Superconductivity-Induced Transfer of In-Plane Spectral Weight in Bi2Sr2CaCu2O8: Resolving a Controversy

We present a detailed analysis of the superconductivity-induced redistribution of optical spectral weight in Bi2Sr2CaCu2O8 near optimal doping. It confirms the previous conclusion by Molegraaf et al. (Science 66, 2239 (2002)), that the integrated low-frequency spectral weight shows an extra increase below Tc. Since the region, where the change of the integrated spectral weight is not compensated, extends well above 2.5 eV, this transfer is caused by the transfer of spectral weight from interband to intraband region and only partially by the narrowing of the intraband peak. We show that the opposite assertion by Boris et al. (Science 304, 708 (2004)) regarding this compound, is unlikely the consequence of any obvious discrepancies between the actual experimental data.Comment: ReVTeX, 9 pages, 8 encapsulated postscript figures, several typo's correcte

In-plane optical spectral weight transfer in optimally doped Bi2_{2}Sr2_{2}Ca2_{2}Cu3_{3}O10_{10}

We examine the redistribution of the in-plane optical spectral weight in the normal and superconducting state in tri-layer \bbb (Bi2223) near optimal doping ($T_c$ = 110 K) on a single crystal via infrared reflectivity and spectroscopic ellipsometry. We report the temperature dependence of the low-frequency integrated spectral weight $W(\Omega_c)$ for different values of the cutoff energy $\Omega_c$. Two different model-independent analyses consistently show that for $\Omega_c$ = 1 eV, which is below the charge transfer gap, $W(\Omega_c)$ increases below $T_c$, implying the lowering of the kinetic energy of the holes. This is opposite to the BCS scenario, but it follows the same trend observed in the bi-layer compound \bb (Bi2212). The size of this effect is larger in Bi2223 than in Bi2212, approximately scaling with the critical temperature. In the normal state, the temperature dependence of $W(\Omega_c)$ is close to $T^2$ up to 300 K

Intraband Optical Spectral Weight in the presence of a van Hove singularity: application to Bi2_2Sr2_2CaCu2_2O8+δ_{8+\delta}

The Kubo single band sum rule is used to determine the optical spectral weight of a tight binding band with further than nearest neighbour hopping. We find for a wide range of parameters and doping concentrations that the change due to superconductivity at low temperature can be either negative or positive. In contrast, the kinetic energy change is always negative. We use an ARPES determined tight binding parametrization of Bi$_2$Sr$_2$CaCu$_2$O$_{8+\delta}$ to investigate whether this can account for recent observations of a positive change in the spectral weight due to the onset of superconductivity. With this band structure we find that in the relevant doping regime a straightforward BCS calculation of the optical spectral weight cannot account for the experimental observations.Comment: 10 page 9 figure

Constraining the Mass Profiles of Stellar Systems: Schwarzschild Modeling of Discrete Velocity Datasets

(ABRIDGED) We present a new Schwarzschild orbit-superposition code designed to model discrete datasets composed of velocities of individual kinematic tracers in a dynamical system. This constitutes an extension of previous implementations that can only address continuous data in the form of (the moments of) velocity distributions, thus avoiding potentially important losses of information due to data binning. Furthermore, the code can handle any combination of available velocity components, i.e., only line-of-sight velocities, only proper motions, or a combination of both. It can also handle a combination of discrete and continuous data. The code finds the distribution function (DF, a function of the three integrals of motion E, Lz, and I3) that best reproduces the available kinematic and photometric observations in a given axisymmetric gravitational potential. The fully numerical approach ensures considerable freedom on the form of the DF f(E,Lz,I3). This allows a very general modeling of the orbital structure, thus avoiding restrictive assumptions about the degree of (an)isotropy of the orbits. We describe the implementation of the discrete code and present a series of tests of its performance based on the modeling of simulated datasets generated from a known DF. We find that the discrete Schwarzschild code recovers the original orbital structure, M/L ratios, and inclination of the input datasets to satisfactory accuracy, as quantified by various statistics. The code will be valuable, e.g., for modeling stellar motions in Galactic globular clusters, and those of individual stars, planetary nebulae, or globular clusters in nearby galaxies. This can shed new light on the total mass distributions of these systems, with central black holes and dark matter halos being of particular interest.Comment: ApJ, in press; 51 pages, 11 figures; manuscript revised following comments by refere

Doping Dependence of the Redistribution of Optical Spectral Weight in Bi2_{2}Sr2_{2}CaCu2_{2}O8+δ_{8+\delta}

We present the ab-plane optical conductivity of four single crystals of Bi$_{2}$Sr$_{2}$CaCu$_{2}$O$_{8+\delta}$ (Bi2212) with different carrier doping levels from the strongly underdoped to the strongly overdoped range with $T_c$=66, 88, 77, and 67 K respectively. We focus on the redistribution of the low frequency optical spectral weight (SW) in the superconducting and normal states. The temperature dependence of the low-frequency spectral weight in the normal state is significantly stronger in the overdoped regime. In agreement with other studies, the superconducting order is marked by an increase of the low frequency SW for low doping, while the SW decreases for the highly overdoped sample. The effect crosses through zero at a doping concentration $\delta$=0.19 which is slightly to the right of the maximum of the superconducting dome. This sign change is not reproduced by the BCS model calculations, assuming the electron-momentum dispersion known from published ARPES data. Recent Cluster Dynamical Mean Field Theory (CDMFT) calculations based on the Hubbard and t-J models, agree in several relevant respects with the experimental data

