A Neptune Mass Planet in the Oort Cloud

[Astrobuff]

Dr Steinn Sigurðsson (Penn State) has been reporting findings announced at the Confererence on Extreme Solar Systems on his blog Speculation of another Neptune in the Solar System at the Conference of Extreme Solar Systems, Santorinibut amongst all the interesting discoveries is this idea raised by planetary dynamicist Dr Ed Thommes:

 

 

"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."

 

 

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:

 

"Undoubtedly, something massive knocked the hell out of the belt, the question is whether it's there now."

 

 

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

 

Links:

*1

Mass Deficit in the Outer Solar System

*2

Eris

*3

Sedna

*4

CR 105

*5

The Calssical EKB

*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

[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

 

 

 

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.

 

 

 

ADDITIONAL INFORMATION:

 

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

[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. 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.

[Martin]

Hello Astrobuff, welcome to SFN.

 

I am glad to see you read Stein's blog----'dynamics of cats'

 

He is calm and reserved about the possibility of there having been a neptunesizer out there at one time (to help somebody's solarsystem model work)

and he says the most likely scenario, if there was such a thing at one time, is that it got subsequently ejected. That is, that the sun formed in a rich enough starforming region to make a onetime flyby by another star at say 100 AU reasonably likely----and that presumed flyby ejected the neptunesize thing (if it was ever there in the first place)

 

IIRC he says, in all fairness, that he is not sure that the search for such things has been thorough enough to absolutely rule out a neptunesizer being still there in the outer Oort but he doesnt suggest much hope of it.

 

I think the point is that Stein is NOT sensationalist. He's a top-quality postdoc at Penn State. He is careful not to let his imagination run away with him and to avoid treating speculation as astrophysical "news".

 

We need to do a certain amount of filtering here at SFN, to keep the crackpot index from getting too high.

 

I've heard Muller talk about Nemesis, but that was a long time ago. It had a certain attention-getting maverick flavor IMO even then. And now it has been kind of discredited or forgotten and consigned to the junkheap of nice ideas that didnt work.

 

Personally I wouldn't welcome anything that looks like a rehash of Muller's Nemesis by changing a few details. In that direction there's too much of the self-important delusional quality that you get with crackpots, and too little real news.

 

I would welcome more straight reporting of the legitimate mainstream academic astrophysics news, if you could keep your own ideas separate from it. that is just my personal view (others may differ)

[Astrobuff]

Martin (Physics Expert)

Unread Today, 12:38 AM Add to Martin's Reputation Report Post #4

Martin's Avatar

Hello Astrobuff, welcome to SFN.

 

I am glad to see you read Stein's blog----'dynamics of cats'

 

He is calm and reserved about the possibility of there having been a neptunesizer out there at one time (to help somebody's solarsystem model work)

and he says the most likely scenario, if there was such a thing at one time, is that it got subsequently ejected. That is, that the sun formed in a rich enough starforming region to make a onetime flyby by another star at say 100 AU reasonably likely----and that presumed flyby ejected the neptunesize thing (if it was ever there in the first place)

 

IIRC he says, in all fairness, that he is not sure that the search for such things has been thorough enough to absolutely rule out a neptunesizer being still there in the outer Oort but he doesnt suggest much hope of it.

 

I think the point is that Stein is NOT sensationalist. He's a top-quality postdoc at Penn State. He is careful not to let his imagination run away with him and to avoid treating speculation as astrophysical "news".

 

We need to do a certain amount of filtering here at SFN, to keep the crackpot index from getting too high.

 

I've heard Muller talk about Nemesis, but that was a long time ago. It had a certain attention-getting maverick flavor IMO even then. And now it has been kind of discredited or forgotten and consigned to the junkheap of nice ideas that didnt work.

 

Personally I wouldn't welcome anything that looks like a rehash of Muller's Nemesis by changing a few details. In that direction there's too much of the self-important delusional quality that you get with crackpots, and too little real news.

 

I would welcome more straight reporting of the legitimate mainstream academic astrophysics news, if you could keep your own ideas separate from it. that is just my personal view (others may differ)

______________

We have calculated Newton's law starting from a world with no space and no time--Carlo Rovelli, August 2006.

