ISSN 1063-7729, Astronomy Reports, 2017, Vol. 61, No. 11, pp. 925–931. c  Pleiades Publishing, Ltd., 2017. Original Russian Text c  D.V. Bisikalo, A.S. Arakcheev, P.V. Kaigorodov, 2017, published in Astronomicheskii Zhurnal, 2017, Vol. 94, No. 11, pp. 920–926. Pulsations in the Atmospheres of Hot Jupiters Possessing Magnetic Fields D. V. Bisikalo * , A. S. Arakcheev, and P. V. Kaigorodov Institute of Astronomy, Russian Academy of Sciences, ul. Pyatnitskaya 48, Moscow, 119017 Russia Received March 15, 2017; in final form, April 20, 2017 Abstract—The discovery of the possible existence of huge quasi-stationary envelopes around a number of hot Jupiters (i.e., with sizes appreciably exceeding their Roche lobes) and the need to correctly take into account their properties when interpreting observational data require a careful analysis of the main physical processes influencing their atmospheres. One important factor is the possibility that the planet has a magnetic field. It was shown earlier that the presence of even a modest dipolar magnetic field of a hot Jupiter (with a magnetic moment approximately 1/10 the magnetic moment of Jupiter) influences the properties of the planetary atmosphere, in particular, leading to expansion of the range of parameters for which a giant, quasi-closed envelope can form around the planet. It was also established that the presence of a planetary magnetic field reduced the mass-loss rate from the envelope, since matter flowing out from the inner Lagrange point moves perpendicular to the field lines. Three-dimensional magnetohydrodynamical (MHD) modeling on time scales appreciably exceeding the time for the formation of the envelope show that pulsations arise in the atmospheres of hot Jupiters possessing dipolar magnetic fields, with characteristic periods ∼0.27P orb . This behavior is easy to understand physically, since even in the case of a spherical atmosphere, the continuous expansion of the ionized atmsphere of a hot Jupiter can lead to the accumulation of matter in regions bounded by closed field lines, and to the periodic rupture of the atmosphere beyond the magnetic field. In the case considered, when the system contains a giant envelope fed by a stream of matter from the inner Lagrange point, the presence of such pulsations gives rise to appreciable variations in the gas-dynamical structure of the flow. In particular, pulsations of the atmosphere lead to tearing off of part of the flow and sharp fluctuations in the size of the envelope, leading to variations in the envelope’s observational properties. DOI: 10.1134/S1063772917110026 1. INTRODUCTION Hot Jupiters are exoplanets with masses of order a Jupiter mass that are located very close to their hosting stars. There are no analogs to hot Jupiters in the solar system, but searches for such planets have shown that they are present around many stars. This poses a number of questions to modern astrophysics. First and foremost is the need to construct models to explain the appearance and evolution of such planets; furthermore, observations have revealed a number of related difficult to explain phenomena. In particular, observations in the near ultraviolet (NUV) show that many hot Jupiters have extended envelopes whose sizes appreciably exceed the sizes of their Roche lobes [1]. As is shown by the estimates of [2], up to one- third of observed hot Jupiters may appreciably over- flow their Roche lobes, which should lead to intense mass loss and short lifetimes. However, the large number of observed hot Jupiters suggests that the lifetimes of these planets are not short. An attempt * E-mail: bisikalo@inasan.ru was made in [3] to resolve this contradiction through analysis of mechanisms for stabilizing the extended envelopes of these planets via the pressure of the stellar wind. As was shown in [4], depending on the parameters of the atmosphere and stellar wind, three types of hot Jupiters are possible: closed, when the size of the envelope does not exceed the size of the Roche lobe; quasi-closed, when the envelope is stabilized by the stellar wind beyond the Roche lobe; and open, when the expansion of the envelope cannot be stopped by the dynamical pressure of the stellar wind. One unresolved question is the influence of the magnetic fields of hot Jupiters on the formation of their extended envelopes. According to most esti- mates (see, e.g., [5–7]), the magnetic fields of hot Jupiters should be weak, since tidal forces from the nearby parent star lead to rapid synchronization of the planet’s rotation and its orbital motion. The method of [8] yields an estimated magnetic moment of WASP 12b of ∼0.14μ Jup , where μ Jup is the mag- netic moment of Jupiter. An attempt to estimate the 925