Velocity fields in stellar atmospheres and the concept of microturbulence

Abstract

The microturbulent addition to thermal Doppler broadening of the line absorption coefficient is always specified by the (Gaussian) velocity distribution function of non-thermal motion. It is shown that this distribution function must be defined in terms of the aggregate amount of the total line of sight within which the velocity is in a particular range. If this distribution function is Gaussian the microturbulent addition follows in the usual way. However, this addition can only be made consistently within the reversing layer concept of line formation, quite apart from the question whether such velocity fields actually occur. The relevant non-thermal velocity distribution function is not definable at a point, unlike the thermal distribution, although it has come to be used in model atmosphere work as if it were so defined. It is shown that the effect on opacity of a small amplitude oscillatory (in space) velocity field can be described as microturbulence, although again only within the reversing layer concept. If the amplitude is large, the line absorption coefficient ceases to be a monotonically decreasing function of wavelength shift from the line centre. Oscillatory velocity fields with amplitude ∼ 1 km/sec should be detectable directly in the cores of strong solar lines even if their wavelength is quite small (∼50 km). A consideration of the directly observed velocity fields in the solar atmosphere, together with a simple hydrodynamic description, strongly suggests that there are no small scale velocity fields with amplitudes large enough to be responsible for microturbulence.