Galilean satellites radial velocity measurements

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Galilean satellites radial velocity measurements

Postby Paolo Berardi » Sat May 28, 2016 3:53 pm

Hi all, I'd like to share an experience regarding radial velocity measurements using the ISIS CCF function (correlation between spectra).

On may 5 I took the spectrum (R~4300, Lhires III with 1200 l/mm grating) of Jovian moon Io (exp 6 x 120s) and Jupiter (12 x 5s). Spectral range was chosen to include a good number of strong absorption lines.

Image

Each satellite sub-exposure profile has been calibrated using two reference lamp spectra taken before and after. Then, the final profile was obtained by adding them. The aim is to reduce the thermoelastic effects on the spectrograph as much as possible.

Jupiter profile was calibrated with only begin/end averaged lamp spectra because the integration time is very short. The wavelength calibration of the planet spectrum is the most critical due to the shift caused by its rotation (spatially extended disk on the slit). The binning zone for the profile extraction was selected in the center of 2d spectrum axis.

Observed relative radial velocity value is as follows:

Io vs Jupiter: -33.7 Km/s

Image

Reflected light doubles (in ideal opposition condition) any observed radial velocity values. We have to consider the Sun->Target->Observer angle. An approximate formula is: 1 + COS(angle). At observing date, the S-T-O angle was 9.5 degree (from ephemeris), so the divisor is very close to 2 (1.986).

The relative radial velocity values corrected for the reflected light becomes:

Io vs Jupiter = -33.7 / 1.986 = -17.0 Km/s

A first check is possibile with ephemeris. I used the NASA Solar System Dynamics (HORIZONS Web-Interface), if anybody knows other ways to verify the results, please let me know.

From SSD, I have referred to “deldot” parameter, which is the radial velocity of the observed target.

deldot Io: 7.1 Km/s
deldot Jupiter: 24.3 Km/s

Relative radial velocity (Io vs Jupiter) from ephemeris is 7.1 - 24.3 = -17.2 Km/s. This is very close to -17.0 Km/s found with ISIS correlation. The velocity value is also compatible with the position along the satellite orbit. Indeed Io had recently passed the maximum elongation point from Jupiter at the observation time, while moving with an orbital velocity, known from literature, of 17.334 km/s (mean value).

Image

The scenario:

Image

Both Io and Jupiter was moving toward the Earth but ephemeris deldot values are positive because the Earth move away faster along its orbit around the Sun. Indeed, the Earth velocity along the Earth-Jupiter direction is 26.2 Km/s (heliocentric correction is negative):

Image

The small velocity component of Jupiter orbital motion along the Jupiter-Earth direction is: 24.3 (from SSD ephemeris.) - 26.2 = -1.9 Km/s.

To try to measure this very modest quantity, we should find the correlation between Jupiter and a reference spectrum (rest wavelengths). As reference profile I averaged six Sun spectral profiles available from Elodie 3.1 library (perhaps there are better ways to find a G2V reference profile…).

Image

ISIS correlation provide the result value -2.6 km/s. Halving it to compensate the light reflection, the measured radial velocity is about -1.3 Km/s.

I realize that these can be measures over the limit of the equipment and techniques used. To check again the method and associated errors, on 21 May (bad weather meanwhile…) I observed again the Jupiter system, this time adding the other Galilean satellites.

The scenario during the observing session:

Image

Time table and results of observations:

Image

Error magnitude (in red) respect to SSD ephemeris seem to me not large again, considering the spectra resolution and the relative small spectral range used for the correlation. Much better results should come out from echelle spectrographs (see the tau Boo exoplanet observation by Christian for example).

I believe the ISIS CCF function is a very powerful tool. Any unexpected error here is due to my not proper conduct of the operations. Relative Rv measurements (i.e. between satellites spectra observed in the same session) are likely easier than absolute estimates. Systematic errors in the calibration of the spectra (offset) are very dangerous (I think to the different injection of light into the slit between star light and the calibration lamp beams).

