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Solar Physics Course Lecture Art PolandPowerPoint Presentation

Solar Physics Course Lecture Art Poland

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Presentation Transcript

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

- 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.

What Quantities Do We Need?

- 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.

Questions

- 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?

Comments

- Equations derived from observations in the lab. of atomic spectra.
- Quantum mechanics gives more precise description.
- What I am showing helps visualize the structure.

Level Splitting, Momentum

- 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

Spin

- 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.

Sample Energy Diagram

- Allowed transitions
- Forbidden transitions
- Magnetic fields can split sub-levels (ie 22s into 2 levels).

Summary

- 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.

How to Use Spectra

- Velocity?
- Doppler shift
- Sometimes just an asymmetry in profile

- What else?
- Temperature – next topic
- Density – next topic

Gas State

- 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)

Get The T

- 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

Line Profile Emission

- Where to measure for T?
- Can get T from line width.

Boltzmann Distribution

- 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

Saha Equation

- 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

How to Get Lines

- 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?

Other issues

- Non-LTE
- A or f values
- Line brightness
- Collision prob.

- Plank function
- Differential emission measure

n

Log Ne2

Summary

- Spectra can give us:
- T via line width, line ratios
- Density via line ratios or diff. emission measure
- Velocity via line shift

MHD Equations

+H-C

- Force Balance or
- Conservation of Momentum

How to Solve

- Depends on the problem
- Near the Sun small area, cartesian
- Whole Sun or Heliosphere, spherical

- Coupled differential equations.
- The big problem is steep gradients.
- Transition region (T gradient)
- Flares (P gradients, shocks)

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

Results

- 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

Other Issues

- Conduction
- Isotropic
- Anisotropic –along B field

- Radiative losses
- Optically thin - collisions
- Non-LTE T(collision) T(radiation)

- Heating
- Constant
- Alfven waves – a function of B

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

Conduction

- Conduction only along B field
- How the grid is oriented with respect to B

Excess heating low down

Numerical diffusion makes it wider.

Model Output

All profiles from same T different v

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