# Another Neptune in the Oort Cloud

1. Jun 30, 2007

### Astrobuff

Dr Steinn Sigurðsson (Penn State) has been reporting findings announced at the Confererence on Extreme Solar Systems on his blog http://scienceblogs.com/catdynamics/2007/06/extreme_solar_systems_v_the_sa.php [Broken]but amongst all the interesting discoveries is this idea raised by planetary dynamicist Dr Ed Thommes:

Now this could really be quite fascinating. I recall reading that the mass of all TNOs, SDOs, and LPCs added up together cannot be more than a few Mearths at best. A far cry from the predicted 10-30 Mearths postulated to have existed in those nether regions i.e. the Edgeworth-Kuiper Belt (EKB), Scattered Disk (SD) in the beginning.

Also Levison et. al., (see *1) have studies which imply that the original mass in planetesimals between 4 and 40 AU was about 4 times the mass in solids in a minimum-mass solar nebula. While this mass is reasonable, he and his team is of the view that the standard model makes predictions that are not borne out by observation. Specifically, this is what he said "(1) the inferred population of the scattered disk is much smaller than predicted ([3],[4]); (2) OC comets appear to form at colder temperatures than our results would suggest ([5]), and (3) models for the origin of Halley-type comets (HTCs) require a massive inner OC or scattered disk as a source region for the HTCs." The unusual path that supercomet 2000 CR105 takes is also suggestive of a perturbative presence somewhere deep within the Scattered Disk IF not beyond, Levison:

So what really did happened to the missing mass (i.e. of these TNOs, SDOs, LPCs, etc) in the EKB, SD and inner Oort cloud? And why do the solar system's outliers like dwarf planet Eris (ex Planet X), Sedna ala 2003 VB12 and CR 105 have such high orbital inclinations (i) of 44.187°, 11.934° and 22.770° (see *2, *3 & *4) respectively? Or why are their orbits so eccentric (e.g. e=0.44177, e=0.855, e=0.798)? Also why the abrupt sharp edge to the Classical EKB at 50 AU (see *5) ? What could have produced it? Could there have been numerous factors at play with regards to these anomalies? Or could any or all of these anomalies be the by-products of a stellar flyby, flybys by BDs or planetary mass (i.e. planemos) interlopers maybe even a Planet X? And why not but the net result of perturbation by a distant substellar mass BD common proper motion solar companion (especially at periastron)?

I have come across a paper by Morbadelli et al., where it was argued that a ~50 MJup rogue BD flyby can account for the perturbed orbits of some of these outer solar system bodies and they even suspect that Sedna could actually be but an extrasolar planetoid captured from this rogue BD. It begets the question i.e. let's assume that they are right, that indeed this BD interloper is the culprit responsible, but what if it wasn't simply just an interloper? What if it was of a lower mass and really but a highly eccentric (0.9 <= eBD <= 0.99), 13 MJup <= Mbd <=20 MJup coeval substellar mass BD companion to our Sun or maybe even a captured ultracool VLM substellar companion (given the likely birth of the Sun in an Orion like open cluster and the case of B1620-26c (see *6), this can't be entirely ruled out or can it?) with a periastron at 100-200 AU instead?

The Teff of such an object is likely to be only about ~369.14 ° K (let's assume that it is of the same age as the sun i.e. 4.6 Gyrs and has a mass of 15 MJup for the sake of discussion) according to Burrows et al., and if it still around, could be near or at apastron at this moment i.e. almost a light year away. Detecting it sure won't be an easy task, for if we are still turning up more M Dwarfs in what is the solar neighborhood's own backyard as evidenced from the RECONS project (see *7) and elsewhere even at this day and age, one can imagine how very much more tedious is the task of locating objects such as BDs with even lower masses, Teffs, and SpTs e.g. T or Y.

Gomes et al., likewise have also come to a rather similar conclusion like Levison et. al., albeit one involving even lower masses perturbers and maybe with particular interest and relevance here is that one of the possibilities involves having a Neptune mass planet out at semiminor axis 2000 AU or a Jovian with semiminor axis at 5000 AU.

References:

Morbidelli, A., & Levison, H. F., 2004, Scenarios for the Origin of the Orbits of the Trans-Neptunian Objects 2000 CR105 and 2003 VB12 (Sedna), AJ, 128, pp. 2564-2576

Burrows, A., Marley, M., Hubbard, W. B., Lunine, J. I., Guillot, T., Saumon, D., Freedman, R.; Sudarsky, D., & Sharp, C., 1997, A Nongray Theory of Extrasolar Giant Planets and Brown Dwarfs, ApJ 491, p.856

Gomes, R. S., Matese, J. J., & Lissauer, J. J., 2006, A distant planetary-mass solar companion may have produced distant detached objects, Icarus, 184, pp. 589-601

*1
http://www.aas.org/publications/baas/v32n3/dps2000/498.htm [Broken]
*2
Eris
*3
Sedna
*4
CR 105
*5
http://www.ifa.hawaii.edu/faculty/jewitt/kb/kb-classical.htm [Broken]
*6
Captured Pulsar Planet
*7
RECONS
*8
The Challenge of Detection Limit

Let us for the sake of convenience, affix a mass of 15 MJup for this hypothetical BD comapnion. And let us also assume that it is an coeval companion to our Sun i.e. age = 4.6 Gyrs. According to Burrows et. al (1997), such a BD has a Teff of 369.14 °K and a luminosity of 7.19179 * 10^-7 Solar.

