The relationship between variable and polarized optical spectral components of luminous type 1 non-blazar quasars

Optical spectropolarimetry carried out by Kishimoto et al. (2004) has shown that several luminous type 1 quasars show a strong decrease of the polarized continuum flux in the rest-frame near-UV wavelengths of $\lambda<4000$\AA. In the literature, this spectral feature is interpreted as evidence of the broadened hydrogen Balmer absorption edge imprinted in the accretion disk thermal emission due to the disk atmospheric opacity effect. On the other hand, the quasar flux variability studies have shown that the variable continuum component in UV-optical spectra of quasars, which is considered to be a good indicator of the intrinsic spectral shape of the accretion disk emission, generally have significantly flat spectral shape throughout the near-UV to optical spectral range. To examine whether the disk continuum spectral shapes revealed as the polarized flux and as the variable component spectra are consistent with each other, we carry out multi-band photometric monitoring observations for a sample of four polarization-decreasing quasars of Kishimoto et al. (2004) (4C09.72, 3C323.1, Ton 202, and B2 1208+32) to derive the variable component spectra and compare the spectral shape of them with that of the polarized flux spectra. Contrary to expectation, we confirm that the two spectral components of these quasars have totally different spectral shape in that the variable component spectra are significantly bluer compared to the polarized flux spectra. This discrepancy in the spectral shape may imply either (1) the decrease of polarization degree in the rest-frame UV wavelengths is not indicating the Balmer absorption edge feature but is induced by some unknown (de)polarization mechanisms, or (2) the UV-optical flux variability is occurring preferentially at the hot inner radii of the accretion disk and thus the variable component spectra do not reflect the whole accretion disk emission.Comment: 12 pages, 5 figures and 3 tables, accepted for publication in Publications of the Astronomical Society of Japan (PASJ) 2016 April 1

Constraints on accretion disk size in the massive type 1 quasar PG 2308+098 from optical continuum reverberation lags

Two years' worth of u-, g-, r-, i-, and z-band optical light curves were obtained for the massive type 1 quasar PG 2308+098 at z=0.433 using the 1.05-m Kiso Schmidt telescope/Kiso Wide Field Camera, and inter-band time lags of the light curves were measured. Wavelength-dependent continuum reverberation lag signals of several tens of days relative to the u-band were detected at g-, r-, i-, and z-bands, where the longer wavelength bands showed larger lags. From the wavelength-dependent lags, and assuming the standard disk temperature radial profile $T \propto R_{\rm disk}^{-3/4}$ and an X-ray/far-ultraviolet reprocessing picture, a constraint on the radius of the accretion disk responsible for the rest-frame 2500 \AA\ disk continuum emission was derived as $R_{\rm disk} = 9.46^{+0.29}_{-3.12}$ light-days. The derived disk size is slightly (1.2-1.8 times) larger than the theoretical disk size of $R_{\rm disk} = 5.46$ light-days predicted from the black hole mass ($M_{\rm BH}$) and Eddington ratio estimates of PG 2308+098. This result is roughly in accordance with previous studies of lower mass active galactic nuclei (AGNs), where measured disk sizes have been found to be larger than the standard disk model predictions by a factor of $\sim 3$; however, the disk size discrepancy is more modest in PG 2308+098. By compiling literature values of the disk size constraints from continuum reverberation and gravitational microlensing observations for AGNs/quasars, we show that the $M_{\rm BH}$ dependence of $R_{\rm disk}$ is weaker than that expected from the standard disk model. These observations suggest that the standard Shakura-Sunyaev accretion disk theory has limitations in describing AGN/quasar accretion disks.Comment: 15 pages, 8 figures and 2 tables, accepted for publication in Publications of the Astronomical Society of Japan (PASJ) 2018 July 3

Constraints on the temperature inhomogeneity in quasar accretion discs from the ultraviolet-optical spectral variability

The physical mechanisms of the quasar ultraviolet (UV)-optical variability are not well understood despite the long history of observations. Recently, Dexter & Agol presented a model of quasar UV-optical variability, which assumes large local temperature fluctuations in the quasar accretion discs. This inhomogeneous accretion disc model is claimed to describe not only the single-band variability amplitude, but also microlensing size constraints and the quasar composite spectral shape. In this work, we examine the validity of the inhomogeneous accretion disc model in the light of quasar UV-optical spectral variability by using five-band multi-epoch light curves for nearly 9 000 quasars in the Sloan Digital Sky Survey (SDSS) Stripe 82 region. By comparing the values of the intrinsic scatter $\sigma_{\text{int}}$ of the two-band magnitude-magnitude plots for the SDSS quasar light curves and for the simulated light curves, we show that Dexter & Agol's inhomogeneous accretion disc model cannot explain the tight inter-band correlation often observed in the SDSS quasar light curves. This result leads us to conclude that the local temperature fluctuations in the accretion discs are not the main driver of the several years' UV-optical variability of quasars, and consequently, that the assumption that the quasar accretion discs have large localized temperature fluctuations is not preferred from the viewpoint of the UV-optical spectral variability.Comment: 14 pages, 7 figures and 2 tables, accepted for publication in MNRAS 2015 February

Dynamics of Porous Dust Aggregates and Gravitational Instability of Their Disk

We consider the dynamics of porous icy dust aggregates in a turbulent gas disk and investigate the stability of the disk. We evaluate the random velocity of porous dust aggregates by considering their self-gravity, collisions, aerodynamic drag, turbulent stirring and scattering due to gas. We extend our previous work by introducing the anisotropic velocity dispersion and the relaxation time of the random velocity. We find the minimum mass solar nebular model to be gravitationally unstable if the turbulent viscosity parameter $\alpha$ is less than about $4 \times 10^{-3}$. The upper limit of $\alpha$ for the onset of gravitational instability is derived as a function of the disk parameters. We discuss the implications of the gravitational instability for planetesimal formation.Comment: 38 pages, 14 figures, accepted for publication in Ap

