An analysis is made of the spectral line shapes of tau Bootis using high resolution (0.026 A) and high signal-to-noise (S/N~400) data in an effort to confirm the planet hypothesis for this star. Changes in the line shape are quantified using spectral line bisectors and line residuals. We detect no variations in either of these quantities above the level of the noise in the data. One spectral line, Fe I 6213 A, does show a hint of sinusoidal variations in the bisector velocity span when phased to the radial velocity period of 3.3 days, but this is not seen in the bisectors for two other lines, nor in the line residuals. Comparisons of the data to the bisector and residual variations expected for nonradial pulsations indicate that we can exclude those sectoral nonradial modes having m>2 and all sectoral modes with k>1, where k is the ratio of the horizontal to vertical velocities for the pulsations. The lack of line shape variability and the 469 m/s radial velocity amplitude is still consistent with nonradial sectoral modes m=1, and possibly m=2, but with k~1, which is at least 3 orders of magnitude less than the predicted value given the 3.3 day period of tau Bootis. Such low values of k can probably be excluded given the lack of photometric variations for this star. Although the measurements presented here do not prove, without any doubt, that tau Boo has a planetary companion, they do add significantly to the increasing body of evidence in favor of this hypothesis.

Artie P. Hatzes William D. Cochran

We introduce a new technique for showing classical knots and links are not slice. As one application we resolve a long-standing question as to whether certain natural families of knots contain topologically slice knots. We also present a simpler proof of the result of Cochran-Teichner that the successive quotients of the integral terms of the Cochran-Orr-Teichner filtration of the knot concordance group have rank 1. For links we have similar results. We show that the iterated Bing doubles of many algebraically slice knots are not topologically slice. Some of the proofs do not use the existence of the Cheeger-Gromov bound, a deep analytical tool used by Cochran-Teichner. Our main examples are actually boundary links but cannot be detected in the algebraic boundary link concordance group, nor by any $\rho$ invariants associated to solvable representations into finite unitary groups.

Tim D. Cochran Shelly Harvey Constance Leidy

We present a detailed study of the cosmic star formation history over $90$ per cent of cosmic time ($0\lesssim z\lesssim4$), using deep, radio continuum observations that probe star formation activity independent of dust. The Low Frequency Array Two Metre Sky Survey has imaged three well-studied extragalactic fields, Elais-N1, Bo\"otes and the Lockman Hole, reaching $\sim20\,\mu\rm{Jy/beam}$ rms sensitivity at $150\,\rm{MHz}$. The availability of high-quality ancillary data from ultraviolet to far-infrared wavelengths has enabled accurate photometric redshifts and the robust separation of radio-bright AGN from their star-forming counterparts. We capitalise on this unique combination of deep, wide fields and robustly-selected star-forming galaxies to construct radio luminosity functions and derive the cosmic star formation rate density. We carefully constrain and correct for scatter in the $L_{150\,\rm{MHz}}-\rm{SFR}$ relation, which we find to be $\sim0.3\,\rm{dex}$. Our derived star formation rate density lies between previous measurements at all redshifts studied. We derive higher star formation rate densities between $z\sim0$ and $z\sim3$ than are typically inferred from short wavelength emission; at earlier times, this discrepancy is reduced. Our measurements are generally in good agreement with far-infrared and radio-based studies, with small offsets resulting from differing star formation rate calibrations.

R. K. Cochrane R. Kondapally P. N. Best J. Sabater K. J. Duncan D. J. B. Smith M. J. Hardcastle H. J. A. Röttgering I. Prandoni P. Haskell G. Gürkan G. K. Miley

In this paper, we apply a direct method instead of a limit approach, for proving the Levin-Cochran-Lee inequalities. First, we state and prove Levin-Cochran-Lee type inequalities on a homogeneous group $\mathbb{G}$ with parameters $0<p\leq q<\infty$. Furthermore, for the case $p=q$, we prove the sharp inequalities with power weights and derive some other new inequalities.

Michael Ruzhansky Markos Fisseha Yimer

We report the detection of a candidate brown dwarf orbiting the metal-rich K dwarf HD 91669, based on radial-velocity data from the McDonald Observatory Planet Search. HD 91669b is a substellar object in an eccentric orbit (e=0.45) at a separation of 1.2 AU. The minimum mass of 30.6 Jupiter masses places this object firmly within the brown dwarf desert for inclinations i>23 degrees. This is the second rare close-in brown dwarf candidate discovered by the McDonald planet search program.

Robert A. Wittenmyer Michael Endl William D. Cochran Ivan Ramirez Sabine Reffert Phillip J. MacQueen Matthew Shetrone

Recently twisted and higher order Alexander polynomials were used by Cochran, Harvey, Friedl--Kim and Turaev to give lower bounds on the Thurston norm. We first show how Reidemeister torsion relates to these Alexander polynomials. We then give lower bounds on the Thurston norm in terms of the Reidemeister torsion which contain and extend all the above lower bounds and give an elegant reformulation of the bounds of Cochran, Harvey and Turaev. The Reidemeister torsion approach also gives a natural approach to proving and extending certain monotonicity results of Cochran and Harvey.

Stefan Friedl

Cochran, Orr and Teichner introduced $L^2$--eta--invariants to detect highly non--trivial examples of non slice knots. Using a recent theorem by L\"uck and Schick we show that their metabelian $L^2$--eta--invariants can be viewed as the limit of finite dimensional unitary representations. We recall a ribbon obstruction theorem proved by the author using finite dimensional unitary eta--invariants. We show that if for a knot $K$ this ribbon obstruction vanishes then the metabelian $L^2$--eta--invariant vanishes too. The converse has been shown by the author not to be true.

Stefan Friedl

We present optical spectra of a flare on Barnard's star. Several photospheric as well as chromospheric species were enhanced by the flare heating. An analysis of the Balmer lines shows that their shapes are best explained by Stark broadening rather than chromospheric mass motions. We estimate the temperature of the flaring region in the lower atmosphere to be >8000 K and the electron density to be ~10^14 cm^{-3}, similar to values observed in other dM flares. Because Barnard's star is considered to be one of our oldest neighbors, a flare of this magnitude is probably quite rare.

D. Paulson J. Allred R. Anderson S. Hawley W. Cochran S. Yelda

We construct a link in the $3$-space that is not isotopic to any PL link (non-ambiently). In fact, there exist uncountably many $I$-equivalence classes of links. The paper also includes some observations on Cochran's invariants $\beta_i$.

Sergey A. Melikhov

We derive optimal cloning limits for finite Gaussian distributions of coherent states, and describe techniques for achieving them. We discuss the relation of these limits to state estimation and the no-cloning limit in teleportation. A qualitatively different cloning limit is derived for a single-quadrature Gaussian quantum cloner.

P. T. Cochrane T. C. Ralph A. Dolinska