Effective temperature (Teff) of the Sun = 5778 °K

Effective temperature (Teff) of this hypothetical BD companion 369.14 °K

Flux 1/Flux 2 = constant * (5778)^4/constant * (369.14)^4

= 1.114577188 * 10^15/1.85679707025 * 10^10

i.e. The SUN is 60026.87278 times BRIGHTER than the hypothetical BD companion

At T = 369.14 ° K

Lamda (Max) = 0.2897/369.14

Lamda (Max) = 0.000784797096 cm K

Now let us also assume the location of our hypothetical BD companion to be 50000 AU. Light has to travel out to 50000 AU, get reflected and come back 50000 AU. This is where the assumption that the planet is in opposition comes in. If the BD is in opposition, then the Earth is in between the Sun and the BD and as the distance between Earth and Sun is 1 AU, the distance between Earth and the BD is 49999AU. Similarly, during opposition, the distance between Earth and Jupiter is 4.2 AU.

Now, by the time the energy of the Sun travels to 50000 AU, the flux is down in comparison to the flux at Jupiter by (50000/5.2)^2. In addition, the reflected light has to travel back 49999 AU from the BD in comparison to only 4.2 AU from Jupiter. Hence, the flux of the reflected sunlight from the planet is below that of Jupiter by a factor of (50000/4.2)^2. Hence, the visual light flux from the planet is below that of Jupiter by a factor (50000/5.2)^2 * (49999/4.2)^2. We know the magnitude of Jupiter (i.e. -2.7 at 5.2 AU). Hence, apply the formula for magnitudes and we'll get the magnitude of the BD companion.

At 50000 AU,

(50000/5.2)^2 * (49999/4.2)^2 = 1.310259681 * 10^16

m1 - m2 = 2.5*log(F2/F1)

m1-(-2.7) = 2.5*(16.11735738)

m1-(-2.7) = 40.29339344

m1 + 2.7 = 40.29339344

m1 = 37.79339344

Apparent Visual Magnitude of this Hypothetical BD companion will be but a DIM 37.79339344 i.e. definitely way beyond the Hubble Space Telescope's (HST) power.

Levison et al's BD Interloper Paper

Burrow et al's Non Gray Theory of EGPs & BDs

Gomes et al's Low Mass Planetary Companion Rogues

Terminology:
TNO = Trans Neptunian Objects
SDO = Scattered Disk Objects
LPCs = Long Period Comets
Mearth = Number of Earth Masses
OC=Oort Cloud
Edgeworth-Kuiper Belt=EKB
SD=Scattered Disk
HTC=Halley-Type Comets
i=Orbital Inclination
e=Orbital Eccentricity
BD= Brown Dwarf
MJup=Jupiter Masses
Mbd=Mass of the BD
eBD=Eccentricity of the BD
Teff=Effective Temperature
VLM=Very Low Mass
Substellar=Of a subsolar value i.e. lower than Sun's value
Gyr=Billion of years
AU = A unit of measure in the cosmos. 1 Astronomical Unit (AU)=the distance of the Earth to the Sun i.e. 146, 900, 000 Km
SpT=Spectral Type

Last edited by a moderator: May 2, 2017
2. Jun 30, 2007

### Astrobuff

http://scienceblogs.com/catdynamics/2007/06/extreme_solar_systems_v_the_sa.php [Broken]

Extreme Solar Systems V: the sacrifices we make

Category: astro
Posted on: June 29, 2007 8:24 AM, by Steinn Sigurðsson

Did I mention that I have been here a week and not got to the beach yet...
One of the penalties of being an organiser. Of course I slept that one free afternoon, but that was after trying to find the Olympic Airways office for 3 hours - they shut it, apparently people kept bothering them or something - did I mention it has been rather hot here?

Then there are these mystery people who keep sending me lengthy snippets of text they claim to be "thesis chapters" or something. Strange behaviour.
The Macs are nice, but the screen contrast is not good enough to read 20-40 pages of text in the afternoon sun, outside, at the beach. Or even the pool...

Ok, some theory speculations:

dynamicists have been playing with formation models, and there is a hint that we can match the observed systems - prescription is that systems form "crowded" - just pack in as many planets as can fit, then let there be some migration, resonant locking and planet-planet scattering, and what emerges has statistical distributions that are not too far off from what is observed.
Now, we could be missing a class of systems more like the Solar System where there was little gross scattering or migration, but probably some, and we are starting to see those systems now.

Ed Thommes had an interesting talk on extensions of his old models and the "Nice" models of Morbadelli et al.
Looks like the outer solar system, with late heavy bombardment, would have come together nicely if there was another Neptune out there to begin with.
So we let debris drag bring Jupiter and Saturn into resonance with a little bit of orbital migration, scatter Uranus and Neptune out (and use the debris to recircularise) and we get the details more or less right if we let a second Neptune have been there and been ejected, either to infinity or outer Oort cloud. Hard to accommodate a planet X that big in the outer system, but maybe possible.

Some interesting news on debris disks, and possible planets around very young stars.
All very preliminary, but clearly something there that can be pushed on with better data.

