TritonHST99 (Cycle 9) -- collaborator's page

Presentation of errors

October 14 2000

The main question remaining that we need to resolve is the presentation of errors in the spectra. For definiteness, I'll only concider visit 2.

Alan, you've seen most of this before. I'm including the full story here though, so you can read this as a single narrative. Alternatively, you can jump around with these links:
Spectrum presented with only random errors
Finding the target offset
Wavelength dependence of slit throughput
Uncertainty of the wavelength dependence of slit throughput

Spectrum presented with only random errors

The first source of error is the random error, provided by the pipeline reduction.

Notice that: (i) The errors increase as the flux drops at shorter wavelenths, as we expect. (ii) The errors are small: 0.3 to 2.5%.

Looking at this version of the plot, we can start to convince ourselves that we see features.

First, there's a very weak feature at 2710 A, maybe.

Also, there's the suggestion of an edge at 2500 A, marking a transition between a red slope (2500 to 3200 A) and a gray albedo (2200 to 2500 A). Alternatively, the red slope may continue all the way across the 2200-3200 A range, and there is a feature at 2400 A.

Finding the target offset

In order to see if any features or drops are real, we have to make sure they are not artifacts caused by uncertainies in the wavelength dependence of the slit-throughput. (All throughputs here are relative to a centered spectrum).

First, let's remember how we calculate the slit throughput from the target offset (e.g.,the miscentering).

We start by knowing the slit throughput at 2710 A, established by ratioing the albedo derived from the spectrum with the albedo derived from the images. For visit 1, this gives a slit throughput of 0.242 -- the flux from spectra lower, by a factor of ~4, from what they would be if the object were centered.

The next step is to determine what offset will give that slit throughput. We use the calibration spectra taken for proposal 7721. This program took deep, well exposed spectra for the explicit purpose of calculating line spread functions (LSFs).

From the spectra observed for proposal 7721, we extract the LSF for the wavelengths observed by the MAMA images: 2710 A with FWHM of 160 A. This LSF is plotted below.

For a centered spectrum, the LSF is integrated from -0.25 to +0.25 arcsec, for our 0.5 arcsec slit.

However, since our target is miscentered, we calculate the slit throughput by integrating the LSF over a region that is the width of the slit (0.5 arcsec) but that is offset from the center of the spectrum. This is then normalized by the centered integral.

The offset is tweaked until we find the offset that gives us a slit throughput of 0.242. We find that the target was miscentered by 0.281 arcsec.

Of course, the target can be miscentered in either direction. We'll address that later. For now, we'll assume that the offset is in the positive direction (as shown in the figure).

Wavelength dependence of slit throughput

As a review, we know the slit throughput at 2710 A, from the MAMA images. We then calculate the offset using the LSF at 2710 A. Once we calculate the offset, we can calculate the slit throughputs at other wavelengths.

The method of calculating throughput vs offset for other wavelengths is the same as for 2710 A: extract a LSF for the appropriate wavelength range, and integrate over the off-center 0.5-arcsec interval.

If only the LSF had no wavelength dependence, then we'd be done! The slit throughput for visit 1 would be 0.242 for all wavelengths.

But since we know the offset, we know how to calculate the wavelength dependence of the slit throughput:

Are we done? Unfortunately not.

Uncertainty of the wavelength dependence of slit throughput

As you've doubtless noticed, we've been looking at offests in the spatial direction (e.g., the cross dispersed direction).

But our target is miscentered side-to-side in the slit (e.g., in the dispersion direction).

If only the PSF were radially symmetric, we'd be done. Our calculations (with spatial offsets) would exactly mimic the behavior of the miscentered target.

How can we see if the PSF is symmetric? Tiny Tim is not accurate for STIS. Images rarely go deep enough to get the wings we need, and are not available at the wavelengths we want.

One way to check the symmetry of the PSF is to recalculate the wavelength dependence of the slit throughput, assuming a negative offset. If we do this, we clearly see that the wavelength dependence of the slit throughtput does depend on the direction of offset, especially near 2500 A.

What's the effect of this on the spectra?

Let's replot albedo vs. wavelength for Visit 2, first repeating the very first plot, and then assuming three different wavelength dependences.

The dotted line uses the throughput that assumes a negative offset, the dashed line uses the throughout that assumes a positive offset, and the middle line uses the mean of the two throughputs.

Look! The feature at 2700 A is probably an artifact of the slit throughput. But, the overall red color is robust, as is the 2500 A drop (or is it a 2300 A feature?).