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Ting Xiao

Publications and source records attributed to Ting Xiao.

64 records · Page 4Linked to original sources

The Host Galaxies of Low-mass Black Holes

Using HST observations of 147 host galaxies of low-mass black holes (BHs), we systematically study the structures and scaling relations of these active galaxies. Our sample is selected to have central BHs with virial masses ~10^5-10^6 solar mass. The host galaxies have total I-band magnitudes of -23.2<M_I<-18.8 mag and bulge magnitudes of -22.9<M_I<-16.1 mag. Detailed bulge-disk-bar decompositions with GALFIT show that 93% of the galaxies have extended disks, 39% have bars and 5% have no bulges at all at the limits of our observations. Based on the Sersic index and bulge-to-total ratio, we conclude that the majority of the galaxies with disks are likely to contain pseudobulges and very few of these low-mass BHs live in classical bulges. The fundamental plane of our sample is offset from classical bulges and ellipticals in a way that is consistent with the scaling relations of pseudobulges. The sample has smaller velocity dispersion at fixed luminosity in the Faber-Jackson plane, compared with classical bulges and elliptical galaxies. The galaxies without disks are structurally more similar to spheroidals than to classical bulges according to their positions in the fundamental plane, especially the Faber-Jackson projection. Overall, we suggest that BHs with mass < 10^6 solar mass live in galaxies that have evolved secularly over the majority of their history. A classical bulge is not a prerequisite to host a black hole.

astro-ph.CO↗

Exploring the Low-Mass End of The M-Sigma Relation with Active Galaxies

We present new measurements of stellar velocity dispersions, using spectra obtained with the Keck Echellette Spectrograph and Imager (ESI) and the Magellan Echellette (MagE), for 76 Seyfert 1 galaxies from the recent catalogue of Greene & Ho. These objects were selected from the Sloan Digital Sky Survey (SDSS) to have estimated black hole (BH) masses below 2\times10^6 M\odot. Combining our results with previous ESI observations of similar objects, we obtain an expanded sample of 93 galaxies and examine the relation between BH mass and velocity dispersion (the M-Sigma relation) for active galaxies with low BH masses. The low-mass active galaxies tend to follow the extrapolation of the M-Sigma relation of inactive galaxies. Including results for active galaxies of higher BH mass from the literature, we find a zero pointα= 7.68\pm0.08 and slope of β= 3.32\pm0.22 for the M-Sigma relation [in the form log Mbh=α+βlog(σ*/200 km s-1)], with intrinsic scatter of 0.46\pm0.03 dex. This result is consistent, within the uncertainties, with the slope of the M-Sigma relation for reverberation-mapped active galaxies with BH masses from 10^6 to 10^9 M\odot. For the subset of our sample having morphological information from Hubble Space Telescope images, we examine the slope of the M-Sigma relation separately for subsamples of barred and unbarred host galaxies, and find no significant evidence for a difference in slope. We do find a mild offset between low-inclination and high-inclination disk galaxies, such that more highly inclined galaxies tend to have larger σ* at a given value of BH mass, presumably due to the contribution of disk rotation within the spectroscopic aperture. We also find that the velocity dispersion of the ionized gas trace the stellar velocity dispersion well for this large sample of low-mass Seyfert 1 galaxies.

astro-ph.CO↗

Bäcklund transformations for the constrained dispersionless hierarchies and dispersionless hierarchies with self-consistent sources

The Bäcklund transformations between the constrained dispersionless KP hierarchy (cdKPH) and the constrained dispersionless mKP hieararchy (cdmKPH) and between the dispersionless KP hieararchy with self-consistent sources (dKPHSCS) and the dispersionless mKP hieararchy with self-consistent sources (dmKPHSCS) are constructed. The auto-Bäcklund transformations for the cdmKPH and for the dmKPHSCS are also formulated.

nlin.SI↗

Integrable dispersionless KdV hierarchy with sources

An integrable dispersionless KdV hierarchy with sources (dKdVHWS) is derived. Lax pair equations and bi-Hamiltonian formulation for dKdVHWS are formulated. Hodograph solution for the dispersionless KdV equation with sources (dKdVWS) is obtained via hodograph transformation. Furthermore, the dispersionless Gelfand-Dickey hierarchy with sources (dGDHWS) is presented.

