Magnetic damping of rotation as a factor in stellar evolution.

Abstract

view Abstract Citations (3) References Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS Magnetic damping of rotation as a factor in stellar evolution. Wilson, Raymond H., Jr. Abstract A thin ring of conducting matter rotating in a magnetic field about an axis in its plane experiences a braking couple given by a well-known function of the area of the ring, its inductance, resistance, and angular velocity, and the effective strength of the magnetic field. Integrating this as an element of a conducting sphere leads to the approximate formula for its angular velocity co as function of time tin seconds: ~p1H2 log5-~1 = (I - to). p Here j (cgs, EMU) is the conductivity of the sphere, p its magnetic permeability, and p its density, while H is the external magnetic field strength in gauss. Such magnetic damping would tend to reduce rotation of all celestial objects in a magnetic field. As explained by Chandrasekhar and Fermi (1953) all present evidence indicates a magnetic field of 7 X 10-6 gauss in the sun's galactic region, due to motions of the ionized galactic plasma. The action of this field on a star like the sun depends partly on its conductivity. A reasonable estimate of the effective conductivity of the sun would be the logarithmic' mean between center and photosphere: (T = 10-6 cgs EMU (Spitzer 1954). Then by the above formula we may derive the sun's period of rotation at, say, 1o = 5 X I& yr. = 1.6 X 1017 sec. ago. Its mean density in this interval could be estimated as perhaps half that at present = 0.7. Assuming the galactic field to have remained constant, the effective component would be about 4 X 10-6 gauss. The result is that loge (coo/ii') = 3.7 so that the rotation period at to would have been 25/40 day = 15 hours. This is on the order of rotational velocities of young stars of early main- sequence type, from which, presumably, the sun and other similar stars have evolved (Struve 1950). Since the conductivity of a star with increasing depth below the photosphere seems to increase more rapidly than its density, the rotation of the interior would be slowed down more rapidly than that of its surface. A result for a fluid or partly fluid sphere would be turbulence, and more rapid rotation at the equator, such as is observed on the sun and the planet Jupiter. In planetary systems and double stars the action of any magnetic fields belonging to the separate members would add its effect to that of the general galactic field. For instance, in the case of close spectroscopic binary stars (Struve 1950), the total effective field might be on the order of 10-i gauss. Assuming other data as above, except the conductivity like that of the solar photosphere, I0-~ cgs EMU, the time required for reduction of rotation by a factor of 100 turns out to be I0~ years. This is the age estimated for such early-type stars (Struve 1950). Thus the theory of magnetic damping alone could possibly explain the abnormally slow rotation of such binary stars compared to that of single stars of the same age. Struve, 0. 1950, Stellar Evolution (Princeton Univ. Press), pp. 130, 83, 244. Chandrasekhar, S. and Fermi, E. 1953, Ap. J. ii8, 113. Spitzer, L. 1954, Smithsonian Physical Tables, p. 502. Naval Research Laboratory, Washington, D. C. Publication: The Astronomical Journal Pub Date: May 1956 DOI: 10.1086/107420 Bibcode: 1956AJ.....61R.193W full text sources ADS |