate a wave scattering problem for Alfv\'en waves. An analysis of the asymptotic solutions of the wave equation and the conservation of the Wronskian give the superradiant condition for Alfv\'en waves, and it will be shown that the condition coincides with that for the Blandford-Znajek process. This means that when Alfv\'enic superradiance occurs, the Blandford-Znajek process also occurs in the force-free magnetosphere. Then, we evaluate the reflection rate of Alfv\'en waves numerically and confirm that Alfv\'enic superradiance is indeed possible in the Kerr spacetime. Moreover, we will discuss a resonant scattering of Alfv\'en waves, which is related to a "quasinormal mode" of the magnetosphere., Comment: 9 pages, 7 figures; matches published version in PRD

We discuss stationary and axisymmetric trans-magnetosonic outflows in the magnetosphere of a rotating black hole (BH). Ejected plasma from the plasma source located near the BH is accelerated far away to form a relativistic jet. In this study, the plasma acceleration efficiency and conversion of fluid energy from electromagnetic energy are considered by employing the trans-fast magnetosonic flow solution derived by Takahashi & Tomimatsu (2008). Considering the parameter dependence of magnetohydrodynamical flows, we search for the parameters of the trans-magnetosonic outflow solution to the recent M87 jet observations and obtain the angular velocity values of the magnetic field line and angular momentum of the outflow in the magnetized jet flow. Therefore, we estimate the locations of the outer light surface, Alfv\'en surface, and separation surface of the flow. We also discuss the electromagnetic energy flux from the rotating BH (i.e., the Blandford-Znajek process), which suggests that the energy extraction mechanism is effective for the M87 relativistic jet., Comment: 16 pages, 7 figures

We performed one-dimensional force-free magnetodynamic numerical simulations of the propagation of Alfven waves along magnetic field lines around a spinning black-hole-like object, the Banados--Teitelboim--Zanelli black string, to investigate the dynamic process of wave propagation and energy transport with Alfven waves. We considered axisymmetric and stationary magnetosphere and perturbed the background magnetosphere to obtain the linear wave equation for the Alfven wave mode. The numerical results show that the energy of Alfven waves monotonically increases as the waves propagate outwardly along the rotating curved magnetic field line around the ergosphere, where energy seems not to be conserved, in the case of energy extraction from the black string by the Blandford--Znajek mechanism. The apparent breakdown of energy conservation suggests the existence of an additional wave induced by the Alfven wave. Considering the additional fast magnetosonic wave induced by the Alfven wave, the energy conservation is recovered. Similar relativistic phenomena, such as the amplification of Alfven waves and induction of fast magnetosonic waves, are expected around a spinning black hole., Comment: 27 pages, 10 figures

Sagittarius A* (Sgr A*) is the central supermassive black hole with the mass $\sim 4\times 10^6 M_{\odot}$ in the Milky Way and stars are orbiting around it. In May 2018, one of the nearest stars to Sgr A* named S0-2/S2 experienced the pericenter passage. The redshift of photons from S0-2 had varied from $4000\>{\rm km\>s^{-1}}$ to $-2000\>{\rm km\>s^{-1}}$ during the pericenter passage, which is within $0.5\>{\rm yr}$. In this paper, we show that this steep variation of the redshift gives a strong constraint on a dark mass distribution inside the orbit of S0-2. By applying a simple $\chi^2$ analysis to the observed redshift, we can easily distinguish between the two models, the point mass model and the point mass plus an extended mass model without the best-fitting parameter search. Our redshift data during the pericenter passage in 2018 with Subaru/IRCS bound the amount of the extended mass inside the orbit of S0-2 less than $0.5\,\%$ ($\sim 2 \times 10^4 M_\odot$) of the mass of Sgr A*. This constraint obtained by our simple analysis is comparable to previous works with the best-fitting parameter search to the motion of S0-2 including the effect of the extended mass. We consider both the power-law and the Plummer models for the dark mass distribution model, but the significant difference between these results is not found., Comment: 10 pages, 9 figures, 2 tables

