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The gravitational index of 5d black holes and black strings
The supersymmetric index of 5d black strings and spinning black holes in M-theory is related to that of 4d black holes in type IIA supergravity when both theories are compactified on the same Calabi-Yau threefold. We find the finite-temperature saddles for the 5d gravitational supersymmetric index by uplifting the recently found attractor saddles of the corresponding 4d index. We study uplifts for two types of geometries: 5d black holes and 5d black strings. For 5d black holes, the uplift guarantees that the index of 4d and 5d black holes match. For 5d black strings, the saddle reproduces the microscopic index at leading order in G N , even without the conventional decoupling limit taken in AdS/CFT. In particular, when the temperature is set to be finite in the 5d flat space region, the black string index is computed from an asymptotically flat solution where the AdS throat is absent. Further, as the temperature is lowered and eventually becomes infinitesimally small in the flat space region, the solution admits a novel decoupling limit in which the AdS 3 throat takes the form of a finite-temperature BTZ black hole that is known to compute the index in AdS 3 /CFT 2 . This represents the first step towards understanding holography for supersymmetric observables in flat space, away from the decoupling limit.
The Asymptotics of Eigenfunctions of the Absolutely Continuous Spectrum. The Scattering Problem of Three One-Dimensional Quantum Particles
In the paper the asymptotic structure of eigenfunctions of the absolutely continuous spectrum of the scattering problem is described. The case of three one-dimensional quantum particles interacting by repulsive pair potentials with a compact support is considered.
Triaxial Constraint and Tensile Strength Enhancement in Brazed Joints
A brazed joint consists of a low-melting point and thin interlayer sandwiched between the high-melting-point base materials, in which the interlayer strength is typically lower than that of the base material. When this butt-joined composite is loaded uniaxially in the direction perpendicular to the plane of the brazing layer, the tensile strength is found to be much higher than that of the braze. This seems to violate the iso-stress condition in such a butt-joint serial configuration. Furthermore, the stress triaxiality has been usually ascribed, but without a quantitative rationalization, as being responsible for this tensile strength enhancement. Here a complete finite element simulation has been conducted to study the dependence of triaxiality and strength enhancement on geometric and material parameters. Two asymptotic limit solutions (based on Bridgman and Xia–Shih solutions, respectively) have been identified to understand the simulation results. The critical role of void evolution has been revealed when making a quantitative comparison to available experiments. In addition, ductility of the brazed joint, which has not been fully addressed in literature, is investigated by the Gurson–Tvergaard–Needleman model.
Flat-space holography and correlators of Robinson–Trautman stress tensor
We propose a quasi-local stress tensor for the four-dimensional asymptotically flat Robinson–Trautman geometries by taking the flat-space limit from the corresponding asymptotically AdS solutions. This stress tensor results in the correct charges of the generators of BMS symmetry if we define conformal infinity by an anisotropic scaling of the metric components. Using flat-space holography this stress tensor is related to expectation values of the stress tensor in a dual field theory called BMS-invariant field theory (BMSFT). We also calculate the two and three point functions of the proposed stress tensor.
Background independent quantum field theory and gravitating vacuum fluctuations
The scale dependent effective average action for quantum gravity complies with the fundamental principle of Background Independence. Ultimately the background metric it formally depends on is selected self-consistently by means of a tadpole condition, a generalization of Einstein’s equation. Self-consistent background spacetimes are scale dependent, and therefore “going on-shell” at the points along a given renormalization group (RG) trajectory requires understanding two types of scale dependencies: the (familiar) direct one carried by the off-shell action functional, and an equally important indirect one related to the continual re-adjustment of the background geometry. This paper is devoted to a careful delineation and analysis of certain general questions concerning the indirect scale dependence, as well as a detailed explicit investigation of the case where the self-consistent metrics are determined predominantly by the RG running of the cosmological constant. Mathematically, the object of interest is the spectral flow induced by the background Laplacian which, on-shell, acquires an explicit scale dependence. Among other things, it encodes the complete information about the specific set of field modes which, at any given scale, are the degrees of freedom constituting the respective effective field theory. For a large class of RG trajectories (Type IIIa) we discover a seemingly paradoxical behavior that differs substantially from the off-shell based expectations: A Background Independent theory of (matter coupled) quantum gravity looses rather than gains degrees of freedom at increasing energies. As an application, we investigate to what extent it is possible to reformulate the exact theory in terms of matter and gravity fluctuations on a rigid flat space. It turns out that, in vacuo, this “rigid picture” breaks down after a very short RG time already (less than one decade of scales) because of a “scale horizon” that forms. Furthermore, we critically reanalyze and refute the frequent claim that the huge energy densities one obtains in standard quantum field theory by summing up to zero-point energies imply a naturalness problem for the observed small value of the cosmological constant.