Last edited by a moderator: May 2, 2017
3. Jun 30, 2007

### Astrobuff

GRAVITATIONAL POTENTIAL OF THE SUN AND WIDELY SEPARATED VLM COMPANIONS

We know that the potential of the Sun extends to Oort Cloud at least i.e. about 100000 AU and this is calculated from Newtonian gravity, except very close to the Sun where general relativistic effects may be significant for sensitive experiments. By Newtonian theory, the potential of a mass M at a distance r is given by -GM/R where G is the gravitational constant. By definition, the potential is zero at r = infinity. Hence the potential well of the Sun extends to infinite distances. However, the effect of Sun's gravity is not unlimited due to the presence of other masses in our galaxy. The gravity well of the Sun will end when its gravity at a certain point in space equals the gravity from another star. At any point further than that point, the gravity well of the other star will be deeper than that of the Sun so that a particle at that point will be in orbit around the other star rather than the Sun. For instance, imagine that the Alpha-Centauri system has a single star of the mass of the Sun (in reality it comprises of three stars). Then, the Sun's gravity will extend exactly to half the distance to this star.

There is an embedded stage in the evolution of a stellar cluster during which the density of normal stars can be as high as a few times 10^4 stars pc^-3 implying an average separation between two stars to be 0.046 pc (1/cube root of 10,000) i.e. this comes up to about 9488.19 AU on average between a star and its neighbor. (Legend: 1 Parsec (pc) = 206265 AU) This figure of 9488.19 AU is well within the halfway point between the Sun and Proxima Centauri (i.e. limit to Sun's gravitational influence) which is 1.29448 pc/2 i.e. 0.64724 pc or 133502.9586 AU.

In light of the above and more to follow below, I'm becomming increasingly skeptical that our Sun is an unique exception i.e. as Duquennoy et al (1991) insists that only about one third of G-dwarf primaries may be real single stars, i.e. having no companions above 0.01 Msun. That the companion masses shows a "continuous increase" towards smaller and smaller values. In fact, Wasserman et al (1991) believes that widely separated companions exist out to distances of distances of 1 pc or more but the "signal" due to binary stars with s >~ 1 pc was swamped by the noise attributable to clustering and thus is a formidable obstacle in determining the widest physical pairs.

There are several well publicized instances of widely separated BD companions e.g. 2MASSI J1022148+411426 at a distance of 2460 AU from its parent F7 IV star HD 89744, the L4.5 dwarf Gl 417b approximately 2000 AU from the G0 Sun-like twin Gl 417A, Gl 584C a L8 V
BD 3600 AU from the G Dwarf pair of Gl 584AB, 2MASSW J1620261-041631 at 1090 AU from the M0 V Gl 618.1 i.e. G17-11, HIP 80053, Gl 570 D some ~1500 AU from the 3 main stars in the system consisting of K4, M1 and M3 stars, and of course Epsilon Indi B (an EARLY T Dwarf i.e. T 2.5 dwarf about 1459 AU from the Spectral Type (SpT) K5 V parent Epsilon Indi A, a star ONLY 3.6 pc away (Kirkpatrick, et al, 2001; Burgasser et al., 2003; Grizis et al, 2001 and *a and *b).

Kirkpatrick (2001) contended that very wide physical separations are possible, like the Gamma Ceti AB + Gl 106.1C system where the components have a separation of ~0.09 pc. And also in Gizis et al. (2001) it was stated that the "observed L and T dwarfs indicate that brown dwarfs are not unusually rare as wide (Delta >1000 A.U.) systems to F-M0 main-sequence stars (M>0.5M_sun, M_V<9.5), even though they are rare at close separation (Delta <3 A.U.), the brown dwarf desert.'' Stellar companions in these separation ranges are equally frequent, but brown dwarfs are >~ 10 times as frequent for wide than close separations."

*a

http://astron.berkeley.edu/~basri/bdwarfs/table1.htm

*b

http://spider.ipac.caltech.edu/staff/davy/STARS_BDS/kirkpatrick.html [Broken]

The idea of a distant BD companion coexisting with and on the whole leaving the planetary zone relatively unscathed is not a radical idea at all and neither will it be a precedence as an example has already been found in the HD 168443 system. There are occasions in this system when the 2 known components i.e. HD 168443 C a ~17 MJup BD and Jovian HD 168443 b are a mere 2.296 AU i.e. when the former happens to be at aphelion and latter is at perihelion. What is of interest is that HD 168443 is not a young system, the star's stellar parameters indicates it is a subgiant star according to its spectral class and weak chromospheric emission, S=0.15, suggestive of an age approximately near 8 Gyrs and an equatorial rotation of under 3 km sec^-1 (Marcy, et al., 1999).

HD 168443 is thus an even older system than our own and the survival of these 2 bodies (if not others, to which we do not have a definite indication to date) illustrates the fact that systems involving planets and a BD companion can coexist relatively peacefully for much of the lifespan of the parent star. Moreover, we are talking about a far flung BD companion here i.e. one located in the order of 10^3 AU distance.

Planet Period T_peri (JD) ecc omega (deg) Velocity Amp, K(m/s) Msini (M_jup) a (AU)

hd168443b 58.10 day 2450047.6 0.53 172.9 472.7 7.73 0.295

hd168443c 4.85 yr 2450250 0.20 63 289 17.2 2.87

Stellar Characteristics

Spectral Type Mass (M_sun) Apparent magnitude Distance (pc) P_rot (d) [Fe/H]

G5 IV 1.01 6.91 38.5 36.76 +0.03

Source: http://exoplanets.org/esp/hd168443/hd168443.shtml

Also in Hogg et al. (1991), the authors higlighted several issues which caught my eye i.e. 4% of sky was not covered by the IRAS survey, and the data from another 4% of the sky near the Galactic plane is ambiguous given the background noise. The authors also noted that should any dark mass have an insignificant proper motion, it would render the dark mass undetectable for it will be "indistinguishable from a stationary source". In the same article, it was also stated that if on the contrary, the dark mass's proper motion is very large, it could have been dismissed as an ingenuine or questionable source.

