The Signature of Microlensing in QSO Variability-Redshift Correlations

A recently discovered inverse correlation between QSO redshift and long-term continuum variability timescales was suggested to be the signature of microlensing on cosmological scales (Hawkins 1993). A general theoretical method for calculating such correlations is presented and applied to various lensing scenarios in the framework of $\Lambda = 0$ Friedmann cosmologies. It is shown that the observed timescales can be strongly influenced by the observational limitations: the finite duration of the monitoring campaign and the finite photometric sensitivity. In most scenarios the timescales increase with source redshift, $z_s$, although slower than the $1+z_s$ time dilation expected of intrinsic variability. A decrease can be obtained for an extended source observed with moderate sensitivity. In this case, only lenses no further away than several hundreds Mpc participate in the lensing. The resulting optical depth is too small to explain the common long-term QSO variability unless an extremely high local lens density is assumed. These results do not support the idea that the reported inverse correlation can be attributed to microlensing of a uniform QSO sample by a uniform distribution of lenses. The possibility of using observations at various wavelengths and QSO samples at various positions to identify microlensing in QSO variability is also discussed.Comment: Self-unpacking, uuencoded postscript file, 10 pages with 7 figures included. Accepted for publication by the MNRAS

Constraining the dark cusp in the Galactic Center by long-period binaries

Massive black holes (MBHs) in galactic nuclei are believed to be surrounded by a high density stellar cluster, whose mass is mostly in hard-to-detect faint stars and compact remnants. Such dark cusps dominate the dynamics near the MBH: a dark cusp in the Galactic center (GC) of the Milky Way would strongly affect orbital tests of General Relativity there; on cosmic scales, dark cusps set the rates of gravitational wave emission events from compact remnants that spiral into MBHs, and they modify the rates of tidal disruption events, to list only some implications. A recently discovered long-period massive young binary (P_12 <~ 1 yr, M_12 ~ O(100 M_sun), T_12 ~ 6x10^6 yr), only ~0.1 pc from the Galactic MBH (Pfuhl et al 2013), sets a lower bound on the 2-body relaxation timescale there, min t_rlx ~ (P_12/M_12)^(2/3)T_12 ~ 10^7 yr, and correspondingly, an upper bound on the stellar number density, max n ~ few x 10^8/ 1/pc^3, based on the binary's survival against evaporation by the dark cusp. However, a conservative dynamical estimate, the drain limit, implies t_rlx > O(10^8) yr. Such massive binaries are thus too short-lived and tightly bound to constrain a dense relaxed dark cusp. We explore here in detail the use of longer-period, less massive and longer-lived binaries (P_12 ~ few yr, M_12 ~ 2-4 M_sun, T_12 ~ 10^8-10^10 yr), presently just below the detection threshold, for probing the dark cusp, and develop the framework for translating their future detections among the giants in the GC into dynamical constraints.Comment: 13 pp. Submitted to Ap

How to Construct Polar Codes

A method for efficiently constructing polar codes is presented and analyzed. Although polar codes are explicitly defined, straightforward construction is intractable since the resulting polar bit-channels have an output alphabet that grows exponentially with he code length. Thus the core problem that needs to be solved is that of faithfully approximating a bit-channel with an intractably large alphabet by another channel having a manageable alphabet size. We devise two approximation methods which "sandwich" the original bit-channel between a degraded and an upgraded version thereof. Both approximations can be efficiently computed, and turn out to be extremely close in practice. We also provide theoretical analysis of our construction algorithms, proving that for any fixed $\epsilon > 0$ and all sufficiently large code lengths $n$, polar codes whose rate is within $\epsilon$ of channel capacity can be constructed in time and space that are both linear in $n$

The torquing of circumnuclear accretion disks by stars and the evolution of massive black holes

An accreting massive black hole (MBH) in a galactic nucleus is surrounded by a dense stellar cluster. We analyze and simulate numerically the evolution of a thin accretion disk due to its internal viscous torques, due to the frame-dragging torques of a spinning MBH (the Bardeen-Petterson effect) and due to the orbit-averaged gravitational torques by the stars (Resonant Relaxation). We show that the evolution of the MBH mass accretion rate, the MBH spin growth rate, and the covering fraction of the disk relative to the central ionizing continuum source, are all strongly coupled to the stochastic fluctuations of the stellar potential via the warps that the stellar torques excite in the disk. These lead to fluctuations by factors of up to a few in these quantities over a wide range of timescales, with most of the power on timescales >~(M_bh/M_d)P(R_d), where M_bh and M_d are the masses of the MBH and disk, and P is the orbital period at the disk's mass-weighted mean radius R_d. The response of the disk is stronger the lighter it is and the more centrally concentrated the stellar cusp. As proof of concept, we simulate the evolution of the low-mass maser disk in NGC4258, and show that its observed O(10 deg) warp can be driven by the stellar torques. We also show that the frame-dragging of a massive AGN disk couples the stochastic stellar torques to the MBH spin and can excite a jitter of a few degrees in its direction relative to that of the disk's outer regions.Comment: ApJ, in press. Updated to reflect published version, including high order viscosity terms, improved variability analysi

Key questions about Galactic Center dynamics

I discuss four key questions about Galactic Center dynamics, their implications for understanding both the environment of the Galactic MBH and galactic nuclei in general, and the progress made in addressing them. The questions are (1) Is the stellar system around the MBH relaxed? (2) Is there a "dark cusp" around the MBH? (3) What is the origin of the stellar disk(s)?, and (4) What is the origin of the S-stars?Comment: Invited overview lecture in "The Galactic Center, a window to the nuclear environment of disk galaxies" (Shanghai 19-23/10/2009). To appear in ASP Conf. Proc. Ser. "Galactic center workshop 2009" ed. Mark Morris (12 pp 5 fig

Stellar dynamics and tidal disruption events in galactic nuclei

The disruption of a star by the tidal field of a massive black hole is the final outcome of a chain of complex dynamical processes in the host galaxy. I introduce the "loss cone problem", and describe the many theoretical and numerical challenges on the path of solving it. I review various dynamical channels by which stars can be supplied to a massive black hole, and the relevant dynamical relaxation / randomization mechanisms. I briefly mention some "exotic" tidal disruption scenarios, and conclude by discussing some new dynamical results that are changing our understanding of dynamics near a massive black hole, and may well be relevant for tidal disruption dynamics.Comment: Invited review talk presented in the "Tidal Disruption events and AGN outbursts" workshop, 25-27 June 2012, ESAC, Madrid, Spain. To appear in the EPJ web of conferences, Editor: R. Saxton. 7 p