A&A 652, A131 (2021) Astronomy https://doi.org/10.1051/0004-6361/202141048 & c A. Czechowski and I. Mann 2021 Astrophysics Dynamics of nanodust in the vicinity of a stellar corona: Effect of plasma corotation A. Czechowski1 and I. Mann2 1 Space Research Centre, Polish Academy of Sciences, Bartycka 18A, 00-716 Warsaw, Poland e-mail: [email protected] 2 Department of Physics and Technology, UiT the Arctic University of Norway, Postboks 6050 Langnes, 9037 Tromso, Norway e-mail: [email protected] Received 11 April 2021 / Accepted 5 June 2021 ABSTRACT Context. In the vicinity of the Sun or other stars, the motion of the coronal and stellar wind plasma must include some amount of corotation, which could affect the dynamics of charged dust particles. In the case of the Sun, this region is now investigated in situ by the Parker Solar Probe. Charged dust particles coming from the vicinity of the Sun can also reach, and possibly be detected by, the Solar Orbiter. Aims. We use numerical simulations and theoretical models to study the effect of plasma corotation on the motion of charged nanodust particles released from the parent bodies moving in Keplerian orbits, with particular attention to the case of trapped particles. Methods. We used two methods: the motion of nanodust is described either by numerical solutions of full equations of motion, or by a two-dimensional (distance vs. radial velocity) model based on the guiding centre approximation. The models of the plasma and magnetic field in the vicinity of the star are based on analytical solutions that satisfy the freezing-in equations. Results. Including plasma corotation does not prevent trapping of nanodust in the vicinity of the Sun or other stars. This result can be understood with the help of the model based on the guiding centre approximation. For the amount of corotation expected near the Sun, the outer limit of the trapped region is almost unaffected. If the corotation persists outside the trapping region, the speed of particles ejected from the Sun is moderately increased. A strong effect of plasma corotation on charged particle dynamics occurs for the star with a high rotation rate and/or a low value of the stellar wind speed. Key words. Sun: heliosphere – solar wind – acceleration of particles – interplanetary medium – circumstellar matter 1. Introduction Our models of nanodust trapping in the vicinity of the Sun were so far restricted to the case of a simple Parker spiral The dynamics of charged dust particles with sizes smaller than a structure of the magnetic field, assuming a radially directed few hundred nanometers is strongly affected by the electromag- solar wind with no plasma corotation. However, as shown by netic force. In particular, nanodust particles can be picked up and Weber & Davis(1967), the plasma flow near the Sun is expected accelerated by the solar wind plasma. In the vicinity of the Sun, to include some amount of corotation. The region affected by these particles can also be trapped by the interplay between the corotation extends approximately to the Alfvén radius, the dis- electromagnetic forces and solar gravity. This could happen pro- tance at which the velocity of the outflowing plasma equals the vided that the ratio of solar radiation to gravity β is lower than Alfvén velocity. The Alfvén radius sets the scale of the region in 0.5 for small dust grains and that the scatter-free approximation which the angular momentum of the solar rotation is transmit- (Luhmann 2003) is applicable. ted to the solar wind plasma, producing a corotating component The process of trapping can be illustrated using the guid- of the solar wind velocity. For the case of the Sun, the order of ing centre approximation, in which the guiding centre moves magnitude of the Alfvén radius (about 0.1 AU) is comparable to along the rotating magnetic field line. The force that governs this the size of the trapping region (0.16 AU near the solar equator). motion can be described in terms of components correspond- It follows that the plasma corotation should not be disregarded ing to an effective gravity force, an effective mirror force, and a in a study of charged dust dynamics. centrifugal force. At the inner limit of the trapping region, the (The value of 0.1 AU was obtained assuming the following effective gravity force acting on the particle is balanced by the values of the slow solar wind parameters: magnetic field radial magnetic mirror force. At the outer limit, the effective gravity and azimuthal