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 Post subject: Line Bisector Analysis
PostPosted: 01. September 2018, 13:59:01 PM 

Joined: 06. October 2016, 15:04:43 PM
Posts: 204

here is an update on what we have done in the last weeks.
We are working current on the idea to do some line bisector analysis.

The aim is to determine at which line and thus which energy and thus which depth the wind starts and whether one can see a development over other lines (atmospheric depths). To this end, we want to search for correlations to pulsation and thus global rv. And finally, examine whether the winds or the special emission phenomenon starts first. This allows conclusions to be drawn about the origin, both spatially and physically.

First we started to write an ESO-MIDAS based tool. This is also still work in progress, but we have already something to show.
In this script first one have to choose the desired line by entering the wavelength. A graph with ± 20 Angstrom around the choosen line will be plotted. Following the line have to be cutted out and a gaussian fit to be done to determine the global rv.

Then the line is plotted and the pixels marked. One can now perform a rebinning in case that the real binning contain not enough data points. After that the script asked for the start value of relative intensity and the step on the intensity-axis for bisecting the line. Now one have to enter the number of bisector-points and the desired polynomial degree for performing the fitting of both line sides.
At least one is asked to enter the start and end pixelnumber of the spectral line.

Out of this information the bisector is calculated of [(blue_side + red_side) / 2] and plotted. The global rv is set as reference for determine the velocitys. At the end there are two more inquirys if one want to plot the visualisation of the quality of the fits. And if one want to plot the bisector in velocity space.

The results are also stored in table-format.

We have to thank Otmar Stahl and Günter Gebhard for advices and help!

But as said there are some things to do, like performing an error estimation and to clear the script up… .

One example of the Fe I 6412 line in rho Cas:

Here the line with bisector
line_bisec.gif [ 6.39 KiB | Viewed 725 times ]
The plot of the performed fits
fit_quality.gif [ 5.21 KiB | Viewed 725 times ]
Bisector in rv space
rv_space.gif [ 4.53 KiB | Viewed 725 times ]


PostPosted: 11. September 2018, 09:39:47 AM 

Joined: 06. October 2016, 15:04:43 PM
Posts: 204
Hello everyone,

now we have implemented an error estimation based on Gray, 2005. It is based on the photometric error and takes into account, that we have two measuring points (blue and red side of the line) and the slope at each flux-level:

Error in km/s = (1/sqrt(2)) * ((1/SNR) / (delta_Flux / delta_lambda_in_km/s)

Delta_lambda we calculated as mean of both sides. Because of the slope of the profile the error is in the line core and at the wings greater than in the middle. Because of the low resolution of about R 12000 and also SNR of about 200 the error is relative large. In literature one can find that are resolutions of about 100.000 and high SNR is used for investigations.

Here is an example of the Si II 6347 line:

Sequence Relative_Flu Wavelength_A rv_km_s error_m_s Line_Positio
-------- ------------ ------------ ------------ ------------ ------------
1 6.00000e-01 6.34598e+03 4.71491e-01 8.29077e+02 6.34597e+03
2 6.20000e-01 6.34597e+03 -5.90517e-02 6.81027e+02 *
3 6.40000e-01 6.34596e+03 -2.89722e-01 5.50395e+02 *
4 6.60000e-01 6.34596e+03 -3.81990e-01 4.51116e+02 *
5 6.80000e-01 6.34596e+03 -2.89722e-01 3.64027e+02 *
6 7.00000e-01 6.34597e+03 -1.05186e-01 3.08291e+02 *
7 7.20000e-01 6.34597e+03 1.25485e-01 2.63005e+02 *
8 7.40000e-01 6.34598e+03 4.02289e-01 2.54297e+02 *
9 7.60000e-01 6.34598e+03 6.32960e-01 2.64747e+02 *
10 7.80000e-01 6.34599e+03 7.25228e-01 2.96099e+02 *
11 8.00000e-01 6.34599e+03 7.71362e-01 3.41385e+02 *
12 8.20000e-01 6.34598e+03 5.86826e-01 4.24989e+02 *
13 8.40000e-01 6.34597e+03 1.48552e-01 5.20785e+02 *
14 8.60000e-01 6.34596e+03 -5.20393e-01 6.46192e+02 *
15 8.80000e-01 6.34594e+03 -1.55841e+00 7.82050e+02 *
16 9.00000e-01 6.34591e+03 -2.94243e+00 9.57967e+02 *
17 9.20000e-01 6.34587e+03 -4.78780e+00 1.14259e+03 *
-------- ------------ ------------ ------------ ------------ ------------

We have to consider a second Problem. That is the instrument profile. The setup itself can also introduce a deformation of the bisector.

To get an idea of the bisector of the instrument profile we took the averaged calibration lamp profile from before_science and after_science and converted it into an absorption line so that the script could handle it. We then measured this. The result is a deformation that is a little less than the flux noise error.

Here the neon 6402 line:
cal_6402.gif [ 6.64 KiB | Viewed 557 times ]
And the bisector of the 6402 line:
rv_space_6402.gif [ 4.59 KiB | Viewed 557 times ]
Then we had considered that the telluric lines could be useful once again. Here we have at most deformations in the range of 10 m/s caused by winds and these deformations are also in the star lines. The advantage should be that these lines went the same way with the same integration time as the star lines through the setup.
So we measured the H2O 6532 and the profile looks very similar to the neon profile:
rv_space_6532.gif [ 4.47 KiB | Viewed 557 times ]

The comparison between the Ca I 6450 line on the left and the H2O line on the right:
6450_comp_6532.gif [ 5.3 KiB | Viewed 557 times ]

So it seems that we can achieve accuracies which are based rather on the photometric error.


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