The same paper also mentioned the following:

- All sources recieved 2 HCONs within 1-2 weeks and a third 6 months aftwerwards but mapping was completed for just 72% of the sky before the IRAS mission came to an abrupt halt.

- If rx >= 2500 AU there would not be any detectable proper motion and hence would not have aroused the attention of anyone unless it happens to be at high galactic latitude even if it were in the IRAS Catalog.

- Detectability will be low if the dark mass is at ecliptic latitudes in the 30-60° range.

- The prospect that IRAS may have missed a dark mass concentration cannot entirely be excluded as the authors have also noted.

And neither can pulsar timing reject totally the possibility for such a VLM BD companion to our sun too as you will see later.

Also a VLM companion (be it a Jovian planet or a full fledged deuterium fusion capable (i.e. 0.012-0.075 Msun (assuming Fe/H = 0.0 i.e. Solar Metallicity), personally I think such a BD comapnion (it should not be more massive than 0.02 Msun though) exist, it could well be picked up by JWST/WISE but maybe not Spitzer, given the latter's smaller field of view. Or it could also be that someone notices an object with an unusually high parallax. The recent discovery of SO025300.5+165258's i.e. a SpT M6.5 Dwarf by Teegarden et al., (2003), proves that relative brightness is NO 100% guarantee of certain detection and positive identification.

For all we know, such a companion could well be sitting as yet unnoticed and buried amongst the countless millions upon millions of objects in the databases (e.g. 2MASS, SDSS, DENIS, SuperCOSMOS, NEAT, LINEAR, etc) aka LP944-20 (i.e. this BD should instead of Gl229b be actually the first BD discoverd. It was first sighted by Luyten and Kowal in 1975 BUT not seen again till about 1997 (Tinney, 1998)) and HD 209458.

I guess some if not all of you have heard of Dr J. D. Kirkpatrick. He is perhaps the world's top BD hunter par excellence. I hope he doesn't mind that I share with you on what he has shared with me and thinks about ultracool VLM BDs and prospects for a distant substellar companion for our Sun along with some other arguments for it from various sources.

In Burrows et al, 2003, the paper states that SIRTF (ala Spitzer)/MIPS should be able to detect at 10 parsecs (i.e. 1 parsec or 1 pc = 206265 A.U. = 3.26162 Light Years) the ~24 µm flux of objects more massive than 2-4 MJ at age 1 Gyr or more massive than 10 MJ at 5 Gyr. In the opinion of the authors, the most relevant channel on MIPS for brown dwarf studies is ~1000 times better in imaging mode than for the pioneering IRAS. While Spitzer is the last of the "Great Observatories," and will view the sky with unprecedented infrared sensitivity, JWST will in turn provide a two- to four-order-of-magnitude gain in sensitivity through much of the mid-infrared up to 27 microns. However the JWST/NIRCam is greater than one hundred times more sensitive than HST/NICMOS at 2.2 µm and enables one to probe deeply in space, as well as broadly in wavelength. In its broadband detection (imaging) mode, JWST/MIRI will be ~100 times more capable than SIRTF from ~5 µm to ~27 µm. Since the mid-IR is one of the spectral regions of choice for the study of the coolest brown dwarfs, MIRI will assume for their characterization a role of dramatic importance.

Kirkpatrick in private, seems especially excited about WISE as he revealed this to me: "The one mission best suited to find ultracool VLM BDs (like the proposed BD companion) is WISE, the Wide Field Infrared Explorer formerly known to all as NGSS. In fact, finding the nearest BD (expected to be closer than Proxima) is one of its two main science goals." He is however, at best, skeptical as to how successful instruments/surveys like Keck Interferometer, SOFIA, SIRTF (ala Spitzer), IRIS and Herschel Space Observatory will be in finding Free Floating Planetary Mass Objects and ultracool BDs (e.g. the proposed BD companion). The Keck Interferometer he asserts doesn't work at those wavelengths (wavelengths that approximates the expected Teffs of these low mass objects e.g. N-band). Herschel works at much longer wavelengths. The others (e.g. SIRTF, SOFIA and IRIS) are in the ballpark, but both SOFIA and SIRTF have very small fields of view. So to find a very low-mass BD and Free Floating non fusors between here and Proxima would require them to get quite lucky. In other words, they'd have to be pointing in just the right spot.

In percentage terms, how many of the BDs found by the various surveys e.g. 2MASS, DENIS, Sloan Digital, NICMOS, SuperCOSMOS, etc have had their stellar types, proper motion and distances determined? How long will it all take for every object currently in the databases to have their stellar types, proper motion and distances measured? Will all the objects in the databases of the above 5 surveys have their nature and other characteristics ascertained before 2010?

Only about thirty or so BDs have had their parallaxes measured. A few more in addition have proper motion measures. It will likely never be the case in his lifetime (in Kirkpatrick's words) that all the known BDs will have their distances measured. Unless there is a dedicated space mission that goes much deeper than Hipparcos and is dedicated to specific targets like BDs, Kirkpatrick does not think this will ever be done completely.

Kirkpatrick shared with me that there are only but a few astronomers around even pursuing parallax measurements, and many of them are meeting resistance because parallax work isn't "sexy". It's of fundamental importance to understanding these objects, though, but not everyone agrees that it's important enough to spare the time and resources on.

