A POSSIBLE ENERGY SOURCE FOR T TAURI STARS Jesse L. Greenstein Mount Wilson and Palomar Observatories The emission spectra of the nebular variables of the T Tauri class, and of the related dwarf stars in dark nebulae, have been described by A. H. Joy. 1 2 They are similar to the spectra of such disturbed regions of the sun as solar flares or the chromosphere. High-excitation lines are seen, such as He i, even He n, together with strong H, Ca n, Fe n, and some forbidden lines, superposed on an underlying late-type dwarf absorption spectrum. Joy, 2 in his Table 2, remarks that in 11 out of 40 stars the absorption spectrum is partially or heavily obscured or filled in by a continuous emission. J. L. Greenstein 3 found that the apparent luminosity of several of the T Tauri group (BD 6 1253, R Mon, R CrA) was greater by about one magnitude than would be predicted from the spectroscopic luminosity, distance, and obscuration of the stars. For example, in spite of their location in dark lanes, the mean obscuration estimated by Joy 2 is less than one magnitude. This is small compared to the total absorption in these dark clouds, and would not suggest the strong observed interaction of star and dense interstellar material. It seems improbable that the short-lived association of these stars with a cloud of interstellar matter can change the actual energy-generation in the interior. The veiling continuum and the emission lines must be produced in a circumstellar fringe or extended chromosphere. The kinetic energy transport by infalling matter has been shown to be small, 4 unless the space density, p, is unexpectedly high, or the relative velocity, V, of star and gas very low. The transport of kinetic energy, E K, per second into a dwarf like the sun in units of the luminosity, L, is : Ek L = 3 X 10 19 p_ V' (i) 1 Mt. Wilson Contr., No. 709; Ap. 102, 168, 1945. 2 Ap. /., 110, 424, 1949. * Ap. /., 107, 375, 1948. 4 J. L. Greenstein, Harvard Obs. Mon., No. 7, p. 19, 1948. 156
ENERGY SOURCE FOR T TAURI STARS 157 For V 10 6 cm/sec, p ^ 10-18 gm/cm 3 ; E K /L ^3 X 10~ 5. This is insufficient as an energy source for the emission lines. However, one rather certain theoretical conclusion 4 may be drawn. Because of the radiation pressure of stars of high luminosity dust and gas cannot easily fall into their atmospheres. The dwarfs considerably fainter than the sun, which most commonly show the T Tauri characteristics, exert negligible radiation pressure on the dust because of their low values of L/M, and can attract the dust. Velocities up to 600 km/sec might be expected under free fall near main-sequence stars ; in dense clouds equipartition of energy between gas and dust is set up within a year or so, i.e., over distances of a few astronomical units ; hence gas and dust fall together. Radiation pressure on the gas will depend on its state of ionization, and on any possible excess ultraviolet emission by the star in the Lyman region. However, the radiation pressure on the gas will also diminish strongly toward later spectral types, as the star s luminous efficiency, L/M, decreases. Let us consider another energy source suggested by recent speculations concerning the existence of an interstellar magnetic field. Interstellar polarization and Fermi s theory of the origin of cosmic rays both suggest that magnetization of a strength, H 0) above 10" 5 /gauss exists in interstellar space. The motion of ionized matter in a magnetic field is such that the magnetic lines of force act as if frozen into the moving material. If the kinetic or potential energies are large compared to those in the magnetic field, the dynamics are essentially Newtonian; if the magnetic energy density, U m = H 2 0 /8k, is much greater than the gravitational energy, the motion is of the type described by H. Alfvén 5 as magneto-hydrodynamic waves. These waves in a field H 0 propagate with a velocity v~h 0 (4 jt p)~ 1/2. At standard conditions H 0 10~ 5, p ~ 10~ 23, the result is v = 11 km/sec in interstellar space. Since this is of the order of gas-cloud peculiar velocities, it is apparent that a real question exists as to whether ordinary dynamics or magneto-hydrodynamics should be applied. During the infall, gas becomes highly compressed com- 5 Cosmical Electrodynamics, Oxford, 1950.