Last edited by Martin : Today at 01:15 AM.

Join Date: May 2004 | Posts: 3,039 | Location: GMT-7 timezone | Martin is offline

 

Martin, I share not with you that this BD companion that I'm talking about is anything but a sensationalist theory nor something but a rehash of Muller's or even Matese's Nemesis. The circumstances that has led to each of us to believe that such a body may yet lie undiscovered are different if only one bothers to read the reasons again. e.g. where in Muller's or Matese's papers on Nemesis mention of 1.) the disturbed orbits of Eris, Sedna, CR 105 or 2.) the mass deficit in the EKB, SD or OC or 3.) the abrupt sharp termination to the Classical EKB at ~50 AU as reasons for their respective Nemeses? If these weren't the grounds on which they built their cases on for Nemesis, how then are their Nameses the same as the hypothetical BD companion I'm espousing here? If it is agreed that this is no rehashing why use the word rehash then?

 

And just to add neither have I said that it is definitely still there. I don't think anyone, no matter how eminent he/she is, can guarantee anything absolutely. Not even a Nobel Prize winner like Prof Steve Thorsett, whom I have also have had the honor of corresponding with on one occasion. Just that it may be there. So in the light of this how than can I or my hypothesis be called a crackpot (see dictionary meaning in Q1) or a rehash (see dictionary meaning in Q2)? I'm not a native speaker of the English language, to that I must readily confess. So for what it is worth, I'm always willing to learn, if you (or others) have something to teach (in addition to what Webster Dictionary has taught me about those 2 words). Damn I think I just lifted an entire line from Martin Gore's song Somebody there me think LOL.

 

Q1

Rehash

Rehash Re*hash" (r?*h?sh"), v. t.

To hash over again; to prepare or use again; as, to rehash

old arguments.

[1913 Webster]

 

Source: -- From The Collaborative International Dictionary of English v.0.48

 

Rehash Re*hash", n.

Something hashed over, or made up from old materials.

[1913 Webster]

 

Source: -- From The Collaborative International Dictionary of English v.0.48

 

Q2

crackpot

crackpot crackpot n.

a whimsically eccentric person.

 

Syn: crank, nut, nutcase, screwball.

[WordNet 1.5]

 

Source: -- From The Collaborative International Dictionary of English v.0.48

 

Both the Muller and Matese groups believed that there was a solid ground to their contention, they both arrived at some kind of a M dwarf companion perturbing the orbits of the LPCs, so much so that there is a periodicity i.e. every 30 million years or so, some great mass extinction event (e.g. like the one that wiped out most of the dinosaurs except for perhaps the crocodile some 65 Myrs ago) happens because of the effect of this M dwarf i.e. Nemesis's orbit. But where in anything that I have written is even remotely suggestive of such a link between my hypothetical BD companion or its orbit to mass extinction events on Earth may I ask? What both the Muller and Matese groups and myself may share in common is a genuine (not for malicious ends) belief that there is an anomaly or that there are anomalies, and they need investigation. we can't just dismiss them as if they don't exist. And to do that, we have to come up with some hypotheses, which can be readily tested, proven or debunked. So why refuse the seeking of answers or be fearful of learning what these answers or whether they turn out one way or the other?

 

I have always believe in a simple philosophy which happens to be that if one has questions, one should raised them even if they happened to be hard questions for those one is directing these questions to. But isn't the very foundation of science based on asking questions, building some hypotheses out of them if needed, arrive at a solution or 2, implement the solution/s, test the solution/s, and revise and improve on the solution/s where needed afterwards. Isn't this what the scientific approach as espoused by George Bernard Shaw is all about?

 

Also the likely birth of the sun in even a moderately rich open cluster like Orion's does not preclude the potential of the sun holding on to any binary companions. Most of the stars around have at least another companion if not more orbiting it (see *1 & *2). Not only of those still enjoying some kind of cluster membership but also amongst the thin and thick disk populations including most of the Sun's immediate neighbors dare I add.

