Thermodynamic Relations in Correlated Systems

Several useful thermodynamic relations are derived for metal-insulator transitions, as generalizations of the Clausius-Clapeyron and Eherenfest theorems. These relations hold in any spatial dimensions and at any temperatures. First, they relate several thermodynamic quantities to the slope of the metal-insulator phase boundary drawn in the plane of the chemical potential and the Coulomb interaction in the phase diagram of the Hubbard model. The relations impose constraints on the critical properties of the Mott transition. These thermodynamic relations are indeed confirmed to be satisfied in the cases of the one- and two-dimensional Hubbard models. One of these relations yields that at the continuous Mott transition with a diverging charge compressibility, the doublon susceptibility also diverges. The constraints on the shapes of the phase boundary containing a first-order metal-insulator transition at finite temperatures are clarified based on the thermodynamic relations. For example, the first-order phase boundary is parallel to the temperature axis asymptotically in the zero temperature limit. The applicability of the thermodynamic relations are not restricted only to the metal-insulator transition of the Hubbard model, but also hold in correlated systems with any types of phases in general. We demonstrate such examples in an extended Hubbard model with intersite Coulomb repulsion containing the charge order phase.Comment: 10 pages, 9 figure

Optical, near-IR and sub-mm IFU Observations of the nearby dual AGN Mrk 463

We present optical and near-IR Integral Field Unit (IFU) and ALMA band 6 observations of the nearby dual Active Galactic Nuclei (AGN) Mrk 463. At a distance of 210 Mpc, and a nuclear separation of $\sim$4 kpc, Mrk 463 is an excellent laboratory to study the gas dynamics, star formation processes and supermassive black hole (SMBH) accretion in a late-stage gas-rich major galaxy merger. The IFU observations reveal a complex morphology, including tidal tails, star-forming clumps, and emission line regions. The optical data, which map the full extent of the merger, show evidence for a biconical outflow and material outflowing at $>$600 km s$^{-1}$, both associated with the Mrk 463E nucleus, together with large scale gradients likely related to the ongoing galaxy merger. We further find an emission line region $\sim$11 kpc south of Mrk 463E that is consistent with being photoionized by an AGN. Compared to the current AGN luminosity, the energy budget of the cloud implies a luminosity drop in Mrk 463E by a factor 3-20 over the last 40,000 years. The ALMA observations of $^{12}$CO(2-1) and adjacent 1mm continuum reveal the presence of $\sim$10$^{9}$M$_\odot$ in molecular gas in the system. The molecular gas shows velocity gradients of $\sim$800 km/s and $\sim$400 km/s around the Mrk 463E and 463W nuclei, respectively. We conclude that in this system the infall of $\sim$100s $M_\odot$/yr of molecular gas is in rough balance with the removal of ionized gas by a biconical outflow being fueled by a relatively small, $<$0.01% of accretion onto each SMBH.Comment: Accepted by The Astrophysical Journal, 23 pages, 19 figure

The masses of Local Group dwarf spheroidal galaxies: The death of the universal mass profile

We investigate the claim that all dwarf spheroidal galaxies (dSphs) reside within halos that share a common, universal mass profile as has been derived for dSphs of the Galaxy. By folding in kinematic information for 25 Andromeda dSphs, more than doubling the previous sample size, we find that a singular mass profile can not be found to fit all the observations well. Further, the best-fit dark matter density profile measured for solely the Milky Way dSphs is marginally discrepant (at just beyond the 1 sigma level) with that of the Andromeda dSphs, where a profile with lower maximum circular velocity, and hence mass, is preferred. The agreement is significantly better when three extreme Andromeda outliers, And XIX, XXI and XXV, all of which have large half-light radii (>600pc) and low velocity dispersions (sigma_v < 5km/s) are omitted from the sample. We argue that the unusual properties of these outliers are likely caused by tidal interactions with the host galaxy.Comment: ApJ in press, 16 pages, 7 figures. Updated to address referee comment

