The Outer Heliosphere On the largest scales, the hot heliosphere encounters the much colder (T 100 K) interstellar medium (ISM).

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1 The Outer Heliosphere On the largest scales, the hot heliosphere encounters the much colder (T 100 K) interstellar medium (ISM). We are in a Local Bubble that s slightly hotter (T up to 10 4 K in places) and lower-density than mean ISM. Still, the conditions inside vs. outside are quite different, so the plasma must readjust itself, in stages. The whole solar system is also in motion with respect to the surrounding Bubble & ISM: u 23 km/s. We can think of u as either a flow coming at us, or as us moving through a static ISM like a bullet. (These views are essentially equivalent!) When two plasma parcels are in relative motion, with supersonic speeds involved, the system forms a series of shocks & other sharp discontinuities: 12.1

2 We ll go through these layers soon, but first it s good to review what shocks really are: the response of a gas to bulk flows faster than the sound speed. Think of an acoustic wave. There are pressure variations along the direction of propagation, and those give rise to longitudinal velocity perturbations δv too. Small-amplitude (linear) waves all drift along with c s δv, but when the velocity amplitude starts to approach c s, then the wave STEEPENS: The region ahead of the shock is unaware that it s coming; i.e., shocks occur when there s insufficient time for the system to react by means of simple linear waves. Shocks are inherently nonlinear... they are entropy increasing engines of the 2nd law of thermodynamics: as gas passes through them, they convert (ordered) kinetic energy into (disordered) thermal energy. In shock s frame, gas flows from upstream (side 1) to downstream (side 2): (1) Upstream/Inflow (2) Downstream/Outflow supersonic (u 1 > c s1 ) subsonic (u 2 < c s2 ) cold hot low ρ, P high ρ,p low entropy high entropy Note: We have seen that nature allows fluids to flow from hot/dense regions to cold/fast regions, but shocks don t form in those cases... rarefaction zones are fanned out & continuous. Mass/momentum/energy conservation laws also apply to shock discontinuities; these form the Rankine-Hugoniot jump conditions. Cravens 4.9 gives them, but we ll just make use of 2 basic ideas: 12.2

3 (1) Mass conservation means ρu = constant across a shock, but the density jump cannot be arbitrarily large. For an ideal gas, ( ) ( ) ρ2 u1 = = γ +1 = 4, for γ = 5/3. γ 1 ρ 1 max u 2 max (2) For B = 0, the total pressure balance across a shock must take into account ram pressure, too... P + ρu 2 = constant across shock. Taking the extreme limit of a very strong shock (u 1 c s1 ), the end result is that all that supersonic motion is converted into heat on the downstream side: k B T 2 = γp 2 = c 2 s2 µm H ρ u2 1 and if u 1 a few hundred km/s, T 2 can be millions of K!... Layers of the Outer Heliosphere Cravens gives a brief overview, but it s showing its age....no spacecraft has yet traveled far enough from the Sun to reach the heliopause. Not anymore! Voyager 1 hit it around r 120 AU. When two flows collide with one another, a steady, stable situation can be attained if the two plasmas can come into total pressure equilibrium. We ve seen that before, but usually for slow/subsonic flows (e.g., convective blobs; static flux tubes) However, the solar wind is locally supersonic. Also: the overall relative flow ( u = 23 km/s) may also be supersonic out in the ISM. If so, then there must be TWO shocks to first decelerate the flows, and then a layer in between where the (subsonic) flows meet, stagnate, and then P tot can be balanced. 12.3

4 Recent observations from IBEX (which detects neutral particles from local ISM) gave evidence there is no Bow Shock. ISM gas gets piled up and deflected by the heliosphere, but it remains subsonic (actually sub-magnetosonic). Cravens summarizes a way of estimating where the heliopause (pressure-balance surface) occurs. P ISM N/m 2 P HS ( ( ) 2 ρ sw u 2 sw )TS ρ 1auu 2 R1au r and for P ISM = P HS, solve for r AU. Really, TS is 95 AU, HP at 120 AU. Breathes in & out with solar cycle. 12.4

5 New development: the 2015 croissant revolution The shape of the heliosphere was assumed to be comet-like (as in the cartoons above) for decades. However, numerical MHD simulations have shown that it may not look quite like that. At r 1 AU, the Parker spiral angle φ p reaches 90, and B B φ ê φ. Opher et al. (2015) realized that the inward magnetic tension ( hoop force ) is strong, and the time-steady heliosheath must heat up even more than we thought (i.e., increase its P gas ) in order to balance it. However, that higher P gas rapidly spreads & fills the whole spherical heliosheath. Over the north & south poles, there s no hoop force, so it drives a collimated jet resembling astrophysical jets above protostars, black holes, etc. There is still comet-like deflection by our motion through the ISM, but instead of the entire region bending back, it s just the jets. This seems to still be controversial

