We give a new algorithm to construct optimal alphabetic ternary trees, where every internal node has at most three children. This algorithm generalizes the classic Hu-Tucker algorithm, though the overall computational complexity has yet to be determined.
We report first results from a large project to measure black hole (BH) mass in high accretion rate active galactic nuclei (AGNs). Such objects may be different from other AGNs in being powered by slim accretion disks and showing saturated accretion
luminosities, but both are not yet fully understood. The results are part of a large reverberation mapping (RM) campaign using the 2.4-m Shangri-La telescope at the Yunnan Observatory in China. The goals are to investigate the gas distribution near the BH and the properties of the central accretion disks, to measure BH mass and Eddington ratios, and to test the feasibility of using such objects as a new type of cosmological candles. The paper presents results for three objects, Mrk 335, Mrk 142 and IRAS F12397+3333 with H$beta$ time lags relative to the 5100AA continuum of $10.6^{+1.7}_{-2.9}$, $6.4^{+0.8}_{-2.2}$ and $11.4^{+2.9}_{-1.9}$ days, respectively. The corresponding BH masses are $(8.3_{-3.2}^{+2.6})times 10^6M_{odot}$, $(3.4_{-1.2}^{+0.5})times 10^6M_{odot}$ and $(7.5_{-4.1}^{+4.3})times 10^6M_{odot}$, and the lower limits on the Eddington ratios 0.6, 2.3, and 4.6 for the minimal radiative efficiency of 0.038. Mrk 142 and IRAS F12397+333 (extinction corrected) clearly deviate from the currently known relation between H$beta$ lag and continuum luminosity. The three Eddington ratios are beyond the values expected in thin accretion disks and two of them are the largest measured so far among objects with RM-based BH masses. We briefly discuss implications for slim disks, BH growth and cosmology.
It has been suggested that the high metallicity generally observed in active galactic nuclei (AGNs) and quasars originates from ongoing star formation in the self-gravitating part of accretion disks around the supermassive black holes. We designate t
his region as the star forming (SF) disk, in which metals are produced from supernova explosions (SNexp) while at the same time inflows are driven by SNexp-excited turbulent viscosity to accrete onto the SMBHs. In this paper, an equation of metallicity governed by SNexp and radial advection is established to describe the metal distribution and evolution in the SF disk. We find that the metal abundance is enriched at different rates at different positions in the disk, and that a metallicity gradient is set up that evolves for steady-state AGNs. Metallicity as an integrated physical parameter can be used as a probe of the SF disk age during one episode of SMBH activity. In the SF disk, evaporation of molecular clouds heated by SNexp blast waves unavoidably forms hot gas. This heating is eventually balanced by the cooling of the hot gas, but we show that the hot gas will escape from the SF disk before being cooled, and diffuse into the BLRs forming with a typical rate of $sim 1sunmyr$. The diffusion of hot gas from a SF disk depends on ongoing star formation, leading to the metallicity gradients in BLR observed in AGNs. We discuss this and other observable consequences of this scenario.
It is found that feii emission contributes significantly to the optical and ultraviolet spectra of most active galactic nuclei. The origin of the optical/UV feii emission is still a question open to debate. The variability of feii would give clues to
this origin. Using 7.5 yr spectroscopic monitoring data of one Palomer-Green (PG) quasi-stellar object (QSO), PG 1700+518, with strong optical feii emission, we obtain the light curves of the continuum lv, feii, the broad component of hb, and the narrow component of hb by the spectral decomposition. Through the interpolation cross-correlation method, we calculate the time lags for light curves of feii, the total hb, the broad component of hb, and the narrow component of hb with respect to the continuum light curve. We find that the feii time lag in PG1700+518 is $209^{+100}_{-147}$ days, and the hb time lag cannot be determined. Assuming that feii and hb emission regions follow the virial relation between the time lag and the FWHM for the hb and feii emission lines, we can derive that the hb time lag is $148^{+72}_{-104}$ days. The hb time lag calculated from the empirical luminosity--size relation is 222 days, which is consistent with our measured feii time lag. Considering the optical feii contribution, PG 1700+518 shares the same characteristic on the spectral slope variability as other 15 PG QSOs in our previous work, i.e., harder spectrum during brighter phase.
Double-peaked [O III]5007, profiles in active galactic nuclei (AGNs) may provide evidence for the existence of dual AGNs, but a good diagnostic for selecting them is currently lacking. Starting from $sim$ 7000 active galaxies in SDSS DR7, we assemble
a sample of 87 type 2 AGNs with double-peaked [O III]5007, profiles. The nuclear obscuration in the type 2 AGNs allows us to determine redshifts of host galaxies through stellar absorption lines. We typically find that one peak is redshifted and another is blueshifted relative to the host galaxy. We find a strong correlation between the ratios of the shifts and the double peak fluxes. The correlation can be naturally explained by the Keplerian relation predicted by models of co-rotating dual AGNs. The current sample statistically favors that most of the [O III] double-peaked sources are dual AGNs and disfavors other explanations, such as rotating disk and outflows. These dual AGNs have a separation distance at $sim 1$ kpc scale, showing an intermediate phase of merging systems. The appearance of dual AGNs is about $sim 10^{-2}$, impacting on the current observational deficit of binary supermassive black holes with a probability of $sim 10^{-4}$ (Boroson & Lauer).
