Water in Emission in the ISO Spectrum of the Early M Supergiant Star mu Cephei

We report a detection of water in emission in the spectrum of the M2 supergiant atar mu Cep (M2Ia) observed by the Short Wavelength Spectrometer (SWS) aboard Infrared Space Observatory (ISO) and now released as the ISO Archives. The emission first appears in the 6 micron region (nu2 fundamental) and then in the 40 micron region (pure rotation lines) despite the rather strong dust emission. The intensity ratios of the emission features are far from those of the optically thin gaseous emission. Instead, we could reproduce the major observed emission features by an optically thick water sphere of the inner radius about two stellar radii (1300Rsun), Tex = 1500K, and Ncol (H2O) = 3.0E+20/cm2. This model also accounts for the H2O absorption bands in the near infrared (1.4, 1.9, and 2.7 micron) as well. The detection of water in emission provides strong constraints on the nature of water in the early M supergiant stars, and especially its origin in the outer atmosphere is confirmed against other models such as the large convective cell model. We finally confirm that the early M supergiant star is surrounded by a huge optically thick sphere of the warm water vapor, which may be referred to as MOLsphere for simplicity. Thus, the outer atmosphere of M supergiant stars should have a complicated hierarchical and/or hybrid structure with at least three major constituents including the warm MOLsphere (T about 1.0E+3K) together with the previously known hot chromosphere (T about 1.0E+4K) and cool expanding gas-dust envelope (T about 1.0E+2K).Comment: 14 pages, 5 postscript figures, to appear in ApJ

On the Determination of an On-Demand Policy for a Multilayer Control System

The cost-performance tradeoff problem associated with a multilayer control system for controlling a class of static, nonlinear, multivariable systems is considered. The multilayer control system has a number of layers of control functions each of which updates different subsets of the manipulated variables at different costs. A favorable cost-performance tradeoff is achieved by determining at each control decision time which subset of the control variables is to be updated. In this paper, we present a mathematical model which describes the operation of the multilayer control system. Also we show that the problem of determining a decision rule (policy) which results in an optimal cost-performance tradeoff can be formulated as a problem in Markovian Decision Processes. Consequently, an optimal policy can be identified by solving a linear program. In order to reduce the computational effort required for identifying the optimal policy, a class of parameterized policies is introduced based on a measure of deviation of the disturbance. This approach provides a designer with a practical method of determining a control policy which achieves a favorable cost-performance tradeoff. An example is given for demonstrating a possible application to process control

Evolutionary models for very-low-mass stars and brown dwarfs with dusty atmospheres

We present evolutionary calculations for very-low-mass stars and brown dwarfs based on synthetic spectra and non-grey atmosphere models which include dust formation and opacity, i.e. objects with \te\simle 2800 K. The interior of the most massive brown dwarfs is shown to develop a conductive core after $\sim 2$ Gyr which slows down their cooling. Comparison is made in optical and infrared color-magnitude diagrams with recent late-M and L-dwarf observations. The saturation in optical colors and the very red near-infrared colors of these objects are well explained by the onset of dust formation in the atmosphere. Comparison of the faintest presently observed L-dwarfs with these dusty evolutionary models suggests that dynamical processes such as turbulent diffusion and gravitational settling are taking place near the photosphere. As the effective temperature decreases below \te\approx 1300-1400 K, the colors of these objects move to very blue near-infrared colors, a consequence of the ongoing methane absorption in the infrared. We suggest the possibility ofa brown dwarf dearth in $J,H,K$ color-magnitude diagrams around this temperature.Comment: 38 pages, Latex file, uses aasms4.sty, accepted for publication in Ap

Dust in the Photospheric Environment: Unified Cloudy Models of M, L, and T Dwarfs

We address the problem of how dust forms and how it could be sustained in the static photospheres of cool dwarfs for a long time. In the cool and dense gas, dust forms easily at the condensation temperature, T_cond, and the dust can be in detailed balance with the ambient gas so long as it remains smaller than the critical radius, r_cr. However, dust will grow larger and segregate from the gas when it will be larger than r_cr somewhere at the lower temperature, which we refer to as the critical temperature, T_cr. Then, the large dust grains will precipitate below the photosphere and only the small dust grains in the region of T_cr < T < T_cond can be sustained in the photosphere. Thus a dust cloud is formed. Incorporating the dust cloud, non-grey model photo- spheres in radiative-convective equilibrium are extended to T_eff as low as 800K. Observed colors and spectra of cool dwarfs can consistently be accounted for by a single grid of our cloudy models. This fact in turn can be regarded as supporting evidence for our basic assumption on the cloud formation.Comment: 50 pages with 14 postscript figures, to be published in Astrophys.