6 Flares and Coronal Mass Ejections (CMEs) These are violent eruptions that range from photosphere to corona to outer heliosphere. Flares & CMEs are related, but they don t always occur together. (Many flares without CMEs... many CMEs without flares) They involve magnetic reconnection, and so we ll go into some detail about what happens there. Observations: Before talking about the eruption, we need to outline what kinds of B configurations exist prior to the eruption. Prominences & filaments: These are twisted strands of magnetic field, seen either off-limb (bright) or on-disk (dark). They re filled with cool (chromospheric) gas, up at coronal heights! Prominences are sometimes loop-like; sometimes spray, hedgerow, surge, fan. These features all have twists & tangles in B. How do they form? 12.6

7 For the footpoints, there are many ideas that involve a combination of: shear & convergence What gets created is a twisted flux rope, with J B 0 but J 0: Cool gas is levitated by the field; collects (in dips ) in local hydrostatic equilibrium often very tangled & turbulent. Overall, though, J B, so in MHD we can write B = αb. 12.7

8 In general, α can be a function of position, but it s been found that many systems like to relax to the so-called LFFF (linear force-free field) that occurs when α = constant. Lundquist (1950) worked out an analytic solution in cylindrical geometry, using Bessel functions J n (x), B r (r) = 0 B φ (r) = ±B 0 J 1 (αr) B z (r) = B 0 J 0 (αr) The constant α is a magnetic torsion parameter that describes how twisted up the field is. The outer edge of the cylinder is the first zero of J 0 (x), which occurs at x = αr edge The Lundquist solution works very well as a fitting formula for twisted magnetic clouds encountered by spacecraft. Those are the interplanetary remnants of CMEs (ICMEs).... However, we re getting ahead of ourselves. Despite the cool prominence gas collected in the dips, these regions tend to have high P mag, so lower P gas than surrounding corona. Thus, flux ropes want to be buoyant and float away. Usually, though, there s lots of nearby potential B (i.e., in an active region) that overlies it. Magnetic tension holds it down. What triggers a release? Still not agreed-upon. Jim Klimchuk (2001) published a set of heuristic cartoons that summarize various ideas from the theorists. 12.8

9 Thermal blast: Sometimes the flare seems to come before the CME? Mass loading: If there s cool, highdensity prominence gas, it may keep the field held down. But as B evolves, there might open up avenues for gas to drain away... Tether-cutting: If the overlying field gets weaker, then magnetic tension nolongercanholddownthebuoyant flux rope. There s a lot of interesting math concerning the catastrophic loss of equilibrium. The model that I think works best is a variant of tether-cutting, developed by Forbes, Isenberg, & Lin (& many others). If the footpoints of the overlying fields are pushed together, then magnetic reconnection cuts the tether: We ll talk more about magnetic reconnection in a bit, but this model seems to account not only for the light-bulb shaped CME, but also for the downward flow of energy (out of the reconnection zone) that powers many solar flares. Flares are bright spikes of emission in just about every spectral band: radio, microwave, IR, visible, UV, X-ray, & gamma-ray! If a supersonic flow of hot coronal gas comes slamming down onto the surface, part of the chromosphere evaporates away quickly, and particles of all kinds get energized. 12.9

10 We re still not quite sure why so much energy gets released by a flare, E J, equivalent to L 1 second! but this is roughly equal to the extra magnetic energy stored in twisted active regions. Getting rid of it relaxes the active-region B back down to a potential field. CMEs expand through the solar wind & heliosphere, creating a strong shock out in front, & pushing everything else out of the way

11 Magnetic Reconnection (Cravens 4.10) What happens when oppositely-directed regions of B are pushed together? If magnetic flux was perfectly frozen-in to the flow, the field would build up in a log-jam. However, we know there s another term in the induction equation: diffusion. B t = (u B) + D B 2 B where D B is the magnetic diffusion coefficient (units of m 2 /s), and it s set by the resistivity of the plasma (depends on ρ, T, composition). Let s look at the magnitudes of the two terms using 1/L. B {FF} + {Diff} where {FF} ub {Diff} D BB t L L 2 The 2 terms have the same units, so their ratio tells us about their relative strengths. Define the magnetic Reynolds number, Rm = {FF} {Diff} ul D B (B cancels out) For most macroscopic/observable spatial scales (L) and speeds (u) in the corona, Rm 1 in fact, Rm ! (so it s a good approximation to think about frozen-in flux!) However, in this problem we re looking at steep variations in the y direction. Define the thickness of the reconnection region (in y) as δ, and assume spatial derivatives are strongest in y. As magnetic flux piles up, gradients get sharper, so δ gets smaller

