Stability of Satellites in Closely Packed Planetary Systems

We perform numerical integrations of four-body (star, planet, planet, satellite) systems to investigate the stability of satellites in planetary Systems with Tightly-packed Inner Planets (STIPs). We find that the majority of closely-spaced stable two-planet systems can stably support satellites across a range of parameter-space which is only slightly decreased compared to that seen for the single-planet case. In particular, circular prograde satellites remain stable out to $\sim 0.4 R_H$ (where $R_H$ is the Hill Radius) as opposed to $\sim 0.5 R_H$ in the single-planet case. A similarly small restriction in the stable parameter-space for retrograde satellites is observed, where planetary close approaches in the range 2.5 to 4.5 mutual Hill radii destabilize most satellites orbits only if $a\sim 0.65 R_H$. In very close planetary pairs (e.g. the 12:11 resonance) the addition of a satellite frequently destabilizes the entire system, causing extreme close-approaches and the loss of satellites over a range of circumplanetary semi-major axes. The majority of systems investigated stably harbored satellites over a wide parameter-space, suggesting that STIPs can generally offer a dynamically stable home for satellites, albeit with a slightly smaller stable parameter-space than the single-planet case. As we demonstrate that multi-planet systems are not a priori poor candidates for hosting satellites, future measurements of satellite occurrence rates in multi-planet systems versus single-planet systems could be used to constrain either satellite formation or past periods of strong dynamical interaction between planets.Comment: 11 pages, 5 figures. Accepted for publication, ApJ

A procedure for implanting a spinal chamber for longitudinal in vivo imaging of the mouse spinal cord.

Studies in the mammalian neocortex have enabled unprecedented resolution of cortical structure, activity, and response to neurodegenerative insults by repeated, time-lapse in vivo imaging in live rodents. These studies were made possible by straightforward surgical procedures, which enabled optical access for a prolonged period of time without repeat surgical procedures. In contrast, analogous studies of the spinal cord have been previously limited to only a few imaging sessions, each of which required an invasive surgery. As previously described, we have developed a spinal chamber that enables continuous optical access for upwards of 8 weeks, preserves mechanical stability of the spinal column, is easily stabilized externally during imaging, and requires only a single surgery. Here, the design of the spinal chamber with its associated surgical implements is reviewed and the surgical procedure is demonstrated in detail. Briefly, this video will demonstrate the preparation of the surgical area and mouse for surgery, exposure of the spinal vertebra and appropriate tissue debridement, the delivery of the implant and vertebral clamping, the completion of the chamber, the removal of the delivery system, sealing of the skin, and finally, post-operative care. The procedure for chronic in vivo imaging using nonlinear microscopy will also be demonstrated. Finally, outcomes, limitations, typical variability, and a guide for troubleshooting are discussed

An Analysis of Jitter and Transit Timing Variations in the HAT-P-13 System

If the two planets in the HAT-P-13 system are coplanar, the orbital states provide a probe of the internal planetary structure. Previous analyses of radial velocity and transit timing data of the system suggested that the observational constraints on the orbital states were rather small. We reanalyze the available data, treating the jitter as an unknown MCMC parameter, and find that a wide range of jitter values are plausible, hence the system parameters are less well constrained than previously suggested. For slightly increased levels of jitter ($\sim 4.5\,m\,s^{-1}$) the eccentricity of the inner planet can be in the range $0<e_{inner}<0.07$, the period and eccentricity of the outer planet can be $440<P_{outer}<470$ days and $0.55<e_{outer}<0.85$ respectively, while the relative pericenter alignment, $\eta$, of the planets can take essentially any value $-180^{\circ}<\eta<+180^{\circ}$. It is therefore difficult to determine whether $e_{inner}$ and $\eta$ have evolved to a fixed-point state or a limit cycle, or to use $e_{inner}$ to probe the internal planetary structure. We perform various transit timing variation (TTV) analyses, demonstrating that current constraints merely restrict $e_{outer}<0.85$, and rule out relative planetary inclinations within $\sim 2^{\circ}$ of $i_{rel}=90^{\circ}$, but that future observations could significantly tighten the restriction on both these parameters. We demonstrate that TTV profiles can readily distinguish the theoretically favored inclinations of i_{rel}=0^{\circ}\,&\,45^{\circ}, provided that sufficiently precise and frequent transit timing observations of HAT-P-13b can be made close to the pericenter passage of HAT-P-13c. We note the relatively high probability that HAT-P-13c transits and suggest observational dates and strategies.Comment: Published in Ap