Power spectrum and form factor in random diagonal matrices and integrable billiards
Triggered by a controversy surrounding a universal behavior of the power spectrum in quantum systems exhibiting regular classical dynamics, we focus on a model of random diagonal matrices (RDM), often associated with the Poisson spectral universality class, and examine how the power spectrum and the form factor get affected by two-sided truncations of RDM spectra. Having developed a nonperturbative description of both statistics, we perform their detailed asymptotic analysis to demonstrate explicitly how a traditional assumption (lying at the heart of the controversy) – that the power spectrum is merely determined by the spectral form factor – breaks down for truncated spectra. This observation has important consequences as we further argue that bounded quantum systems with integrable classical dynamics are described by heavily truncated rather than complete RDM spectra. High-precision numerical simulations of semicircular and irrational rectangular billiards lend independent support to these conclusions.
Gravitational wave scattering theory without large-distance asymptotics
In conventional gravitational wave scattering theory, a large-distance asymptotic approximation is employed. In this approximation, the gravitational wave is approximated by its large-distance asymptotics. In this paper, we establish a gravitational wave scattering theory without the large-distance asymptotic approximation.
Sum of oscillator-strength moments and asymptotic behaviour of thermally induced broadening and shift of energy levels of Rydberg atom circular states
Based on the rules for summing oscillator-strength moments, we derive analytical expressions for environmentally (thermally) induced energy-level shifts and broadenings of circular Rydberg states with maximum orbital (l) and magnetic (m) quantum numbers, l = |m| = n – 1. The formulae for the energy of interaction with blackbody radiation are presented in the form of series expansion in even powers of the small parameter η = Z{sup 2}/(n{sup 3}k{sub B}T) ≪ 1 in the region of high temperatures T and principal quantum numbers n (Z is the charge of the residual ion). The expression for the thermally induced width contains a negative temperature-independent term coinciding in absolute value with the spontaneous width, so that the temperature-independent term is absent in the expression for the sum of the spontaneous and thermally induced widths. A similar expansion in powers of η for the thermally induced shift also contains a temperature-independent term proportional to 1/n{sup 6}. (paper)
Effect of boundary conditions on fluctuations of the Bose condensate of interacting atoms
For a gas of trapped interacting atoms forming a Bose condensate, we demonstrate a possibility of a significant influence of the boundary conditions on the statistics of the number of particles in the fundamental mode of the system. The analysis is carried out in the Bogoliubov – Popov low-temperature approximation for model homogeneous cubic traps with periodic or combined periodic and zero boundary conditions. It is shown that the effect of the boundary conditions does not weaken even in the region of parameters corresponding to the relatively strong interaction in the Thomas – Fermi asymptotic case, and does not disappear when proceeding to the thermodynamic limit. (paper)
Cosmological consequences of first-order general-relativistic viscous fluid dynamics
In this work, we investigate the out-of-equilibrium dynamics of viscous fluids in a spatially flat Friedmann-LemaîtreRobertson-Walker cosmology using the most general causal and stable viscous energy-momentum tensor defined at first order in spacetime derivatives. In this new framework a pressureless viscous fluid having equilibrium energy density ρ can evolve to an asymptotic future solution in which the Hubble parameter approaches a constant while ρ → 0, even in the absence of a cosmological constant (i.e., Λ = 0). Thus, while viscous effects in this model drive an accelerated expansion of the universe, the equilibrium energy density itself vanishes, leaving behind only the acceleration. This behavior emerges as a consequence of causality in first-order theories of relativistic fluid dynamics and it is fully consistent with Einstein’s equations.