 

Also I'm not sure how propounding any theory perhaps calling that may be a bit ill advised, given that this suspicion of mine is not a a fully matured one like several of Matese's/Whitmire's or those of Levison's. But certainly they are all based on true phenomenons that can readily be verified to truly exist e.g. the abrupt edge of the Classical EKB at ~50 AU, the mass deficit in the EKB, SD and OC, the seemingly disturbed orbits (as evidenced in their unusually high orbital inclinations and eccentricities vis-a-vis other solar system planets including the planets and asteroids in the Main Belt) of outliers like Eris, Sedna and CR 105. So I don't see how my belief can be suggested to be something coming from that of a crackpot or charlatan. A crackpot certainly won't go to the extent go to the extent that I have gone in painfully digging around for academic literature published by renowned journals like AJ, ApJ, MNRAS, Icarus, Nature, etc., reading them, digesting & understanding them (and if failing to do so consult distinguished astro Profs) does he/she?

 

A crackpot also bothers not to badger almost each and every Prof and Dr listed in the Astronomy and Astrophysics Dept of any a prestigious Uni like Ucolick, Univ Arizona, UCLA, etc., or even institutions like Max Planck does he/she? I'm sure if you were to write in to people like Prof Gibor Basri if he can recall someone who used to pester him on his email by sending without fail some 30-50 questions with several sub-questions in them each time, he will know who you are talking about. The same goes for the likes of Profs Colin Scarfe & Robert Mathieu, Profs Shri Kulkarni & Scott Tremaine who also taught me bits on pulsar timing, dark masses in the solar system, etc; planetary dynamicists Drs Paul Wiegert and Matt Holman; formation of planetary systems around binaries expert Prof Willy Kley, Astronomie & Astrophysik, Computational Physics, Universität Tübingen, Auf der Morgenstelle 10, 72076 Tübingen, Germany; Jeff Mangum from NRAO who was patient and taught me tons on Pulsar Timing over email; Dr Peter Hauschildt & Prof Dimitar Sasselov - BD & EGP Theoreticians; Everyone is entitled to his or her opinion on things, you are to yours and I'm to mine but we can beg to differ, can we not?

 

I guess I'm not being overly unreal here in saying that I'm no crackpot but am really serious in trying to understand and work on the problems we have in the outer solar system from the EKB outwards. Seeking whatever literature from whichever eminent expert there is in the fields I'm concerned with or need to understand in order for me to conjure up a credible hypothesis. Note perhaps a hypothesis is perhaps a better term to describe what I have presented here indeed.

 

Ref:

 

*1

 

http://www.cfht.hawaii.edu/Reference/Bulletin/Bull39/bulleti4.htm

 

 

 

Accretion in PMS binaries : high angular resolution spectra with OSIS

 

J.-L. Monin and G. Duchêne (Grenoble).

 

During the past five years, many studies have addressed the question of the multiplicity in star-forming regions (SFR). While about 60% of G-K main sequence dwarfs belong to multiple systems in the solar vicinity (Duquennoy & Mayor 1991), several papers (e.g. Leinert et al. 1993) have pointed out that 80%, and maybe up to 100%, of Taurus young stars are not formed singly. More recently, this binarity excess has been found in other SFR (e.g. Ghez et al. 1997). It is a major theoretical challenge to explain several points including why do stars form in multiple system, and why is the degree of multiplicity different in different SFR and in the solar environment.

 

*2

http://etacha.as.arizona.edu/~eem/ttau/

 

Most T Tauri stars are in BINARY star systems

 

They have temperatures and masses similar to the Sun, but they are BRIGHTER. They have FAST ROTATION rates (few days compared to a month for the Sun). They are ACTIVE, VARIABLE stars (few days compared to a month for the Sun) Variable X-ray and radio emission (Solar-like activity X 1000!)

[Astrobuff]

Some examples of the questions I have sent to various astronomers and astrophysicists over the years below:

 

From: Peter Hauschildt <yeti@hobbes.physast.uga.edu> [save Address] [block Sender]

 

Cc:

Subject: Re: Some Question on Brown Dwarfs and Infrared Astronomy

Date: Wed, 6 Aug 2003 09:17:58 +0200

 

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> Question 1.)

