A MAGYAR MITTEILUNGEN TUDOMANYOS AKADEMIA DER CSILLAGVIZSGALO STERNWARTE INTEZETENEK DER UNGARISCHEN AKADEMIE KOZLEMENYEI DER WISSENSCHAFTEN BUDAPEST-SZABADSAGHEGY Nr. 68. L. G. BALAZS DISTRIBUTION OF STARS OF SPECTRAL TYPES F7 AND EARLIER IN A LYRA REGION BUDAPEST, 1975 DISTRIBUTION OF STARS OF SPECTRAL TYPES F7 AND EARLIER IN A LYRA REGION SUMMARY A study has been made of the spatial distribution of early type stars in a region of intermediate galactic latitude. Objective prism plates were used to survey an area of 19.5 sq.deg in Lyra for all stars of spectral type F7 and earlier down to 13^th photographic magnitude. 524 stars were detected, for which spectral types and photographic UBV colours were obtained. The stars were separated into four groups - spectral class A1 and earlier, A2-A7, A8-F2, and F3-F7 - and the space densities determined for each group. The space density curves show that the first two groups both appear to be composed of two kinematically distinct subsystems, each having a Gaussian velocity distribution but with a ratio of the velocity dispersions of 1.8:1. These two subsystems probably differ in age and it may be significant that the derived age difference, about 3x10^8 years, is close to the time-difference between two consecutive periods of star formation predicted by the density wave theory of spiral structure. Further observations, however, are needed to rule out other birth mechanisms having the same characteristic time. INTRODUCTION The distribution of the stars off the galactic plane is of considerable interest in order to understand some of the dynamical properties of our stellar system. To derive the three-dimensional distribution, we must analyse data concerning the apparent surface distribution in those galactic latitudes that are usually called "high" (|b| approx.>=40deg) and "intermediate" (approx. 40deg>=|b|>=10deg). The overwhelming majority of objects recognisable in high and intermediate galactic latitudes belongs to mean main-sequence stars and ordinary giants of spectral types A - K. In this paper we analyse stars F7 and earlier in an area of 19.5 sq.deg in Lyra. OBSERVATIONAL MATERIAL An area of 19.5 square degrees centred on l = 62.69deg, b = +15.99deg (alpha = 18h 42m, delta = +33deg 20') was chosen for investigation. The observations were carried out with the 60/90/180 cm Schmidt telescope of the mountain station of the Konkoly Observatory. Spectral types and UBV colours were derived for 524 stars brighter than 13^th photographic magnitude. The spectral classes are based on three objective prism plates taken with a 5deg UBK7 (uv transmitting) prism that gives a dispersion of 580 A/mm at Hgamma. Kodak OaO emulsions were used, and the widening was 18", equivalent to 0.16 mm on the plate. The classification criteria were those given. by STOCK and SLETTEBAK (1959) and STOCK (1971). The plates were made with double exposures of 6m and 24m so that any systematic variations in the classification with photographic density could be estimated. The UBV photometry is based on four plates taken in each colour. The filters, emulsion types, and exposure times used are given in the following table: U: Kodak OaO + Schott UG1 2 mm filter exp. time: 10m B: Kodak OaO + Schott GG13 2 mm filter " 5m V: Kodak OaD + Schott GG14 2 mm filter " 4m The international system is connected with the instrumental system according to the equations: V_instr = V - 0.05(B-V) - 0.01 (B-V)_instr = 1.08(B-V) + 0.04 (U-B)_instr = 1.11(U-B) - 0.04(B-V) + 0.02 The plates were measured with the Becker-type iris photometer of the Konkoly Observatory, using a photoelectric sequence obtained with the Konkoly Observatory 60 cm photometric telescope. The mean errors of the photographically determined colours are +- 0.08m, 0.07m and 0.06m for U, B, and V, respectively. Figure 1.a-d. The distribution of the stars against V magnitude. THE SPACE DISTRIBUTION OF THE STARS According to the sharpness of the classificational criteria and to the number of stars in each subclass four subgroups were determined: Stars earlier than A2, A2-A7, A8-F2, and F3-F7. The distribution of the stars against the V magnitude, in the subgroups defined, are demonstrated in Figs. 1a-1d. For determining the interstellar absorption the stars in each subgroup were divided into five groups according to their visual brightness: <7; 7-9; 9-11; 11-12; and >12. For each subgroup mean spectral types and colour indices were determined. Adopting JOHNSON's (1963) relation between intrinsic colour indices and spectral types the E_B-V and E_U-B colour excesses were obtained. The colour excesses determined by this method are plotted in Fig. 2, as a function of the distance modulus obtained by subtracting from the mean V magnitude of each subgroup the absolute magnitude belonging to the mean spectral type. Adopting a ratio of total to selective absorption R = A_V/E_B-V = 3 for the total absorption a value A_V = 0.06 rho could be obtained, where rho = V-M_V. According to this formula the absorption in the observed direction at a distance of 300 pc amounts to 75% of the absorption at 1000 pc indicating that the interstellar dust is concentrated in a 80 pc half thick layer along the galactic plane for this galactic longitude. Our determination is in good agreement with FITZGERALD's (1968) data ( 0.1<=E_y<0.2 ) for this area. Figure 2. The colour excesses (E_B-V and E_U-B) as functions of uncorrected distance modulus. The space densities were derived by grouping the stars in order of the distance modulus, obtained from the measured V magnitude and the mean absolute magnitude of the spectral type, corrected for the absorption and dividing the number of stars by the volume containing them. Assuming a Gaussian distribution of absolute magnitudes at a given spectral type the mean absolute magnitude at a given visual brightness can be obtained using the basic convolution equation of stellar statistics. The computation results the formula (MALMQUIST 1936) mean(M(m)) = M_0 - sigma^2/A(m) dA(m)/dm where M_0, sigma, and A(m) are the intrinsic absolute magnitude, the standard deviation of the Gaussian distribution, and the number