Pitch Angle of Galactic Spiral Arms

One of the key parameters that characterize spiral arms in disk galaxies is a pitch angle that measures the inclination of a spiral arm to the direction of galactic rotation. The pitch angle differs from galaxy to galaxy, which suggests that the rotation law of galactic disks determines it. In order to investigate the relation between the pitch angle of spiral arms and the shear rate of galactic differential rotation, we perform local $N$-body simulations of pure stellar disks. We find that the pitch angle increases with the epicycle frequency and decreases with the shear rate and obtain the fitting formula. This dependence is explained by the swing amplification mechanism.Comment: 17 pages, 8 figures, accepted for publication in Ap

Swing Amplification of Galactic Spiral Arms: Phase Synchronization of Stellar Epicycle Motion

We revisit the swing amplification model of galactic spiral arms proposed by Toomre (1981). We describe the derivation of the perturbation equation in detail and investigate the amplification process of stellar spirals. We find that the elementary process of the swing amplification is the phase synchronization of the stellar epicycle motion. Regardless of the initial epicycle phase, the epicycle phases of stars in a spiral are synchronized during the amplification. Based on the phase synchronization, we explain the dependence of the pitch angle of spirals on the epicycle frequency. We find the most amplified spiral mode and calculate its pitch angle, wavelengths, and amplification factor, which are consistent with those obtained by the more rigorous model based on the Boltzmann equation by Julian and Toomre (1966).Comment: 31 pages, 11 figures, accepted for publication in Ap

Dynamics and Accretion of Planetesimals

We review the basic dynamics and accretion of planetesimals by showing N-body simulations. The orbits of planetesimals evolve through two-body gravitational relaxation: viscous stirring increases the random velocity and dynamical friction realizes the equiparation of the random energy. In the early stage of planetesimal accretion the growth mode of planetesimals is runaway growth where larger planetesimals grow faster than smaller ones. When a protoplanet (runaway-growing planetesimal) exceeds a critical mass the growth mode shifts to oligarchic growth where similar-sized protoplanets grow keeping a certain orbital separation. The final stage of terrestrial planet formation is collision among protoplanets known as giant impacts. We also summarize the dynamical effects of disk gas on planets and the core accretion model for formation of gas giants and discuss the diversity of planetary systems

Effect of Stellar Encounters on Comet Cloud Formation

We have investigated the effect of stellar encounters on the formation and disruption of the Oort cloud using the classical impulse approximation. We calculate the evolution of a planetesimal disk into a spherical Oort cloud due to the perturbation from passing stars for 10 Gyr. We obtain the empirical fits of the $e$-folding time for the number of Oort cloud comets using the standard exponential and Kohlrausch formulae as functions of the stellar parameters and the initial semimajor axes of planetesimals. The $e$-folding time and the evolution timescales of the orbital elements are also analytically derived. In some calculations, the effect of the Galactic tide is additionally considered. We also show the radial variations of the $e$-folding times to the Oort cloud. From these timescales, we show that if the initial planetesimal disk has the semimajor axes distribution ${\rm d}n/{\rm d}a\propto a^{-2}$, which is produced by planetary scattering (Higuchi et al. 2006), the $e$-folding time for planetesimals in the Oort cloud is $\sim$10 Gyr at any heliocentric distance $r$. This uniform $e$-folding time over the Oort cloud means that the supply of comets from the inner Oort cloud to the outer Oort cloud is sufficiently effective to keep the comet distribution as ${\rm d}n/{\rm d}r\propto r^{-2}$. We also show that the final distribution of the semimajor axes in the Oort cloud is approximately proportional to $a^{-2}$ for any initial distribution.Comment: Accepted for publication in AJ, 15 figures, 3 table

Planetesimal Formation by Gravitational Instability of a Porous-Dust Disk

Recently it is proposed that porous icy dust aggregates are formed by pairwise accretion of dust aggregates beyond the snowline. We calculate the equilibrium random velocity of porous dust aggregates taking into account mutual gravitational scattering, collisions, gas drag, and turbulent stirring and scattering. We find that the disk of porous dust aggregates becomes gravitationally unstable as they evolve through gravitational compression in the minimum-mass solar nebula model for a reasonable range of turbulence strength, which leads to rapid formation of planetesimals.Comment: 14 pages, 5 figures, accepted for publication in ApJ Letter

Galactic Spiral Arms by Swing Amplification

Based on the swing amplification model of Julian and Toomre (1966), we investigate the formation and structure of stellar spirals in disk galaxies. We calculate the pitch angle, wavelengths, and amplification factor of the most amplified mode. We also obtain the fitting formulae of these quantities as a function of the epicycle frequency and Toomre's $Q$. As the epicycle frequency increases, the pitch angle and radial wavelength increases, while the azimuthal wavelength decreases. The pitch angle and radial wavelength increases with $Q$, while the azimuthal wavelength weakly depends on $Q$. The amplification factor decreases with $Q$ rapidly. In order to confirm the swing amplification model, we perform local $N$-body simulations. The wavelengths and pitch angle by the swing amplification model are in good agreement with those by $N$-body simulations. The dependence of the amplification factor on the epicycle frequency in $N$-body simulations is generally consistent with that in the swing amplification model. Using these results, we estimate the number of spiral arms as a function of the shear rate. The number of spiral arms increases with the shear rate if the disk to halo mass ratio is fixed.Comment: 23 pages, 10 figures, accepted for publication in Ap