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Suprathermal Electrons in the Solar Corona: Can Nonlocal Transport Explain Heliospheric Charge States?  

Steven R Cranmer   Submitted: 2014-08-27 14:24

There have been several ideas proposed to explain how the Sun's corona is heated and how the solar wind is accelerated. Some models assume that open magnetic field lines are heated by Alfvén waves driven by photospheric motions and dissipated after undergoing a turbulent cascade. Other models posit that much of the solar wind's mass and energy is injected via magnetic reconnection from closed coronal loops. The latter idea is motivated by observations of reconnecting jets and also by similarities of ion composition between closed loops and the slow wind. Wave/turbulence models have also succeeded in reproducing observed trends in ion composition signatures versus wind speed. However, the absolute values of the charge-state ratios predicted by those models tended to be too low in comparison with observations. This letter refines these predictions by taking better account of weak Coulomb collisions for coronal electrons, whose thermodynamic properties determine the ion charge states in the low corona. A perturbative description of nonlocal electron transport is applied to an existing set of wave/turbulence models. The resulting electron velocity distributions in the low corona exhibit mild suprathermal tails characterized by "kappa" exponents between 10 and 25. These suprathermal electrons are found to be sufficiently energetic to enhance the charge states of oxygen ions, while maintaining the same relative trend with wind speed that was found when the distribution was assumed to be Maxwellian. The updated wave/turbulence models are in excellent agreement with solar wind ion composition measurements.

Authors: Steven R. Cranmer
Projects: None

Publication Status: ApJ Letters, 791, L31 (2014 August 20)
Last Modified: 2014-08-28 09:53
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Connecting the Sun's High-Resolution Magnetic Carpet to the Turbulent Heliosphere  

Steven R Cranmer   Submitted: 2013-03-05 13:17

The solar wind is connected to the Sun's atmosphere by flux tubes that are rooted in an ever-changing pattern of positive and negative magnetic polarities on the surface. Observations indicate that the magnetic field is filamentary and intermittent across a wide range of spatial scales. However, we do not know to what extent the complex flux tube topology seen near the Sun survives as the wind expands into interplanetary space. In order to study the possible long-distance connections between the corona and the heliosphere, we developed new models of turbulence-driven solar wind acceleration along empirically constrained field lines. We used a potential-field model of the Quiet Sun to trace field lines into the ecliptic plane with unprecedented spatial resolution at their footpoints. For each flux tube, a one-dimensional model was created with an existing wave/turbulence code that solves equations of mass, momentum, and energy conservation from the photosphere to 4 AU. To take account of stream-stream interactions between flux tubes, we used those models as inner boundary conditions for a time-steady MHD description of radial and longitudinal structure in the ecliptic. Corotating stream interactions smear out much of the smallest-scale variability, making it difficult to see how individual flux tubes on granular or supergranular scales can survive out to 1 AU. However, our models help clarify the level of ''background'' variability with which waves and turbulent eddies should be expected to interact. Also, the modeled fluctuations in magnetic field magnitude were seen to match measured power spectra quite well.

Authors: S. R. Cranmer, A. A. van Ballegooijen, L. N. Woolsey
Projects: National Solar Observatory (Sac Peak)

Publication Status: ApJ, in press for April 20, 2013 issue, arXiv:1303.0563
Last Modified: 2013-03-06 08:54
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Tangled Magnetic Fields in Solar Prominences  

Steven R Cranmer   Submitted: 2010-01-18 12:06

Solar prominences are an important tool for studying the structure and evolution of the coronal magnetic field. Here we consider so-called ''hedgerow'' prominences, which consist of thin vertical threads. We explore the possibility that such prominences are supported by tangled magnetic fields. A variety of different approaches are used. First, the dynamics of plasma within a tangled field is considered. We find that the contorted shape of the flux tubes significantly reduces the flow velocity compared to the supersonic free fall that would occur in a straight vertical tube. Second, linear force-free models of tangled fields are developed, and the elastic response of such fields to gravitational forces is considered. We demonstrate that the prominence plasma can be supported by the magnetic pressure of a tangled field that pervades not only the observed dense threads but also their local surroundings. Tangled fields with field strengths of about 10 G are able to support prominence threads with observed hydrogen density of the order of 1011 cm-3. Finally, we suggest that the observed vertical threads are the result of Rayleigh-Taylor instability. Simulations of the density distribution within a prominence thread indicate that the peak density is much larger than the average density. We conclude that tangled fields provide a viable mechanism for magnetic support of hedgerow prominences.

