On this page are abstracts and links to preprints and reprints of papers submitted or accepted for publication in refereed journals. Online copies of other published papers and meeting presentations are linked (where available) on other pages. In some cases, there are also online data or computer codes linked with one of these papers.

**
"Proton, Electron, and Ion Heating in the Fast Solar Wind from
Nonlinear Coupling Between Alfvenic and Fast-Mode Turbulence,"
**
Cranmer, S. R., and van Ballegooijen, A. A. 2012,
*Ap. J.,* **754**, 92.
[see also
arXiv:1205.4613]

This paper is available in PDF format (2.0 Mbytes).

*ABSTRACT:*

In the parts of the solar corona and solar wind that experience the fewest Coulomb collisions, the component proton, electron, and heavy ion populations are not in thermal equilibrium with one another. Observed differences in temperatures, outflow speeds, and velocity distribution anisotropies are useful constraints on proposed explanations for how the plasma is heated and accelerated. This paper presents new predictions of the rates of collisionless heating for each particle species, in which the energy input is assumed to come from magnetohydrodynamic (MHD) turbulence. We first created an empirical description of the radial evolution of Alfven, fast-mode, and slow-mode MHD waves. This model provides the total wave power in each mode as a function of distance along an expanding flux tube in the high-speed solar wind. Next we solved a set of cascade advection-diffusion equations that give the time-steady wavenumber spectra at each distance. An approximate term for nonlinear coupling between the Alfven and fast-mode fluctuations is included. For reasonable choices of the parameters, our model contains enough energy transfer from the fast mode to the Alfven mode to excite the high-frequency ion cyclotron resonance. This resonance is efficient at heating protons and other ions in the direction perpendicular to the background magnetic field, and our model predicts heating rates for these species that agree well with both spectroscopic and in~situ measurements. Nonetheless, the high-frequency waves comprise only a small part of the total Alfvenic fluctuation spectrum, which remains highly two-dimensional as is observed in interplanetary space.

**
"Testing a Predictive Theoretical Model for the Mass Loss Rates
of Cool Stars,"
**
Cranmer, S. R., and Saar, S. H. 2011,
*Ap. J.,* **741**, 54.
[see also
arXiv:1108.4369]

This paper is available in PDF format (1.4 Mbytes).

*ABSTRACT:*

The basic mechanisms responsible for producing winds from cool, late-type stars are still largely unknown. We take inspiration from recent progress in understanding solar wind acceleration to develop a physically motivated model of the time-steady mass loss rates of cool main-sequence stars and evolved giants. This model follows the energy flux of magnetohydrodynamic turbulence from a subsurface convection zone to its eventual dissipation and escape through open magnetic flux tubes. We show how Alfven waves and turbulence can produce winds in either a hot corona or a cool extended chromosphere, and we specify the conditions that determine whether or not coronal heating occurs. These models do not utilize arbitrary normalization factors, but instead predict the mass loss rate directly from a star's fundamental properties. We take account of stellar magnetic activity by extending standard age-activity-rotation indicators to include the evolution of the filling factor of strong photospheric magnetic fields. We compared the predicted mass loss rates with observed values for 47 stars and found significantly better agreement than was obtained from the popular scaling laws of Reimers, Schroeder, and Cuntz. The algorithm used to compute cool-star mass loss rates is provided as a self-contained and efficient computer code. We anticipate that the results from this kind of model can be incorporated straightforwardly into stellar evolution calculations and population synthesis techniques.

**
"Can the Solar Wind be Driven by Magnetic Reconnection in
the Sun's Magnetic Carpet?"
**
Cranmer, S. R., and van Ballegooijen, A. A. 2010,
*Ap. J.,* **720**, 824.
[see also arXiv:1007.2383]

This paper is available in PDF format (2.2 Mbytes).

