KID 8018547 - KOI 902

K00902.01, P1=83.9250821 days, R1=5.05 R_Earth

Posted June 21, 2015 1:13 PM

This is a relatively large PC for an M-dwarf, and it looks like it has sinusoidal TTVs with a semi-amplitude of about 45 minutes which don't seem to have been studied. Perhaps this is a resonant planetary system? It might be worth looking for other transits here, and analysing those TTVs would be interesting.

Posted June 21, 2015 4:36 PM

by ajamyajax

KIC 8018547 KOI 902: yes indeed significant TTV transits here. And I don't know how we missed this one on PH1(?)... Anyway a few plots using 0.51X R_Sol suggests to me this is a Neptune class planet with some inclination that is highly perturbed by an unseen larger gas giant with a period of several years.

8018547,KOI 902.01,CANDIDATE,83.9250821,152.8365979,6.84 (0.285 BJD)

ttv1 = [152.907,236.809,320.705,404.626,488.537,572.44,656.37,740.287,824.21,908.133,992.074,1076.013,1159.963,1243.896,1327.84,1411.778,1495.728,1579.68]

F1a
OC1

Posted June 21, 2015 9:33 PM

by Shellface

I just checked on KOINet, and this is on their target list (see here). The TTVs look perfectly parabolic over the Kepler timescale - its super-period must be huge!

Though the star is faint, the deep transits mean these TTVs will be amenable for study from the ground. The (fairly) short transits mean that they can be observed from a single site, which is not common for a planet with an orbital period as long as Mercury. Very interesting!

As the TTV super-period is very long, either the planet is in a near-perfect low-order resonance, or the TTVs are non-resonant, in which case the TTVs cycle with the period of the outer companion. If this is true, then the other companion would probably be a giant planet with an orbital period of most of a decade. from the plot on the KOINet page, there does appear to be some short-period variation in the transit times near minimum, which is more in favour of a resonant scenario. Further transit observations would be highly valuable here.

Posted June 21, 2015 10:05 PM

by JKD

Posted June 22, 2015 5:51 AM

by zoo3hans

Hm, I do not see anything special in the light curve by a visual check (with LcViewer). So I assume the outer companion is non-transiting.

Posted June 22, 2015 2:53 PM

by ajamyajax

Update: experimenting with this TTV cycle stuff a bit, I get a bit longer possible than the second chart on KOINet.. But I get what plots. And don't know why they zero centered that O-C plot ~80 to -80 since observed is ~0 to -160 but at least we get the same approx delta. Anyway FWIW (as usual).

OCX1

Posted June 22, 2015 8:40 PM

by Shellface in response to ajamyajax's comment.

The periodic fit in their plot looks pretty bad; I imagine it's the shortest period with an acceptable goodness of fit. Your plot is probably more representative of reality.

As it's about day 2363 or so on the Kepler data scale now, it looks like it's towards the last time that the transit times can be extrapolated to a reasonable accuracy without further transit observations.

Also, for variations like this where one of the extrema cannot be definitively given a value, the zero-point of the data is arbitrary (it can technically take an infinite range of values, but realistically will not). I imagine they wanted to plot zero at the middle of the curve for simplicity.

Some preliminary estimates of the system parameters can be made, even with a limited TTV cycle. First, the super-period can have its minimum value estimated (~3500 days), which gives the minimum semi-amplitude of the TTVs (~250 minutes). If we assume the resonance that the system is in, then further parameters can be estimated. For example, if we assume a 2:1 resonance, the outer period is ~171.98 days, and the period ratio is ~2.049. Solving for the TTV amplitude, and given a stellar mass of 0.53 Msol, gives a mass for the second planet of ~0.12 Mjup, under the assumption of zero eccentricity. Though this is extremely preliminary, the result is plausible; in this case, the mass for the second planet seems compatible with the expected mass for the first one, given a radius of 5 Rearth. A low-order resonant, two planet system (where only one transits) seems to be a good working model until future observations can be secured, and the system solved properly.

Posted June 22, 2015 9:51 PM

by ajamyajax in response to Shellface's comment.

Thanks for that. Had a new thought this morning: the nature of the TTV here reminds me of our find and PH paper (below) where a highly perturbed low-density planet is gravitationally sandwiched between two others of different masses in perfect resonance. So I think we should consider the possibility the same is going on here, and look for some sign of an inner companion. Also this might be a good excuse to try the TTV calcs again as well.. So we'll see. 😃

"Planet Hunters VII. Discovery of a New Low-Mass, Low-Density Planet (PH3 c) Orbiting Kepler-289 with Mass Measurements of Two Additional Planets (PH3 b and d)"

Joseph R. Schmitt, Eric Agol, Katherine M. Deck, Leslie A. Rogers, J. Zachary Gazak, Debra A. Fischer, Ji Wang, Matthew J. Holman, Kian J. Jek, Charles Margossian, Mark R. Omohundro, Troy Winarski, John M. Brewer, Matthew J. Giguere, Chris Lintott, Stuart Lynn, Michael Parrish, Kevin Schawinski, Megan E. Schwamb, Robert Simpson, Arfon M. Smith

http://arxiv.org/abs/1410.8114

Posted June 23, 2015 1:35 PM

by ajamyajax in response to ajamyajax's comment.