I attach the relevant profiles if anybody want to play with:

http://quasar.teoth.it/html/jup/spec_jup.zip

Please let me know for any mistake I might’ve done, suggestion or other…
Clear skies,
Paolo
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Re: Galilean satellites radial velocity measurements

Postby Olivier GARDE » Sun May 29, 2016 7:00 am

Hi Paolo,

A great chalenge and wonderful results specially with a LHIRES III and 1200 l/mm grating...
LHIRES III #5, LISA, e-Shel, C14, RC400 Astrosib, AP1600
http://o.garde.free.fr/astro/Spectro1/Bienvenue.html
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Re: Galilean satellites radial velocity measurements

Postby Martin Dubs » Sun May 29, 2016 7:49 am

Hi Paolo,

a great result and a good analysis.
In one point I would differ. To get the Doppler shift from SSD, I think you should add the radial velocity of the sun - moon leg (rdot) and the radial velocity on the moon earth leg (deldot) which you can obtain by selecting heliocentric and observer range-rate in the settings.
For your date I then get 24.6 km/sec for Jupiter for location Falera (which I mostly use) and -10.0 km/sec for Jo or a difference of 34.6 km/sec for the combined sun - moon - earth Doppler shift. This takes into account the different direction of the light from the sun and towards the earth.
With a circular orbit the radial velocity difference viewed from the earth is zero when the moon is in conjunction with the planet, the radial velocity of the sun -moon leg is zero when the shadow of the moon is crossing Jupiter. At greatest elongation of the moon the motion is mostly radial, so your values are correct. At other times there is a small phase shift of radial velocities, disappearing near opposition of Jupiter.

Regards,

Martin
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Re: Galilean satellites radial velocity measurements

Postby Joan Guarro Flo » Sun May 29, 2016 10:47 am

Buon lavoro, Paolo !!
Joan.
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Re: Galilean satellites radial velocity measurements

Postby Benjamin Mauclaire » Sun May 29, 2016 10:35 pm

Hello Paolo,

Great observations and results!
Could you give Rv uncertinties in order to make comparaison to SDD ephemeris quantitatively realiable?

Benji
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Re: Galilean satellites radial velocity measurements

Postby Paolo Berardi » Mon May 30, 2016 4:26 pm

Dear friends, thanks a lot for your comments and suggestions!

Martin, yours is the best method to perform a check for the observations. I didn't think that SSD can provides all we need to obtain a reference value to be compared with the observed Rv (CCF spectra correlation related to the total Doppler shift).

Follows the new comparison table:

Image

Benji, I don't know how to estimate the Rv associated error, especially for any sistematic error (i.e. the example that I put about the injection of the light into the slit). Concerning random errors I thought about the follow solution. Since I calibrated each sub-exposure profile with dedicated reference lamp spectra (preceding and following), I could compare (CCF) the average/sum profile with each single sub-exposure profiles and analyse the data dispersion. For example, Io moon spectra taken in the first session (may 6) vs the first sub-exposure profile:

Image

Table with the results:

Image

Sigma of that data set is about 0.9 Km/s. Could be valid for statistical errors?

Paolo
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Re: Galilean satellites radial velocity measurements

Postby Martin Dubs » Tue May 31, 2016 8:29 am

Hello Paolo,

I am glad that you found my comment useful. Too bad that with the better velocities from SSD the agreement did not improve. Nevertheless I think the results are excellent for a slit spectrograph where the slightest uneven illumination of the slit can lead to larger errors.

Congratulations,

Martin
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Re: Galilean satellites radial velocity measurements

Postby Paolo Berardi » Wed Jun 01, 2016 4:18 pm

Thanks Martin, look like there is a progressive sistematic error (observations are in chronological order). Anyway it was fun to have this experience. Might be a didactic exercise to observe the moons at their maximum elongation time from the planet, then measure the Jupiter mass from orbital velocity and period using the Newton's law of universal gravitation (from Io orbiting at 17 Km/s can be deduced an approximate planet mass of 1.8x10^27 Kg).

Paolo
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