Authors: A. A. van Ballegooijen and S. R. Cranmer
Projects: None

Publication Status: ApJ, in press.
Last Modified: 2010-01-18 13:06
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An Efficient Approximation of the Coronal Heating Rate for Use in Global Sun-Heliosphere Simulations  

Steven R Cranmer   Submitted: 2010-01-04 08:45

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 Alfvén 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 Alfvén 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 Alfvén 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.

Authors: S. R. Cranmer
Projects: None

Publication Status: ApJ, in press, arXiv:0912.5333
Last Modified: 2010-01-04 09:31
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Coronal Holes  

Steven R Cranmer   Submitted: 2009-09-16 09:07

Coronal holes are the darkest and least active regions of the Sun, as observed both on the solar disk and above the solar limb. Coronal holes are associated with rapidly expanding open magnetic fields and the acceleration of the high-speed solar wind. This paper reviews measurements of the plasma properties in coronal holes and how these measurements are used to reveal details about the physical processes that heat the solar corona and accelerate the solar wind. It is still unknown to what extent the solar wind is fed by flux tubes that remain open (and are energized by footpoint-driven wave-like fluctuations), and to what extent much of the mass and energy is input intermittently from closed loops into the open-field regions. Evidence for both paradigms is summarized in this paper. Special emphasis is also given to spectroscopic and coronagraphic measurements that allow the highly dynamic non-equilibrium evolution of the plasma to be followed as the asymptotic conditions in interplanetary space are established in the extended corona. For example, the importance of kinetic plasma physics and turbulence in coronal holes has been affirmed by surprising measurements from the UVCS instrument on SOHO that heavy ions are heated to hundreds of times the temperatures of protons and electrons. These observations point to specific kinds of collisionless Alfvén wave damping (i.e., ion cyclotron resonance), but complete theoretical models do not yet exist. Despite our incomplete knowledge of the complex multi-scale plasma physics, however, much progress has been made toward the goal of understanding the mechanisms ultimately responsible for producing the observed properties of coronal holes.

Authors: Steven R. Cranmer
Projects: None

Publication Status: Living Reviews in Solar Physics, in press. (61-page review paper)
Last Modified: 2009-09-17 11:00
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Empirical Constraints on Proton and Electron Heating in the Fast Solar Wind  

Steven R Cranmer   Submitted: 2009-07-16 05:14

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 Alfvénic fluctuations, the best agreement was found for a distribution of wavenumber vectors that evolves toward isotropy as distance increases.

Authors: Cranmer, S. R., Matthaeus, W. H., Breech, B. A., and Kasper, J. C.
Projects: None

Publication Status: ApJ, in press, arXiv:0907.2650
Last Modified: 2009-07-16 08:34
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Ion Temperatures in the Low Solar Corona: Polar Coronal Holes at Solar Minimum  

Steven R Cranmer   Submitted: 2008-10-03 04:05

In the present work we use a deep-exposure spectrum taken by the SUMER spectrometer in a polar coronal hole in 1996 to measure the ion temperatures of a large number of ions at many different heights above the limb between 0.03 and 0.17 solar radii. We find that the measured ion temperatures are almost always larger than the electron temperatures and exhibit a non-monotonic dependence on the charge-to-mass ratio. We use these measurements to provide empirical constraints to a theoretical model of ion heating and acceleration based on gradually replenished ion-cyclotron waves. We compare the wave power required to heat the ions to the observed levels to a prediction based on a model of anisotropic magnetohydrodynamic turbulence. We find that the empirical heating model and the turbulent cascade model agree with one another, and explain the measured ion temperatures, for charge-to-mass ratios smaller than about 0.25. However, ions with charge-to-mass ratios exceeding 0.25 disagree with the model; the wave power they require to be heated to the measured ion temperatures shows an increase with charge-to-mass ratio (i.e., with increasing frequency) that cannot be explained by a traditional cascade model. We discuss possible additional processes that might be responsible for the inferred surplus of wave power.