*ABSTRACT:*

The physical processes that heat the solar corona and accelerate the solar wind remain unknown after many years of study. Some have suggested that the wind is driven by waves and turbulence in open magnetic flux tubes, and others have suggested that plasma is injected into the open tubes by magnetic reconnection with closed loops. In order to test the latter idea, we developed Monte Carlo simulations of the photospheric "magnetic carpet" and extrapolated the time-varying coronal field. These models were constructed for a range of different magnetic flux imbalance ratios. Completely balanced models represent quiet regions on the Sun and source regions of slow solar wind streams. Highly imbalanced models represent coronal holes and source regions of fast wind streams. The models agree with observed emergence rates, surface flux densities, and number distributions of magnetic elements. Despite having no imposed supergranular motions, a realistic network of magnetic "funnels" appeared spontaneously. We computed the rate at which closed field lines open up (i.e., recycling times for open flux), and we estimated the energy flux released in reconnection events involving the opening up of closed flux tubes. For quiet regions and mixed-polarity coronal holes, these energy fluxes were found to be much lower than required to accelerate the solar wind. For the most imbalanced coronal holes, the energy fluxes may be large enough to power the solar wind, but the recycling times are far longer than the time it takes the solar wind to accelerate into the low corona. Thus, it is unlikely that either the slow or fast solar wind is driven by reconnection and loop-opening processes in the magnetic carpet.

**
"An Efficient Approximation of the Coronal Heating Rate
for Use in Global Sun-Heliosphere Simulations,"
**
Cranmer, S. R. 2010,
*Ap. J.,* **710**, 676.
[see also
arXiv:0912.5333]

This paper is available in PDF format (1.0 Mbytes).

*ABSTRACT:*

The origins of the hot solar corona and the supersonically expanding solar wind are still the subject of debate. A key obstacle in the way of producing realistic simulations of the Sun-heliosphere system is the lack of a physically motivated way of specifying the coronal heating rate. Recent one-dimensional models have been found to reproduce many observed features of the solar wind by assuming the energy comes from Alfven waves that are partially reflected, then dissipated by magnetohydrodynamic turbulence. However, the nonlocal physics of wave reflection has made it difficult to apply these processes to more sophisticated (three-dimensional) models. This paper presents a set of robust approximations to the solutions of the linear Alfven wave reflection equations. A key ingredient to the turbulent heating rate is the ratio of inward to outward wave power, and the approximations developed here allow this to be written explicitly in terms of local plasma properties at any given location. The coronal heating also depends on the frequency spectrum of Alfven waves in the open-field corona, which has not yet been measured directly. A model-based assumption is used here for the spectrum, but the results of future measurements can be incorporated easily. The resulting expression for the coronal heating rate is self-contained, computationally efficient, and applicable directly to global models of the corona and heliosphere. This paper tests and validates the approximations by comparing the results to exact solutions of the wave transport equations in several cases relevant to the fast and slow solar wind.

**
"Testing Models of Accretion-driven Coronal Heating and
Stellar Wind Acceleration for T Tauri Stars,"
**
Cranmer, S. R. 2009,
*Ap. J.,* **706**, 824.
[see also
arXiv:0910.2686]

This paper is available in PDF format (1.1 Mbytes).

*ABSTRACT:*

Classical T Tauri stars are pre-main-sequence objects that undergo simultaneous accretion, wind outflow, and coronal X-ray emission. The impact of plasma on the stellar surface from magnetospheric accretion streams is likely to be a dominant source of energy and momentum in the upper atmospheres of these stars. This paper presents a set of models for the dynamics and heating of three distinct regions on T Tauri stars that are affected by accretion: (1) the shocked plasmas directly beneath the magnetospheric accretion streams, (2) stellar winds that are accelerated along open magnetic flux tubes, and (3) closed magnetic loops that resemble the Sun's coronal active regions. For the loops, a self-consistent model of coronal heating was derived from numerical simulations of solar field-line tangling and turbulent dissipation. Individual models are constructed for the properties of 14 well-observed stars in the Taurus-Auriga star-forming region. Predictions for the wind mass loss rates are, on average, slightly lower than the observations, which suggests that disk winds or X-winds may also contribute to the measured outflows. For some of the stars, however, the modeled stellar winds do appear to contribute significantly to the measured mass fluxes. Predictions for X-ray luminosities from the shocks and loops are in general agreement with existing observations. The stars with the highest accretion rates tend to have X-ray luminosities dominated by the high-temperature (5-10 MK) loops. The X-ray luminosities for the stars having lower accretion rates are dominated by the cooler accretion shocks.