In our numerous correspondence, I asked Kirkpatrick this: Given that the Universe is ~14 Gyrs old, what is the likelihood that old i.e. >10 Gyrs VLM stars with Masses in between 75 to 80 MJup may lurk as yet undiscovered or their nature as yet unresolved within 1-10 Light Years (L.Y.) of the Sun? This is what he said there are still a few of those out there, but it's solely because our searches are incomplete and not because these objects are harder to find than BDs. They're actually a lot easier to find because they're hydrogen burners and emit more light than the BDs.

Dr. J.D. Kirkpatrick in private email correspondence and also Kirkpatrick (2003) has related i.e. that the population census of Very Low Mass objects like Late Type dwarfs e.g. M and stellar L dwarfs (i.e. SpT <L5) and especially that of BDs is as yet incomplete perhaps by as much as 50%.

While undoubtedly, the technology available is getting better and better with each passing day, scarce resources e.g. manpower and money; human prejudices and carelessness (i.e. in overlooking potential discoveries) can all render the BEST intentioned efforts useless.

An outline on the NGSS/WISE mission (Kirkpatrick, 2003) in which it was stated that the census of Low mass and cool BDs in the space between the Solar System and Proxima Centauri with Teff down to about 150°K is probably incomplete. i.e. quote from article: "there should be at least ~200 brown dwarfs with M > 10 MJup within 8 pc of the Sun."

If there are 200 BDs within 8 pc, then each BD occupies its own [(4/3) * pi * (8pc)^3]/200 = 10.7 pc^3. Out to Proxima Centauri there is a volume of space equal to [(4/3) * pi * (1.3pc)^3] = 9.2 pc^3. So, if we get lucky, there might be one BD closer than Proxima since the sphere of space centered on the Sun ought to have one such object in a volume slightly larger than that out to Proxima. So, if there are actually more than 200 BDs within 8pc (and what Kirkpatrick quoted here was just a lower limit to the expected numbers i.e. there are probably >200 BDs within 8 pc), then the likelihood of a BD closer than Proxima goes up.

Thus, it's still within the realm of possibility that the Sun could indeed have a very cold BD companion that we haven't discovered yet. Kirkpatrick also disclosed that it's things like that that keeps him going sometimes, too!

PULSAR TIMING

How it works:

Accurate timings of millisecond pulsars can provide a potential reference for the motions of the Sun, using the light time delay effects in various directions to define the motions and accelerations of the Sun. The motions of the Sun around the centre of mass of the Solar System, induced by the planets, can already be seen reflected in pulsar timings.

In principle, given a long enough baseline in time and enough timing accuracy, one could detect as-yet-unknown companions to the Sun which would exert a gravitational influence on the centre of mass.

FINDINGS

In Thornburg (1985), an upper limit was placed on the solar system acceleration at 10^-9 m/s^2

To find acceleration of solar system towards any a dark mass, we apply the following formula:

vdot = 0.6 m/a^2 ------------------- Equation (1)

The expression vdot = 0.6 m/a^2 is just Newton's law of gravity (where m is expressed in solar masses (Msun), a is the Semimajor axis in AU and vdot is in cm/s^2), this expression does not subject to the shape of the orbit i.e. it is independent of the ellipticity of any object under consideration.

Mass of Sun (Msun) = 1.989 * 10^30 kg, Mass of Jupiter (MJup) = 1.9 * 10^27 kg, Mass of Earth (Mearth) = 5.98 * 10^24 kg and Mass of BD companion = 2.85 * 10^28 kg.

The proposed BD companion has a Mass = 0.014328808 Msun (i.e. 15 MJup) and for the sake of facilitating the discussion let's assign an arbitrary semimajor axis (a) = 27500 AU

Substituting m = 0.014328808 and a = 27500 AU into ------------------- Equation (1)

We have,

vdot = 0.6 (0.014328808/27500^2)

vdot = 1.136831048 * 10^-11 cm/s^2

1 cm/(s^2) = 0.01 m/(s^2)

vdot = 1.136831048 * 10^-13 m/s^2

This acceleration value of 1.136831048 * 10^-13 m/s^2 is inside of Thornburg's upper Limit of 10^-9 m/s^2 i.e. what it shows is that a 0.014328808 Msun BD companion is still very much within the realm of possibility.

LIMITATION OF PULSAR TIMING SURVEYS

Due to the distribution of pulsars (they are found mainly in the galactic plane), there are areas in the sky where these timing surveys are rendered almost effectively useless. Thus for all we know, some dark masses in the outer perimenters of the solar system may still yet escape detection if they aren't anywhere near the galactic plane including a ~15 MJup BD.

References:
Burgasser, A. J.; Kirkpatrick, J. D., McElwain, M. W., Cutri, R. M., Burgasser, A. J., Skrutskie, M. F., 2003, AJ, 125, pp. 850-857

Burrows, A., Sudarsky, D., Lunine, J. I., 2003, Beyond the T Dwarfs: Theoretical Spectra, Colors, and Detectability of the Coolest Brown Dwarfs, ApJ, 596, pp. 587-596

Duquennoy A., Mayor M., 1991, A&A, 248, 485

Gizis, J. E., Kirkpatrick, J. D., Burgasser, A., Reid, I. N., Monet, D. G., 2001 ApJ, 551, pp. L163-L166

Hogg, D. W.; Quinlan, G. D. & Tremaine, S. 1991, AJ 101, p2274-2286

Kirkpatrick, J. D., Dahn, C. C., Monet, D. G., Reid, I. N., Gizis, J. E., Liebert, J., Burgasser, A. J., 2001 ApJ.121, pp. 3235-3253

