New views of the solar wind with the Lambert W function

This paper presents closed-form analytic solutions to two illustrative problems in solar physics that have been considered not solvable in this way previously. Both the outflow speed and the mass loss rate of the solar wind of plasma particles ejected by the Sun are derived analytically for certain illustrative approximations. The calculated radial dependence of the flow speed applies to both Parker's isothermal solar wind equation and Bondi's equation of spherical accretion. These problems involve the solution of transcendental equations containing products of variables and their logarithms. Such equations appear in many fields of physics and are solvable by use of the Lambert W function, which is briefly described. This paper is an example of how new functions can be applied to existing problems.Comment: 16 pages (revtex4), 3 figures, American J. Phys., in press (2004

Neutral interstellar He parameters in front of the heliosphere 1994--2007

Analysis of IBEX measurements of neutral interstellar He flux brought the inflow velocity vector different from the results of earlier analysis of observations from GAS/Ulysses. Recapitulation of results on the helium inflow direction from the past ~40 years suggested that the inflow direction may be changing with time. We reanalyze the old Ulysses data and reprocess them to increase the accuracy of the instrument pointing to investigate if the GAS observations support the hypothesis that the interstellar helium inflow direction is changing. We employ a similar analysis method as in the analysis of the IBEX data. We seek a parameter set that minimizes reduced chi-squared, using the Warsaw Test Particle Model for the interstellar He flux at Ulysses with a state of the art model of neutral He ionization in the heliosphere, and precisely reproducing the observation conditions. We also propose a supplementary method of constraining the parameters based on cross-correlations of parameters obtained from analysis of carefully selected subsets of data. We find that the ecliptic longitude and speed of interstellar He are in a very good agreement with the values reported in the original GAS analysis. We find, however, that the temperature is markedly higher. The 3-seasons optimum parameter set is lambda = 255.3, beta = 6, v = 26.0 km/s, T = 7500 K. We find no evidence that it is varying with time, but the uncertainty range is larger than originally reported. The originally-derived parameters of interstellar He from GAS are in good agreement with presently derived, except for the temperature, which seems to be appreciably higher, in good agreement with interstellar absorption line results. While the results of the present analysis are in marginal agreement with the earlier reported results from IBEX, the most likely values from the two analyses differ for reasons that are still not understood.Comment: submitted for publication in Astronomy & Astrophysic

Modeling the Sun's open magnetic flux and the heliospheric current sheet

By coupling a solar surface flux transport model with an extrapolation of the heliospheric field, we simulate the evolution of the Sun's open magnetic flux and the heliospheric current sheet (HCS) based on observational data of sunspot groups since 1976. The results are consistent with measurements of the interplanetary magnetic field near Earth and with the tilt angle of the HCS as derived from extrapolation of the observed solar surface field. This opens the possibility for an improved reconstruction of the Sun's open flux and the HCS into the past on the basis of empirical sunspot data.Comment: 16 pages, 5 figures, Accepted for publication in Ap

A turbulence-driven model for heating and acceleration of the fast wind in coronal holes

A model is presented for generation of fast solar wind in coronal holes, relying on heating that is dominated by turbulent dissipation of MHD fluctuations transported upwards in the solar atmosphere. Scale-separated transport equations include large-scale fields, transverse Alfvenic fluctuations, and a small compressive dissipation due to parallel shears near the transition region. The model accounts for proton temperature, density, wind speed, and fluctuation amplitude as observed in remote sensing and in situ satellite data.Comment: accepted for publication in ApJ

On Collisionless Electron-Ion Temperature Equilibration in the Fast Solar Wind

We explore a mechanism, entirely new to the fast solar wind, of electron heating by lower hybrid waves to explain the shift to higher charge states observed in various elements in the fast wind at 1 A.U. relative to the original coronal hole plasma. This process is a variation on that previously discussed for two temperature accretion flows by Begelman & Chiueh. Lower hybrid waves are generated by gyrating minor ions (mainly alpha-particles) and become significant once strong ion cyclotron heating sets in beyond 1.5 R_sun. In this way the model avoids conflict with SUMER electron temperature diagnostic measurements between 1 and 1.5 R_sun. The principal requirement for such a process to work is the existence of density gradients in the fast solar wind, with scale length of similar order to the proton inertial length. Similar size structures have previously been inferred by other authors from radio scintillation observations and considerations of ion cyclotron wave generation by global resonant MHD waves.Comment: 32 pages including 11 figures, 4 tables, accepted by Ap

Assessing the tilt of the solar magnetic field axis through Faraday rotation observations