Authors: E. Landi and S. R. Cranmer
Projects: SoHO-SUMER

Publication Status: ApJ, in press (for January 20, 2009)
Last Modified: 2008-10-03 09:29
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Plasmoids in Reconnecting Current Sheets: Solar and Terrestrial Contexts Compared  

Steven R Cranmer   Submitted: 2008-09-23 10:41

Magnetic reconnection plays a crucial role in violent energy conversion occurring in the environments of high electrical conductivity, such as the solar atmosphere, magnetosphere, and fusion devices. We focus on the morphological features of the process in two different environments, the solar atmosphere and the geomagnetic tail. In addition to indirect evidence that indicates reconnection in progress or having just taken place, such as auroral manifestations in the magnetosphere and the flare loop system in the solar atmosphere, more direct evidence of reconnection in the solar and terrestrial environments is being collected. Such evidence includes the reconnection inflow near the reconnecting current sheet, and the outflow along the sheet characterized by a sequence of plasmoids. Both turbulent and unsteady Petschek-type reconnection processes could account for the observations. We also discuss other relevant observational consequences of both mechanisms in these two settings. While on face value, these are two completely different physical environments, there emerge many commonalities, for example, an Alfvén speed of the same order of magnitude, a key parameter determining the reconnection rate. This comparative study is meant as a contribution to current efforts aimed at isolating similarities in processes occurring in very different contexts in the heliosphere, and even in the universe.

Authors: J. Lin, S. R. Cranmer, and C. J. Farrugia
Projects: None

Publication Status: JGR, in press for special NESSC section on Comparative Aspects of Magnetic Reconnection.
Last Modified: 2008-09-23 18:09
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Subject will be restored when possible  

Steven R Cranmer   Submitted: 2008-04-30 11:19

In preparation for lively debate at the May 2008 SPD/AGU Meeting in Fort Lauderdale, this document attempts to briefly lay out my own view of the evolving controversy over how the solar wind is accelerated. It is still unknown to what extent the solar wind is fed by flux tubes that remain open (and are energized by footpoint-driven wavelike fluctuations), and to what extent much of the mass and energy is input more intermittently from closed loops into the open-field regions. It may turn out that a combination of the two ideas is needed to explain the full range of observed solar wind phenomena.

Authors: Steven R. Cranmer
Projects: None

Publication Status: Background document for 2008 Spring AGU talk SH34B-03.
Last Modified: 2008-09-23 21:02
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Subject will be restored when possible  

Steven R Cranmer   Submitted: 2008-02-14 08:16

A theory for the heating of coronal magnetic flux ropes is developed. The dissipated magnetic energy has two distinct contributions: (1) energy injected into the corona as a result of granule-scale, random footpoint motions, and (2) energy from the large-scale, nonpotential magnetic field of the flux rope. The second type of dissipation can be described in term of hyperdiffusion, a type of magnetic diffusion in which the helicity of the mean magnetic field is conserved. The associated heating rate depends on the gradient of the torsion parameter of the mean magnetic field. A simple model of an active region containing a coronal flux rope is constructed. We find that the temperature and density on the axis of the flux rope are lower than in the local surroundings, consistent with observations of coronal cavities. The model requires that the magnetic field in the flux rope is stochastic in nature, with a perpendicular length scale of the magnetic fluctuations of order 1000 km.

Authors: A. A. van Ballegooijen and S. R. Cranmer
Projects: None

Publication Status: ApJ, in press (v. 679, June 1, 2008), arXiv:0802.1751
Last Modified: 2008-02-14 09:53
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Subject will be restored when possible  

Steven R Cranmer   Submitted: 2008-02-06 08:08

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 O5+ ion concentration in the extended corona; the resulting range of values is roughly consistent with recent downward revisions in the oxygen abundance.