nlin.SI↗

The constrained dispersionless mKP hierarchy and the dispersionless mKP hierarchy with self-consistent sources

We first show that the quasiclassical limit of the squared eigenfunction symmetry constraint of the Sato operator for the mKP hierarchy leads to a reduction of the Sato function for the dispersionless mKP hierarchy. The constrained dispersionless mKP hierarchy (cdmKPH) is obtained and it is shown that the (2+1)-dimensional dispersionless mKP hierarchy is decomposed to two (1+1)-dimensional hierarchies of hydrodynamical type. The dispersionless mKP hierarchy with self-consistent sources (dmKPHSCS) together with its associated conservation equations are also constructed. Some solutions of dmKPESCS are obtained by hodograph reduction method.

nlin.SI↗

Bäcklund transformations for the KP and mKP hierarchies with self-consistent sources

Using gauge transformations for the corresponding generating pseudo-differential operators $L^n$ in terms of eigenfunctions and adjoint eigenfunctions, we construct several types of auto-Bäcklund transformations for the KP hierarchy with self-consistent sources (KPHSCS) and mKP hierarchy with self-consistent sources (mKPHSCS) respectively. The Bäcklund transformations from the KPHSCS to mKPHSCS are also constructed in this way.

nlin.SI↗

The quasiclassical limit of the symmetry constraint of the KP hierarchy and the dispersionless KP hierarchy with self-consistent sources

For the first time we show that the quasiclassical limit of the symmetry constraint of the KP hierarchy leads to the generalized Zakharov reduction of the dispersionless KP (dKP) hierarchy which has been proved to be result of symmetry constraint of the dKP hierarchy recently. By either regarding the constrained dKP hierarchy as its stationary case or taking the dispersionless limit of the KP hierarchy with self-consistent sources directly, we construct a new integrable dispersionless hierarchy, i.e., the dKP hierarchy with self-consistent sources and find its associated conservation equations (or equations of Hamilton-Jacobi type). Some solutions of the dKP equation with self-consistent sources are also obtained by hodograph transformations.

nlin.SI↗

A new constrained mKP hierarchy and the generalized Darboux transformation for the mKP equation with self-consistent sources

The mKP equation with self-consistent sources (mKPESCS) is treated in the framework of the constrained mKP hierarchy. We introduce a new constrained mKP hierarchy which may be viewed as the stationary hierarchy of the mKP hierarchy with self-consistent sources. This offers a natural way to obtain the Lax representation for the mKPESCS. Based on the conjugate Lax pairs, we construct the generalized Darboux transformation with arbitrary functions in time $t$ for the mKPESCS which, in contrast with the Darboux transformation for the mKP equation, provides a non-auto-Bäcklund transformation between two mKPESCSs with different degrees. The formula for $n$-times repeated generalized Darboux transformation is proposed and enables us to find the rational solutions (including the lump solutions), soliton solutions and the solutions of breather type of the mKPESCS.

nlin.SI↗

Generalized Darboux transformations for the KP equation with self-consistent sources

The KP equation with self-consistent sources (KPESCS) is treated in the framework of the constrained KP equation. This offers a natural way to obtain the Lax representation for the KPESCS. Based on the conjugate Lax pairs, we construct the generalized binary Darboux transformation with arbitrary functions in time $t$ for the KPESCS which, in contrast with the binary Darboux transformation of the KP equation, provides a non-auto-Bäcklund transformation between two KPESCSs with different degrees. The formula for N-times repeated generalized binary Darboux transformation is proposed and enables us to find the N-soliton solution and lump solution as well as some other solutions of the KPESCS.

nlin.SI↗

Canonical explicit Bäcklund transformations with spectrality for constrained flows of soliton hierarchies

It is shown that explicit Bäcklund transformations (BTs) for the high-order constrained flows of soliton hierarchy can be constructed via their Darboux transformations and Lax representation, and these BTs are canonical transformations including Bäcklund parameter $η$ and possess a spectrality property with respect to $η$ and the 'conjugated' variable $μ$ for which the pair $(η, μ)$ lies on the spectral curve. As model we present the canonical explicit BTs with the spectrality for high-order constrained flows of the Kaup-Newell hierarchy and the KdV hierarchy.

nlin.SI↗