Analysis into Asymptotic Convergence to Full Nonlinear Solutions and Exploration of the Implication of Numerical Operator Mutation of Differential Systems
A robust, sufficiently accurate and practical hydrodynamic simulation toolset is required as a key component of the modeling and simulation of air-gap electrostatic discharge events. This work was performed to complement these ongoing efforts. In particular, hydrodynamic simulations must be vetted to ensure they are robust and sufficiently accurate over relevant characteristic scales. Verification models were generated in order to cultivate the technical knowledge and expertise needed to properly create, implement and execute numerical simulations. Furthermore, this effort was utilized extensively to educate students on the mathematical and numerical principles underlying hydrodynamic simulations. This education opportunity, provided in a holistic and rigorous manner, has greatly benefited developing scientists and engineers with the necessary understandings and toolsets required to excel at accomplishing the task at hand, and, more generally, it has enabled them to generate key programmatic deliverables. This report articulates several subtilties; specifically, how perturbations, nonlinear behavior, and dissipative mechanisms influence numerical stability, how to properly structure mathematical and numerical solutions, and how to properly generate error estimation/assignment. A more rigorous discussion of the consequences of such topics can be found in the body of this report in Chapters 2 and 3 with qualitative findings discussed in Chapter 4.
The Red Supergiant Content of M31 and M33
We identify red supergiants (RSGs) in our spiral neighbors M31 and M33 using near-IR (NIR) photometry complete to a luminosity limit of logL/L{sub ⊙}=4.0. Our archival survey data cover 5 deg{sup 2} of M31, and 3 deg{sup 2} for M33, and are likely spatially complete for these massive stars. Gaia is used to remove foreground stars, after which the RSGs can be separated from asymptotic giant branch (AGB) stars in the color–magnitude diagram. The photometry is used to derive effective temperatures and bolometric luminosities via MARCS stellar atmosphere models. The resulting H-R diagrams show superb agreement with the evolutionary tracks of the Geneva evolutionary group. Our census includes 6400 RSGs in M31 and 2850 RSGs in M33 within their Holmberg radii; by contrast, only a few hundred RSGs are known so far in the Milky Way. Our catalog serves as the basis for a study of the RSG binary frequency being published separately, as well as future studies relating to the evolution of massive stars. Here we use the matches between the NIR-selected RSGs and their optical counterparts to show that the apparent similarity in the reddening of OB stars in M31 and M33 is the result of Malmquist bias; the average extinction in M31 is likely higher than that of M33. As expected, the distribution of RSGs follows that of the spiral arms, while the much older AGB population is more uniformly spread across each galaxy’s disk.
Ground Vibrational State SiO Emission in the VLA BAaDE Survey
Using a subsample of the Bulge Asymmetries and Dynamical Evolution (BAaDE) survey of stellar SiO masers, we explore the prevalence and characteristics of {sup 28}SiO J = 1 − 0, v = 0 emission. We identify 90 detections of maser, thermal, or composite {sup 28}SiO J = 1 − 0, v = 0 emission out of approximately 13,000 candidate spectra from the National Science Foundation’s Karl G. Jansky Very Large Array (VLA). We find that the detected sources are likely asymptotic giant branch stars belonging to a bright, foreground Milky Way stellar disk population. For the 32 sources showing thermal components, we extract values for outflow velocity by fitting thermal line profiles. We find a range of circumstellar envelope expansion velocities, and compare to previously recorded OH and CO expansion velocities. This preliminary survey is already the largest study of stellar ground vibrational state SiO masers to date, and will be expanded to include the entire VLA BAaDE data set when data reduction for the 18,988 target sources is completed.
Anomalous Stellar Populations in Low-surface-brightness Galaxies
We present new Hubble Space Telescope WFC3 near-IR observations of the color–magnitude diagrams (CMDs) in two low-surface-brightness galaxies, F575-3 and F615-1, notable for having no current star formation based on a lack of Hα emission. Key features of the near-IR CMDs are resolved, such as the red giant branch (RGB), the asymptotic giant branch (AGB) region, and the top of the blue main sequence. F575-3 has the bluest RGB of any CMD in the literature, indicating an extremely low mean metallicity. F615-1 has unusually wide RGB and AGB sequences, suggesting multiple episodes of star formation from metal-poor gas, and possibly infalling material. Both galaxies have an unusual population of stars to the red of the RGB and lower in luminosity than typical AGB stars. These stars have normal optical colors but abnormal near-IR colors. We suggest that this population of stars might be analogous to local peculiar stars like Be stars with strong near-IR excesses owing to a surrounding disk of hot gas.