Traveling across several order of magnitude in distance, relativistic jets from strong gravity region to asymptotic flat spacetime region are believed to consist of several general relativistic magnetohydrodynamic (GRMHD) processes. We present a semi-analytical approach for modeling the global structures of a trans-fast magnetosonic relativistic jet, which should be ejected from a plasma source nearby a black hole in a funnel region enclosed by dense accreting flow and also disk corona around the black hole. Our model consistently includes the inflow and outflow part of the GRMHD solution along the magnetic field lines penetrating the black hole horizon. After the rotational energy of the black hole is extracted electromagnetically by the negative energy GRMHD inflow, the huge electromagnetic energy flux then propagates from the inflow to the outflow region across the plasma source, and in the outflow region the electromagnetic energy converts to the fluid kinetic energy. Eventually, the accelerated outflow must exceed the fast-magnetosonic wave speed. We apply the semi-analytical trans-fast magnetosonic flow model to the black hole magnetosphere for both parabolic and split-monopole magnetic field configurations, and discuss the general flow properties; that is, jet acceleration, jet magnetization, and the locations of some characteristic surfaces of the black hole magnetosphere. We have confirmed that, at large distance, the GRMHD jet solutions are in good agreement with the previously known trans-fast special relativistic magnetohydrodynamic (SRMHD) jet properties, as expected. The flexibility of the model provides a prompt and heuristic way to approximate the global GRMHD trans-fast magnetosonic jet properties., Comment: accpeted for publication in the Astrophysical Journal

The star S0-2, orbiting the Galactic central massive black hole candidate Sgr A*, passed its pericenter in May 2018. This event is the first chance to detect the general relativistic (GR) effect of a massive black hole, free from non-gravitational physics. The observable GR evidence in the event is the difference between the GR redshift and the Newtonian redshift of photons coming from S0-2. Within the present observational precision, the 1st post-Newtonian (1PN) GR evidence is detectable. In this paper, we give a theoretical analysis of the time evolution of the 1PN GR evidence, under a presupposition that is different from used in previous papers. Our presupposition is that the GR/Newtonian redshift is always calculated with the parameter values (the mass of Sgr A*, the initial conditions of S0-2, and so on) determined by fitting the GR/Newtonian motion of S0-2 with the observational data. It is then revealed that the difference of the GR redshift and the Newtonian one shows two peaks before and after the pericenter passage. This double-peak-appearance is due to our presupposition, and reduces to a single peak if the same parameter values are used in both GR and Newtonian redshifts as considered in previous papers. In addition to this theoretical discussion, we report our observational data obtained with the Subaru telescope by 2018. The quality and the number of Subaru data in 2018 are not sufficient to confirm the detection of the double-peak-appearance., Comment: Accepted for publication in PASJ (Publications of the Astronomical Society of Japan), 23 pages, 11 figures, 6 tables

The superradiant scattering of Alfv\'en waves (Alfv\'enic superradiance) in a forcefree magnetosphere is discussed to reveal the relationship between the Blandford-Znajek (BZ) process and superradiance. For simplicity, we consider a four-dimensional rotating black string spacetime of which each $z=\text{const}$ slice is a Ba\~nados-Teitelboim-Zanelli solution as an analogy of the equatorial plane of the Kerr spacetime. Then, it is confirmed that the condition for Alfv\'enic superradiance coincides with that for the BZ process, and the wave amplification can be very large due to a resonant scattering for some parameter sets of the wave frequency and the angular velocity of the magnetic field line. Moreover, by analysis of the Poynting flux, we first show that the BZ process can be interpreted as the long wavelength limit of Alfv\'enic superradiance., Comment: 7 pages, 5 figures, Matched to published version