Well, maybe some progress with TTVFast as I think I have plotted their example output data correctly after a program run. That part is (usually) my forte, while the astrophysics component of all this is not.. So I still have to decipher their input parameters and so forth, and then see if I can estimate possible unseen companions masses from the results. But I'll see if I can come up with anything more here.

TTV1

"TTVFast: An efficient and accurate code for transit timing inversion problems"

Katherine M. Deck, Eric Agol, Matthew J. Holman, David Nesvorny

http://arxiv.org/abs/1403.1895

"KOI-142, the King of Transit Variations, is a Pair of Planets near the 2:1 Resonance"

David Nesvorny, David Kipping, Dirk Terrell, Joel Hartman, Gaspar A. Bakos, Lars A. Buchhave

http://arxiv.org/abs/1304.4283

"The transit timing is modulated with a TTV period of PTTV ~≃ 630 days."

"... In any case, we predict that KOI-142b should stop transiting within the next 10-25 years. The reason for that is the the orbital plane KOI-142b is inclined relative to the more massive KOI-142c, must precess around KOI-142c’s orbital plane."

Posted June 25, 2015 5:33 PM

by Shellface in response to ajamyajax's comment.

Ahaha. I was interested in that paper - but, seeing as my programming knowledge is… a few years behind my physics, their code was unambiguously beyond my abilities to use. I suppose it's suitable that we have the inverse problems!

There's something I'll be posting in a day or two which, I believe, would be highly suitable for that code. I am aware that both some of the old Planet Hunters folks and the science team behind it have had names on papers regarding TTVs, so hopefully this will be applicable here…

Anyway. Let's not get sidetracked; this is probably not the best thread for general TTV stuff.

Posted June 26, 2015 12:19 AM

by ajamyajax in response to Shellface's comment.

Sounds good. I'll see if I can convert what you post into TTVFast results + my plots on a separate thread whenever you get to it. With a few questions along the way most likely.

Posted June 26, 2015 2:33 AM

by ajamyajax in response to Shellface's comment.

SF, a TTVFast question right from the top: I am puzzled by most of the example input parameters for KOI142.in, even though they seem to plot ok. They should be listed below (in order). Stellar mass is the only obvious one, and my planet mass conversions didn't match what they have. So I am hoping you might recognize what conversion they are using here. Thanks.

(1) Planet Mass, (2) Stellar Mass, (3) Period, (4) Eccentricity, (5) Inclination, (6) Longnode

(1) 0.000295994511

(2) 0.95573417954

(3) 0.00002878248

(4) 1.0917340278625494e+01 5.6159310042858110e-02 9.0921164935951211e+01 -1.1729336712101943e-18 1.8094838714599581e+02 -8.7093652691581923e+01

(5) 0.00061895914

(6) 2.2266898036209028e+01 5.6691301931178648e-02 8.7598285693573246e+01 4.6220554014026838e-01 1.6437004273382669e+00 -1.9584857031843157e+01

The NEA confirmed planet values for KOI 142.01 are:

Planet Mass (M_jup) 0.027

Stellar Mass (M_sun) 0.956

Period 10.95416

Eccentricity 0.05593

Inclination (deg) 89.055

Longnode (?)

Posted June 26, 2015 3:22 PM

by ajamyajax

Update: I just e-mailed my question to Katherine Deck, so hopefully she can help us out with this.

Posted June 26, 2015 8:49 PM

by Shellface in response to ajamyajax's comment.

Well, it looks like the stellar mass is the only one that follows the labels. To my eye, it looks like (4) and (6) represents parameters of the planets, period (days), eccentricity, inclination (degrees), and then some things I don't recognise. It looks like the different inclination for b follows that it is largely impossible to determine the sense of orbital inclination through transit observations - as in, inclinations of x degrees and 180-x degrees give the same goodness of fit.

I'm not sure what (1), (3) and (5) are. Given their placement I expect they are something to do with the star, first planet and second planet, respectively, but I don't know what.

Also, "Longnode" must refer to the longitude of the ascending node. Values of the parameter for both planets are given in the discovery paper, though I don't really see any relation between them and those inputs.

Posted June 26, 2015 9:58 PM

by ajamyajax in response to Shellface's comment.

(CORRECTED) SF, heard back from Kat Deck who corrected some of my parameters here. Sorry about my earlier confusion with these. I am still fuzzy about 'G' however since my calc doesn't produce the same results as the KOI 142 example. (Update) each of the two planets has sets of values indicated by parameter (n).01 and (n).02. Hope this helps.