Kirkpatrick, J. D., 2003, The Next Generation Sky Survey and the Quest for Cooler Brown Dwarfs, IAU Symposium Vol. 211 ("Brown Dwarfs")

Marcy, G. W., Butler, R. P., Vogt, S. S., Fischer, D., Liu, M. C., 1999 ApJ 520, p239-247

Teegarden, B. J., Pravdo, S. H., Hicks, M., Shaklan, S. B., Covey, K., Fraser, O., Hawley, S.L., McGlynn, T., & Reid, I. N., 2003, "Discovery of a New Nearby Star", ApJ 589, pp. L51-L53

Thornburg, J. 1985, An upper limit for the solar acceleration, MNRAS, 213, 27P-28P

Tinney, C. G., 1998, "The intermediate-age brown dwarf LP944-20", MNRAS 296, L42-L44

Wasserman, I., Weinberg, M. D., 1991 ApJ 382, p149-167

Last edited by a moderator: May 2, 2017
4. Jun 30, 2007

### Astrobuff

And guys, just in case you all get to think that this is nothing new but a rehash of Hut's/Muller's Nemesis Theory. I suggest you think again. There are a few things here that distinguishes the object that I am proposing here has an orbit nowhere bear that of Hut's/Muller's Nemesis.

1.
It certainly does not goes out anywhere near halfway between Sol and Proxima.

2.
The original Nemesis was supposed to have been a M Dwarf. I know Muller and team later suggested that a BD is a distinct possibility too. But my object is definitely a BD.

3.
This BD companion I'm proposing is in no way responsible for any of the major mass extinction episodes in the Earth's history. It certainly has not the 26-32 million years orbital period of Nemesis.

4.
My arguments thus are not because of the mass extinction episodes that we need this BD but because of the missing mass in the EKB, SD, OC and the excited even disturbed orbits of objects like Eris, Sedna and CR 105.

5.
While I do not claim that I'm the 1st one to have proposed that our Sun has anything else that is more massive than the planets known to orbit it, as is evidenced by me quoting Morbadelli and Gomez amongst others, my reasons while some of them may overlap with those of Morbadelli/Levison or those of Gomez et al., others are unique e.g. the missing mass in the above mentioned regions and the sharp edge to the Classical EKB at ~50 AU.

Hope this clears things up.

5. Jun 30, 2007

### tony873004

You might enjoy my computer program, Gravity Simulator, where you can actually set up these scenerios and watch them happen. The install even comes with a simulation of Morbadelli's "Captured Sedna" scenerio:

http://www.orbitsimulator.com/gravity/articles/sedna.html

6. Jun 30, 2007

### Astrobuff

Thanks Tony. :) I'm actually still waiting for Dr Paul Wiegert. For what it is worth, he and Dr Matt Holman once co-wrote a paper ( see Long-Term Stability of Planets in Binary Systems ) on the stability of planets in binary systems to get back to me. He promised me years ago to run some simulations for me on his Uni's supercomputers. It has been a long wait I must say. And yes the parameters of this hypothetical BD companion that I'm proposing has changed markedly since I last communicated with him - which incidentally was some 3-4 years ago now :surprised :tongue2:

Holman, M. J., Wiegert, P. A., 1999, Astron. Journal, vol 117, pp 621-628

Below are transcripts of what some of our numerous correspondence contained.

----- Original Message -----
From: Paul Wiegert <wiegert@astro.queensu.ca>
Date: Mon, 23 Jun 2003 15:56:48 -0400 (EDT)
Subject: Re: Question on Long Term Stability of Planets in Binary Systems

>
>
> Hi XXX. Sorry for the slow reply. Things have been busy here and I wanted
> to think about your e-mail a bit. I've also been interested in the
> question of what happened to the mass in the Kuiper Belt. And I think most
> would agree that its not impossible that there is a BD out there, though
> we would have had to be unlucky not to have seen it.
>
> I suspect the major objection would be that a body that massive passing
> through the Kuiper Belt would perturb the orbits of the planets more than
> is observed. I'd be happy to run a few simulations to take a quick look,
> in fact, maybe I'll through a couple on right now. These will be just
> rough and ready first looks, but they should tell us if the BD will
> destabilize the planets. They'll probably take a day or two to run. I'll
> let you know how they turn out.
>
> cheers
> paul
>
>
> ----------------------------------------------------------------------
> Paul Wiegert Tel: (613) 533-2684
> Department of Physics Fax: (613) 533-6463
> Queens University www.astro.queensu.ca/~wiegert/[/URL]
> Kingston Ontario K7L 3N6 CANADA [email]wiegert@astro.queensu.ca[/email]
>
> I must go down to the seas again, to the lonely sea and the sky
> And all I ask is a tall ship and a star to steer her by
> -John Masefield
> ----------------------------------------------------------------------
>

Also this,

Hi. In the limit where the secondary is small, we expect that the Hill sphere defines the maximum distance in which planets could be stable. Well, actually its about half the Hill sphere, less if you want to stay on a reasonably circular orbit (the Moon is about at about 1/5 of the
Earth's Hill sphere radius. When we say O[mu^1/3] and such, O just means "of order", which means, like some small constant times it, eg O[mu^1/3] = k mu^1/3, where k is some small constant (whose exact value we are not interested in here, just the dependence on mu).

However, in the case of very eccentric orbits, the Hill sphere is no longer a good approximation. We don't have an exact expression, but probably if the secondary has a larger mass than the planets, they can't expect to be stable much beyond about half the closest approach distance.