Using Transit Timing Observations to Search for Trojans of Transiting Extrasolar Planets

Theoretical studies predict that Trojans are likely a frequent byproduct of planet formation and evolution. We examine the sensitivity of transit timing observations for detecting Trojan companions to transiting extrasolar planets. We demonstrate that this method offers the potential to detect terrestrial-mass Trojans using existing ground-based observatories. We compare the transit timing variation (TTV) method with other techniques for detecting extrasolar Trojans and outline the future prospects for this method.Comment: submitted to ApJL, 12 pages, 2 figure

Tri-Dirac Surface Modes in Topological Superconductors

We propose a new type of topological surface modes having cubic dispersion in three-dimensional topological superconductors. Lower order dispersions are prohibited by the threefold rotational symmetry and time-reversal symmetry. Cooper pairing in the bulk changes sign under improper rotations, akin to$^{3}$He-B. The surface manifestations are a divergent surface density of states at the Fermi level and isospins that rotate three times as they circle the origin in momentum space. We propose that Heusler alloys with band inversion are candidate materials to harbor the novel topological superconductivity.Comment: Five-page main text plus five-page supplementary materials; three figure

Entanglement Spectrum Classification of CnC_n-invariant Noninteracting Topological Insulators in Two Dimensions

We study the single particle entanglement spectrum in 2D topological insulators which possess $n$-fold rotation symmetry. By defining a series of special choices of subsystems on which the entanglement is calculated, or real space cuts, we find that the number of protected in-gap states for each type of these real space cuts is a quantum number indexing (if any) non-trivial topology in these insulators. We explicitly show the number of protected in-gap states is determined by a $Z^n$-index, $(z_1,...,z_n)$, where $z_m$ is the number of occupied states that transform according to $m$-th one-dimensional representation of the $C_n$ point group. We find that the entanglement spectrum contains in-gap states pinned in an interval of entanglement eigenvalues $[1/n,1-1/n]$. We determine the number of such in-gap states for an exhaustive variety of cuts, in terms of the $Z_m$ quantum numbers. Furthermore, we show that in a homogeneous system, the $Z^n$ index can be determined through an evaluation of the eigenvalues of point group symmetry operators at all high-symmetry points in the Brillouin zone. When disordered $n$-fold rotationally symmetric systems are considered, we find that the number of protected in-gap states is identical to that in the clean limit as long as the disorder preserves the underlying point group symmetry and does not close the bulk insulating gap.Comment: 14.2 pages for main text, 4.8 pages for Appendices, four figures and two table

Large Chern Number Quantum Anomalous Hall Effect In Thin-film Topological Crystalline Insulators

Quantum anomalous Hall (QAH) insulators are two-dimensional (2D) insulating states exhibiting properties similar to those of quantum Hall states but without external magnetic field. They have quantized Hall conductance $\sigma^H=Ce^2/h$, where integer $C$ is called the Chern number, and represents the number of gapless edge modes. Recent experiments demonstrated that chromium doped thin-film (Bi,Sb)$_2$Te$_3$ is a QAH insulator with Chern number $C=\pm1$. Here we theoretically predict that thin-film topological crystalline insulators (TCI) can host various QAH phases, when doped by ferromagnetically ordered dopants. Any Chern number between $\pm4$ can, in principle, be reached as a result of the interplay between (a) the induced Zeeman field, depending on the magnetic doping concentration, (b) the structural distortion, either intrinsic or induced by a piezoelectric material through proximity effect and (c) the thickness of the thin film. The tunable Chern numbers found in TCI possess significant potential for ultra-low power information processing applications.Comment: References update

New class of topological superconductors protected by magnetic group symmetries

We study a new type of three-dimensional topological superconductors that exhibit Majorana zero modes (MZM) protected by a magnetic group symmetry, a combined antiunitary symmetry composed of a mirror reflection and time-reversal. This new symmetry enhances the noninteracting topological classification of a superconducting vortex from $Z_2$ to $Z$, indicating that multiple MZMs can coexist at the end of one magnetic vortex of unit flux. Specially, we show that a vortex binding two MZMs can be realized on the $(001)$-surface of a topological crystalline insulator SnTe with proximity induced BCS Cooper pairing, or in bulk superconductor In$_x$Sn$_{1-x}$Te.Comment: Accepted version to appear in PRL: 4-page text plus 4-page supplementary materials, two figure