Last summer and fall I participated in the “BRITE Stars in Cygnus” campaign monitoring the radial pulsations of Deneb’s atmosphere. This involved measuring radial velocities by determining the wavelength shifts of the Si II λλ 6347 & 6371 lines, where expected velocity differences might be 10 km/sec or less. After measuring a number of nights’ data it appears I’ve achieved less than “stellar” results. On most nights the standard deviation in my data was around 2 to 3 km/sec where my goal was for a precision of 1 km/sec or better. So I began to wonder about the wavelength stability of the LHiRes III and read a couple of posts from other observers who shared the same concern. So I decided to conduct a few tests. This article presents the results of a couple of those tests.
The first test was very simple. I took a series of calibration lamp exposures over the course of about an hour. The spectrograph was on the telescope and the telescope pointed at the pole with the drive turned off. That is, the telescope was not moving. I turned on the lamp and took an image about every two minutes. I then measured the mean shift of the three Neon lines visible in the wavelength range (Ne 6532, 6598, & 6678) recorded using an ST8 camera and the 2400 lines/mm grating, resulting in a measured dispersion of about 0.11A per pixel. Using the IRAF task “reidentify” I measured the shift from the first image and created the plot shown in Figure #1.
Figure 1: The measured shifts of calibration lines from frames taken while the telescope was “parked” – standing still, and not touching the spectrograph.
Note that, except for the very beginning, the shift in positions for the Neon lines was fairly constant wrt time. I show two linear least-squares fits – one for the entire data set and one “cherry picking” the final 3000 seconds or so. Basically the only thing this should be showing is the effects of changing temperature since nothing else was moved, other than to switch on the lamp at the beginning of the test. The telescope had been parked for over a day at the time of the test. Since the test was taken in the late afternoon the temperatures were falling – around 2 degrees C over the course of the test. The cause of the rapid drop in the roughly six-minute span near the beginning of the sequence is a mystery.
Test #1 should give an idea of “best case scenario”. The telescope was standing still and the spectrograph was not touched throughout the duration of the test. When I’m gathering actual “science” data I always take calibration images before and after each spectrum, or around every 30 minutes in cases where I have a bright target for which I take several images within that time. Using two calibration images the wavelength solutions for surrounding calibrations are interpolated over time to match the time of mid exposure of the science image. Of course that means I need to switch the lamp on, rotate the source onto the slit, take the calibration image, rotate the source back away from the slit and turn the lamp off for each calibration image, all of which involves manipulating items which are parts of the spectrograph. Furthermore, the telescope is moving from east to west causing the direction of pull due to gravity to change throughout the sequence. So a second, more “real world” test was conducted monitoring a star with a well-determined radial velocity (HD 82885 = 11 LMi) over the course of four hours comprising a total of 11 images.
The second plot shows heliocentric-corrected measurements of radial velocity using the H-alpha line in the spectrum of HD82885. In this case the standard deviation of the measurements was 1.13 km/second. Which, to be honest, I found quite surprising. I took an additional step and used the telluric correction task in ISIS to determine the precision of the wavelength solutions and found a standard deviation of 0.04 Angstroms with a mean of essentially zero. Obviously my skill at trying to “eyeball” match the telluric lines was not all that good on an individual basis, but on average they confirmed the wavelength solutions as being generally good.
So, again, I find this result very encouraging. During the sequence of spectra the star passed across the meridian. The sequence began at hour angle -2.6 hours and finished at hour angle +1.5 hours, so a little over four hours. That means the stresses due to gravity on the spectrograph and camera changed a lot throughout the sequence. Note how the slope of the measurement curve changes at meridian crossing, hinting at slightly non-linear changes wrt hour angle likely due to gravity.
The one thing that is quite puzzling, however, was that my mean radial velocity determined from the experiment was 17.5 +/- 1.1 km/second – the published radial velocity for HD82885 is 14.4km/second. So my measurement is about 3.1 km/sec (or nearly three sigma) from the star’s known radial velocity. On the other hand, using Telluric lines in ISIS seems to agree with my wavelength solutions since, on average (despite a larger scatter in the measurements) the mean difference was zero (actually about 6e-10 Angstroms – WAY down in the noise). I have no idea what the source of the 3.1 km/sec difference is. I used 6562.801 Angstroms for the in-air wavelength of H-alpha. And I’m almost certain I measured the correct star; 11 LMi is the only 5th magnitudes star in the near vicinity and the spectra I measured match those of the star’s published G8+V spectral type.
Figure 2: Radial velocity measurements based on a four-hour sequence of 11 spectra of HD82885, a star whose radial velocity is well-known to be 14.4 km/sec. My result of 17.5 km/sec, while consistent, is consistently off by an average of 3.1 km/sec.
As a final check I used the cross-correlation task in ISIS to measure the differences of each reduced spectrum against the first spectrum. In each case ISIS reported shifts wrt the first spectrum which agreed with those I’d determined by simply measuring the position (in IRAF) of the H-alpha line.
So, in summation – it appears the LHiRes, at least for the duration of these two experiments, behaved rather well. Really surprisingly well given my previous attempts at radial velocity measurements. However, despite the standard deviation of the 11 measurements I made being just slightly above 1 km/sec, the mean ws off by 3.1 km/sec
Harboring a bit of doubt about the result, above, I re-ran the experiment on the night of 2015 January 15/16. This time I only acquired 7 spectra of HD82885, but they were all a bit better S/N as I took 1800 second exposures each, as opposed to 1200 seconds for the December data. The results were even, to me, simultaneously more astonishing and perplexing. I basically found the same radial velocity, this time Vr=17.18 +/- 0.39 km/sec. So while the mean radial velocity was not significantly different the standard deviation of the measurements was even better. Note that, in both cases, I had to actually hold the knob that rotates the Neon lamp onto the slit each time. It was fairly cold outside (around -7C) and the wires inside the spectrograph that attach to the Neon source were stiff and would, if I did not hold it, cause the Neon lamp to spring back out of the light path. So I actually had to hold on to the knob during the short (2-second) calibration exposures. Figure 3 illustrates the result.
Figure 3: Result from re-running the radial velocity test illustrated in Figure 2. Within the error margins the mean radial velocity found here is the same as for the previous test, but the standard deviation is even better.
Based on these two experiments (hardly an exhaustive sample):
- I seem to have a systematic offset of around 0.065 Angstroms, resulting in a roughly +3 km/sec error (or a bit more than 1/2 a pixel for my setup) in the region of 6600 Angstroms. I’m not sure if that arises from instrumental issues or from my method of measuring the H-alpha absorption line in my spectra. All measurements were done using the IRAF “splot” task. For H-alpha in air I used 6562.801 Angstroms, and c=299700 km/sec
- The LHiRes III can be used to measure radial velocities within +/- 1 km/sec, perhaps better, at ~6500 Angstroms.
- While there is some movement within the instrument those movements seem largely linear over time. Note this says nothing about the source of such movements just that they can be calibrated out by using surrounding calibration exposures and interpolating the wavelength solutions to the central time of exposure of the “science” image.
- The only explanation I have for the much higher standard errors I found in my Deneb measurements is that I was adjusting the grating twice each night in order to capture both H-alpha and Si II λλ 6347 & 6371 lines. My current working theory is that after moving the grating micrometer it takes some time for things to settle.