> I understand that any Object of Solar metallicity once they

attain

> about 13 Mj in mass, they are capable of some deuterium fusion.

> However, what if the metallicity of the object is zero or twice

that

> of the Sun? What are the theoretical minimum masses for

deuterium

> burning for such objects (i.e. metallicity = zero and

metallicity > twice

 

No idea, I'm not doing stellar evolution models.

>

> Question 2.)

 

> DISEQUILIBIUM chemistry i.e. molecular species predicted by

models to

> have disappeared at such low tempearatures apparently are still

> lingering around*1,*2&*3. From theory, it is understood that

Brown

> dwarfs (BDs) are FULLY CONVECTIVE objects

 

Actually, it L & T dwarfs the convection zones retracts ever more

from

the

outer atmosphere. fully convective is an interior term that describes

that

once convection stars, it keeps going to the center of the object.

The atmosphere is far more complex.

 

> and thus vertical transport of heat and material is rather

EFFICIENT.

> My question then is would not the combination of dredging up

from the

> interior of these metals with the HEAT that BDs possess and

> interaction with water/ice crystals especially in ul

> tracool BDs (i.e. those with Teff <500 K) produce perhaps

not flares

> BUT visible fiery amber color aurorae-like displays? Also I'm

curious

> IF the dark reddish-magenta

 

The energy densities of chemical reactions are likely far too low for

that

to be visible. Mag. fields or just the internal radiation have

probably

far higher energy densities.

 

Cheers,

Peter

--

************************* Note new Address

*******************************

========================================================================

 

==

Peter H. Hauschildt Phone: +49 40 42891-4013

Hamburger Sternwarte Fax: +49 40 42891-4198

Gojenbergsweg 112 Email: yeti@hs.uni-hamburg.de

 

21029 Hamburg, Germany

http://www.hs.uni-hamburg.de/~stcd101/

 

========================================================================

 

==

PGP public key available at pgp-public-keys@pgp.ai.mit.edu

 

PGP fingerprint: A6 4A 37 AC 15 96 E7 E7 83 99 DB AE 7F 19 D5 35

========================================================================

 

==

= "Prepare For More Mowing!!" (1)

= "Scientific Progress Goes 'Boink'?!" (2)

= "Real Programmers Don't use Pascal!!!" (3)

 

 

 

==================================================================================================

 

 

 

Subject: Re: Re: Astronomy Questions

From: Greg Novak <novak@ucolick.org> Add to Contacts

Date: Mon, 4 Aug 2003 17:58:25 -0700 (PDT)

View Message Source

 

I see. Unfortunately the Ask an Astronomer page isn't an appropriate

resource for the kind of help you're looking for. The questions you're

asking are too detailed for this forum and could be written up as a

research paper themselves. It seems that you're looking for a research

collaborator.

 

I can point you toward a few resources: For your questions about radial

velocities, I suggest you look at "Solar System Dynamics" by Murray and

Dermott. There's also a book called "Stellar Structure and Evolution" by

Kippenhahn and Wiegert that handles the details of the structure of stars

(including brown dwarfs).

 

Good luck,

Greg

 

==========================================================

 

Subject: Re: Questions on Truncation radiis in Eccentric & Extreme mass ratio systems

From: "Robert D. Mathieu" <mathieu@astro.wisc.edu> Add to Contacts

Date: Mon, 04 Aug 2003 07:41:54 -0500

Cc: kley@tat.physik.uni-tuebingen.de

View Message Source

 

Dear John,

 

Many thanks for your message, and your interest in the exciting work

of Dr. Kley at our Symposium. Your questions are rather specific and

technical, so I would encourage you to send your message to him

directly. I will also copy Willy with this message.

 

Sincerely,

 

Bob Mathieu

 

 

John Stimson wrote:

>

> Hello there Professor Mathieu, I am a marketing

> manager by profession

> but I do have an intense interest in astronomy.

