A small magnetosphere-solar wind interaction for northward and southward interplanetary magnetic field: Hybrid simulation results Pavel M. Trávníček Institute of Geophysics and Planetary Physics, UCLA, Los Angeles, CA 90095, USA; Yosemite reconnection meeting, U.S.A., February, 2010
Table of contents Spatio-temporal scaling of objects and processes in space plasmas How to make a global kinetic simulation less or more kinetic Downscaling real objects into a global kinetic simulation Global simulation of the interaction between solar wind and for northward and southward orientation of the interplanetary magnetic field (Travnicek et al., 2010). Yosemite reconnection meeting, U.S.A., February, 2010
Planets of our Solar system Name distance n psw B SW Λ isw v ASW radius R v sw = 300km/s dipole moment M [AU] [cm 3 ] [nt] [km] [km s 1 ] [km] [Λ i ] [v A ] [M Earth ] [Λ 3 i B sw/µ 0 ] Mercury 0.31 73 46 26.7 118 2 439 91 2.5 4.7 10 4 5.4 10 7 0.47 32 21 40 82 2 439 60 3.6 4.7 10 4 3.5 10 7 Venus 0.72 14 10 61 59 6 052 99 5 - - Earth 1.0 7 6 86 50 6 378 74 6 1.0 2.6 10 9 Mars 1.5 3.1 3.4 129 42 3 397 26 7 - - Jupiter 5.2 0.26 0.83 447 36 71 398 160 8 20.000 2.7 10 13 Saturn 9.6 0.076 0.44 827 35 60 000 73 9 540 2.16 10 11 Uranus 19.1 0.019 0.22 1 654 35 25 400 15 9 48 4.8 10 9 Neptune 30.2 0.0077 0.14 2 599 35 24 300 9 9 26 1.0 10 9 Pluto 39.4 35 2 500 9 unknown unknown The Earth magnetic dipole moment is M Earth = 8 10 22 Am 2. Mercury is the most likely (magnetized) candidate to be studied by a global kinetic numerical model beside unmagnetized planets Venus and Mars Effect of denser stellar flow at Mercury: from physical point of view the size of Mercury is comparable to Earth Mercury also changes its diameter in the stellar flow of given desity thanks to its eccentric Solar orbit Pluto almost can not be simulated by a hybrid code and its study requires a full particle in cell code RPWI meeting, Uppsala, Sweden, November, 2009
Solar wind expansion A homogeneous slowly expanding plasma (without any fluctuating wave energy) evolves adiabatically. The ion parallel and perpendicular temperatures T and T satisfy the CGL equations T B and T n 2 /B 2, respectively. Plasma temperature anisotropies naturally develop. Temperature anisotropy (i.e. departure from Maxwellian particle distribution function) represent a possible source of free energy for many different instabilities. RPWI meeting, Uppsala, Sweden, November, 2009
Solar wind protons Both panels show a color scale plot of the relative frequency of (β p,t p /T p ) in the WIND/SWE data (1995-2001) for the solar wind v SW < 600 km/s The over plotted curves show the contours of the maximum growth rate (in units ω cp ) in the corresponding [Hellinger et al., 2006] bi-maxwellian plasma proton cyclotron instability (solid curves) parallel fire hose instability (dashed curves) proton mirror instability (dotted curves) oblique fire hose instability (dash-dotted curves) RPWI meeting, Uppsala, Sweden, November, 2009
Solar wind electrons [Stverak et al., 2008] Panel shows a gray shaded scale plot of the relative frequency of (β p,t p /T p ) in the Helios data for the solar wind v SW < 600 km/s The over plotted curves show the contours of the maximum growth rate (in units ω ce ) in the corresponding bi-maxwellian plasma whistler instability (dash-dotted curves) parallel electron fire hose instability (dashed curves) RPWI meeting, Uppsala, Sweden, November, 2009
Global simulations to date All (global) numerical models / techniques employ some compromises: MHD 3D simulations [Kabin et al., 2001]. Hybrid models with spatial resolution of several c/ω pi [Kalio and Janhunen, 2003] (typical Larmor radius at Mercury is 2-3 c/ω pi ). Global 2D hybrid models of solar wind interacting with magnetized obstacles have been also considered [Omidi et al., 2002]. Scaled down model with spatial resolution of the order c/ω pi and reasonable ratio between Larmor radius and the scaled down size of the planet [Travnicek et al., 2007, 2009]. RPWI meeting, Uppsala, Sweden, November, 2009
Scaling down the model We use a scaled down model of Mercury with a magnetic moment M = 50,000B sw (c/ω ppsw ) 3 4π/µ 0 = 3.76 10 19 /ε Am 2 for both studies. The downscaling preserves the stand-off distance of the magnetopause predicted by R mp = (2B 2 eq/(µ 0 P ram,sw )) 1/6 R M, where B eq is the magnetic field at the equator of the planet with radius R M and P ram,sw is solar wind ram pressure n sw m p v 2 sw, where m p is the proton mass (m p = 1 in simulation units). Although scaled down, the radius R M is always sufficiently larger than the local Larmor radius r L. The scaling factor of the physical space equals to 3-4. RPWI meeting, Uppsala, Sweden, November, 2009
Quasi-parallel magnetosheath plasma RPWI meeting, Uppsala, Sweden, November, 2009
A qualitative agreement... Upper panels shows several observables from a global simulation along virtual M1 flyby trajectory of virtual MESSENGER. Bottom panel shows in situ observed magnitude of the magnetic field and the amplitide of magnetic field oscilations. (Travnicek et al., 2009) Yosemite reconnection meeting, U.S.A., February, 2010
Figure 1: Schematic views of for (left) a northward IMF highlighting the features and phenomena observed by MESSEN- GER during its flyby of 14 January 2008 (from Slavin et al., 2008) and for (right) a southward IMF as observed by MESSENGER on 6 October 2008 (from Slavin et al., 2009).
