Kinematics of the Broad-line Region of 3C 273 from a Ten-year Reverberation Mapping Campaign

Despite many decades of study, the kinematics of the broad-line region of 3C~273 are still poorly understood. We report a new, high signal-to-noise, reverberation mapping campaign carried out from November 2008 to March 2018 that allows the determination of time lags between emission lines and the variable continuum with high precision. The time lag of variations in H$\beta$ relative to those of the 5100 Angstrom continuum is $146.8_{-12.1}^{+8.3}$ days in the rest frame, which agrees very well with the Paschen-$\alpha$ region measured by the GRAVITY at The Very Large Telescope Interferometer. The time lag of the H$\gamma$ emission line is found to be nearly the same as for H$\beta$. The lag of the Fe II emission is $322.0_{-57.9}^{+55.5}$ days, longer by a factor of $\sim$2 than that of the Balmer lines. The velocity-resolved lag measurements of the H$\beta$ line show a complex structure which can be possibly explained by a rotation-dominated disk with some inflowing radial velocity in the H$\beta$-emitting region. Taking the virial factor of $f_{\rm BLR} = 1.3$, we derive a BH mass of $M_{\bullet} = 4.1_{-0.4}^{+0.3} \times 10^8 M_{\odot}$ and an accretion rate of $9.3\,L_{\rm Edd}\,c^{-2}$ from the H$\beta$ line. The decomposition of its $HST$ images yields a host stellar mass of $M_* = 10^{11.3 \pm 0.7} M_\odot$, and a ratio of $M_{\bullet}/M_*\approx 2.0\times 10^{-3}$ in agreement with the Magorrian relation. In the near future, it is expected to compare the geometrically-thick BLR discovered by the GRAVITY in 3C 273 with its spatially-resolved torus in order to understand the potential connection between the BLR and the torus.Comment: 17 pages, 12 figures, 6 tables, accepted for publication in The Astrophysical Journa

Multi-mode entanglement of N harmonic oscillators coupled to a non-Markovian reservoir

Multi-mode entanglement is investigated in the system composed of $N$ coupled identical harmonic oscillators interacting with a common environment. We treat the problem very general by working with the Hamiltonian without the rotating-wave approximation and by considering the environment as a non-Markovian reservoir to the oscillators. We invoke an $N$-mode unitary transformation of the position and momentum operators and find that in the transformed basis the system is represented by a set of independent harmonic oscillators with only one of them coupled to the environment. Working in the Wigner representation of the density operator, we find that the covariance matrix has a block diagonal form that it can be expressed in terms of multiples of $3\times 3$ and $4\times 4$ matrices. This simple property allows to treat the problem to some extend analytically. We illustrate the advantage of working in the transformed basis on a simple example of three harmonic oscillators and find that the entanglement can persists for long times due to presence of constants of motion for the covariance matrix elements. We find that, in contrast to what one could expect, a strong damping of the oscillators leads to a better stationary entanglement than in the case of a weak damping.Comment: 21 pages, 4 figure

Beyond spectroscopy. II. Stellar parameters for over twenty million stars in the northern sky from SAGES DR1 and Gaia DR3

We present precise photometric estimates of stellar parameters, including effective temperature, metallicity, luminosity classification, distance, and stellar age, for nearly 26 million stars using the methodology developed in the first paper of this series, based on the stellar colors from the Stellar Abundances and Galactic Evolution Survey (SAGES) DR1 and Gaia EDR3. The optimal design of stellar-parameter sensitive $uv$ filters by SAGES has enabled us to determine photometric-metallicity estimates down to $-3.5$, similar to our previous results with the SkyMapper Southern Survey (SMSS), yielding a large sample of over five million metal-poor (MP; [Fe/H]$\le -1.0$) stars and nearly one million very metal-poor (VMP; [Fe/H]$\le -2.0$) stars. The typical precision is around $0.1$ dex for both dwarf and giant stars with [Fe/H]$>-1.0$, and 0.15-0.25/0.3-0.4 dex for dwarf/giant stars with [Fe/H]$<-1.0$. Using the precise parallax measurements and stellar colors from Gaia, effective temperature, luminosity classification, distance and stellar age are further derived for our sample stars. This huge data set in the Northern sky from SAGES, together with similar data in the Southern sky from SMSS, will greatly advance our understanding of the Milky Way, in particular its formation and evolution.Comment: 14 pages, 14 figures, 3 tables, accepted by ApJ. arXiv admin note: text overlap with arXiv:2104.1415