> However, I'm at best,

> very much a novice still. I hope you can offer

> advise on some

> questions that I have with regards to a paper by

> Mr. Wilhelm Kley

> that you co-edited.

>

> Question (1)

> In Kley, 2001, it is stated : "As the ratio of

> distance d of the

> secondary over the semimajor axis a of the planets

> falls into the

> range d/a = 400-10000 the companion has very

> little influence on the

> eccentricity of the planet."

>

> Does this rule (i.e. d/a = 400-10000) apply to

> components of near

> equal masses only? What aboutin a system where the

> primary is a solar

> mass star (i.e. Mprimary = Msun = 1.989 * 10^30

> kg) and a binary

> companion with a mass as tiny as a mere

> 0.016239316 Msun, does it

> apply as well?

>

> Question (2)

> From Kley, 2001 again, I quote:

> "The presence of a companion excites tidal waves

> in the disk around

> the primary which, for a star on a circular orbit

> are stationary in a

> frame corotating with the binary period. These

> spiral waves carries

> angular momentum and energy (see e.g. Lin &

> Papaloizou, 1993). As the

> star orbits the disk beyond the outer disk radius,

> its keplerian

> velocity is smaller than that of the disk and the

> angular momentum

> carried by the spiral wave is negative with

> respect to the disk

> material. Dissipation of the wave, for example

> through shock waves,

> will slow down the matter in the disk and lead to

> an inward drift of

> the material. This in turn truncates the outer

> edges of the disk."

>

> ASSUMING primary is a Solar mass star (i.e.

> Mprimary=1.989 * 10^30

> kg) and the binary has a mass i.e.

> Msecondary=0.016239316 Msun.

> Question is what happens IF binary is on an

> eccentric orbit (i.e.

> when e=0.3, e=0.5, e=0.7, e=0.9 or e=0.98)? What

> will the excitation

> for these tidal waves be like on the circumprimary

> disk? How will it

> affect the outer radius radius of the

> circumprimary disk? Will the

> truncation be even more or less dramatic or

> neutralized (i.e.

> EXTREMELY low mass of the secondary and the very

> HIGH eccentricity of

> the binary cancelling one another out)?

>

> Question (3)

>

> In the same paper Kley, 2001, this was mentioned:

> "Their main results are displayed in Fig. 1. the

> label µ = M2/M1+M2.

> In the case of the circumprimary disk, a larger

> viscosity (Reynolds

> number) leads to a larger truncation radius rt,

> while for a

> circumbinary disk, it reduces the truncation

> radius. For typical

> values of protostellar disks Re~10^5, and for

> typical binary

> parameter (see above q = 0.5, e = 0.5) we obtain

> for the

> circumprimary disk rt/a = 0.17 and for the

> circumbinary disk rt/a =

> 3.0."

>

> Assuming a Vicosity SIMILAR to that in the

> primodial Solar Nebula,

> and µ = 0.15979814 what would the truncation

> radiis be like for both

> the circumprimary and the circumbinary disks for

> various values of

> Eccentricity (e) of the secondary (e.g. e = 0.3,

> 0.5, 0.7, 0.9 &

> 0.98)?

>

> Reference:

>

> Kley, W., 2001, Planet Formation in Binary

> Systems, In Birth and

> Evolution of Binary Stars, Proceedings of IAU

> Symposium No. 200 Eds.

> Zinnecker, H. & Mathieu, R. D., p.511

>

> Thanks for your time. Hope to hear from you soon.

> Regards,

 

 

==========================================================

 

Correspondence with Prof. Colin Scarfe

 

> Q1.