12 Thus, the dominant terms in the derivatives are the ones with the smallest spatial scales, so, e.g., B x y B x. δ Replacing u by u in (fixed speed at which fields are pushed together) and L by δ (which is shrinking), we find that eventually, Rm 1... i.e., diffusion starts to beat flux freezing, i.e., the thickness of a reconnection region is δ D B u in and once the region gets this thin, diffusion starts to annihilate magnetic energy and convert it to heat. Problem: We don t know either δ or u in! In order to figure out what s really going on when B starts to get destroyed, we need to bring in more information. This step is still unsolved & controversial. Aside: The sharp, flattened region where opposing fields meet is often called a current sheet. Why? In MHD, J = 1 µ 0 B and in this geometry, J z B x µ 0 δ because the / y term dominates. Outside the current sheet, J 0. Also, in the reference frame moving with the flow, E = ηj, so E z ηb µ 0 δ D BB δ i.e., u in E B so the faster the reconnection inflow, the more of a DC electric field is built up in the current sheet. Thus, once we know all the parameters, the volumetric heating rate inside the current sheet can be computed; Q heat = J E = J z E z. I ll go over one of the earliest models of what happens when incoming field lines are broken and reconnected to field lines from the opposite side. In the 2D Sweet Parker model (1957), the reconnection region can be thought of as flattened & rectangular

13 The large-scale length L of the system is something we already know, like ρ (which we can assume is uniform everywhere). If it s steady-state, then the total mass coming in must balance the mass going out, in proportion to the dimensions, u in L z u out δ z i.e., mass flux depends on ρua, but the full A depends on the z extent in/out of the board. That s the same for both in & out motions. We can also make use of energy conservation, (E kin +E mag +E thermal ) in = (E kin +E mag +E thermal ) out In the low-β corona, we ignore E thermal (not true inside diffusion region, but we re staying outside for now). Also, assume that slow inflow dominated by magnetic energy, and fast outflow dominated by kinetic energy: E = volume energy density, so E in = x y z U B ( ) B 2 = L(u in t) z 2µ 0 E out = x y z U K = (u out t)δ z ( ) 1 2 ρu2 out If E in = E out, then u out = B µ0 ρ = V A (the Alfvén speed). In the corona, V A c s, so the reconnection outflow is strongly supersonic

14 Some context: Note that V A is showing up as a characteristic macroscopic/large-scale speed of the system. It s not just a wave phase speed. Really, E in E out, since a part of E in must go into heating up the diffusion region! We shouldn t ignore E thermal. Note that a larger u in means larger E in, so the total reconnection heating rate scales with u in. Finally, we can put together everything we know to write u in = u outδ (from mass conservation) L = V A(D B /u in ) (from energy conservation & Rm 1 in box) L Multiplying the right side by V A /V A, we can write u 2 in = V 2 A Rm 0 where Rm 0 = V AL D B is the macroscopic/large-scale magnetic Reynolds number. Thus, u in V A δ L 1 Rm0 Unfortunately, this is extremely slow. If Rm , then u in is 10 5 times the local Alfvén speed. In the solar corona, it would take months years to fully process an active region s worth of B via reconnection this way. However, we see in flares that it can all happen in 5 10 minutes! Observations (and more detailed computer simulations) show that real reconnecting systems often find their way to u in V A 0.01 to 0.1 which is sufficiently fast and efficient to account for what we see. The details (how the universe gets around Sweet-Parker constraints ) are still unclear

15 Ideas include: The thin current sheet (diffusion region) can be turbulent, in which small magnetic islands can form & grow along the thin interface region. Chaotic eddies produce extra anomalous diffusion: larger D B smaller effective Rm 0 thicker δ, faster u in Maybe the reconnecting fields come together in a series of X-points rather than all along a parallel line. Petschek proposed a model where not all reconnecting plasma has to go through the diffusion region. Some plasma short-circuits the diffusion region and forms SHOCKS along the inflow/outflow interface. Petschek s u in V A 1 ln(rm 0 ) which isn t as tiny as Sweet-Parker s. If the diffusion region wants to get smaller than the particle Larmor radii, then non-mhd collisionless effects can take over. (Electrons and ions decouple from a common fluid motion.) This is called the Hall effect. Now that we know more about reconnection, we can explore more about the space weather consequences of flares & CMEs

16 1. Coronal reconnection regions have DC E-fields, so some particles can get accelerated to relativistic speeds (energies of order MeV GeV!). The ones that propagate down hit the chromosphere, produce solar flares, and are rapidly decelerated via collisions with atoms/ions. Some of that energy goes into producing X-rays & gamma-rays, some of which can reach the Earth. Dangerous to life & technology! Some of the Solar Energetic Particles (SEPs) can escape, too. In-situ detectors see impulsive SEP events: 2. Once CME flux ropes are ejected, they accelerate to speeds > V A. (Continual injection of nonthermal particles from below helps to heat & accelerate flux rope plasma!) CMEs form shocks ahead of them; high-energy SEPs tend to cross shocks multiple times, and get accelerated at each crossing. These generate gradual SEP events (see above). 3. CMEs also disturb the background solar wind s B(r, θ, φ). Since Earth s field points northward, if a CME produces swings between northward & southward B, the ability to reconnect with Earth s magnetosphere swings around wildly, producing geomagnetic storms