Hope this helps!
paul

By the way, I am using GNU/Linux at home these days. Used to have a FreeBSD partition lying around but did away with it. Just could not stand having to sit around a day or so for a package like ruby1.8 to get compiled from source especially on my ancient machine. But running a program like Xorsa (see *1) be it on Debian or FreeBSD can be quite demanding on my pathetic system's meagre resources I must readily confess. ;)

*1

penanshin@debian> apt-cache show xorsa
Package: xorsa
Priority: optional
Section: science
Installed-Size: 4092
Maintainer: Frank S. Thomas <frank@thomas-alfeld.de>
Architecture: i386
Source: orsa
Version: 0.7.0-8
Depends: fftw2, libc6 (>= 2.5-5), libcln4, libgcc1 (>= 1:4.2-20070516), libginac1.3c2a (>= 1.3.0), libgl1-mesa-glx | libgl1, libglu1-mesa | libglu1, libgmp3c2, libgsl0 (>= 1.4), libice6 (>= 1:1.0.0), liborsa0c2a, libpng12-0 (>= 1.2.13-4), libqt3-mt (>= 3:3.3.7), libsm6, libstdc++6 (>= 4.2-20070516), libx11-6, libxext6, zlib1g (>= 1:1.2.1)
Filename: pool/main/o/orsa/xorsa_0.7.0-8_i386.deb
Size: 1255964
SHA256: 007496dfe733e2e970d323649d65b88a8dae03bcf433afb7de176c9a08166d09
Description: tool for Celestial Mechanics investigations
Orbit Reconstruction, Simulation and Analysis (ORSA) is a framework
for Celestial Mechanics investigations. The main goals of the project
are the implementation of state of the art orbit integration
algorithms, with concerns on accuracy and performance, and the
development of a number of analysis tools.
.
This package contains xorsa, the main graphical application provided
by the ORSA project. It is an interactive tool for scientific grade
Celestial Mechanics computations. Asteroids, comets, artificial
satellites, Solar, and extra-Solar planetary systems can be
accurately reproduced, simulated and analyzed.
.
Homepage: [url]http://orsa.sourceforge.net[/url]
Tag: field::astronomy, implemented-in::c++, interface::x11, role::program, uitoolkit::qt, x11::application

Last edited by a moderator: Apr 22, 2017
7. Jul 1, 2007

### tony873004

I find Dr. Wiegert quite helpful. He usually is slow to respond to e-mails, but he always responds. There are a few simulations on my website that are inspired by his work:

http://www.orbitsimulator.com/gravity/articles/cruithne.html
http://www.orbitsimulator.com/cgi-bin/yabb/YaBB.pl?num=1176415775/30

I would guess the same reason for both. It has been theorized that a close stellar encounter early in the Sun's history caused these. The Sun might have been part of a star cluster in a star forming region for the first few hundred million years of its existance. During such a time it may have had several close and slow encounters with other stars which scrambled the solar system beyond a certain point.

This is wrong. This is like saying that the gravity well of the Earth will end when its gravity at a certain point in space equals the gravity from the Sun. But the Sun's gravity pulls the Moon more than twice as hard as the Earth's gravity, yet the Moon remains firmly in Earth orbit. The Hill Sphere is what you need to compute.

If it exists, I would agree with you, or it would have been stripped away a long time ago. Proxima is simply the closest star NOW. In a million years Gliese ??? will pass only 1 LY from Earth.
[quote =Dr. Wiegert]I'd be happy to run a few simulations to take a quick look,
> in fact, maybe I'll through a couple on right now. These will be just
> rough and ready first looks, but they should tell us if the BD will
> destabilize the planets. They'll probably take a day or two to run.
[/quote]
I suspect he meant that it would take a day or two to get back to you. You don't need a supercomputer to do these types of simulations. The program I wrote ( www.gravitysimulator.com ) can perform these types of simulations in a matter of minutes to hours (although properly setting up the simulation can take some time).

You'll commonly see this approximated as (50000/5.2)^4, although your was is a little more accurate.
Here's a link to some calculators I wrote that you may find useful. There's a stellar encounter calculator, as well as a Hill Sphere calculator, and some Kozai mechanism calculators which you may want to consider since the Kozai mechanism permits a massive body orbiting out of plane to tamper with the orbits of the objects interior to it without ever coming close: http://orbitsimulator.com/formulas

8. Jul 1, 2007

### Astrobuff

Yes it has been theorized by several e.g. Shigeru Ida, Kenyon or Bromley (either or both) but in the Morbadelli paper, I think both Morbadelli and Levison have run their own simulations (see their paper) to show that such encounters (although they are sure to have occurred on many occasions before) could not have produced so many anomalies in so many objects (e.g. Eris, Sedna, CR 105, the thousands if not millions or billions of bodies where in the few tenths or few Earth masses of material in the EKB and SD; the thousands if not millions or billions of bodies where in the few Mearth or MJup of masses in the OC) who may I gently remind, are ALL on different orbits all and also it is inconceivable that all are in or around the same place centered or in the vicinity of the encounter trajectory of any of the stars that may have passed closeby. While not totally demolishing the case for close stellar encounters, I think Morbadelli et al did a reasonably good job in rendering such encounters as a cause for the above mentioned orbital disruptions rather dubious. And just for the record, may I add that in that same paper mentioned, Morbadelli and Levison also precluded any likelihood that a migrating Neptune is the cause for the disrupted orbits of Sedna and CR 105 as well.