 

>

 

> With G = 6.672 * 10^-11 Nm^2/kg^2, all the masses must be in kg, the period

 

> in seconds and all distances in metres 1 Year = 365.2568983 days

 

> a = 6500 AU = 9.724 * 10^14 m

 

> P = 515672.5836 years = 515672.5836 * 365.2568983 * 24 * 60 * 60 s

 

> P = 1.627369647 * 10^13 s

 

> Position Angle (x) at Apastron = 180º

 

>

 

> V1 = 2 * pi * a/(P sqrt (1 - e^2)) -----------------------------------

 

> Equation (1) Substituting pi = 3.1415926, a = 9.724 * 10^14 m, P =

 

> 1.627369647 * 10^13 s & e = 0.98801923 into Equation (1), we have, V1 = 2 *

 

> 3.1415926 * 9.724 * 10^14/(1.627369647 * 10^13 sqrt(1 - 0.98801923^2)) m/s

 

> V1 = 6.109769288 * 10^15/(1.627369647 * 10^13 * 0.154330817)

 

> V1 = 6.109769288 * 10^15/2.511532872 * 10^12

 

> V1 = 2432.685376 m/s

 

> V1 = 2.432685376 km/s

 

>

 

> V2 = e * V1 ----------------------------------- Equation (2)

 

> Substituting V1 = 2432.685376 m/s & e = 0.98801923 into Equation (2), we

 

> have, V2 = 0.98801923 * 2432.685376 m/s

 

> V2 = 2403.539932 m/s

 

> V2 = 2.403539932 km/s

 

>

 

> At Apastron i.e. 12922.125 AU, Angle x = 180º

 

> Radial Velocity (RV) = V2 sin x ------------------------------Equation (3)

 

> Substituting V2 = 2403.539932 m/s and x = 180º into Equation (3)

 

> RV = 2.403539932 sin 180º

 

> Therefore RV = 0 m/s

 

>

 

Correct.

 

>

 

> Tangential Velocity (Vt) = V1 + V2 cos x ----------------------Equation (4)

 

> Substituting V1 = 2432.685376 m/s, V2 = 2403.539932 m/s & x = 180º

 

> Vt = 2.432685376 + 2.403539932 cos 180º

 

 

 

This is already in km/s

 

 

 

> Vt = 2432.685376 + 2403.539932(-1)

 

> Therefore Vt = 0.029145444 m/s = 2.94145444 * 10^-5 km/s

 

 

 

So there was no need for this - your answer is too small by a factor 1000.

 

 

 

Tangential Velocity (Vt) = V1 + V2 cos x ----------------------Equation (4)

 

Substituting V1 = 2432.685376 m/s, V2 = 2403.539932 m/s & x = 180º

 

Vt = 2.432685376 + 2.403539932 cos 180º

 

vt = 2432.685376 + 2403.539932(-1)

 

vt = 29.145444 m/s = 0.029145444 km/s

 

 

 

>

 

> At apastron (d) = 12922.125 AU = 1.9331499 * 10^12 km

 

> µ = Vt/d ----------------------------------- Equation (5)

 

> Substituting Vt = 2.94145444 * 10^-5 km/s and d = 1.9331499 * 10^12 km into

 

> Equation (5) µ = 2.94145444 * 10^-5/1.9331499 * 10^12

 

> µ = 1.507666012 * 10^-17 radians/s

 

> As 1 radian = 206265''

 

> Thus,

 

> µ = 3.1097873 * 10^-12 ''/s

 

> µ = 3.1097873 * 10^-12 * 60 * 60 * 24 * 365.2568983 ''/yr

 

> µ = 9.813927716 * 10^-5 ''/yr i.e. 0.098139277 mas/yr

 

>

 

> Are my calculations for RV, Vt and µ (mu) correct? Also these values as

 

> computed above are for heliocentric RV, VT and µ aren't they?

 

>

 

Vt and mu are too small by a factor 1000, as mentioned above.

 

 

 

At apastron (d) = 12922.125 AU = 1.9331499 * 10^12 km

 

µ = Vt/d ----------------------------------- Equation (5)

 

Substituting Vt = 0.029145444 km/s and d = 1.9331499 * 10^12 km into Equation (5)

 

µ = 0.029145444/1.9331499 * 10^12

 

µ = 1.507666012 * 10^-14 radians/s

 

As 1 radian = 206265''

 

Thus,

 

µ = 3.109787299 * 10^-9 ''/s

 

µ = 3.109787299 * 10^-12 * 60 * 60 * 24 * 365.2568983 ''/yr

 

µ = 9.813927716 * 10^-2 ''/yr i.e. 0.098139277 ''/yr

 

µ = 98.13927715 mas/yr

 

 

 

> Q2.

