Psi Capricorni

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Psi Capricorni

Post by Sunchaser on 28th February 2012, 8:33 pm

This is probably a stupid question, but here goes.

I'm making what I would hope to be a realistic solar system for Celestia around Psi Capricorni, but according to this

http://stars.astro.illinois.edu/sow/psicap.html

there is no indication of anything-dust, planets, nada.

While I know the system is still fictitious, I would like to utilize the real world data. What would be the best way to do this?


thanks for your help

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Re: Psi Capricorni

Post by Sirius_Alpha on 28th February 2012, 10:25 pm

Keep your planet's masses (or more accurately their predicted radial velocity semi-amplitudes) below the detection limits published so far. That will hold until those detection limits push further down. Without knowing what literature or study they're referring to, I couldn't tell you anything more specific than that.

Follow-up: Researching the star a bit, I find it hard to believe a rotational velocity of v sin i = 37 km s-1 would permit radial velocity -derived limits to be stringent enough to rule out a system of planets. The wording of the article you cite seems presumptuous. A lack of evidence for planets is not evidence for a lack of planets.

Follow-up2:
Taking information from this paper, which gives the RV amplitudes of several A-F stars observed with HARPS, it looks like the maximum radial velocity amplitude an orbiting planet could have would be 118 m s-1, assuming I understood their table at the end of the document correctly. Otherwise, it would have been detected. So as long as your fictional planets exert RV semi-amplitudes of K < 118 m s-1, then they are not explicitly ruled out by the data available.

And that's a lot of room to work with, too.

K is calculated by

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Re: Psi Capricorni

Post by Sunchaser on 28th February 2012, 10:40 pm

The article itself could be outdated. However, it wouldn't make sense to have a gigantic solar system with asteroid belt around it, would it? I was shooting for something sparse. I'm utilizing a tweaked version of StarGen.

Thanks

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Re: Psi Capricorni

Post by Sirius_Alpha on 29th February 2012, 8:23 am

If Psi Cap has an exact replica of the solar system orbiting it, none of its planets would have been detected in the current data set.

As for debris disks, again I wouldn't know without seeing the paper they reference. But if I understand right, debris disks like those in our solar system (similar mass and infrared brightness) are fairly difficult to detect around other stars.

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Re: Psi Capricorni

Post by Sunchaser on 29th February 2012, 8:44 am

Thank you for being so patient...but you're dealing w/ someone who for all intents and purposes flunked Algebra 2...was more of an art student who fell in love with astronomy.

I'm afraid I'm going to need some explanation on the formula. I think the only thing I got was P=orbital period of the body, right? I'm not sure what other numbers I'd enter.

Also, not having a scientific calculator, (trying to use one online) and never having had to use one (see par. 1) I'm not sure how to enter said equation.

Thank you for indulging me.

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Re: Psi Capricorni

Post by Sirius_Alpha on 29th February 2012, 1:31 pm

a* is the semi-major axis of the star (remember that what we're observing with radial velocity is the star's barycentric motion, due to the influence of a planet). i is the inclination of the orbit of the star (which will be equivalent to the inclination of the orbit of the planet), with 90 being edge-on to us, and 0 or 180 being face-on (and undetectable with radial velocity, as sin(0) = sin(180) = 0). P is the orbital period of the star and planet about the barycentre, and e is the eccentricity of those orbits.

you're dealing w/ someone who for all intents and purposes flunked Algebra 2...was more of an art student who fell in love with astronomy.
Keeping this in mind, I created a graph of the detection limits, giving 118 m/s for K, giving the star a mass of 1.1 Msol, and keeping the eccentricity of the orbit to 0.


The orbital period is in days, and the mass is in Jupiter-masses. Any planets below that curve would have evaded detection. Bear in mind this is simplified. The real detection limit is not a smoothe curve, as there are aliases that can hide planets (if the planet's orbital period is almost exactly a day/year, then because the star is only observed at certain times of the day/year, the full RV curve is never measured and some of it can remain hidden). Also, this assumes a long enough coverage of the star to make such authoritative statements about the detection limits at a given orbital period. The observation baseline, if significantly smaller than 1,000 days, will be unable to put strong constraints on the mass of planets at 1,000 days, as only a small amount of the exerted RV curve was observed.

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Re: Psi Capricorni

Post by Sunchaser on 29th February 2012, 1:55 pm

Thank you.

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Re: Psi Capricorni

Post by Sunchaser on 29th February 2012, 2:15 pm

Here's what I came up with...the planet in question is a terrestrial-type world orbiting Psi Cap (which is 1.35 solar masses) at a distance of 1.8228 AU and an orbital period of 2.12 years. The eccentricity is .0569. I input an arbitrary inclination of 75 (wasn't sure on the amount.) The number I came up with was this....

K=-2.091539574975037

Needless to say, I'm not sure if I did this correctly.

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Re: Psi Capricorni

Post by Sirius_Alpha on 29th February 2012, 2:29 pm

Putting K in terms of the mass of the planet (instead of the reflex motion of the star), the equation above, in terms of something that could be put into a calculator, can be approximated as as:

=28.4*(((PERIOD*24*3600)/(365.25*24*3600))^(-1/3))*(((SIN((PI/180)*INCLINATION))*PLANET_MASS)*(STAR_MASS)^(-2/3))

And you can just replace "PERIOD", "INCLINATION", "PLANET_MASS" and "STAR_MASS" with whatever you wish. The orbital period should be given in days, the inclination in degrees, the mass of the star in solar masses, and the mass of the planet in Jupiter-masses.

For a planet like the one you mentioned, given a stellar mass of 1.35 solar masses, an orbital period of 800 days (rough calculation from the semi-major axis you gave), and a mass of 0.003 Jupiter-masses (to make it about an Earth-mass, just a guess on my part since you did not give the mass of the plaent), and an inclination of 75, I get an RV semi-amplitude of K ~ 0.052 m s-1.

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Re: Psi Capricorni

Post by Sunchaser on 29th February 2012, 4:52 pm

After re-entering with new figures (planetary mass was 1.161 Earth mass), I came up with the following.....

K=0.638281863587437

Would this be more accurate? I'm not sure if this number is expressing km or m. I would assume that if it's m, it's under 118, and if it's km, it's still well under 118.

41 and still doing homework....sigh.

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Re: Psi Capricorni

Post by Sunchaser on 9th March 2012, 8:34 am

I'm trying to make heads or tails of the data that is found here:

http://simbad.u-strasbg.fr/simbad/sim-id?Ident=@2398339&Name=*+psi+Cap&submit=display+all+measurements

One weird thing I found had to do with the velocity measurements...they were all in the positive, but varied wildly. How should such data be interpreted?

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Re: Psi Capricorni

Post by Sirius_Alpha on 10th March 2012, 1:37 am

Sunchaser wrote:One weird thing I found had to do with the velocity measurements...they were all in the positive, but varied wildly. How should such data be interpreted?
Failure to include the error margins on those measurements.

50 5, 45 9, 52 5, and 49 3, are all consistent with each other. But 50, 45, 52, and 49 are not. The error margins make a difference, and it doesn't seem that they have been included on the SIMBAD page.


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