Engineering topics

Hammer, R.

Publications and source records attributed to Hammer, R..

10 records

NASA NTRS1992

A new way to convert Alfven waves into heat in solar coronal holes - Intermittent magnetic levitation

In our recent analysis of Alfven wave reflection in solar coronal holes, we found evidence that coronal holes are heated by reflected Alfven waves. This result suggests that the reflection is inherent to the process that dissipates these Alfven waves into heat. We propose a novel dissipation process that is driven by the reflection, and that plausibly dominates the heating in coronal holes.

Moore, R. L.↗

NASA NTRS1985

The Scaling of Coronal Models from One Star to Another

The requirements that must be met in order that stationary numerical corona models can be scaled from one star to another are discussed. A corona model is a solution of the conservation equations for mass, momentum, and energy, subject to appropriate boundary conditions, and of the equation of state. In general, the mass M and radius R of the star enter these equations and boundary conditions as free parameters. A given solution can be scaled to other stars only if all equations can be rewritten in such a form that M and R do no longer appear explicitly as free parameters, but only implicitly as scaling factors of the variables. An adequate means to find these scaling factors is a homologous transformation: one multiplies all variables and parameters by separate constants (i.e., scaling factors) and requires that the equations and boundary conditions remain valid. This leads to a set of nonlinear relations between the transformation constants. Only if in this set the two constants associated with M and R can be chosen independently, can a given numerical corona model be scaled to arbitrary stars.

Hammer, R.↗

NASA NTRS1985

Overheated Open Coronal Regions

The physics of compact, hydrostatic coronal shells formed from the collapse of overheated coronae is addressed. A large number of hydrostatic shells was computed for the usual exponential heating law with constant damping length. The boundary conditions were that on both sides of a shell the conductive flux at chromospheric temperatures is small. The boundary value problem was solved with a shooting technique. The main goal of the calculations was to determine the dependence of the shells on coronal heating flux (F sub Mo) and damping length (L); and in particular, to localize the boundary line in the parameter space (F sub Mo, L) that separates normal extended coronae from coronal shells.

Hammer, R.↗

NASA NTRS1984

Corona models tested with IUE and Einstein observations

Compilations of IUE and Einstein observations which show that the emissions from the outer layers of cool stars are nonlinearly correlated are discussed. This result can be used to test theoretical corona models as well as hypotheses on the mechanism that determines the location of the transition region. In stars in which most of the X-ray emission originates in small coronal loops it may be necessary that part of the emitting plasma is hotter than 20 million K or that the transition region is not only heated by thermal conduction, but also by downflows. Observational evidence for both these effects, and methods for analyzing the geometrical structure of outer stellar atmospheres are considered.

Hammer, R.↗

NASA NTRS1984

Energy balance of stellar coronae. III - Effect of stellar mass and radius

A homologous transformation is derived which permits the application of the numerical coronal models of Hammer from a star with solar mass and radius to other stars. This scaling requires a few approximations concerning the lower boundary conditions and the temperature dependence of the conductivity and emissivity. These approximations are discussed and found to be surprisingly mild. Therefore, the scaling of the coronal models to other stars is rather accurate; it is found to be particularly accurate for main-sequence stars. The transformation is used to derive an equation that gives the maximum temperature of open coronal regions as a function of stellar mass and radius, the coronal heating flux, and the characteristic damping length over which the corona is heated.

Hammer, R.↗

NASA NTRS1983

Stellar coronae - What can be predicted with minimum flux models?

In order to determine the possible errors of various minimum flux corona (MFC) predictions, MFC models are compared with a grid of detailed coronal models covering a range of two orders of magnitude in coronal heating and damping length values. The MFC concept is totally unreliable in the prediction of mass loss and the relative importance of various kinds of energy losses, and MFC predictions for the mass loss rate and energy losses due to stellar wind can be wrong by many orders of magnitude. It is suggested that for future applications, the unreliable MFC formulas should be replaced by a grid of related models accounting for the coronal dependence on damping length, such as the models underlying the present study.

Hammer, R.↗

NASA NTRS1982

Energy balance of stellar coronae. I - Methods and examples. II - Effect of coronal heating

Simplified models of magnetically open coronal regions are computed, with the aim of fulfilling appropriate boundary conditions at the base of the atmosphere, at the critical point, and at infinity. The models are determined by the stellar mass and radius and by the amount and location of coronal heating, and this dependence is analyzed in terms of pressure, temperature, characteristic heights, energy losses, mass loss, and asymptotic behavior. The results are used to classify the magnetically open coronal regions according to the energy loss mechanism that dominates in the region between the base and the critical point, and it is shown that more complicated heating mechanisms may be replaced by the presented exponential heating law, provided that the damping length is suitably chosen.

Hammer, R.↗

NASA NTRS1982

On the correlation between chromospheric and coronal emission

It is shown that with increasing stellar activity the emission of the transition region and corona increases faster than the emission of the chromosphere. It is also explained why the pressure of the transition region increases with increasing stellar activity. Further, it is shown that this relation is a necessary requirement for the global stability of the chromosphere/transition region/corona system.

Hammer, R.↗

NASA NTRS1982

Energy balance and stability

The energy balance of the outer atmospheres of solarlike stars is discussed. The energy balance of open coronal regions is considered, discussing the construction and characteristics of models of such regions in some detail. In particular, the temperature as a function of height is considered, as are the damping length dependence of the global energy balance in the region between the base of the transition region and the critical point, and the effects of changing the amount of coronal heating, the stellar mass, and the stellar radius. Models of coronal loops are more briefly discussed. The chromosphere is then included in the discussion of the energy balance, and the connection between global energy balance and global thermal stability is addressed. The observed positive correlations between the chromospheric and coronal energy losses and the pressure of the transition region is qualitatively explained.

Hammer, R.↗

NASA NTRS1981

Dependence of open stellar coronal regions on coronal heating

Models of open regions in hot stellar coronae are presented. For a given star these regions depend on the total amount phi sub Mo of coronal heating and on the characteristic length (L) over which this energy is dissipated. The height of the temperature maximum is mainly determined by L. The coronal temperature, the mass loss rate, and the relative fraction of wind energy losses increase strongly with L as long as L is much smaller than the stellar radius. For large L, however, these quantities are only weak functions of L, while they still increase with increasing phi sub Mo. Thus, if the heating occurs close to the stellar surface, the open coronal regions are cool, and most of the energy is used for radiation. Extended coronal heating, on the other hand, leads to hot coronal regions with small base pressure and predominating energy losses due to stellar wind (for large phi sub Mo and/or outward thermal conduction (for small phi sub Mo).

Hammer, R.↗