158 JESSE L. GREENSTEIN pared with normal interstellar densities; the magnetic field will be carried inward, will resist compression somewhat, but must undoubtedly increase inward. The emission line widths correspond to gas motions of 100 km/sec; in my analysis 3 of the emission lines of BD 6 1253 I derived a density of about 10-14 gm/cm 3 at 10 RO from the star. If we assume that the gas velocity is controlled by the magnetic forces, a field of 3 gauss is required. Since the gas density and field are so high, it is apparent that conditions are quite similar to those in the upper chromosphere; the motions would be like those in prominences carrying magnetic energy downward. A theory of the intensity of the magnetic field to be expected as the gas is compressed would be extremely difficult. The properties of magneto-hydrodynamic waves have been studied only in an incompressible medium. If the change of p and of H 0 are both small over a wave length of the disturbance (i.e., a dense patch of moving gas), and if the motion is determined by a preexistent magnetic field, Alfvén 6 showed that the induced field varies quite slowly, as p 1/4. On the other hand, if it is gravity that brings the matter, with its magnetic field, inward, the compression increases the field steeply. Imagine a spherical shell uniformly shrinking ; all dimensions change as r -1, the gas density as r -3, the number of lines of force crossing a cm 2 as ^3/2 ; then the energy density of the field U m varies as i.e., as the density p. Under the acceleration of free fall, the density increases inward less rapidly than in the above model, but it seems that for an order-of-magnitude estimate we may use the relation that U m is proportional to p. Then taking an initial interstellar field of 10-5 gauss at standard density p = 10~ 23 gm/cm 3 we obtain after compression : Um = 4 x 10 11 p, ff 0 = 3X 10 6 PK (2) (3) Under the physical conditions obtained for BD 6 1253 equation (3) gives a field of 0.3 gauss. This differs by only a factor of ten from the field derived previously as necessary to maintain 6 Op. cit., p. 90.
ENERGY SOURCE FOR T TAURI STARS 159 velocities of 100 km/sec in random magneto-hydrodynamic waves. Thus in the outer envelope of such a star a field near 1 gauss does not seem impossible. The thermal energy density Ut for a gas is : U t = 2 X 10 8 T P. (4) The gravitational potential energy U gr convertible into kinetic energy when matter falls into a star like the sun is : U gr = 2 X 10 15 P. (5) It can be seen that U m < U gr, and also U m < Ut when T > 2000. Only if the initial magnetization is much greater than average could U m exceed U gr. If the star possessed a magnetic field, or if turbulent eddies could build up larger fields in the gas, magnetic effects could also be increased. The most interesting effect is not in the direct addition of the magnetic field energy to that of the star but in the possibility of the rapid release of stellar energy in a flare process. Solar flares have emission lines of H, He i, and the ionized metals, and some intense flares have a continuous spectrum. Radio fadeouts show that ultraviolet radiation is very intense in flares. The flare process has been ascribed by R. G. Giovanelli 7 to the flow of intense electric discharges in regions where a fixed and a variable magnetic field cross under favorable geometric conditions. Mass motion of ionized material as a sunspot grows produces favorable conditions for such discharges; not only the static field but the direction of the variable field and its rate of change is important. The emission does not necessarily correspond to thermal equilibrium, but resembles that in discharge tubes in that collisional excitation becomes important. A continuous spectrum could well occur in intense discharges ; the lines will be broadened by the strong electric fields. Flares occur low in the chromosphere; perhaps Ellerman s bombs occur inside the reversing layer. According to R. S. Richardson, flares cover up to 2.5 X 10" 8 of the solar disk, or about 4 X 10 19 cm 2. In an average strong solar flare, Ha emits about as much energy as 4 A of the continuous spectrum of the sun; the total Ha 7 M.N., 108, 163, 1948.
