Stellar Winds on the Main-Sequence II: the Evolution of Rotation and Winds

Aims: We study the evolution of stellar rotation and wind properties for low-mass main-sequence stars. Our aim is to use rotational evolution models to constrain the mass loss rates in stellar winds and to predict how their properties evolve with time on the main-sequence. Methods: We construct a rotational evolution model that is driven by observed rotational distributions of young stellar clusters. Fitting the free parameters in our model allows us to predict how wind mass loss rate depends on stellar mass, radius, and rotation. We couple the results to the wind model developed in Paper I of this series to predict how wind properties evolve on the main-sequence. Results: We estimate that wind mass loss rate scales with stellar parameters as $\dot{M}_\star \propto R_\star^2 \Omega_\star^{1.33} M_\star^{-3.36}$. We estimate that at young ages, the solar wind likely had a mass loss rate that is an order of magnitude higher than that of the current solar wind. This leads to the wind having a higher density at younger ages; however, the magnitude of this change depends strongly on how we scale wind temperature. Due to the spread in rotation rates, young stars show a large range of wind properties at a given age. This spread in wind properties disappears as the stars age. Conclusions: There is a large uncertainty in our knowledge of the evolution of stellar winds on the main-sequence, due both to our lack of knowledge of stellar winds and the large spread in rotation rates at young ages. Given the sensitivity of planetary atmospheres to stellar wind and radiation conditions, these uncertainties can be significant for our understanding of the evolution of planetary environments.Comment: 26 pages, 14 figures, 2 tables, to be published in A&

Stellar Winds on the Main-Sequence I: Wind Model

Aims: We develop a method for estimating the properties of stellar winds for low-mass main-sequence stars between masses of 0.4 and 1.1 solar masses at a range of distances from the star. Methods: We use 1D thermal pressure driven hydrodynamic wind models run using the Versatile Advection Code. Using in situ measurements of the solar wind, we produce models for the slow and fast components of the solar wind. We consider two radically different methods for scaling the base temperature of the wind to other stars: in Model A, we assume that wind temperatures are fundamentally linked to coronal temperatures, and in Model B, we assume that the sound speed at the base of the wind is a fixed fraction of the escape velocity. In Paper II of this series, we use observationally constrained rotational evolution models to derive wind mass loss rates. Results: Our model for the solar wind provides an excellent description of the real solar wind far from the solar surface, but is unrealistic within the solar corona. We run a grid of 1200 wind models to derive relations for the wind properties as a function of stellar mass, radius, and wind temperature. Using these results, we explore how wind properties depend on stellar mass and rotation. Conclusions: Based on our two assumptions about the scaling of the wind temperature, we argue that there is still significant uncertainty in how these properties should be determined. Resolution of this uncertainty will probably require both the application of solar wind physics to other stars and detailed observational constraints on the properties of stellar winds. In the final section of this paper, we give step by step instructions for how to apply our results to calculate the stellar wind conditions far from the stellar surface.Comment: 24 pages, 13 figures, 2 tables, Accepted for publication in A&

Testing in High-Dimensional Spiked Models

We consider the five classes of multivariate statistical problems identified by James (1964), which together cover much of classical multivariate analysis, plus a simpler limiting case, symmetric matrix denoising. Each of James' problems involves the eigenvalues of {code} where H and E are proportional to high dimensional Wishart matrices. Under the null hypothesis, both Wisharts are central with identity covariance. Under the alternative, the non-centrality or the covariance parameter of H has a single eigenvalue, a spike, that stands alone. When the spike is smaller than a case-specific phase transition threshold, none of the sample eigenvalues separate from the bulk, making the testing problem challenging. Using a unified strategy for the six cases, we show that the log likelihood ratio processes parameterized by the value of the sub-critical spike converge to Gaussian processes with logarithmic correlation. We then derive asymptotic power envelopes for tests for the presence of a spike

Mid-J CO Shock Tracing Observations of Infrared Dark Clouds I

Infrared dark clouds (IRDCs) are dense, molecular structures in the interstellar medium that can harbour sites of high-mass star formation. IRDCs contain supersonic turbulence, which is expected to generate shocks that locally heat pockets of gas within the clouds. We present observations of the CO J = 8-7, 9-8, and 10-9 transitions, taken with the Herschel Space Observatory, towards four dense, starless clumps within IRDCs (C1 in G028.37+00.07, F1 and F2 in G034.43+0007, and G2 in G034.77-0.55). We detect the CO J = 8-7 and 9-8 transitions towards three of the clumps (C1, F1, and F2) at intensity levels greater than expected from photodissociation region (PDR) models. The average ratio of the 8-7 to 9-8 lines is also found to be between 1.6 and 2.6 in the three clumps with detections, significantly smaller than expected from PDR models. These low line ratios and large line intensities strongly suggest that the C1, F1, and F2 clumps contain a hot gas component not accounted for by standard PDR models. Such a hot gas component could be generated by turbulence dissipating in low velocity shocks.Comment: 14 pages, 8 figures, 5 tables, accepted by A&A, minor updates to match the final published versio

