Radial velocity errors

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Radial velocity errors

Postby Tim Lester » Thu Sep 03, 2015 2:53 am

Last night was very hazy but the seeing was good at 1.6 arcsec FWHM so I decided to do an experiment that I have wanted to do for some time.
I have wanted to determine just how sensitive the wavelength calibration is to small position changes of the star image
relative to the center of the slit. My slit width is 23 um or 1.8 arcsec on the sky.

I acquired 4 spectra of P_Cyg while it was near the zenith. Each spectra used 5 x 30 sec exposures with a Relco lamp calibration before and after.
1 - star centered on slit
2 - star offset by 20% of the slit width to the left (1/2 pixel)
3 - star offset by 20% of the slit width to the right (1/2 pixel)
4 - star centered on slit
I established the center of the slit by imaging the evening sky and adjusting the guide camera so that a pixel column was exactly centered.

For each of the 4 conditions above I produced two sets of spectra.
Set (A) had no HRV correction and no removal of the H2O lines.
Set (B) had the HRV correction and the H2O removed (but with no additional shift).
The integrated intensities for the case of the star shifted left or right dropped by only 2 to 4%.

I used the radial velocity tool in ISIS to calculate the velocity differences.

For set (A) a synthetic H2O spectra was used for the reference spectrum (adjusted to match the resolution and intensity of the water lines).
Using the water lines in this way to calculate the errors in calibration produced the following (in Km/sec):

star on center -0.8
star to left 1.37
star to right -2.75
star on center(2) -0.61

For set (B) the spectra #1 "star centered on slit" was used as the reference.
Using the P Cyg lines in this way to calculate relative errors in calibration produced the following (in Km/sec):

star on center 0
star to left 1.82
star to right -1.60
star on center(2) -0.04

Both sets tell the same story. Offsetting the star by only 20% of the slit width produces aprox. 2 km/sec errors!
Set (A) indicates that I have an error of about -0.7 Km/sec when using my Relco lamp to calibrate if the star is perfectly centered. But it is also possible that what I considered to be perfectly centred was actually off by about 7% of the slit width.

Obviously keeping the star precisely centered on the slit is ultra important if one wants accurate radial velocities.
Dithering the star back and forth across the full slit width may be another option but this would reduce the efficiency greatly and the dithering itself would have to be done very uniformly.

Now I am beginning to see just how difficult it is to get accurate radial velocities! Anyway I thought these results may be of interest.

Tim
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Re: Radial velocity errors

Postby Francois Teyssier » Thu Sep 03, 2015 7:17 am

Hi Tim,
Thank you for sharing ; very interesting
Of course, this is with the 1800 l/mm grating at R = 9000 ?
François
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Re: Radial velocity errors

Postby Tim Lester » Thu Sep 03, 2015 8:51 pm

Yes your right François. I neglected the important detail that the spectra were centred on Ha using an 1800 l/mm grating giving R = 9000.

Tim
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Re: Radial velocity errors

Postby Robin Leadbeater » Mon Sep 07, 2015 11:20 am

Hi Tim,

I measured my long term RV calibration stability with a LHIRES at R~15000 at 0.5 km/s std devn
viewtopic.php?f=10&t=1111#p5011
This includes all effects though, not just position of the star on the slit. My guiding stability is not good though so there is probably good averaging across the slit.
I can see how you can get errors if the slit is on the slope of the star PSF. This would produce asymmetry in the line profile rather than an actual shift in line position. Is this what you are seeing? What technique are you using to measure the line wavelength? A gaussian fit might be less sensitive to line asymmetry than a barycentre measurement for example.

Cheers
Robin
LHIRES III #29 ATIK314 ALPY 600/200 ATIK428 Star Analyser 100/200 C11 EQ6
http://www.threehillsobservatory.co.uk
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Re: Radial velocity errors

Postby Robin Leadbeater » Mon Sep 07, 2015 4:56 pm

I would also be interested to hear if there are any other solutions to this but I suspect to improve the precision of RV measurements with a slit spectrograph you would either need to use a slit which is significantly narrower than the star PSF or dither the star across the slit. Both of these reduce throughput though of course. I think the problem is less with a fibre feed where the star PSF shape is scrambled by the fibre. This would explain why a much higher precision can be obtained for example in Christian Buil's exoplanet measurements using an eShel.

Robin
LHIRES III #29 ATIK314 ALPY 600/200 ATIK428 Star Analyser 100/200 C11 EQ6
http://www.threehillsobservatory.co.uk
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Re: Radial velocity errors

Postby Tim Lester » Wed Sep 09, 2015 2:12 am

Hi Robin,

I used the radial velocity tool in ISIS to measure the shifts by cross correlation. For the shifts measured from the H2O lines I used the region 6470 to 6550 ang. only, for the shifts measured from the P Cygni lines I used the region 6360 to 6760 ang.

I had wanted to do this experiment because the seeing is often quite good at my location at 1.8 to 2.2 arcsec FWHM. My slit is 2.3 arcsec on the sky (I had stated incorrectly that it was 1.8 arcsec) and my sampling factor is 2.4 so I had been worried that a slightly off center star would give an RV error due to asymmetry of the line shape as you suggested. And indeed it does. I consider my slit width a good match for my conditions as far as sampling and spectrograph efficiency is concerned but there is a trade-off when it comes to accurate radial velocities. I think I would prefer a narrower slit rather than trying to dither or defocus the star to help eliminate this effect (provided my sampling did not drop below 2.2).

However, as you point out, a fiber feed may be the best option for accurate radial velocities. It can effectively scramble the light uniformly across the exit face of the fiber if precautions are taken to make sure the various fiber modes are constantly being mixed by continuously bending the fiber in a random fashion as Christian did.

I too would be interested in any other ideas for those of us that are not fiber fed.

Tim
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Re: Radial velocity errors

Postby Peter Somogyi » Thu Sep 10, 2015 12:31 pm

If there was a reference database for RV, then maybe we could even fix the errors by shooting before & after, with the same guiding.
Does anybody know such database?
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Re: Radial velocity errors

Postby Filipe Dias » Fri Sep 23, 2016 8:29 pm

I autoguide using PHD2, which can oscilate like crazy when the slit that cuts a star image into two, and when the seeing is not that super. I think this clearly fits the problem mentioned!

Up to now, I only know two alternatives (guide on a field star, or use a beam-splitter)... Maybe PHD2 will get smarter soon...
Fil
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