**
"Empirical Constraints on Proton and Electron Heating in
the Fast Solar Wind,"
**
Cranmer, S. R., Matthaeus, W. H., Breech, B. A., and Kasper, J. C.
2009, *Ap. J.,* **702**, 1604.
[see also arXiv preprint:
arXiv:0907.2650]

This paper is available in PDF format (0.9 Mbytes).

*ABSTRACT:*

We analyze measured proton and electron temperatures in the high-speed solar wind in order to calculate the separate rates of heat deposition for protons and electrons. When comparing with other regions of the heliosphere, the fast solar wind has the lowest density and the least frequent Coulomb collisions. This makes the fast wind an optimal testing ground for studies of collisionless kinetic processes associated with the dissipation of plasma turbulence. Data from the Helios and Ulysses plasma instruments were collected to determine mean radial trends in the temperatures and the electron heat conduction flux between 0.29 and 5.4 AU. The derived heating rates apply specifically for these mean plasma properties and not for the full range of measured values around the mean. We found that the protons receive about 60% of the total plasma heating in the inner heliosphere, and that this fraction increases to approximately 80% by the orbit of Jupiter. A major factor affecting the uncertainty in this fraction is the uncertainty in the measured radial gradient of the electron heat conduction flux. The empirically derived partitioning of heat between protons and electrons is in rough agreement with theoretical predictions from a model of linear Vlasov wave damping. For a modeled power spectrum consisting only of Alfvenic fluctuations, the best agreement was found for a distribution of wavenumber vectors that evolves toward isotropy as distance increases.

**
"A Pulsational Mechanism for Producing Keplerian Disks around Be Stars,"
**
Cranmer, S. R. 2009,
*Ap. J.,* **701**, 396.
[see also arXiv preprint:
arXiv:0906.2772]

This paper is available in PDF format (0.9 Mbytes).

*ABSTRACT:*

Classical Be stars are an enigmatic subclass of rapidly rotating hot stars characterized by dense equatorial disks of gas that have been inferred to orbit with Keplerian velocities. Although these disks seem to be ejected from the star and not accreted, there is substantial observational evidence to show that the stars rotate more slowly than required for centrifugally driven mass loss. This paper develops an idea (proposed originally by Hiroyasu Ando and colleagues) that nonradial stellar pulsations inject enough angular momentum into the upper atmosphere to spin up a Keplerian disk. The pulsations themselves are evanescent in the stellar photosphere, but they may be unstable to the generation of resonant oscillations at the acoustic cutoff frequency. A detailed theory of the conversion from pulsations to resonant waves does not yet exist for realistic hot-star atmospheres, so the current models depend on a parameterized approximation for the efficiency of wave excitation. Once resonant waves have been formed, however, they grow in amplitude with increasing height, steepen into shocks, and exert radial and azimuthal Reynolds stresses on the mean fluid. Using reasonable assumptions for the stellar parameters, these processes were found to naturally create the inner boundary conditions required for dense Keplerian disks, even when the underlying B-star photosphere is rotating as slowly as 60% of its critical rotation speed. Because there is evidence for long-term changes in Be-star pulsational properties, this model may also account for the long-term variability of Be stars, including transitions between normal, Be, and shell phases.