(1) G = AU^3/day^2/M_sun, (2) Stellar Mass, (3) Planetary Mass, (4) Period, (5) Eccentricity, (6) Inclination, (7) Longnode (8) Argument (9) Mean anomaly

(1) 0.000295994511

(2) 0.95573417954

(3.01) 0.00002878248

(4.01) 1.0917340278625494e+01 (5.01) 5.6159310042858110e-02 (6.01) 9.0921164935951211e+01 (7.01) -1.1729336712101943e-18 (8.01) 1.8094838714599581e+02 (9.01) -8.7093652691581923e+01

(3.02) 0.00061895914

(4.02) 2.2266898036209028e+01 (5.02) 5.6691301931178648e-02 (6.02) 8.7598285693573246e+01 (7.02) 4.6220554014026838e-01 (8.02) 1.6437004273382669e+00 (9.02) -1.9584857031843157e+01

The NEA confirmed planet values for KOI 142.01 are:

Planet Mass (M_jup) 0.027

Stellar Mass (M_sun) 0.956

Period 10.95416

Eccentricity 0.05593 (note 0.056159x for .01 in file above, but values from paper may differ with NEA data)

Inclination (deg) 89.055 (note 90.9x for .01 in file above)

p.s. Kat's additional comments might help also:

Inclination (degrees) = 90.9... (this is measured relative to the sky-plane
(plane of reference), so 90* exactly is an exactly edge-on orbit)
Longitude of ascending node (Omega): Tells you how the orbit is oriented
in the sky-plane. For example, here long_node ~0, which implies the
ascending node is along the x-axis (reference direction in figure on
wikipedia). (the sky plane is X Y plane, Z is towards observer along line
of sight).
Argument (w) = argument of pericenter: the angle between the ascending
node & the pericenter, measured in the plane of orbit, in the direction of
the motion of the planet.
Mean anomaly: initial angle of the plane measured from pericenter, again
in the plane of the orbit, in the direction of the motion.
Then repeat but for the second planet.

Posted June 30, 2015 3:10 PM

by ajamyajax in response to ajamyajax's comment.

Ok, I got more help from Kat on "G" already. Here is her reply:

The way to convert G from m/kg/s to AU/day/M_sun is like this:
G(m/kg/s) = 6.6710^-11 m^3/kg/s^2
G (Au/day/Msun) = G (m/kg/s)(1
AU/1.49610^11m)^3(1.989110^30kg/Msun)(606024 sec/day)^2

(there are 1.510^11 meters in 1 AU, 1.98910^30 kg in 1 Msun, and
606064 seconds in 1 day)
If you calculate this exactly in google (which has the more exact units in
it)
G = 0.000295994511

G is the gravitational constant appearing in the gravitational force, so
it will be the same for every system you use TTVFast.

Posted June 30, 2015 3:35 PM

by ajamyajax

SF: all right, I think we are ready now to use TTVFast for our own calcs! I think there are a few ways we can both do this. You will need to prepare your own input file values as described above for each system you want to evaluate of course. You can either (a) post these values so I can run them through the programs for you, or (b) I can post the compiled EXE programs here with Dropbox or something so you can run TTVFast yourself (they only posted the source on their website). And then most likely you can chart your own results as I do. So let me know.

Posted June 30, 2015 4:20 PM

by Shellface

(I am slightly… very sleep-deprived right now, so I'm probably not exactly cognitive)

Alright. I ought to be able to work with an executable, and it'd be easier to be able to do things on my own. I can… PM you my email address? That should work.

Do you know if the planetary masses are in units of solar mass or respective stellar mass? It's hard to tell when the stellar mass is almost solar.

Posted June 30, 2015 4:47 PM

by ajamyajax in response to Shellface's comment.

Sure email is fine. I will include a few tips also in a bit. And about the masses, "all masses are in units of M_sun" per Kat.

Posted June 30, 2015 4:56 PM

by JKD

Posted June 30, 2015 7:31 PM

by ajamyajax

KIC 8018547 KOI 902 update / TTVFast batch test #1: just ran a (new) simple two planet probability fit out to ~2000 days for 1x P1 mass object with a slight inclination of 89.0 degrees (just to maybe put a possible unseen companion's transit out of sight). The results were kind of as expected, but not but quite. In order to get the anti-correlated fit I tested for, the estimated period range had to be 163.9 to 164.9 days which is just less than 2x KOI 902.01's period of 83.92x.

So if my fitted test period is close with a possible second and unseen planet's period being just less than 2:1 resonance, perhaps there is a third longer-period planet that is perturbing it slightly? If I add a theoretical third planet of the same mass with P=657.6 (4x P=164.4) and a similar inclination, TTVFast appears to plot a nice resonance between all three calculated objects. And yes all this is still experimental, but I think also means TTVFast can be useful to us here.

PB1

TTVF1
TTVF2

TTVFast credit: Deck, Agol, Holman & Nesvorny, 2014, ApJ, 787, 132, arXiv:1403.1895

Posted July 4, 2015 11:38 PM

by ajamyajax in response to ajamyajax's comment.

Update: with the limited data we have (not even a full TTV cycle here) important to mention this first experiment just one possible scenario.. I also remembered this morning that I changed my TTVFast setup_file start time to 0 from 131.5 to closer match my O-C plot's curve, but I should batch run the other parameter also, and more probably. So the interesting tests continue. 😃

Posted July 5, 2015 1:42 PM

KID 8018547 - KOI 902 - APH00004rq