 

> Let's suppose then that this hypothetical BD companion's current equatorial

 

> coordinates are centered on RA 19h30m55.00000s, DEC +17d30m33.0000s (UT

 

> Date (yymmdd) 991024) which, when converted to ecliptic coordinates

 

> (J2000.0) translates into Longitude 298.19484499º, Latitude 38.74976534º

 

> and PA (East of North) 11.365602º (Source: NED Coordinate & Extinction

 

> Calculator Results) with interstellar reddening E(B-V) = 14.468 mag

 

> (believe this is within the confines of the Galactic Plane) i.e. a region

 

> of space where much interstellar dust. Sir, from your previous reply, you

 

> mentioned this,

 

>

 

> QUOTE: "We can assume that the direction to the object from the earth is

 

> the same as it is from the sun, to a very good approximation, and that the

 

> earth's orbit is a circle. If then the object's celestial latitude and

 

> longitude are l and b, and the sun's celestial longitude is lsun, while the

 

> earth's velocity is Ve, then the component of Ve in the line of sight to

 

> the object is Vc, where

 

>

 

> Vc = Ve * sin (l - lsun) * cos b.

 

>

 

> Celestial latitude and longitude are similar to terrestrial ones, but are

 

> based on the ecliptic, not the equator. This means that the sun's celestial

 

> latitude is always zero, which explains why it doesn't appear in the above

 

> equation."

 

>

 

> what should we input for the Sun's celestial longitude i.e. lsun given the

 

> above RA and DEC coordinates for the hypothetical BD companion so as to

 

> enable me to derive Vc (i.e. geocentric radial velocity)? In general, how

 

> do we go about determining the Sun's celestial longitude when a Solar

 

> System object's celestial longitude and latitude are known? Is there a

 

> general equation of some sort around?

 

>

 

The sun's celestial longitude changes continuously, so you would need to look

 

it up in an Almanac, such as the one put out jointly by the Royal Observatory

 

and the U.S. Naval Observatory for the date you want. You can interpolate for

 

fractions of a day. Alternatively you can be reasonably accurate by assuming

 

that the longitude is zero on March 21 and increases just under one degree

 

per day after that (360 degrees in 365 days).

 

 

 

 

 

> Q4.

 

> In the last month or so, I recieved the following from a friend:

 

> "Harrison (Nature 270, 324, 1977) measured pulsar period changes and said

 

> they could be due to the Sun's acceleration due its orbiting with a

 

> companion. His accerlation was vdot = 10^-6 cm/s^2. For circular orbits

 

> vdot relates to distance and mass. vdot = 0.6 m /a^2, where m is the mass

 

> of the companion star in solar masses and a is the semi-major axis (radius

 

> for a circle) in AU (distance of Earth to Sun is 1 AU). Thus with vdot =

 

> 10^-6 and m = 1, the distance to the companion star was a = 775 AU, and the

 

> orbital period is tau = 22000 years. (Use the formula tau = a^1.5).

 

> Henricks and Staller (Nature 273, 132, 1978) complained that stars so close

 

> would be very bright (brighter than Venus!) and be seen. Even if the star

 

> were less massive than 1 solar mass, and therefore dimmer than the Sun, it

 

> would be closer and therefore bright." i.

 

> I was thinking what IF the companion has a mass = 0.016239316 Msun and is

 

> in a NON-circular, HIGHLY ELLIPTICAL orbit (e = 0.98801923) with a

 

> semimajor axis = 6500 AU, would the above statement then NOT be applicable

 

> i.e. Am I right to say that for elliptical orbits vdot is NOT exactly

 

> equals to distance and mass?

 

 

 

No. The expression vdot = 0.6 m/a^2 is just Newton's law of gravity if m is in

 

Msun, a is in AU and vdot is in cm/s^2. So it doesn't depend on the shape of

 

the orbit at all.

 

ii.

