1. Line Profiles of Magnetically Confined Winds Stephanie Tonnesen

2. The Numerical Method The original r, ,  coordinates are aligned with the magnetic coordinate system. The z-axis is aligned with the magnetic poles In order to make my program more universally applicable I have allowed for the observer’s coordinate system to be tilted with respect to the magnetic coordinate system. In order to find the line of sight velocities necessary for the observer I need to do a coordinate transformation. v los =- (v x-mag )*sin(tilt) +(v z-mag )*cos(tilt) I sum the emission of gridpoints that correspond to v los values that go into the same bin. The bins are all the same range of velocity values. This histogram is my line profile. The emission is found by multiplying the volume of each element around my gridpoint by the emissivity constant by the density at the gridpoint squared. This causes the potential for noise in my line profile because normally at every point in the wind there would be a different emissivity. The finer my grid, the better the resolution in my line profile. My volume element size is very dependent on the number of both r and  zones: vol(i) =((r edge (i)+r step ) 3 - (r edge (i)) 3 )*(cos(t edge (i))-cos(t edge (i)+t step ))*(p edge (i)+p step -p edge (i))/3 Where the edge variables are the values that mark the “sides” of my volume elements, and the step variables are the size of the step between consecutive variables.

3. Smoothing Another change to the program that I made to smooth the profile had to do with seperating the emission into different velocity bins. A velocity was assigned to a bin no matter where it fell in the range, and all the emission from that gridvolume was added into that bin. This caused jagged peaks in my line profiles that were only the result of a small difference in the number of emission volumes put into each particular bin. The new method splits each velocity into the bin that it is in and the bin it is closest to. This is done by finding how close the velocity is to the center velocity of the two bins and splitting the emissivity into the two bins by the same fraction. You can see the results to the right.

4. There are other effects that cause noise, namely the number of gridpoints. Until you use about 70 r gridpoints, there is a stair-step appearance to the profile that is reminiscent to a stack of the rectangles you get when looking at a single shell. The number of phi points has a large affect on the smoothness of the top of the profile, and you need about 60 phi points to get a smooth top.

5. Fitting the General Model The first task was to make sure that my program was able to match the analytic solution I had previously found for a spherically symmetric wind model. Note that the inner line is always the numerical solution.

6. Occultation Next I added occultation to make sure that as expected, it would only cause asymmetry in the profile.

7. Flared Equatorial Disk The MCWS model on which my line profiles will be based shows that the x-ray producing shocks occur around the magnetic equator, so I will cut off the emissivity around the poles. So the emission from the star only comes from an equatorial disk.

8. I can rotate my viewing axis to look at this radially flowing wind from different angles. This will give me different line profiles, both from what emission exists at what doppler shifts, and because different amounts of emitting wind will be occulted. 0º (pole-on) 45º 90º Along magnetic equator

9. Future Work Currently I am working on adding a phi velocity component, and I will try and get more realistic equations to describe what may be happening in the phi component. Later I will add a theta velocity component. I will then postprocess Asif’s simulations. Finally, I will add absorption into my program.