Context: Faraday rotation measurements of extragalactic radio sources during coronal occultation allow assessment of both the electron density distribution and the three-dimensional magnetic field topology in the outer solar corona. Aims: We simulate the three-dimensional structure of both the coronal magnetic field and the electron density distribution in order to reproduce the excess Faraday rotation measures (RMs) of the occulted radio sources observed during solar activity minimum. In particular, we infer the tilt of the solar magnetic axis with respect to the rotation axis. Methods: We compare the output of the model with Very Large Array (VLA) radio polarimetric measurements of a sample of extragalactic sources observed in May 1997. Information on the magnetic field geometry can be retrieved by fine-tuning the set of model free parameters that best describe the observations. Results: We find that predicted and observed Faraday rotation measures are in excellent agreement, thus supporting the model. Our best-fitting model yields a tilt angle $\theta_{RB}=3.3^{\circ}$ of the solar magnetic axis with respect to the solar rotation axis around Carrington Rotation 1923. This result is consistent with analogous but independent estimates computed from the expansion coefficients of the photospheric field observed at the Wilcox Solar Observatory (WSO).Comment: 8 pages, 5 figures, accepted for publication in A&

Improved Constraints on the Preferential Heating and Acceleration of Oxygen Ions in the Extended Solar Corona

We present a detailed analysis of oxygen ion velocity distributions in the extended solar corona, based on observations made with the Ultraviolet Coronagraph Spectrometer (UVCS) on the SOHO spacecraft. Polar coronal holes at solar minimum are known to exhibit broad line widths and unusual intensity ratios of the O VI 1032, 1037 emission line doublet. The traditional interpretation of these features has been that oxygen ions have a strong temperature anisotropy, with the temperature perpendicular to the magnetic field being much larger than the temperature parallel to the field. However, recent work by Raouafi and Solanki suggested that it may be possible to model the observations using an isotropic velocity distribution. In this paper we analyze an expanded data set to show that the original interpretation of an anisotropic distribution is the only one that is fully consistent with the observations. It is necessary to search the full range of ion plasma parameters to determine the values with the highest probability of agreement with the UVCS data. The derived ion outflow speeds and perpendicular kinetic temperatures are consistent with earlier results, and there continues to be strong evidence for preferential ion heating and acceleration with respect to hydrogen. At heliocentric heights above 2.1 solar radii, every UVCS data point is more consistent with an anisotropic distribution than with an isotropic distribution. At heights above 3 solar radii, the exact probability of isotropy depends on the electron density chosen to simulate the line-of-sight distribution of O VI emissivity. (abridged abstract)Comment: 19 pages (emulateapj style), 13 figures, ApJ, in press (v. 679; May 20, 2008

Disk Formation by AGB Winds in Dipole Magnetic Fields

We present a simple, robust mechanism by which an isolated star can produce an equatorial disk. The mechanism requires that the star have a simple dipole magnetic field on the surface and an isotropic wind acceleration mechanism. The wind couples to the field, stretching it until the field lines become mostly radial and oppositely directed above and below the magnetic equator, as occurs in the solar wind. The interaction between the wind plasma and magnetic field near the star produces a steady outflow in which magnetic forces direct plasma toward the equator, constructing a disk. In the context of a slow (10 km/s) outflow (10^{-5} M_sun/yr) from an AGB star, MHD simulations demonstrate that a dense equatorial disk will be produced for dipole field strengths of only a few Gauss on the surface of the star. A disk formed by this model can be dynamically important for the shaping of Planetary Nebulae.Comment: 14 pages, 8 figures, 1 table, accepted by Ap

Molecular subtyping of bladder cancer using Kohonen self-organizing maps

Kohonen self-organizing maps (SOMs) are unsupervised Artificial Neural Networks (ANNs) that are good for low-density data visualization. They easily deal with complex and nonlinear relationships between variables. We evaluated molecular events that characterize high- and low-grade BC pathways in the tumors from 104 patients. We compared the ability of statistical clustering with a SOM to stratify tumors according to the risk of progression to more advanced disease. In univariable analysis, tumor stage (log rank P = 0.006) and grade (P < 0.001), HPV DNA (P < 0.004), Chromosome 9 loss (P = 0.04) and the A148T polymorphism (rs 3731249) in CDKN2A (P = 0.02) were associated with progression. Multivariable analysis of these parameters identified that tumor grade (Cox regression, P = 0.001, OR.2.9 (95% CI 1.6–5.2)) and the presence of HPV DNA (P = 0.017, OR 3.8 (95% CI 1.3–11.4)) were the only independent predictors of progression. Unsupervised hierarchical clustering grouped the tumors into discreet branches but did not stratify according to progression free survival (log rank P = 0.39). These genetic variables were presented to SOM input neurons. SOMs are suitable for complex data integration, allow easy visualization of outcomes, and may stratify BC progression more robustly than hierarchical clustering