Also your contention that some of these closeby stars near the Sun when it was still part of some open cluster has slow and close encounters with it, would not such slow encounters have consequenced in a capture by the Sun especially if they happened to be of a lesser mass than the Sun? And if these rogue stars are much more massive than the Sun, would not the Sun and our solar system especially the outer planets have been severely disrupted? And if not why not? I do not deny that there have been encounters but question is at what distance, the sizes of these interlopers, the trajectory angle, velocity of these interlopers, duration of the encounters as well as the frequency of such encounters (i.e. every few thousand years, Myrs, Gyrs or what)? Also you mentioned that these encounters kinda scrambled the solar system into what we see today but again it begets another question. Why stop? Why did it not scramble the solar system totally?

Given the situation and premises laid out as it is, I suppose I'm not being too unreal here to suggest that a permanent binary companion even if it happens to be a VLM BD best fits the bill as the solution. Like what the folks on the centauri-dreams website (or something along the same lines and to the same effect) have said, some object rushing in at 4000 km/s is NOT as threatening as another plodding along at a relative snail's pace at but mere 4 m/s. It is the relative permanence i.e. length of stay that inflicts the DAMAGE i.e. by slowly, gradually, painstakingly grinding away, removing masses by directly ejecting them into even further reaches of the OC or into infinity. Or by perturbing their orbits so much so that they become chaotic and mutually collisional. I guess honestly speaking, this presents the most plausible explanation and solution to the above mentioned problems in in the EKB and beyond.

Want to place a bet on who related to me that (i.e. about the half way point between the Sun and our nearest star as the relative end point of the Sun's gravitational potential? It was some Astronomy Professor into Celestial Mechanics over an email. :tongue: I'll double check with a few more Profs to see who is right. Stay tune! But wait...ah...before I forget, you may also need to correct what you think about the relative importance of the Hill Sphere in situations like these after reading what Dr Paul Wiegert has to say here:

Yes. I do concede that this is a possible scenario given the frequency of close stellar passages past and present. I'm not saying and have never said that this BD companion is still defintely there and will stay there till time immemorial. Mind you, it it not a requirement for the Sun to be in an open cluster, forget about a GC to have such encounters. The Sun is for the moment, a solitary star (till as and when proven to be otherwise) but in its journey around the Galactic Center, there have been and will be such close encounters with other stars, BDs and other exotic entities e.g. GMCs. As you have noted, one such encounter will be GL 710, a 0.5 Msun M dwarf who will be heading this way in about...hold onto your seats folks!...1.4 Myrs time. But its closest approach will come NO further in than ~1.1 LYs at about ~70,000 AU.

Anyway back to what we are discussing at hand, such encounters can eject whatever that is out there in the OC to infinity or if not completely to the very outskirts at the very least. This is where I argue that I and others including Hut and Wasserman, etc have a case for real outliers of a binary companion i.e. that such encounters may produce binary companions at even LY distances from their primaries. The only reason why we have not detected many thus far is because of the tedious job of ascertaining common proper motion, parallaxes, time, etc.

Proxima Centauri is indeed the closest KNOWN star for the time being yes. No doubts about it for now that is. But it may not be in a few years or a few decades time if JWST/WISE has anything to do about it. See what Dr J. D. Kirkpatrick has to say about BDs within the space from here to Proxima. And also those few hydrogen burning VLM M dwarfs. I have prepared my ground quite extensibly in preparation of such questions Tony :tongue:. OK I'll not put you through the pain of what is admittedly a rather tedious task of sifting through the wordy stuff I wrote above. Check this out! It is from the horse's own mouth i.e. Dr J. D. Kirkpatrick the man himself and I think Principal Investigator behind WISE >

1.
2.
He may or he may not. I also once communicated with Dr Levison, the man who together with Morbadelli came up with the BD interloper as the most likely cause for the disturbed orbits of Sedna and CR 105 (Eris the dwarf planet wasn't discovered then, so bad of you Dr Brown! :P), wanted to do some simulations to check for stability over Myrs or Gyrs timeline not just a few simple simulations using some rudimentary software downloadable that can be run so easily on a x86, MIPS, MIPSEL, Alpha, PPC, Sparc, etc. He wanted to factor in things like secular perturbation by other masses, etc you see.

Also getting back to what Dr Wiegert actually did say,

From what is implied in that paragraph, he wanted to run a few simulations not simply one or two. And that will be just rough and ready first looks and also They'll probably take a day or two to run. The latter sentence implies that he's probably churning them with some kind of software on some kind of high end machine. And even with such a machine, it'll take a day or two NOT something that will produce tangible results in minutes or hours. I'm not sure how much advances both the software and hardware have made in the time since 23 Jun 2003 15:56:48 -0400 (EDT) but I seriously doubt that for the kind of output desired by Dr Wiegert i.e. to rule it either way, the improvements made cannot have been so remarkable as to have cut down the time from a day or two to but hours or even minutes. And then he ended by saying that he'll get back to me i.e. I'll let you know how they turn out I'm still waiting some 3 years and 1 week on :surprised:tongue2:. Although to be absolutely fair, he did not spell out a definite date.

Thanks. I'll check them out. Although admittedly, I'm pretty reliant on different Profs and Drs to run the simulations on my behalf. :tongue:

Reference:
Kirkpatrick, J. D., 2003, The Next Generation Sky Survey and the Quest for Cooler Brown Dwarfs, IAU Symposium Vol. 211 ("Brown Dwarfs")

Last edited: Jul 1, 2007