Astronomy Reports, Vol. 45, No. 11, 2001, pp. 861–864. Translated from Astronomicheski˘ ı Zhurnal, Vol. 78, No. 11, 2001, pp. 985–989. Original Russian Text Copyright c  2001 by Khoperskov. Do the Galaxies NGC 936 and NGC 3198 Possess Massive Spheroidal Subsystems? A. V. Khoperskov Sternberg Astronomical Institute, Universitetski ˘ ı pr. 13, Moscow, 119899 Russia Received March 5, 2001 Abstract—The condition for gravitational stability of the stellar disks of the galaxies NGC 936 and NGC 3198 makes maximum disk models unacceptable. We present mass estimates for these objects’ spheroidal components. The mass of the dark halo of NGC 3198, within four disk radial scale lengths, ex- ceeds its disk mass by a factor of 1.6 to 2. The masses of the disk and spheroidal subsystem (halo +bulge), within four radial scale lengths, are approximately the same for NGC 936. c  2001 MAIK “Nau- ka/Interperiodica”. 1. INTRODUCTION The possible existence of an invisible massive component in S galaxies is one of the most important problems in the physics of galaxies. The presence of extended regions in the gas rotation curves showing no decrease with radius beyond the optical radius are among the features that provide evidence for the presence of massive halos, whose mass may appreciably exceed that of the visible matter in the disk, M d . Withintheopticalradius,thehalomass M h can be comparable to and even exceed M d . Among other signatures, this is suggested by the efficient stabilization of the global bar mode by the massive spheroidal subsystem [1–3], but here the situation is more complex: the asymmetrical bar forming in the disk leads to a gravitational interaction with the halo matter, resulting in a transfer of angular momentum from the disk to the spheroidal subsystem [4]. Analyzing the results of dynamical modeling of interacting disk/bar/halo subsystems, Dabattista and Sellwood [5] concluded that the halo mass within theopticalradiushadtobesmallcomparedtothedisk mass and, in particular, that maximum disk models (MDMs) were suitable for the galaxies NGC 936 and NGC 3198. The MDM is based on the observed rotation curve of the gaseous subsystem, V gas , and the condition that the disk mass be the maximum possible for the case when the mass-to-luminosity ratio in the disk population is approximately constant and the circular velocity in the galaxy’s equatorial plane V c is equal to V gas . The observed radial distribution of stellar veloc- ity dispersions constrains the value of µ ≡ M s /M d , where M s isthemassofthespheroidalhalo + bulge + core subsystem. For the stellar disk to be gravitation- ally stable, the system must not be cool: c r >c crit r , where c r is the stellar radial velocity dispersion [6– 9]. The velocity dispersions in the stellar disks of NGC 936 and NGC 3198 are known. Earlier [10], we considered a model that satisfactorily described the velocity curve and stellar velocity dispersion in NGC 3198. Here, we show that the gravitational stability condition for the stellar disks makes max- imum disk models unacceptable for NGC 936 and NGC 3198 and leads to underestimated masses for their spheroidal subsystems. 2. GRAVITATIONAL STABILITY OF A STELLAR DISK Weassume that there is an exponential dis- tribution of matter in the disk, (r, z)=  0 sech 2 (z/h) exp(-r/L), so that the disk subsys- tem is governed by three parameters: the disk’s radial scale length L, vertical scale length h, and central surface density σ 0 =2h 0 . We will describe the spheroidal components (halo, bulge, core) with the masses M h ,M b ,M c and scale lengths a, b, c, respectively. The matter of the bulge and core will be assumed to be confined to radii (r b ) max and (r c ) max , respectively. We will not con- sider the density distributions of the individual com- ponents but instead restrict our treatment to the inte- grated density µ = M s /M d =(M h + M b + M c )/M d . For the disk to be gravitationally stable to non- axially symmetrical perturbations, it is necessary that c r ≥ c crit r . The minimum stellar radial velocity dispersion required for stability, c crit r , is traditionally described using Toomre’s parameter Q T = c crit r /c T , 1063-7729/01/4511-0861$21.00 c  2001 MAIK “Nauka/Interperiodica”