**
"Turbulence-driven Polar Winds from T Tauri Stars Energized by
Magnetospheric Accretion,"
**
Cranmer, S. R. 2008,
*Ap. J.,* **689**, 316.
[see also arXiv preprint:
arXiv:0808.2250]

This paper is available in PDF format (1.0 Mbytes).

*ABSTRACT:*

Pre-main-sequence stars are observed to be surrounded by both accretion flows and some kind of wind or jet-like outflow. Recent work by Matt and Pudritz has suggested that if classical T Tauri stars exhibit stellar winds with mass loss rates about 0.1 times their accretion rates, the wind can carry away enough angular momentum to keep the stars from being spun up unrealistically by accretion. This paper presents a preliminary set of theoretical models of accretion-driven winds from the polar regions of T Tauri stars. These models are based on recently published self-consistent simulations of the Sun's coronal heating and wind acceleration. In addition to the convection-driven MHD turbulence (which dominates in the solar case), we add another source of wave energy at the photosphere that is driven by the impact of plasma in neighboring flux tubes undergoing magnetospheric accretion. This added energy, determined quantitatively from the far-field theory of MHD wave generation, is sufficient to produce T Tauri-like mass loss rates of at least 0.01 times the accretion rate. While still about an order of magnitude below the level required for efficient angular momentum removal, these are the first self-consistent models of T Tauri winds that agree reasonably well with a range of observational mass loss constraints. The youngest modeled stellar winds are supported by Alfven wave pressure, they have low temperatures ("extended chromospheres"), and they are likely to be unstable to the formation of counterpropagating shocks and clumps far from the star.

**
"Improved Constraints on the Preferential Heating and
Acceleration of Oxygen Ions in the Extended Solar Corona,"
**
Cranmer, S. R., Panasyuk, A. V., and Kohl, J. L. 2008,
*Ap. J.,* **678**, 1480.
[see also arXiv preprint:
arXiv:0802.0144]

This paper is available in PDF format (0.7 Mbytes).

*ABSTRACT:*

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.
The most realistic electron densities (which decrease steeply
from 3 to 6 solar radii) produce the lowest probabilities of
isotropy and most-probable temperature anisotropy ratios that
exceed 10.
We also use UVCS O VI absolute intensities to compute the
frozen-in O^(5+) ion concentration in the extended corona;
the resulting range of values is roughly consistent with recent
downward revisions in the oxygen abundance.

**
"Self-consistent Coronal Heating and Solar Wind Acceleration
from Anisotropic Magnetohydrodynamic Turbulence,"
**
Cranmer, S. R., van Ballegooijen, A. A., and Edgar, R. J. 2007,
*Ap. J. Suppl.,* **171**, 520.
[see also arXiv preprint:
astro-ph/0703333]

This paper is available in PDF format (1.2 Mbytes).

*ABSTRACT:*

We present a series of models for the plasma properties along
open magnetic flux tubes rooted in solar coronal holes,
streamers, and active regions.
These models represent the first self-consistent solutions that
combine: (1) chromospheric heating driven by an empirically
guided acoustic wave spectrum, (2) coronal heating from
Alfven waves that have been partially reflected, then damped
by anisotropic turbulent cascade, and (3) solar wind acceleration
from gradients of gas pressure, acoustic wave pressure, and
Alfven wave pressure.
The only input parameters are the photospheric lower boundary
conditions for the waves and the radial dependence of the
background magnetic field along the flux tube.
We have not included multifluid or collisionless effects (e.g.,
preferential ion heating) which are not yet fully understood.
For a single choice for the photospheric wave properties, our
models produce a realistic range of slow and fast solar wind
conditions by varying only the coronal magnetic field.
Specifically, a two-dimensional model of coronal holes and
streamers at solar minimum reproduces the latitudinal
bifurcation of slow and fast streams seen by *Ulysses.*
The radial gradient of the Alfven speed affects where the
waves are reflected and damped, and thus whether energy
is deposited below or above the Parker critical point.
As predicted by earlier studies, a larger coronal "expansion
factor" gives rise to a slower and denser wind, higher
temperature at the coronal base, less intense Alfven waves
at 1 AU, and correlative trends for commonly measured ratios
of ion charge states and FIP-sensitive abundances that are in
general agreement with observations.
These models offer supporting evidence for the idea that
coronal heating and solar wind acceleration (in open magnetic
flux tubes) can occur as a result of wave dissipation and
turbulent cascade.