160 JESSE L. GREENSTEIN energy output is thus near 10 27 ergs/sec, and may last for from a few minutes to an hour. Unfortunately this does not provide even an order of magnitude estimate of the total luminosity of the flare. A continuum 0.01 as bright per angstrom unit as Ha would never be detected, but over 1000 A it would give ten times as much light. M. A. Ellison 8 reports observation of a continu- ous spectrum 10 percent as bright as that of the sunspot penum- bra in a flare that had an Ha emission 15 A wide and three times as bright as the penumbral continuum. In another flare, No- vember 19, 1949, the flare continuum 9 was observed 8 percent as bright as the photosphere and was photographed over at least a 150 angstrom range of wave length. Such a flare would have been visible in white light ; a list of flares visible in white light has been given. 10 Let us assume that per unit area these emit 10 percent as much radiation as a black body at 5000 ; over an area 2.5 X 10~ 3 of the solar disk, this is 1.5 X 10 25 per angstrom. Over 1000 A about 10 28 ergs/sec is emitted. ergs/sec At the Tucson meeting of the American Astronomical So- ciety it was pointed out by F. L. Whipple and seconded by several speakers, including Joy and Kron, that the short-lived increases of brightness observed in late-type dwarf stars such as L726-8 11 12 and -f-20 2465 13 resemble solar flares. Kron and Kron 13 showed that the observed increase and decrease in light could be explained if a hot spot covering 0.02 of the dme star s disk appeared with a continuous spectrum corresponding to a temperature of 10,000 and then cooled by radiation. Humason and Joy found that in a flaring of L 726-8 the absorption spec- trum was blotted out by a blue continuum and emission lines of H, He i and He n appeared. Luyten 12 found a flare in L 726-8 which lasted about twenty minutes and had an energy output of 4 X 10 31 i.e., 3 X 10 28 ergs/sec. We see that while an average solar flare does not release energy comparable to the 8 Observatory, 66, 357, 1946. 9 Ellison and Conway, Observatory, 70, 78, 1950. 10 Observatory, 67, 156, 1947. 11 Joy and Humason, Pub. A.S.P., 61, 133, 1949. is W. J. Luyten, Ap. J., 109, 532, 1949. 13 K. C. and G. E. Kron, Pub. A.S.P., 61, 210, 1949.
ENERGY SOURCE FOR T TAURI STARS 161 flaring brightness changes of the late dwarfs, the bright flares visible in white light on the sun have radiation comparable to that in the flare of Luyten s star. The very bright solar flares, if they occurred on M dwarfs, would double the star s brightness for short periods! They would probably be most conspicuous in the violet, because of the steep drop of the stellar continuum. The blue continuum observed by Joy and Humason 11 is not a normal Paschen recombination continuum. This was shown 3 to be true in BD 6 1253, where Ha is 119 times as strong as one angstrom of the neighboring continuum. Even though at stellar temperatures, Ha is as bright theoretically as 500 A of Balmer continuous emission, the great intensity of Ha and the weak violet continuum of a dk star lead to a prediction that the Balmer continuous emission should be visible. The expected Paschen continuum is much weaker, and cannot be identified with the radiation which veils the T Tauri absorption spectrum. If strong electric discharges occur, this blue continuum may have quite a different origin, like that in Ellison s great flares. Near the T Tauri stars ionized material is falling in at considerable speeds, and can carry magnetic fields in from the interstellar gas. If the star has spots with associated magnetic fields like the sun, the production of bright flares would be on a much greater scale and more frequent than in the sun. Thus we can picture the T Tauri stars as surrounded by extended chromospheres of interstellar matter at high kinetic temperatures. The strength of the emission lines in T Tauri stars compared to the stellar continuum is large relative to that of the lines produced in the solar chromosphere. This can be interpreted as arising from a much larger and denser chromosphere surrounding these objects. The downward motions commonly observed in solar prominences would also occur on a larger scale. Such downward motions may possibly be indicated by Joy s observation 1 that the mean absorption-line velocity of eight T Tauri stars is algebraically greater by (-25 km/sec than the mean emission velocity. The emission lines would have their origin in the chromosphere and sometimes in the rapidly but steadily occurring flares. Broadened emission could also result from the electrical discharge mechanism. We have seen that the incoming material appar-
162 JESSE L. GREENSTEIN ently does not itself carry sufficient energy to the star, but it seems well suited as a source of the high kinetic temperature and as a trigger mechanism for the release of excess energy from star spots, in the form of flares bright enough to affect the total spectrum of the object. I am indebted to Dr. A. H. Joy and Dr. R. S. Richardson for helpful criticism and advice. [Note added in proof.] After the completion of the above, D. H. Menzel published a brief account of his theory of solar prominences in Nature, 166, 31, 1950. He finds that the magnetic field in a collapsing prominence varies in proportion to the gas density. This would greatly increase our estimate of the magnetic field of the compressed interstellar material and make the magnetic energy density exceed U gr or Ut- Thus chromospheric phenomena and flare production would occur on a much greater scale.