General Relativity predicts that a star passing close to a supermassive black hole should exhibit a relativistic redshift. We test this using observations of the Galactic center star S0-2. We combine existing spectroscopic and astrometric measurements from 1995-2017, which cover S0-2's 16-year orbit, with measurements in 2018 March to September which cover three events during its closest approach to the black hole. We detect the combination of special relativistic- and gravitational-redshift, quantified using a redshift parameter, $\Upsilon$. Our result, $\Upsilon=0.88 \pm 0.17$, is consistent with General Relativity ($\Upsilon=1$) and excludes a Newtonian model ($\Upsilon=0$ ) with a statistical significance of 5 $\sigma$., Comment: 78 pages, 21 figures, accepted to Science, astrometry and radial velocity measurements, and posterior chains available here, http://www.astro.ucla.edu/~ghezgroup/gc/gr/data.zip

We study the effects of frame-dragging on the structure of force-free magnetospheres around rotating black holes. For slowly rotating black holes, analytic explorations often focus on transforming an exact force-free solution applicable to a static black hole into a solution approximately applicable to a slowly-rotating black hole via perturbations in black hole spin. We show that the single perturbed monopolar solution most commonly arrived at using such techniques is in fact a separatrix between two broad classes of solutions: those with poloidal magnetic fields that bend upwards towards the azimuthal axis and those that bend downwards towards the equatorial plane. This is because frame-dragging affects the toroidal magnetic field distributions, changing the force balance between poloidal magnetic field lines., Comment: Appendix with alternate derivations and further explanations added

If a magnetically dominated magnetosphere is to extract a black hole's rotational energy and transmit it to distant regions, then the inner light surface of that magnetosphere must lie within the ergoregion. That inner light surface condition limits the angular velocity of magnetic field lines. We take the distribution of magnetic field line angular velocity on the horizon to be a useful proxy for inner light surface location and study how different distributions affect the structure of energy-extracting magnetospheres. Within magnetospheres that exhibit differential field line bending towards both the azimuthal axis and the equatorial plane, we find that the total Poynting flux energy directed outward along the azimuthal axis can vary by over a factor of 100 for a single value of black hole spin., Comment: Updated to accepted version

We propose a new acceleration mechanism for charged particles by using cylindrical or spherical non-linear acoustic waves propagating in ion-electron plasma. The acoustic wave, which is described by the cylindrical or spherical Kortweg-de Vries equation, grows in its wave height as the wave shrinks to the center. Charged particles confined by the electric potential accompanied with the shrinking wave get energy by repetition of reflections. We obtain power law spectrums of energy for accelerated particles. As an application, we discuss briefly that high energy particles coming from the Sun are produced by the present mechanism., Comment: 17 pages, 18 figures

During the next closest approach of the orbiting star S2/S0-2 to the Galactic supermassive black hole (SMBH), it is estimated that RV uncertainties of ~ 10 km/s allow us to detect post-Newtonian effects throughout 2018. To evaluate an achievable uncertainty in RV and its stability, we have carried out near-infrared, high resolution (R ~ 20,000) spectroscopic monitoring observations of S2 using the Subaru telescope and the near-infrared spectrograph IRCS from 2014 to 2016. The Br-gamma absorption lines are used to determine the RVs of S2. The RVs we obtained are 497 km/s, 877 km/s, and 1108 km/s in 2014, 2015, and 2016, respectively. The statistical uncertainties are derived using the jackknife analysis. The wavelength calibrations in our three-year monitoring are stable: short-term (hours to days) uncertainties in RVs are < 0.5 km/s, and a long-term (three years) uncertainty is 1.2 km/s. The uncertainties from different smoothing parameter, and from the partial exclusion of the spectra, are found to be a few km/s. The final results using the Br-gamma line are 497 +- 17 (stat.) +- 3 (sys.) km/s in 2014, 877 +- 15 (stat.) +- 4 (sys.) km/s in 2015, and 1108 +- 12 (stat.) +- 4 (sys.) km/s in 2016. When we use two He I lines at 2.113\mum in addition to Br-gamma, the mean RVs are 513 km/s and 1114 km/s for 2014 and 2016, respectively. The standard errors of the mean are 16.2 km/s (2014) and 5.4 km/s (2016), confirming the reliability of our measurements. The difference between the RVs estimated by Newtonian mechanics and general relativity will reach about 200 km/s near the next pericenter passage in 2018. Therefore our RV uncertainties of 13 - 17 km/s with Subaru enable us to detect the general relativistic effects in the RV measurements with more than 10 sigma in 2018., Comment: 27 pages, 14 figures, 8 tables, submitted to PASJ