components Br = Bφ = 35 µG at 1 AU, number force is equal to the centrifugal force term. density 5 cm−3 at 1 AU, and a wind speed of 350 km s−1). The trapping of nanodust particles in the vicinity of the Sun The study of dust dynamics near the Sun are at present being was studied in a number of works (Czechowski & Mann 2010, compared with observations. The Parker Solar Probe (PSP) 2011, 2012, 2018; Czechowski & Kleimann 2017). A similar is now passing through the regions of high dust fluxes near phenomenon may occur near other stars (cf. Su et al. 2013, 2020; the Sun. The Electromagnetic Fields Investigation (FIELDS) Rieke et al. 2015; Kimura et al. 2020). Calculations of the nan- antenna instrument package (Bale et al. 2016) during the first odust trajectories were also made for nanodust around Vega and PSP orbits measured impact events that are consistent with Fomalhaut (Stamm et al. 2019), two stars with a planetary debris the trajectories of particles under the effect of gravity and disk. radiation pressure force (Page et al. 2020; Szalay et al. 2020; A131, page 1 of9 Open Access article, published by EDP Sciences, under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. A&A 652, A131 (2021) Malaspina et al. 2020). Comparison to a dust collision and Our treatment of plasma corotation is based on that of dynamics model suggests that the majority of detected particles Weber & Davis(1967). The main di fference is that we did not are 30 nm and larger (Mann & Czechowski 2021). The trajec- restrict our model to the solar equator plane, but assumed that tory of the PSP is evolving, with the orbit perihelion approach- the latitudinal (θ) components of B and V are zero. The mag- ing the Sun. In 2020, the perihelion of the PSP orbit came below netic field and plasma flow lines lie then on θ = const cones. ∼0.15 AU, the outer limit of the region in which the trapped nan- The simple models such as the radially directed solar wind flow, odust particles can be present. At the end of the year, it also the Parker spiral magnetic field, as well as their modification approached 0.1 AU, the usual estimate of the Alfvén radius. In by various models of plasma corotation are consistent with our 2021, the spacecraft will approach the Sun to within 0.08 AU, assumptions. the middle point of the trapped region. Although it is not clear With the assumptions listed above, the magnetic field and the whether the impacts of nanodust particles can be detected by the plasma velocity can be written as PSP, the observations of the dust distribution may be helpful to understand what is happening in the trapping region. B = Br(r; θ)eˆr + Bφ(r; θ)eˆφ = Br(r; θ)(eˆr − aeˆφ) (2) Another opportunity to study the effects of plasma corotation on trapped dust follows from the discovery of hot dust around V = Vr(r; θ)eˆr + Vφ(r; θ)eˆφ = Vr(r; θ)(eˆr + ceˆφ); (3) early-type stars surrounded by debris disks (Su et al. 2013, 2020; Rieke et al. 2015; Kimura et al. 2020). This case is of particular where a = a(r; θ) ≡ −Bφ=Br and c = c(r; θ) ≡ Vφ=Vr. The form interest to us because (as we show in this paper) the high rotation of a(r; θ) and c(r; θ) depends on the model of corotation. Because of the r · B = 0 condition, the radial component of rate of a star strengthens the effects of corotation more than for 2 the case of the Sun. the magnetic field must behave as Br = b=r , where b can depend We show that trapping of the nanodust particles in the vicin- on θ. In our calculations we specified the r dependence of the ity of the Sun or other stars is not adversely affected by plasma radial plasma velocity component Vr = Vr(r). In most calcula- corotation. Some of our preliminary results were included in tions referring to the case of the Sun, we used the radial velocity Stamm et al.(2019). The argument relies on the model of nan- profile (Model 3 in Czechowski & Mann 2018), based on obser- odust motion (Czechowski & Mann 2010, 2011, 2018) based vations by Sheeley et al.(1997). Alternatively, we assumed that on the guiding centre approximation. The model was used suc- the radial component of the solar or stellar wind velocity is a distance- and latitude-independent constant. The value of this cessfully to interpret the results of numerical simulations of −1 charged dust motion. Assuming that the particle motion can constant we took to be 400 km s for the case of the Sun. For be regarded as scatter free, the conditions for the guiding cen- other stars, we used the values listed in Table 2 of Kimura et al.