**
"On the Generation, Propagation, and Reflection of Alfven Waves
from the Solar Photosphere to the Distant Heliosphere,"
**
Cranmer, S. R., and van Ballegooijen, A. A. 2005,
*Ap. J. Suppl.,* **156**, 265.
[see also arXiv preprint
astro-ph/0410639]

This paper is available in PDF format (1.92 Mbytes).

*ABSTRACT:*

We present a comprehensive model of the global properties of Alfven waves in the solar atmosphere and the fast solar wind. Linear non-WKB wave transport equations are solved from the photosphere to a distance past the orbit of the Earth, and for wave periods ranging from 3 seconds to 3 days. We derive a radially varying power spectrum of kinetic and magnetic energy fluctuations for waves propagating in both directions along a superradially expanding magnetic flux tube. This work differs from previous models in three major ways. (1) In the chromosphere and low corona, the successive merging of flux tubes on granular and supergranular scales is described using a two-dimensional magnetostatic model of a network element. Below a critical flux-tube merging height the waves are modeled as thin-tube kink modes, and we assume that all of the kink-mode wave energy is transformed into volume-filling Alfven waves above the merging height. (2) The frequency power spectrum of horizontal motions is specified only at the photosphere, based on prior analyses of G-band bright point kinematics. Everywhere else in the model the amplitudes of outward and inward propagating waves are computed with no free parameters. We find that the wave amplitudes in the corona agree well with off-limb nonthermal line-width constraints. (3) Nonlinear turbulent damping is applied to the results of the linear model using a phenomenological energy loss term. A single choice for the normalization of the turbulent outer-scale length produces both the right amount of damping at large distances (to agree with in situ measurements) and the right amount of heating in the extended corona (to agree with empirically constrained solar wind acceleration models). In the corona, the modeled heating rate differs by more than an order of magnitude from a rate based on isotropic Kolmogorov turbulence.

**
"A Statistical Study of Threshold Rotation Rates for the Formation
of Disks around Be Stars,"
**
Cranmer, S. R. 2005,
*Ap. J.,* **634**, 585.
[see arXiv preprint:
astro-ph/0507718]

*ABSTRACT:*

This paper presents a detailed statistical determination of
the equatorial rotation rates of classical Be stars.
The rapid rotation of Be stars is likely to be linked to
the ejection of gas that forms dense circumstellar disks.
The physical origins of these disks are not understood, though
it is generally believed that the ability to spin up matter
into a Keplerian disk depends on how close the stellar rotation
speed is to the critical speed at which the centrifugal force
cancels gravity.
There has been recent disagreement between the traditional
idea that Be stars rotate between 50% and 80% of their
critical speeds and new ideas (inspired by the tendency for
gravity darkening to mask rapid rotation at the equator) that
their rotation may be very nearly critical.
This paper utilizes Monte Carlo forward modeling to
simulate distributions of the projected rotation speed
*v sin i,* taking into account gravity darkening,
limb darkening, and observational uncertainties.
A chi-squared minimization procedure was used to find the
distribution parameters that best reproduce observed
*v sin i* distributions from R. Yudin's database.
Early-type (O7e-B2e) Be stars were found to exhibit a
roughly uniform spread of intrinsic rotation speed that
extends from 40-60% up to 100% of critical.
Late-type (B3e-A0e) Be stars exhibit progressively narrower
ranges of rotation speed as the effective temperature
decreases; the lower limit rises to reach critical rotation
for the coolest Be stars.
The derived lower limits on equatorial rotation speed
represent conservative threshold rotation rates for the onset
of the Be phenomenon.
The significantly subcritical speeds found for early-type Be
stars represent strong constraints on physical models of
angular momentum deposition in Be star disks.