Water vapor on supergiants. The 12 micron TEXES spectra of mu Cephei

Several recent papers have argued for warm, semi-detached, molecular layers surrounding red giant and supergiant stars, a concept known as a MOLsphere. Spectroscopic and interferometric analyses have often corroborated this general picture. Here, we present high-resolution spectroscopic data of pure rotational lines of water vapor at 12 microns for the supergiant mu Cephei. This star has often been used to test the concept of molecular layers around supergiants. Given the prediction of an isothermal, optically thick water-vapor layer in Local Thermodynamic Equilibrium around the star (MOLsphere), we expected the 12 micron lines to be in emission or at least in absorption but filled in by emission from the molecular layer around the star. Our data, however, show the contrary; we find definite absorption. Thus, our data do not easily fit into the suggested isothermal MOLsphere scenario. The 12 micron lines, therefore, put new, strong constraints on the MOLsphere concept and on the nature of water seen in signatures across the spectra of early M supergiants. We also find that the absorption is even stronger than that calculated from a standard, spherically symmetric model photosphere without any surrounding layers. A cool model photosphere, representing cool outer layers is, however, able to reproduce the lines, but this model does not account for water vapor emission at 6 microns. Thus, a unified model for water vapor on mu Cephei appears to be lacking. It does seem necessary to model the underlying photospheres of these supergiants in their whole complexity. The strong water vapor lines clearly reveal inadequacies of classical model atmospheres.Comment: Accepted for publication in the Astrophysical Journa

Identification of SH Δv=1\Delta v=1 ro-vibrational lines in R And

We report the identification of SH $\Delta v=1$ ro-vibrational lines in the published high-resolution infrared spectrum of the S-type star, R And. This is the first astronomical detection of this molecule. The lines show inverse P-Cygni profiles, indicating infall motion of the molecular layer due to stellar pulsation. A simple spherical shell model with a constant infall velocity is adopted to determine the condition of the layer. It is found that a single excitation temperature of 2200 K reproduces the observed line intensities satisfactory. SH is located in a layer from 1.0 to ~1.1 stellar radii, which is moving inward with a velocity of 9 km s-1. These results are consistent with the previous measurements of CO $\Delta v=3$ transitions. The estimated molecular abundance SH/H is 1x10^-7, consistent with a thermal equilibrium calculation.Comment: 10 pages, 2 figures. Accepted for publication in ApJ Letter

Quantitative estimates of discrete harmonic measures

A theorem of Bourgain states that the harmonic measure for a domain in $\R^d$ is supported on a set of Hausdorff dimension strictly less than $d$ \cite{Bourgain}. We apply Bourgain's method to the discrete case, i.e., to the distribution of the first entrance point of a random walk into a subset of $\Z ^d$, $d\geq 2$. By refining the argument, we prove that for all \b>0 there exists \rho (d,\b)N(d,\b), any $x \in \Z^d$, and any $A\subset \{1,..., n\}^d$ | \{y\in\Z^d\colon \nu_{A,x}(y) \geq n^{-\b} \}| \leq n^{\rho(d,\b)}, where $\nu_{A,x} (y)$ denotes the probability that $y$ is the first entrance point of the simple random walk starting at $x$ into $A$. Furthermore, $\rho$ must converge to $d$ as \b \to \infty.Comment: 16 pages, 2 figures. Part (B) of the theorem is ne

5-micron photometry of late-type dwarfs

We present narrowband-M photometry of nine low-mass dwarfs with spectral types ranging from M2.5 to L0.5. Combining the (L'-M') colours derived from our observations with data from the literature, we find colours consistent with a Rayleigh-Jeans flux distribution for spectral types earlier than M5, but enhanced F_3.8/F_4.7 flux ratios (negative (L'-M') colours) at later spectral types. This probably reflects increased absorption at M' due to the CO fundamental band. We compare our results against recent model predictions and briefly discuss the implications.Comment: accepted for the Astronomical Journa

Four nearby L dwarfs

We present spectroscopic, photometric and astrometric observations of four bright L dwarfs identified in the course of the 2MASS near-infrared survey. Our spectroscopic data extend to wavelengths shortward of 5000\AA in the L0 dwarf 2MASSJ0746+2000 and the L4 dwarf 2MASSJ0036+1840, allowing the identification of absorption bands due to MgH and CaOH. The atomic resonance lines Ca I 4227\AA and Na I 5890/5896\AA are extremely strong, with the latter having an equivalent width of 240\AA in the L4 dwarf. By spectral type L5, the D lines extend over $\sim1000$\AA and absorb a substantial fraction of the flux emitted in the V band, with a corresponding effect on the (V-I) broadband colour. The KI resonance doublet at 7665/7699\AA increases in equivalent width from spectral type M3 to M7, but decreases in strength from M7 to L0 before broadening substantially at later types. These variations are likely driven by dust formation in these cool atmospheres.Comment: to appear in AJ, January 2000; 27 pages, including 3 tables and 7 figures embedded in the tex

Photometric Variability in the Ultracool Dwarf BRI 0021-0214: Possible Evidence for Dust Clouds

We report CCD photometric monitoring of the nonemission ultracool dwarf BRI 0021-0214 (M9.5) obtained during 10 nights in 1995 November and 4 nights in 1996 August, with CCD cameras at 1 m class telescopes on the observatories of the Canary Islands. We present differential photometry of BRI 0021-0214, and we report significant variability in the I-band light curve obtained in 1995. A periodogram analysis finds a strong peak at a period of 0.84 day. This modulation appears to be transient because it is present in the 1995 data but not in the 1996 data. We also find a possible period of 0.20 day, which appears to be present in both the 1995 and 1996 datasets. However, we do not find any periodicity close to the rotation period expected from the spectroscopic rotational broadening (< 0.14 day). BRI 0021-0214 is a very inactive object, with extremely low levels of Halpha and X-ray emission. Thus, it is unlikely that magnetically induced cool spots can account for the photometric variability. The photometric variability of BRI 0021-0214 could be explained by the presence of an active meteorology that leads to inhomogeneous clouds on the surface. The lack of photometric modulation at the expected rotational period suggests that the pattern of surface features may be more complicated than previously anticipated.Comment: Accepted for publication in ApJ. 26 pages, 13 figures include