Two Luminous Post-AGB Stars in the Galactic Globular Cluster M19
We report the discovery of a luminous “yellow” post–asymptotic giant branch (PAGB) star in the globular cluster (GC) M19 (NGC 6273), identified during our uBVI survey of Galactic GCs. The uBVI photometric system is optimized to detect stars with large Balmer discontinuities, indicating very low surface gravities and high luminosities. The spectral energy distribution (SED) of the star is consistent with an effective temperature of about 6250 K and a surface gravity of logg=0.5. We use Gaia data to show that the star’s proper motion and radial velocity are consistent with cluster membership. One aim of our program is to test yellow PAGB stars as candidate Population II standard candles for determining extragalactic distances. We derive a visual absolute magnitude of M {sub V} = − 3.39 ± 0.09 for the M19 star. This is in close agreement with the M {sub V} values found for yellow PAGB stars in the GCs ω Cen, NGC 5986, and M79, indicating a very narrow luminosity function. These objects are 4 mag brighter than RR Lyrae variables, and they can largely avoid the issues of interstellar extinction that are a problem for Population I distance indicators. We also identified a second luminous PAGB object in M19, this one a hotter “UV-bright” star. Its SED is consistent with an effective temperature of about 11,750 K and logg=2.0. The two objects have nearly identical bolometric luminosities, logL/L{sub ⊙}=3.24 and 3.22, respectively.
Astrometric Membership Tests for the Zinn–Newell–Gibson UV-bright Stars in Galactic Globular Clusters
In 1972, Zinn, Newell, & Gibson (ZNG) published a list of 156 candidate UV-bright stars they had found in 27 Galactic globular clusters (GCs), based on photographs in the U and V bands. UV-bright stars lie above the horizontal branch (HB) and blueward of the asymptotic giant branch (AGB) and red giant branch in the clusters’ color–magnitude diagrams. They are in rapid evolutionary phases—if they are members and not unrelated bright foreground stars. The ZNG list has inspired numerous follow-up studies, aimed at understanding late stages of stellar evolution. However, the ZNG candidates were presented only in finding charts, and celestial coordinates were not given. Using my own collection of CCD frames in u and V, I have identified all of the ZNG objects, and have assembled their coordinates, parallaxes, and proper motions from the recent Gaia Early Data Release 3 (EDR3). Based on the Gaia astrometry, I have determined which objects are probable cluster members (45% of the sample). For the members, using photometry from EDR3, I have assigned the stars to various evolutionary stages, including luminous post-AGB stars, and stars above the HB. I point out several ZNG stars of special interest that have still, to my knowledge, never been studied in detail. This study is an adjunct to a forthcoming survey of the Galactic GCs in the uBVI photometric system, designed for detection of low-gravity stars with large Balmer discontinuities.
Light Element Abundances and Multiple Populations in M53
We present results from a study of 94 red giant stars in the globular cluster M53. We use low-resolution spectra to measure the strength of CN and CH features at ∼3800 and 4300 Å, respectively. The strengths of these features are used to classify stars into a CN-enhanced and CN-normal population and to measure C and N abundances in all 94 stars. We find the red giant branch stars to be evenly split between the two populations identified, and observe the presence of CN-enhanced stars on the asymptotic giant branch. In addition, we identify five CH star candidates based on the strength of their CN and CH band features, and the presence of a P-branch in their CH band. We compare our identification of multiple populations to those based on the Na–O anticorrelation and pseudo-color indices in Hubble Space Telescope UV photometry, and find general agreement between all three methods. Our large sample size also allows us to study the radial distribution of each population, and we find that the CN-enhanced population is more centrally concentrated. We use our C and N measurements to compare the evolutionary changes in these elements as a function of magnitude between the two populations, and show that both populations experience similar evolutionary changes to the surface abundances of C and N. Finally, we calculate C+N+O abundances for each population and compare them to similar measurements made in M10; we find that in both clusters, CN-enhanced stars have a slightly enhanced C+N+O (Δ(C+N+O) ∼ 0.2 dex).