of stars in a m +-1/2 interval, respectively. The densities derived by this method are plotted in Figs. 3a-3d. The dashed lines show the limit of the completeness of the sample caused by the limiting magnitude of classification. We shall discuss in the following section the spatial-distribution of the stars of each subclass separately and in more detail. DISCUSSION OF THE SPACE DENSITIES The density-gradients ( delta nu/delta r ) of the different subgroups are nearly the same up to 600 pc, except for the break-down caused by the plate limit. At about 600pc the density-gradient of the A2-A7 stars changes and becomes smaller. A similar change is visible in the distribution of stars younger than A2 at 1000 pc but it is based on a small number of stars and therefore its significance is questionable. Other authors ( VAN RHIJN 1955, KUROCHKIN 1958, PERRY 1969, WOOLLEY and STEWARD 1967), however, derived a similar change in the density gradient at stars younger than A2 so this effect in our case seems to be realistic. The spatial distribution of the A stars near the galactic poles shows a similar space density curve as those stars in our case. The similarity between this distributions and those obtained by the present investigation suggests that the observed density gradients of stars younger than A2, and A2-A7, in our case, are mainly due to the contributions of the gradients perpendicular to the galactic plane to the gradient in the line of sight. Figure 3.a.-d. The derived space densities of the different subgroups. (The dashed lines show the limit of the completness of the sample.) Supposing that the distribution of stars in the phase space is an even function of the Z velocity component we can derive the following relation connecting the spatial density, the standard deviation of the Z velocity component and the gravitational potential (OGORODNIKOV 1965): After integration and elementary computations we obtain: In our case we can take nu from our observations making the assumption that nu depends mainly on the z coordinate. We assume that the same holds for delta Phi / delta z in the direction observed and take it from the observations in the galactic caps (reviewed by OORT 1965). sigma_z(0) may be varied inside reasonable limits according to the observed data. If the formula given above has resulted a horizontal straight line in the sigma_z(z);z diagram we should assume that the velocity distribution, in the area observed, is Gaussian, since in that case sigma_z(z) is independent of z. Using the eye-estimated density curve of the stars A2-A7 derived from our observations and substituting sigma_z(0)=6.8 km/sec we get the curve plotted in Fig.4. The curve runs approximately horizontally up to 70 pc and above 180 pc, and the ratio of the velocity dispersions characterising the two horizontal parts of the curve equals to 1:1.8. Nearly the same ratio ( 1:2 ) was observed by WOOLLEY et al. ( 1969 ) and HARDING et al. ( 1971 ) for A0 stars in the south galactic cap. For sigma_z (0) they obtained 9 km/sec. Therefore the shape of the density curve may be explained as a superposition of two Gaussian velocity distributions having the above ratio of the velocity dispersions. At z = 0 the ratio of the densities of the two subsystems equals to about 1:7, and 1:70 in the case of stars younger than A2 if we adopt the change of the density gradient at r = 1.000 pc as a real effect. It is to be mentioned that JONES ( 1972 ) found that the M giants in the south galactic cap had a similar dispersion dependence to those plotted in Fig.4. His sigma_z(0)= 7 km/sec agrees very well with our value but the increase of velocity dispersion is stronger than in our case. Figure 4. The sigma_z(z)/sigma_z(0) ratio computed from the density curve of A2-A7 stars plotted against the height (z) above the galactic plane. The explanation that the shape of the density curve and the z dependence of the velocity dispersion of the A type stars caused by a condensation of those stars around the sun seems to be improbable, because the search for determining the spatial density of these stars, reported by McCUSKEY (1965), does not show significant condensation in the direction of our observed area projected onto the galactic plane. Moreover the condensations are different at different spectral types but in our case the density gradients are nearly independent of the spectral type at the first part of the density curves. The less compact subsystem is more prominent among the A2-A7 stars than among stars earlier than A2, which have mostly a spectral type B8 or later. Fig. 5 shows the logarithmic ratio of the density of the less compact component to the total density at z=0 using the data of different investigators. The most prominent feature in this figure is the "break" at A0 in the values of the ratios. Figure 5. The logarithm of the ratio of the density of the less compact component to the total density at z=0 using the data of different investigators. If stars are born continuously the existence of two kinematically different subsystems would be difficult to explain. This supports the idea of steplike birth. Taking into account that the young stars are more concentrated to the galactic plane than the older stars and that the less compact subsystem increases in its prominence towards stars having longer lifetimes it is reasonable to suppose that the two kinematically different subsystems differ in age, too. The time difference between two "birth events" may be estimated by the lifetime of the stars at which the "break" appears in Fig. 5. Using the theoretical lifetimes published by IBEN ( 1967 ) and the empirical bolometric absolute magnitudes of DAVIS and WEBB ( 1970 ) and the absolute visual magnitudes of JUNG ( 1970, 1971 ) the lifetimes of the A0 stars are about 3x10^8 years. The uncertainties of the spectral classification of the late type B and early type A stars on spectrograms of small scale determine a confidence interval around A0 in Fig. 5. The edges of this interval are the spectral types B8 and A2. The lifetime tau of the stars at which the "break" appears lies therefore in the interval: 1.5x10^8yrs