run Hyb1 run Hyb2 Spatial resolution x 0.4 d psw Spatial resolution y = z 1.0 d psw Spatial size of the system L x = N x x 237.6 d psw Spatial size of the system L y = L z = N y y 288 d psw Mercury s radius R M 15.32d psw Temporal resolution (simulation time step) t 0.02 ωgpsw 1 Time sub-stepping for electromagnetic fields t B t/20 = 0.001 ωgpsw 1 Simulation box transition time 59.4 ωgpsw 1 Duration of each simulation 120.0 ωgpsw 1 β psw 1.0 β esw 1.0 Number of macro-particles per cell (specie 0) 80 50 Number of macro-particles per cell (specie 1) 100 100 Total number of macro-particles 3.9 10 9 2.5 10 9 Solar wind velocity v psw 4.0 v Asw Orientation of IMF in (X,Z) plane + 20-20 Mercury s magnetic moment M 250 nt R 3 M 4π/µ 0 (no tilt) n psw, B sw, v Asw, d psw, ω gpsw = 1 (in simulation units)
Figure 2: Upper panels show the simulated proton density n p in two planes: (a) the equatorial plane (X, Y) and (b) the plane of main meridian (X, Z) from simulation Hyb1 (northward IMF) at t = 100ωgpsw. 1 Bottom panels (c) and (d) show the same information from simulation Hyb2 (southward IMF).
Table: List of markers used for the orientation along the (virtual) M1 and M2 trajectories Marker description color r/r M for M1 r/r M for M2 SI shock inbound yellow 8.0-1 white 5.5 - MI magnetopause inbound green 2.9 3.9 2 white 2.6 2.7 3 white 1.3 1.4 CA closest approach red 0.1 0.1 MO magnetopause inbound green 1.2 0.9 4 white 1.6 1.2 SO shock outbound yellow 2.1 1.6
Figure 3: An example of a plasmoid formed in the magnetotail marked by a white arrow on panel (a) which shows simulated proton density n p in the equatorial plane (X, Y) (southward IMF). The plasmoid structure has roughly 0.5R M in diameter (see panels b-d) and its life-span from time of its formation to its dissipation is 10 20ωgpsw. 1 The plasmoid tends to move slowly down the magnetotail away from the planet.
Figure 4: Simulation results at time t = 100ω 1 gpsw in the two-dimensional curved sectional planes of the simulation box for (a) Hyb1 and (b) Hyb2; these planes contain the corresponding spacecraft trajectories M1 and M2, respectively, and are perpendicular to the equatorial plane (X, Y): Shown are color-scale plots of the simulated proton density n p. as a function of r and Z, where r is the distance of the corresponding position of the spacecraft from Mercury s surface.
Figure 5: Simulation results at time t = 100ω 1 gpsw in the two-dimensional curved sectional planes of the simulation box for (a) Hyb1 and (b) Hyb2 simulation; these planes contain the corresponding spacecraft trajectories M1 and M2, respectively, and are perpendicular to the equatorial plane (X,Y). Shown are gray-scale plots of the magnitude of the simulated magnetic field B as a function of r and Z.
Figure 6: Panels a and g show the density n p /n psw, panels b and h show magnitude of the magnetic field B/B sw, panels c and i display the proton plasma temperature T p /T psw, panels d and j show the proton temperature anisotropy T p /T p, panels e and k show the X-component of the plasma bulk velocity v px /v Apsw, and panels f and l displays the proton kinetic pressure p p /p psw.
