Modeling Solar Eruptions

The  big  ques+ons  about  solar  erup+ons:   • How  is  energy  built  up  and  stored? • How  is  energy  released  so  quickly? • How  are  par+cles  accelerated?   • How  do  they  propagate  into  the  heliosphere   and  affect  humans  and  technology?   Can  numerical  simula+ons  answer  these   ques+ons?  Of  course!   Outline   • CME/erup+ve  flare  basics   • Overview  of  breakout  model   • Global  evolu+on     • Breakout  current  sheet  forma+on  and  evolu+on   • Flare  current  sheet  forma+on  and  evolu+on   • Energe+cs  –  implica+ons  for  erup+on  mechanism   • Conclusions   Sources  of  Solar  Erup+ons   SDO/AIA (1600Å) – line of sight along Earth-Sun line T < 100,000K Solar  Erup*ons  =  Flares  +  CMEs   STEREO  A  304A  and  coronagraph–  line  of  sight  perpendicular  to   Earth-­‐Sun  line,  bright  =  dense   How  can  we  understand  the   underlying  physics?   • Propose  a  theory  that  meets  the  requirements   set  by  observa+ons  and  physical  laws   • Test  this  theory  by  modeling  simplest  possible   system  with  essen+al  proper+es   • Compare  simula+on  results  with  theore+cal   predic+ons  and  observa+ons:  CME  speeds,   energe+cs,  +mings,  magnitude,  etc.     • Test  robustness:  successful  explana+on  of   progressively  more  complex/realis+c  systems?     Updated  “Standard” CME-­‐Flare  Cartoon   Observed  to  date   • • • • • • • • Coronal  mass  ejec+on  (CME)   Current  sheet  (UVCS)     Electron  beams  (HXR,  µιχροwave,   Type  III  emissions)   Reconnec+on  inflows  &  ou^lows   Fast  shock  above  post-­‐erup+on   loops  (standing  Type  II,  superhot   HXRs)?   Flare  ribbons  (Hα,  etc.)   Post-­‐erup+on  loops  (newly   formed,  filling,  and  cooling)   plasmoids  in  current  sheet   Key  Point:    Need  physical  insight  to  develop  theories  before  tes+ng   by  numerical  modeling  and  comparison  with  observa+ons   Fundamental  Ques+ons   § What  is  the  pre-­‐erup+on  magne+c  configura+on?   • filament  channel:  sheared  arcade  or  twisted  flux  rope   § How  is  free  energy  injected  and  stored?   • photospheric  mo+ons:  shearing,  emergence     § How  is  energy  suddenly  released?   • magne+c  reconnec+on  or  ideal  instability  or  …     • How  is  this  energy  par++oned  and  transported  to   yield  observable  signatures?     Solar  Erup*ons  =  Volcanoes?   • Energy  storage:  increasing  pressure  (rising  magma)   held  back  by  overlying  magne+c  field  (rock  cap)   • Energy  release  can  be  gradual  or  sudden   • Intense  erup+ons  can  drive  shock  waves   But,  volcanoes  are  not  magne+cally  driven  or  released   Breakout  Model  for  Fast  CME  Ini+a+on   (b)Three  Simple  Requirements:   (c) (a) 4 1 2 3 null point § Mul+polar  topology       breakout CS § Sheared   filament   channel   (forma+on  mechanism   unimportant)   sheared § Scale-­‐dependent   resis+vity     prominence field   fla b Breakout  Model  Overview   (b) (a) 4 1 2 (c) breakout CS null point 3 sheared prominence field flare CS breakout CS • Ini+al  field  from  two  dipoles  –  axisymmetric  4  flux  system • Slow  footpoint  mo+ons  create  sheared  filament  channel • Outward  expansion  drives  breakout  current  sheet  forma8on  at the  null,  followed  by  reconnec8on  (flux  transfer)   • Expanding  sheared  core  field  creates  thinning  flare  current  sheet     • Flare  reconnec8on  in  lower  current  sheet  forms  CME  flux  rope   • Fast  CME  is  launched,  post-­‐flare  arcade  builds  up   Approach   2.5D  numerical  experiments  with  ARMS  in  spherical   geometry.   • Adap+vely  refined   • Refinement  criteria:    gradient  in  one  or  more  J   components  exceeds  specified  value,  in  specified  |B|   range   • Outer  boundary  at  125  Rsun   • Filament  channel  formed  by  slow  an+parallel   photospheric  mo+ons  around  equatorial  PIL     • Null  finder  subrou+ne  iden+fies  and  tracks  nulls  (X   and  O  points),  and  assesses  their  robustness   ARMS   ∂ρ + ∇ • ρv = 0 ∂t 1 ∂ρ v + ∇ • ρ vv = −∇P + (∇ × B ) × B + ρ g 4π ∂t ∂T + ∇ • Tv = ( 2 − γ ) T ∇ • v ∂t ∂B − ∇ × ( v × B) = 0 ∂t All of the symbols have their standard meanings: ρ is the mass density, v the velocity, • Finite  volume,  Flux  Corrected  Transport-­‐based  solver     P the thermal pressure, T the temperature, B the magnetic induction, and t the time. We • Fixed   and  dynamically   adap+ve   grids    (PARAMESH)   assumed• a fully ionized hydrogen plasmacriteria   whosedratio of b specific Refinement/derefinement   efined   y  user  heats γ = 5/3 and used • gravitational Ini+al  condi+ons:   the solar acceleration g = −GMsr/r3, where Ms is the solar mass, G the –  current-­‐free   mul+polar   field,   hydrosta+c   spherical   universal gravitational constant, and r the position vector.atmosphere,   The temperature equation • simple Boundary   Condi+ons:   describes adiabatic heating or cooling of the plasma as it compresses or expands, – radial:  line-­‐+ed,  no-­‐flow-­‐through,  with  specified  photospheric  shear   respectively. There are necessary, stabilizing numerical diffusion terms implicit in all of – open  condi+ons  at  all  other  boundaries   these equations; those in the induction equation permit magnetic reconnection to occur at Why  AMR  is  Important   Currents and grid at 102500 s: block boundaries shown in global view at left; cell boundaries shown in closeup below Numerical resistivity is scale dependent: smaller cells higher Rm