Outflow forces of low mass embedded objects in Ophiuchus: a quantitative comparison of analysis methods

The outflow force of molecular bipolar outflows is a key parameter in theories of young stellar feedback on their surroundings. The focus of many outflow studies is the correlation between the outflow force, bolometric luminosity and envelope mass. However, it is difficult to combine the results of different studies in large evolutionary plots over many orders of magnitude due to the range of data quality, analysis methods and corrections for observational effects such as opacity and inclination. We aim to determine the outflow force for a sample of low luminosity embedded sources. We will quantify the influence of the analysis method and the assumptions entering the calculation of the outflow force. We use the James Clerk Maxwell Telescope to map 12CO J=3-2 over 2'x2' regions around 16 Class I sources of a well-defined sample in Ophiuchus at 15" resolution. The outflow force is then calculated using seven different methods differing e.g. in the use of intensity-weighted emission and correction factors for inclination. The results from the analysis methods differ from each other by up to a factor of 6, whereas observational properties and choices in the analysis procedure affect the outflow force by up to a factor of 4. For the sample of Class I objects, bipolar outflows are detected around 13 sources including 5 new detections, where the three non-detections are confused by nearby outflows from other sources. When combining outflow forces from different studies, a scatter by up to a factor of 5 can be expected. Although the true outflow force remains unknown, the separation method (separate calculation of dynamical time and momentum) is least affected by the uncertain observational parameters. The correlations between outflow force, bolometric luminosity and envelope mass are further confirmed down to low luminosity sources.Comment: 24 pages, 13 figures, Accepted by A&

An ALMA Survey of Protoplanetary Disks in the σ\sigma Orionis Cluster

The $\sigma$ Orionis cluster is important for studying protoplanetary disk evolution, as its intermediate age ($\sim$3-5 Myr) is comparable to the median disk lifetime. We use ALMA to conduct a high-sensitivity survey of dust and gas in 92 protoplanetary disks around $\sigma$ Orionis members with $M_{\ast}\gtrsim0.1 M_{\odot}$. Our observations cover the 1.33 mm continuum and several CO $J=2-1$ lines: out of 92 sources, we detect 37 in the mm continuum and six in $^{12}$CO, three in $^{13}$CO, and none in C$^{18}$O. Using the continuum emission to estimate dust mass, we find only 11 disks with $M_{\rm dust}\gtrsim10 M_{\oplus}$, indicating that after only a few Myr of evolution most disks lack sufficient dust to form giant planet cores. Stacking the individually undetected continuum sources limits their average dust mass to 5$\times$ lower than that of the faintest detected disk, supporting theoretical models that indicate rapid dissipation once disk clearing begins. Comparing the protoplanetary disk population in $\sigma$ Orionis to those of other star-forming regions supports the steady decline in average dust mass and the steepening of the $M_{\rm dust}$-$M_{\ast}$ relation with age; studying these evolutionary trends can inform the relative importance of different disk processes during key eras of planet formation. External photoevaporation from the central O9 star is influencing disk evolution throughout the region: dust masses clearly decline with decreasing separation from the photoionizing source, and the handful of CO detections exist at projected separations $>1.5$ pc. Collectively, our findings indicate that giant planet formation is inherently rare and/or well underway by a few Myr of age.Comment: 16 pages, 9 figures; published in AJ; The full machine readable tables can be obtained by downloading and extracting the gzipped tar source file listed under "Other formats.

Warm formaldehyde in the Oph IRS 48 transitional disk

Simple molecules like H2CO and CH3OH in protoplanetary disks are the starting point for the production of more complex organic molecules. So far, the observed chemical complexity in disks has been limited due to freeze out of molecules onto grains in the bulk of the cold outer disk. Complex molecules can be studied more directly in transitional disks with large inner holes, as these have a higher potential of detection, through UV heating of the outer disk and the directly exposed midplane at the wall. We use Atacama Large Millimeter/submillimeter Array (ALMA) Band 9 (~680 GHz) line data of the transitional disk Oph IRS 48, previously shown to have a large dust trap, to search for complex molecules in regions where planetesimals are forming. We report the detection of the H2CO 9(1,8)-8(1,7) line at 674 GHz, which is spatially resolved as a semi-ring at ~60 AU radius centered south from the star. The inferred H2CO abundance is ~10^{-8} derived by combining a physical disk model of the source with a non-LTE excitation calculation. Upper limits for CH3OH lines in the same disk give an abundance ratio H2CO/CH3OH>0.3, which points to both ice formation and gas-phase routes playing a role in the H2CO production. Upper limits on the abundances of H13CO+, CN and several other molecules in the disk are also derived and found to be consistent with full chemical models. The detection of the H2CO line demonstrates the start of complex organic molecules in a planet-forming disk. Future ALMA observations should be able to push down the abundance detection limits of other molecules by 1-2 orders of magnitude and test chemical models of organic molecules in (transitional) disks.Comment: Updated references and minor changes to text, approved by language edito