Figure 7: Proton velocity distribution function f p along the M1 trajectory from simulation Hyb1 with northward IMF (left panels) and along the M2 trajectory in simulation Hyb2 with southward IMF (right panels). Panels show different cuts of f p calculated along the corresponding spacecraft trajectory from all macro-particles within a sphere with radius r vdf = 0.9d psw.
Figure 8: Precipitation of solar wind protons onto the surface of Mercury as seen in our simulation with (a) northward IMF and with (b) southward IMF. Macro-particles were collected over a time period of T = ωgpsw 1 at t = 100 ωgpsw. 1 The longitude 0 and the latitude 0 correspond to the dayside subsolar point. Both panels show the number of protons n p in the units of the solar wind proton density n psw absorbed by Mercury s surface at the given location per accumulation time ωgpsw 1 per (c/ω ppsw ) 2.
Figure 9: Distance from marginal stability criteria given by ( a Γ = sgn(a) (β p β 0 ) b T ) p + 1 T p along spacecraft trajectory M1 in simulation Hyb1 (left panels) and along M2 in Hyb2 (right panels) for (a and e) the proton cyclotron instability, Γ pc, (b and f) the mirror instability, Γ mir, (c and g) the parallel fire hose, Γ pf, and (d and h) the oblique fire hose, Γ of.
Table: Fitted parameters for marginal stability states of different instabilities Instability a b β 0 Proton cyclotron instability 0.43 0.42-0.0004 Mirror instability 0.77 0.76-0.016 Parallel fire hose -0.47 0.53 0.59 Oblique fire hose -1.4 1.0-0.11
Figure 10: On first six panels the three time-averaged magnetic components are shown: B x (a/h, red line), B y (b/i, green line), and B z (c/j, blue line). The second six panels displays relative variations of the three magnetic components from the averaged value at time t = 100ωgpsw 1 δb x / B (d/k, red line), δb y / B (e/l, green line), and δb z / B (f/m, blue line). The last two panels (g/n) show the relative fluctuating magnetic energy δb 2 / B 2.
Figure 11: Time evolution of the absolute value of (a and e) electric E(r,t)/(B sw v Asw ) and (b and f) magnetic B(r,t)/B sw fields and the corresponding spectra (c and g) E(r,ω) and (d and h) B(r,ω) from simulation Hyb1 with northward IMF along the M1 trajectory (left) and from simulation Hyb2 with southward IMF along the M2 trajectory (right).
Figure 12: Correlation between the proton density n p /n psw and the magnitude of the magnetic field B/B sw along the M2 trajectory from simulation Hyb2 with southward IMF. The correlation was calculated at each measurement point over 200 nearest points and over 256 time steps.
Summary 1 of 3 The overall magnetospheric features of the simulated system are similar to those in the terrestrial magnetosphere. We observe typical series of thin and thick transition regions appear including bow shock, magnetosheath, magnetopause, magnetotail, magnetosphere itself, plasma belt, etc. The simulated results are in a good qualitative agreement with in situ observations of MESSENGER. The oblique/quasi-parallel bow shock region is a source of backstreaming protons filling the foreshock where they generate strong wave activity. These large-amplitude waves are transported with the solar wind to the adjacent magnetosheath. In the quasi-perpendicular magnetosheath, waves are generated near the bow shock and locally by the proton temperature anisotropy. Yosemite reconnection meeting, U.S.A., February, 2010
Summary 2 of 3 For the low-β plasma considered here, the dominant instability in the quasi-perpendicular magnetosheath is the proton cyclotron instability, a result confirmed by the density-magnetic field n p,b correlation analysis. The positions of the foreshock and the quasi-parallel and quasi-perpendicular bow shock regions are controlled by the IMF orientation. Magnetospheric plasma also exhibits a proton temperature anisotropy (loss cone) with a signature of (drift) mirror mode activity. For both orientations magnetospheric cusps form on the day side, at higher latitudes for northward IMF compared to southward IMF. The day side magnetosphere has a smaller size for southward IMF. These differences are likely related to different locations of reconnection regions for the two orientations. Yosemite reconnection meeting, U.S.A., February, 2010
Summary 3 of 3 In the case of southward IMF the night-side magnetospheric cavity in the Z direction is wider. We found strong sunward plasma flows within Mercury s magnetotail. For southward IMF the sunward plasma flows is stronger owing to a presence a strong sunward proton beam, a signature of the reconnection process occured further downtail in the thin current sheet (along with the formation of plasmoids). These energetic protons likely contribute to the thermal and dynamic pressure of the magnetospheric plasma widening the magnetospheric cavity in the case of southward IMF. Both IMF configurations lead to a quasi-trapped plasma belt around the planet. Such a belt may account for the diamagnetic decreases observed on the inbound passes of both MESSENGER flybys. Yosemite reconnection meeting, U.S.A., February, 2010