Keck HIRES Temperature Data: Wavelength Dependence (as of October 1999)

Abstract:
The temperature effects on the HIRES wavelength scale is discussed. The conclusion is that the temperature variations for all practical purposes will almost certainly have a negligible affect on the wavelength scale for any conceivable experiment.

Air-to-Vacuum Conversion:

The air-to-vacuum conversion in the makee program is correct for 15 degrees Celsius and 76 cm Hg pressure. These values are used since the Thorium wavelengths in the data file "ThAr.dat" are valid for 15 degrees, 76 cm. The air-to-vacuum conversion is used to convert the Thorium lines in the data file back into vacuum wavelengths.

As long as vacuum positions are used for the Thorium lines, then the vacuum wavelength scales are correct regardless of the local air pressure and temperature since the arc lamp and object light are affected in the same manner. This assumes that the temperature remains constant between the time the arc lamp is taken and the object.

```Programming note: I actually use the 15deg/76cm Thorium line positions for the wavelength fit and then correct back to vacuum from 15deg/76cm on the final (object) wavelength scale. The reason I do this is because most Thorium plots are given in 15deg/76cm wavelengths, so it is convenient to have the arc lamp spectra in 15deg/76cm wavelengths. Also note that the sky spectra (Sky-###.fits) have wavelengths in air (15deg/76cm). The object spectrum (Flux-###.fits, Err-###.fits) wavelengths are in vacuum and also have a heliocentric correction. ```

Temperature Effects on the Index of Refraction:

The index of refraction of air at 0 degrees Celsius and 76 cm Hg is given by the CRC handbook as approximately:

```   n = 2875.66 +(13.412/(w*w*1.0d-8)) +(0.3777/(w*w*w*w*1.0d-16))

where "w" is the wavelength in Angstroms.
```
at 15 degrees Celsius this becomes:
```   n = 2726.43 +(12.288/(w*w*1.0d-8)) +(0.3555/(w*w*w*w*1.0d-16))
```

The wavelength difference between light which is at 3500 and 6500 Angstroms in vacuum, is actually 2999.162 at 0deg/76cm and 2999.205 at 15deg/76cm. The difference between the two cases is 0.043 Angstroms (or about 2.6 km/s at 5000 Angstroms or about 1.2 pixels (unbinned).)

Assuming that this difference is comparable (probably smaller?) at the lower air pressure of 14,000 feet elevation, this means that an Arc lamp taken at 15 degrees is used to calibrate an object taken at 0 degrees, there will be an approximately 1 pixel error in the wavelength spread between 3500 and 6500 Angstroms.

Note that the absolute scale is usually shifted to sky lines taken with the object, and so the absolute scale is not affected, but the relative scale will be wrong.

Absolute Wavelength Shift vs. Temperature:

The vacuum wavelengths of 3500.0 and 6500.0 will appear at 3498.9464 and 6498.1088 at 0deg/76cm, 3499.0023 and 6498.2076 at 15deg/76cm, and 3499.0526 and 6498.2969 at 30deg/76cm.

If the temperature varies by 2 degrees (see below), then an absolute shift of about 0.01 Angstroms (about 0.2 pixels (unbinned)) may occur due to this temperature variation. However, slight shifts in the echelle grating angle may cause a pixel or more shift in the wavelengths and will usually dominant any possible temperature shift. Also note that if you use an arclamp exposure taken next to the object to set the absolute scale or (better yet) use the night sky lines in the background of the object exposure to set the absolute scale, then temperature effects will certainly be negligible for the absolute wavelength scale.

Temperature Variations Inside HIRES:

To determine the temperature variations inside HIRES, I have made a plot of a few temperatures given by the FITS header from images taken over several observing runs in 1998. Here is a plot of the temperatures versus day of year: kht1.ps . Here is a plot of the temperatures during an October 1998 observing run versus Hawaii Standard Time: kht-oct98.ps . And in December 1998: kht-dec98.ps . And here is all the raw data: kht.data.txt .

Note that the inside temperature can vary by more than 1 degree during the night and more than 2 degrees during an observing run. A very rough linear approximation of the calculations above suggest that a 0.1 to 0.2 pixel error in the relative wavelength scale (across 3000 Angstroms) can occur if an arc lamp is used for wavelength scale fitting which is not taken near the time of the object exposure.