Measuring Organic Molecular Emission in Disks with Low Resolution Spitzer Spectroscopy

We explore the extent to which Spitzer IRS spectra taken at low spectral resolution can be used in quantitative studies of organic molecular emission from disks surrounding low mass young stars. We use Spitzer IRS spectra taken in both the high and low resolution modules for the same sources to investigate whether it is possible to define line indices that can measure trends in the strength of the molecular features in low resolution data. We find that trends in HCN emission strength seen in the high resolution data can be recovered in low resolution data. In examining the factors that influence the HCN emission strength, we find that the low resolution HCN flux is modestly correlated with stellar accretion rate and X-ray luminosity. Correlations of this kind are perhaps expected based on recent observational and theoretical studies of inner disk atmospheres. Our results demonstrate the potential of using the large number of low resolution disk spectra that reside in the Spitzer archive to study the factors that influence the strength of molecular emission from disks. Such studies would complement results for the much smaller number of circumstellar disks that have been observed at high resolution with IRS

Model predictions of wind and turbulence profiles associated with an ensemble of aircraft accidents

The feasibility of predicting conditions under which wind/turbulence environments hazardous to aviation operations exist is studied by examining a number of different accidents in detail. A model of turbulent flow in the atmospheric boundary layer is used to reconstruct wind and turbulence profiles which may have existed at low altitudes at the time of the accidents. The predictions are consistent with available flight recorder data, but neither the input boundary conditions nor the flight recorder observations are sufficiently precise for these studies to be interpreted as verification tests of the model predictions

Baby-Step Giant-Step Algorithms for the Symmetric Group

We study discrete logarithms in the setting of group actions. Suppose that $G$ is a group that acts on a set $S$. When $r,s \in S$, a solution $g \in G$ to $r^g = s$ can be thought of as a kind of logarithm. In this paper, we study the case where $G = S_n$, and develop analogs to the Shanks baby-step / giant-step procedure for ordinary discrete logarithms. Specifically, we compute two sets $A, B \subseteq S_n$ such that every permutation of $S_n$ can be written as a product $ab$ of elements $a \in A$ and $b \in B$. Our deterministic procedure is optimal up to constant factors, in the sense that $A$ and $B$ can be computed in optimal asymptotic complexity, and $|A|$ and $|B|$ are a small constant from $\sqrt{n!}$ in size. We also analyze randomized "collision" algorithms for the same problem

The test case of HD26965: difficulties disentangling weak Doppler signals from stellar activity

We report the discovery of a radial velocity signal that can be interpreted as a planetary-mass candidate orbiting the K dwarf HD26965, with an orbital period of 42.364$\pm$0.015 days, or alternatively, as the presence of residual, uncorrected rotational activity in the data. Observations include data from HIRES, PFS, CHIRON, and HARPS, where 1,111 measurements were made over 16 years. Our best solution for HD26965 $b$ is consistent with a super-Earth that has a minimum mass of 6.92$\pm$0.79 M$_{\oplus}$ orbiting at a distance of 0.215$\pm$0.008 AU from its host star. We have analyzed the correlation between spectral activity indicators and the radial velocities from each instrument, showing moderate correlations that we include in our model. From this analysis, we recover a $\sim$38 day signal, which matches some literature values of the stellar rotation period. However, from independent Mt. Wilson HK data for this star, we find evidence for a significant 42 day signal after subtraction of longer period magnetic cycles, casting doubt on the planetary hypothesis for this period. Although our statistical model strongly suggests that the 42-day signal is Doppler in origin, we conclude that the residual effects of stellar rotation are difficult to fully model and remove from this dataset, highlighting the difficulties to disentangle small planetary signals and photospheric noise, particularly when the orbital periods are close to the rotation period of the star. This study serves as an excellent test case for future works that aim to detect small planets orbiting `Sun-like' stars using radial velocity measurements.Comment: 16 pages, 10 figures, 13 tables, accepted for publication in A