Authors: Steven R. Cranmer, Alexander V. Panasyuk, and John L. Kohl
Projects: None

Publication Status: ApJ, in press (v. 679; May 20, 2008), arXiv:0802.0144
Last Modified: 2008-02-06 13:42
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Self-consistent Coronal Heating and Solar Wind Acceleration from Anisotropic Magnetohydrodynamic Turbulence  

Steven R Cranmer   Submitted: 2007-03-13 14:09

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 Alfvén 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 Alfvén 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 Alfvén 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 Alfvén 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.

Authors: Steven R. Cranmer, Adriaan A. van Ballegooijen, and Richard J. Edgar
Projects: None

Publication Status: ApJ Supplement, in press (v. 171, August 2007), astro-ph/0703333
Last Modified: 2007-03-14 10:56
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On the Generation, Propagation, and Reflection of Alfvén Waves from the Solar Photosphere to the Distant Heliosphere  

Steven R Cranmer   Submitted: 2004-10-27 08:17

We present a comprehensive model of the global properties of Alfvén 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 Alfvén 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.

Authors: S. R. Cranmer and A. A. van Ballegooijen
Projects: None

Publication Status: ApJS, in press (February 2005)
Last Modified: 2004-10-27 08:17
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New views of the solar wind with the Lambert W function  

Steven R Cranmer   Submitted: 2004-06-14 14:22

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.

Authors: Steven R. Cranmer
Projects: None

Publication Status: American J. Phys., in press (2004)
Last Modified: 2004-06-14 14:22
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Ion Cyclotron Wave Dissipation in the Solar Corona: The Summed Effect of More than 2000 Ion Species  

Steven R Cranmer   Submitted: 2000-01-05 17:04

In this paper the dissipation of ion cyclotron resonant Alfvén waves in the extended solar corona is examined in detail. For the first time, the wave damping arising from more than 2000 low-abundance ion species is taken into account. Useful approximations for the computation of coronal ionization equilibria for elements heavier than nickel are presented. Also, the Sobolev approximation from the theory of hot-star winds is applied to the resonant wave dissipation in the solar wind, and the surprisingly effective damping ability of ``minor'' ions is explained in simple terms. High-frequency (10 to 10, 000 Hz) waves propagating up from the base of the corona are damped significantly when they resonate with ions having charge-to-mass ratios of about 0.1, and negligible wave power would then be available to resonate with higher charge-to- charge-to-mass ratio ions at larger heights. This result confirms preliminary suggestions from earlier work that the waves that heat and accelerate the high-speed solar wind must be generated throughout the extended corona. The competition and eventual equilibrium between wave damping and wave replenishment may explain observed differences in coronal O VI and Mg X emission line widths.

Authors: Cranmer, S. R.
Projects:

Publication Status: ApJ, 532 (in press for 1 April 2000)
Last Modified: 2000-01-05 17:04
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Abstracts by Author
Suprathermal Electrons in the Solar Corona: Can Nonlocal Transport Explain Heliospheric Charge States?
Connecting the Sun's High-Resolution Magnetic Carpet to the Turbulent Heliosphere
Tangled Magnetic Fields in Solar Prominences
An Efficient Approximation of the Coronal Heating Rate for Use in Global Sun-Heliosphere Simulations
Coronal Holes
Empirical Constraints on Proton and Electron Heating in the Fast Solar Wind
Ion Temperatures in the Low Solar Corona: Polar Coronal Holes at Solar Minimum
Plasmoids in Reconnecting Current Sheets: Solar and Terrestrial Contexts Compared
Subject will be restored when possible
Subject will be restored when possible
Subject will be restored when possible
Self-consistent Coronal Heating and Solar Wind Acceleration from Anisotropic Magnetohydrodynamic Turbulence
On the Generation, Propagation, and Reflection of Alfven Waves from the Solar Photosphere to the Distant Heliosphere
New views of the solar wind with the Lambert W function
Ion Cyclotron Wave Dissipation in the Solar Corona: The Summed Effect of More than 2000 Ion Species

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