An energy extracting black hole magnetosphere can be defined by the location of its inner Alfv\'{e}n surface, which determines the rate of black hole energy extraction along a given magnetic field line. We study how the location of the inner Alfv\'{e}n surface can modify the structure of energy extracting black hole magnetospheres in the force-free limit. Hundreds of magnetospheres are numerically computed via a general relativistic extension of the Newtonian magnetofrictional method for a full range of black hole spins and flow parameters. We find that jet-like structures naturally form very close to the horizon for Alfv\'{e}n surfaces near the boundary of the ergosphere and that energy is extracted towards the equatorial plane for Alfv\'{e}n surfaces close to the horizon. This suggests that two broad classes of energy extracting black hole magnetospheres might exist; those that transmit extracted energy directly to distant observers, and those that transmit extracted energy to nearby accreting matter. Applied to transient high energy phenomena, we find that they might also differ in timescale by a factor of 20 or more., Comment: 23 Pages, 9 Figures

We present a model of the analog geometry in a magnetohydrodynamic (MHD) flow. For the MHD flow with magnetic pressure-dominated and gas pressure-dominated conditions, we obtain the magnetoacoustic metric for the fast MHD mode. For the slow MHD mode, on the other hand, the wave is governed by the advective-type equation without an isotropic dispersion term. Thus, the "distance" perpendicular to the wave propagation is not defined and the magnetoacoustic metric cannot be introduced. To investigate the properties of the magnetoacoustic geometry for the fast mode, we prepare a two-dimensional axisymmetric inflow and examine the behavior of magnetoacoustic rays which is a counterpart of the MHD waves in the eikonal limit. We find that the magnetoacoustic geometry is classified into three types depending on two parameters characterizing the background flow:~analog spacetimes of rotating black holes, ultra spinning stars with ergoregions, and spinning stars without ergoregions. We address the effects of the magnetic pressure on the effective geometries., Comment: 17 pages, 5 figures, final version to match the published version

We propose a novel theoretical model to describe a physical identity of the soft X-ray excess, ubiquitously detected in many Seyfert galaxies, by considering a steady-state, axisymmetric plasma accretion within the innermost stable circular orbit (ISCO) around a black hole (BH) accretion disk. We extend our earlier theoretical investigations on general relativistic magnetohydrodynamic (GRMHD) accretion which has implied that the accreting plasma can develop into a standing shock for suitable physical conditions causing the downstream flow to be sufficiently hot due to shock compression. We numerically calculate to examine, for sets of fiducial plasma parameters, a physical nature of fast MHD shocks under strong gravity for different BH spins. We show that thermal seed photons from the standard accretion disk can be effectively Compton up-scattered by the energized sub-relativistic electrons in the hot downstream plasma to produce the soft excess feature in X-rays. As a case study, we construct a three-parameter Comptonization model of inclination angle $\theta_{\rm obs}$, disk photon temperature $kT_{\rm in}$ and downstream electron energy $kT_e$ to calculate the predicted spectra in comparison with a 60 ks {\it XMM-Newton}/EPIC-pn spectrum of a typical radio-quiet Seyfert 1 AGN, Ark~120. Our $\chi^2$-analyses demonstrate that the model is plausible in successfully describing data for both non-spinning and spinning BHs with the derived range of $61.3~{\rm keV} \lesssim kT_e \lesssim 144.3~{\rm keV}$, $21.6~{\rm eV} \lesssim kT_{\rm in} \lesssim 34.0~{\rm eV}$ and $17.5\degr \lesssim \theta_{\rm obs} \lesssim 42.6\degr$ indicating a compact Comptonizing region of $3-4$ gravitational radii that resembles the putative X-ray coronae., Comment: accepted to ApJ; 39 pages, 11 figures