A kinematic study of the Andromeda dwarf spheroidal system

We present a homogeneous kinematic analysis of red giant branch stars within 18 of the 28 Andromeda dwarf spheroidal (dSph) galaxies, obtained using the Keck I LRIS and Keck II DEIMOS spectrographs. Based on their g-i colors (taken with the CFHT MegaCam imager), physical positions on the sky, and radial velocities, we assign probabilities of dSph membership to each observed star. Using this information, the velocity dispersions, central masses and central densities of the dark matter halos are calculated for these objects, and compared with the properties of the Milky Way dSph population. We also measure the average metallicity ([Fe/H]) from the co-added spectra of member stars for each M31 dSph and find that they are consistent with the trend of decreasing [Fe/H] with luminosity observed in the Milky Way population. We find that three of our studied M31 dSphs appear as significant outliers in terms of their central velocity dispersion, And XIX, XXI and XXV, all of which have large half-light radii (>700 pc) and low velocity dispersions (sigma_v<5 km/s). In addition, And XXV has a mass-to-light ratio within its half-light radius of just [M/L]_{half}=10.3^{+7.0}_{-6.7}, making it consistent with a simple stellar system with no appreciable dark matter component within its 1 sigma uncertainties. We suggest that the structure of the dark matter halos of these outliers have been significantly altered by tides.Comment: 41 pages, 23 figures. Accepted for publication in Ap

Discovery of an extremely bright submillimeter galaxy at z=3.93

Serendipitously we have discovered a rare, bright submillimeter galaxy (SMG) with a flux density of 30 +/- 2 mJy at lambda=1.2mm, using MAMBO2 at the IRAM 30-meter millimeter telescope. Although no optical counterpart is known for MM18423+5938, we were able to measure the redshift z=3.92960 +/- 0.00013 from the detection of CO lines using the IRAM Eight MIxer Receiver (EMIR). In addition, by collecting all available photometric data in the far-infrared and radio to constrain its spectral energy distribution, we derive the FIR luminosity 4.8 10^14/m Lsol and mass 6.0 10^9/m Msol for its dust, allowing for a magnification factor m caused by a probable gravitational lens. The corresponding star-formation rate is 8.3 10^4/m Msol/yr. The detection of three lines of the CO rotational ladder, and a significant upper limit for a fourth CO line, allow us to estimate an H2 mass of between 1.9 10^11/m Msol and 1.1 10^12/m Msol. The two lines CI(3p1-3p0) and CI(3p2-3p1) were clearly detected and yield a [CI]/[H2] number abundance between 1.4 10^-5 and 8.0 10^-5. Upper limits are presented for emission lines of HCN, HCO^+, HNC, H_2O and other molecules observed. The moderate excitation of the CO lines is indicative of an extended starburst, and excludes the dominance of an AGN in heating this high-redshift SMG.Comment: Model revised. Accepted as an Astronomy and Astrophysics Letter, 4 pages, 3 figure

VLT/NACO adaptive optics imaging of the TY CrA system - A fourth stellar component candidate detected

We report the detection of a possible subsolar mass companion to the triple young system TY CrA using the NACO instrument at the VLT UT4 during its commissioning. Assuming for TY CrA a distance similar to that of the close binary system HD 176386, the photometric spectral type of this fourth stellar component candidate is consistent with an ~M4 star. We discuss the dynamical stability of this possible quadruple system as well as the possible location of dusty particles inside or outside the system.Comment: 4 pages, 2 figures postscrip

Personal history of my engagement with cuprate superconductivity, 1986-2010

Six months ago I was asked to write a personal history of my engagement with the high-Tc problem of the cuprate superconductors, in rather informal and autobiographical style. As the work proceeded I realized that it was impossible and would have been dishonest to separate out my rather amusing but seminal early fumblings from the complete restructuring of the problem which I have achieved during the past decade. But the result became considerably too long, by over half, for its intended recipient. The assignment had left me with no obligation to deal with all the fascinating but irrelevant phenomenology which I had more or less instinctively ignored on my way, but that feature also fails to endear the article to any conceivable editorial board containing knowledgeable experts on the subject. Also, their purpose was for it to serve as a (quote) introduction to the more technical debates, but its message is that almost all of these are not relevant. They are not, on the whole, focused on achieving understanding of the crucial experimental anomalies, many, if not most, of which are now understood. The key to the problem is a new method of dealing with the constrained Hilbert space which follows from the necessity of Gutzwiller projection