## Overall

We have data from the Keck telescope of quasar PHL957. There has been interest in using the spacing of quasar absorption lines to determine if the fine-structure constant had a different value in the past. Extremely precise spectral data is required to detect possible changes.

The data we have includes many exposures of the quasar with an iodine cell in the line of sight. The iodine cell imposes a dense forest of absorption lines across all of the data. The iodine lines are known to a very high precision.

The basic idea is that we might be able to wavelength calibrate the quasar data to a greater precision than other calibration methods (namely Thorium-Argon lines).

## Initial data

There were two rounds of data taken.

The first on 2002-November-01.

The second round of data was taken across 3 days: 2004-October-0[3,4,5].

There were 13 half-hour runs taken across the 3 days. 6 of these runs had the iodine cell in place. Table of runs.

Species that we'll use to look for a variable fine structure constant:

Mg I, Mg II, Al II, Al III, Si II, Cr II, Fe II, Ni II, and Zn II

### Iodine Lines

This is the raw data of the absorption lines from an iodine cell. You are seeing data from laboratory measurements. The dense lines are closely spaced absorption lines.

I fit a continuum to the Marcy Iodine lines by average the three largest flux values (and their corresponding wavelengths) to get a single number for every 300 data points (about 1 angstrom).

I then fit a spline through these averaged points and evaluated the spline at each Marcy Iodine data point. This became the continuum for this data set.

An IDL cubic spline was fit through these points — the spline was then used as the continuum.

To normalize this data, the flux values were divided by the continuum.

I then divided the flux of the data points by the continuum that I fit to get:

I then inverted the normalized Iodine lines and subtracted so that a data point that lies directly on the continuum line would add no signal to anything being considered, while a clear absorption line would give a clear signal.

### Keck Data

This is the data of quasar PHL957 from 2004 (new chip) taken by the Keck telescope.

First, look at what an exposure looks like without the iodine cell:

With the iodine cell in place, the dense iodine absorption lines (that we saw in the above section) are imposed on top of the Keck data across the entire order.

Fitting the nickel absorption lines and a continuum across the entire order looks like the following:

What looks like an increase in noise is mostly real signal from the iodine cell.

Now a zoomed in section to give a better idea of what this looks like:

First, a zoom in without the Iodine cell in place:

And now, a zoom in with the Iodine cell in place:

I then divide out the data by the continuum. (The errors are the original errors divided by the continuum as well).

Again to show how much signal we get from the iodine lines, I first show an exposure that doesn't have the iodine cell in it:

With the iodine cell in place:

I next subtract the fit parameter from the data points and then divided by continuum.

What this process looks like without the iodine cell in place:

What this looks like with the iodine cell in place:

This last step essentially leaves me with only the signal from the iodine lines (in the form of deviation from some somewhat arbitrary zero-line).

One has to be careful if there are saturated lines in a specific order, although that's not a concern for this particular order.

### Wavelength Calibrating the Keck Data

Now, to compare this to the Iodine lines from the Keck Telescope several things had to happen.

First, to get the shapes to line up, I had to invert the end result of the Keck data. Next, I had to make sure that they are lined up in a possibly sensible manner. So, I had to make sure that the total offset was equivalent, and the total area under the curves were the same.

Here is a copy of essentially what I do: Convolution

Now, since the Iodine lines have way more resolution, we have to convolve the iodine lines with the resolution of the Keck telescope so that we could look for what the Keck telescope would see when it looked at iodine lines.

We convolve the iodine lines with a Gaussian evaluated at the wavelength of the Keck data points.

We then take the difference between the Keck line and the convolved iodine line and square the difference, and divide by the error on the Keck data point squared (the Iodine errors are negligible).

I then shift the raw iodine lines by a small amount, and reconvolve and re-difference/square it.

I print all this calculation to an ascii file where I deal with analysis at a later point.

I read in the calculated file, and I add up the value of the chi square for each data point, and for a specific bin, I take a look at when, for a given shift, the chi squared is a minimum.

So, for the minimum chi squared for a given bin size across those data points, we know how much to shift the iodine lines to line up the best with the Iodine lines imprinted on the Keck data — which, if the Iodine lines are correct, really tells us how much to shift the Keck lines.

I did several attempts at changing the continuum to see how sensitive my wavelength calibration is to continuum fitting parameters.

I found that the wavelength correction was consistent for all even remotely plausible continuum.

So here is a picture of some various continuums I tried:

And here are the various wavelength calibrations for each of these continuums:

As you can see, the corrections are extremely robust for widely differing continuums.

To give you an idea of what the convolution process looks like, watch this looping video of essentially what goes on.

The following image shows the calculated convolution for each shift in the iodine lines laid on top of the stationary Keck data.

Notice that the convolved data points can only move vertically because the iodine convolution is calculated for the x-values of the Keck data.

If you watch the red peak just to the right of 5320.5, you can see how the convolution evolves as an iodine line moves from one side of a particular Keck data point, to the other.

The best fit is at around a shift of 0.06025 angstroms.

This means that the convolved iodine lines fit what was seen through the telescope the best when 0.06025 angstroms was added (before being convolved) to the wavelength values of the laboratory iodine lines.

Assuming that the laboratory iodine lines are known to a way higher degree of precision than the telescope data, then to correctly calibrate the Keck data, we would have to subtract 0.06025 angstroms from the Keck telescope wavelength values in this portion of the order.

After all this work is done, here are the Results.