**
"New views of the solar wind with the Lambert W function,"
**
Cranmer, S. R. 2004,
*American J. Phys.,* **72**, 1397.
[see also arXiv preprint
astro-ph/0406176]

This paper is available as:

- gzipped Postscript (0.30 Mbytes)
- PDF format (0.26 Mbytes), which can be viewed by the free Adobe Acrobat Reader

*ABSTRACT:*

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.

**
"Alfvenic Turbulence in the Extended Solar Corona:
Kinetic Effects and Proton Heating,"
**
Cranmer, S. R. and van Ballegooijen, A. A., 2003,
*Ap. J.,* **594**, 573.

This paper is available as:

- gzipped Postscript (0.67 Mbytes)
- PDF format (0.63 Mbytes), which can be viewed by the free Adobe Acrobat Reader

*ABSTRACT:*

We present a model of magnetohydrodynamic (MHD) turbulence in the extended solar corona that contains the effects of collisionless dissipation and anisotropic particle heating. Recent observations have shown that preferential heating and acceleration of positive ions occurs in the first few solar radii of the high-speed solar wind. Measurements made by the Ultraviolet Coronagraph Spectrometer aboard SOHO have revived interest in the idea that ions are energized by the dissipation of ion cyclotron resonant waves, but such high-frequency (i.e., small wavelength) fluctuations have not been observed. A turbulent cascade is one possible way of generating small-scale fluctuations from a pre-existing population of low-frequency MHD waves. We model this cascade as a combination of advection and diffusion in wavenumber space. The dominant spectral transfer occurs in the direction perpendicular to the background magnetic field. As expected from earlier models, this leads to a highly anisotropic fluctuation spectrum with a rapidly decaying tail in the parallel wavenumber direction. The wave power that decays to high enough frequencies to become ion cyclotron resonant depends on the relative strengths of advection and diffusion in the cascade. For the most realistic values of these parameters, though, there is insufficient power to heat protons and heavy ions. The dominant oblique fluctuations (with dispersion properties of kinetic Alfven waves) undergo Landau damping, which implies strong parallel electron heating. We discuss the probable nonlinear evolution of the electron velocity distributions into parallel beams and discrete phase-space holes (similar to those seen in the terrestrial magnetosphere) which can possibly heat protons via stochastic interactions.

**
"Coronal Holes and the High-Speed Solar Wind,"
**
Cranmer, S. R. 2002,
*Space Science Reviews,* **101**, 229
(65-page review paper).

This paper is available in PDF format (1.51 Mbytes), which can be viewed by the free Adobe Acrobat Reader

*ABSTRACT:*

Coronal holes are the lowest density plasma components of the
Sun's outer atmosphere, and are associated with rapidly
expanding magnetic fields and the acceleration of the
high-speed solar wind.
Spectroscopic and polarimetric observations of the extended
corona, coupled with interplanetary particle and radio
sounding measurements going back several decades, have put
strong constraints on possible explanations for how the plasma
in coronal holes receives its extreme kinetic properties.
The Ultraviolet Coronagraph Spectrometer (UVCS) aboard the
*Solar and Heliospheric Observatory (SOHO)*
spacecraft has revealed
surprisingly large temperatures, outflow speeds, and velocity
distribution anisotropies for positive ions in coronal holes.
We review recent observations, modeling techniques, and
proposed heating and acceleration processes for protons,
electrons, and heavy ions.
We emphasize that an understanding of the acceleration region
of the wind (in the nearly collisionless extended corona) is
indispensable for building a complete picture of the physics
of coronal holes.

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