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Solar Physics Course Lecture Art Poland - PowerPoint PPT Presentation

Solar Physics Course Lecture Art Poland. Modeling MHD equations And Spectroscopy. Why. What I am going to talk about should lead to our understanding of physical processes in outer solar atmosphere: Heating Energy transport Solar wind acceleration Magnetic field evolution. Overview.

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Solar Physics CourseLectureArt Poland

Modeling MHD equations

And

Spectroscopy

• What I am going to talk about should lead to our understanding of physical processes in outer solar atmosphere:

• Heating

• Energy transport

• Solar wind acceleration

• Magnetic field evolution

• Modeling features in the solar atmosphere involves solving the full MHD equations.

• The solution of these equations needs initial conditions and boundary conditions.

• To get realistic values, you need observations.

• In this lecture I will first talk about how to get the observations, and then how they are used in the solution of the equations.

Open magnetic field

What Features

• The equations tell us we need to observe

• Temperature

• Density

• Velocity

• Magnetic field

• To do time dependence we need each as a function of time.

• How can we measure these quantities at the Sun?

• Spectroscopic observations

• What causes an absorbtion line? How is one formed?

• Why are some lines in emission?

• Equations derived from observations in the lab. of atomic spectra.

• Quantum mechanics gives more precise description.

• What I am showing helps visualize the structure.

• When there are multiple electrons in an atom, the n levels are split.

• The split levels are referred to as s,p,d,f,

• For n=1 there are only s levels

• For n=2 there are s and p levels

• For n=3 there are s,p,and d levels

• etc

• The other quantity is electron spin.

• He for example has 2 electrons, both can occupy the n=1 level because one has a spin of +1/2 and the other a spin of -1/2

• Transitions between spin level have a very low probability, and are referred to as forbidden transitions.

• When they are opposite to each other they are referred to as singlets

• When they are the same, triplets

• Spin combined with momentum can also give doublets.

• Allowed transitions

• Forbidden transitions

• Magnetic fields can split sub-levels (ie 22s into 2 levels).

• Atomic structure - Spectral lines

• Electron transitions

• N levels

• Momentum s,p,d,f

• Spin

• Momentum and spin splitting occurs in magnetic field – can use splitting to measure strength of field.

• Velocity?

• Doppler shift

• Sometimes just an asymmetry in profile

• What else?

• Temperature – next topic

• Density – next topic

• 1) The basic observed equation is P=NkT, N=ρ/uMH

• a. This is important: if you know two, you know the third.

• b. Can make observations that yield T, and ρ so you can get P.

• 2) Temperature and mean velocity – visualization again

• a. Perfect box with perfect collisions: collision momentum with wall is 2mvx

• b. Number of collisions vx/2L L is size of box

• c. Total of all momentum is ΣΜvx2/L

• d. Momentum is pressure so P=ML-3Σvx2

• e. Define mean vx2=n-1Σvx2

• f. vx2=vy2=vz2=1/3v2

• g. P=n/3L3(Mv2)=1/3(NMv2)

• h. So average energy ½ Mv2=3/2 kT This is important because it relates energy, velocity, to temperature. (not bulk velocity)

• Velocity of atoms and electrons related to T was just shown.

• What do we need to get the temperature of the gas? First assumption?

• Assume a Maxwellian velocity distribution

• What must be assumed for this to be valid?

• Collisions (not so good at very low r)

• f(v,T)= (M/2πkT)3/2v2e-(Mv2/2kT)

• Maxwellian tail of distribution

• Where to measure for T?

• Can get T from line width.

• a. Ni/N=gi/ue-ε/kT ε=hν

• b. Can use the ratio for 2 energy levels to get relative populations between two energy levels.

• c. Measure two lines from same atom to get T

• d. Ni/Nj=gi/gje-δε/kT

• a. equation of ionization state:

• Ni/Nj(Ne)=(2πmkT)3/2/h3(2(ui(T)/uj(T))e-ε/kT

• b. Used to determine gas temperature

FeIII FeIV

N

T

• I is the intensity you observe

• S is emission/cm3

• t is optical depth n is frequency

• How do you get an absorption line from this?

• How do you get an emission line?

• Non-LTE

• A or f values

• Line brightness

• Collision prob.

• Plank function

• Differential emission measure

n

Log Ne2

• Spectra can give us:

• T via line width, line ratios

• Density via line ratios or diff. emission measure

• Velocity via line shift

+H-C

• Depends on the problem

• Near the Sun small area, cartesian

• Whole Sun or Heliosphere, spherical

• Coupled differential equations.

• The big problem is steep gradients.

• The boundary conditions you choose almost always dictate the solution.

• The output of these programs are table of numbers, T(x,y,z,t), P(x,y,z,t),etc.

• Need to visualize the results

• Need to make visualizations something that you can compare with observations.

Variable Grid MeshMajor Breakthrough

• Paramesh

• Steep T gradient in transition region.

• Almost no gradient in corona.

Gridding Changes as Calculation progresses

• Conduction

• Isotropic

• Anisotropic –along B field

• Optically thin - collisions

• Heating

• Constant

• Alfven waves – a function of B

• Make each of these a replaceable module in your program.

• Conduction only along B field

• How the grid is oriented with respect to B

Excess heating low down

Numerical diffusion makes it wider.

All profiles from same T different v