Emergence of fractal behavior in condensation-driven aggregation

We investigate a model in which an ensemble of chemically identical Brownian particles are continuously growing by condensation and at the same time undergo irreversible aggregation whenever two particles come into contact upon collision. We solved the model exactly by using scaling theory for the case whereby a particle, say of size $x$, grows by an amount $\alpha x$ over the time it takes to collide with another particle of any size. It is shown that the particle size spectra of such system exhibit transition to dynamic scaling $c(x,t)\sim t^{-\beta}\phi(x/t^z)$ accompanied by the emergence of fractal of dimension $d_f={{1}\over{1+2\alpha}}$. One of the remarkable feature of this model is that it is governed by a non-trivial conservation law, namely, the $d_f^{th}$ moment of $c(x,t)$ is time invariant regardless of the choice of the initial conditions. The reason why it remains conserved is explained by using a simple dimensional analysis. We show that the scaling exponents $\beta$ and $z$ are locked with the fractal dimension $d_f$ via a generalized scaling relation $\beta=(1+d_f)z$.Comment: 8 pages, 6 figures, to appear in Phys. Rev.

High-Dimensional Inference with the generalized Hopfield Model: Principal Component Analysis and Corrections

We consider the problem of inferring the interactions between a set of N binary variables from the knowledge of their frequencies and pairwise correlations. The inference framework is based on the Hopfield model, a special case of the Ising model where the interaction matrix is defined through a set of patterns in the variable space, and is of rank much smaller than N. We show that Maximum Lik elihood inference is deeply related to Principal Component Analysis when the amp litude of the pattern components, xi, is negligible compared to N^1/2. Using techniques from statistical mechanics, we calculate the corrections to the patterns to the first order in xi/N^1/2. We stress that it is important to generalize the Hopfield model and include both attractive and repulsive patterns, to correctly infer networks with sparse and strong interactions. We present a simple geometrical criterion to decide how many attractive and repulsive patterns should be considered as a function of the sampling noise. We moreover discuss how many sampled configurations are required for a good inference, as a function of the system size, N and of the amplitude, xi. The inference approach is illustrated on synthetic and biological data.Comment: Physical Review E: Statistical, Nonlinear, and Soft Matter Physics (2011) to appea

A Critique of Current Magnetic-Accretion Models for Classical T-Tauri Stars

Current magnetic-accretion models for classical T-Tauri stars rely on a strong, dipolar magnetic field of stellar origin to funnel the disk material onto the star, and assume a steady-state. In this paper, I critically examine the physical basis of these models in light of the observational evidence and our knowledge of magnetic fields in low-mass stars, and find it lacking. I also argue that magnetic accretion onto these stars is inherently a time-dependent problem, and that a steady-state is not warranted. Finally, directions for future work towards fully-consistent models are pointed out.Comment: 2 figure

Effect of stellar wind induced magnetic fields on planetary obstacles of non-magnetized hot Jupiters

We investigate the interaction between the magnetized stellar wind plasma and the partially ionized hydrodynamic hydrogen outflow from the escaping upper atmosphere of non- or weakly magnetized hot Jupiters. We use the well-studied hot Jupiter HD 209458b as an example for similar exoplanets, assuming a negligible intrinsic magnetic moment. For this planet, the stellar wind plasma interaction forms an obstacle in the planet's upper atmosphere, in which the position of the magnetopause is determined by the condition of pressure balance between the stellar wind and the expanded atmosphere, heated by the stellar extreme ultraviolet (EUV) radiation. We show that the neutral atmospheric atoms penetrate into the region dominated by the stellar wind, where they are ionized by photo-ionization and charge exchange, and then mixed with the stellar wind flow. Using a 3D magnetohydrodynamic (MHD) model, we show that an induced magnetic field forms in front of the planetary obstacle, which appears to be much stronger compared to those produced by the solar wind interaction with Venus and Mars. Depending on the stellar wind parameters, because of the induced magnetic field, the planetary obstacle can move up to ~0.5-1 planetary radii closer to the planet. Finally, we discuss how estimations of the intrinsic magnetic moment of hot Jupiters can be inferred by coupling hydrodynamic upper planetary atmosphere and MHD stellar wind interaction models together with UV observations. In particular, we find that HD 209458b should likely have an intrinsic magnetic moment of 10-20% that of Jupiter.Comment: 8 pages, 6 figures, 2 tables, accepted to MNRA

Hitting Time of Quantum Walks with Perturbation

The hitting time is the required minimum time for a Markov chain-based walk (classical or quantum) to reach a target state in the state space. We investigate the effect of the perturbation on the hitting time of a quantum walk. We obtain an upper bound for the perturbed quantum walk hitting time by applying Szegedy's work and the perturbation bounds with Weyl's perturbation theorem on classical matrix. Based on the definition of quantum hitting time given in MNRS algorithm, we further compute the delayed perturbed hitting time (DPHT) and delayed perturbed quantum hitting time (DPQHT). We show that the upper bound for DPQHT is actually greater than the difference between the square root of the upper bound for a perturbed random walk and the square root of the lower bound for a random walk.Comment: 9 page