 

> What is the formula for vdot for elliptical orbits like the one at hand

 

> (i.e. e = 0.98801923 for a 0.016239316 Msun substellar companion with

 

> semimajor axis (a) at 6500 AU)?

 

 

 

See above.

 

 

 

vdot = 0.6 (0.016239316/6500^2)

 

vdot = 2.306175053 * 10^-10 cm/s^2

 

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

 

vdot = 2.306175053 * 10^-12 m/s^2

 

 

 

iii.

 

> While this companion may be bright when it is at perihelion, if instead it

 

> happens to be at opposition, its apparent magnitude would be a prohibitive

 

> +27.81163876 in the V-band. While in the infrared bandpasses, its magnitude

 

> in e.g. the J band is half of +27.81163876, but does not the recent

 

> discovery of SO025300.5+165258's i.e. a SpT M6.5 Dwarf by Teegarden et al.,

 

> 2003 (recognized now as the 3rd NEAREST star at 5.87092 Light Years away

 

> with a Proper Motion (µ) of 5.06 +/- 0.03 arcsec/yr) proves that relative

 

> brightness is NO 100% guarantee of CERTAIN detection and identification?

 

>

 

Within reason, yes. But since a solar-mass object would have to be only 775 AU

 

away to produce an acceleration of 10^-6 cm/s^2 and indeed it would be so

 

bright as to be obvious if it were a normal star, Henricks and Staller's

 

comment demolishes that hypothesis completely. Even a white dwarf would be

 

easy to detect there, and it would have a large proper motion due to its

 

mutual orbit with the sun. The direction of the acceleration would therefore

 

change noticeably. Harrison may have detected an acceleration, but that's not

 

its cause. (I don't know where you get the numbers in the above paragraph.)

 

 

 

 

 

> b.

 

> In Thornburg, 1985 (MNRAS, 213, 27P-28P) an upper limit was placed on the

 

> solar system acceleration at 10^-9 m/s^2 BUT given the orbital period of

 

> this 0.01623 Msun companion at 6500 AU is 515672.5836 years and a near

 

> parabolic elliptical orbit (i.e. e = 0.98801923), would NOT Thornburg's

 

> limit of 10^-9 m/s^2 be SEVERELY WEAKENED?

 

>

 

 

 

I don't see why. It is the other way around. The upper limit restricts the

 

possibilities for a solar companion.

 

 

 

 

 

> Q5. As with Q1., this question has to do with the precision of calculations

 

> and units. Sir, I understand that Specific Angular Momentum (h) = Angular

 

> Momentum (J)/Mass and thus (h) should have units of m^2/s. Also if G =

 

> 6.672 * 10^-11 Nm^2/kg^2, all the masses must be in kg, the period in

 

> seconds and distances in metres.

 

>

 

> Let a = Semimajor axis of BD, b = Semiminor axis of BD, Msun = Mass of

 

> Sun, Mbd = Mass of BD, Rmin = Periastron of BD, e = Eccentricity of BD &

 

> G = Gravitational Constant

 

> Let M1 = Msun = 1.989 * 10^30 kg

 

> Let M2 = Mbd = 3.23 * 10^28 kg

 

> G = 6.672 * 10^-11 Nm^2/kg^2

 

> a = 6500 AU

 

> e = 0.98801923

 

>

 

> From standard two-body classical mechanics in an inverse square law

 

> potential (Goldstein 1980), it is defined that the angular momentum of a

 

> binary system is completely specified by the semi-major and semi-minor axes

 

> of the bound orbit, as well as the reduced mass of the two-body system µ =

 

> M1M2/(M1+M2), and the inverse square law constant of proportionality k:

 

>

 

> Given that Angular Momentum (J) = (b/a^1/2)(µk)^1/2

 

> ----------------------------------- Equation (1) b = a(1 - e^2)^1/2

 

> ----------------------------------- Equation (2) k = G * Msun * Mbd

 

> ----------------------------------- Equation (3) µ = (Msun * Mbd)/(Msun +

 

> Mbd) ----------------------------------- Equation (4) where b is the

 

> semiminor axis, k is the reduced mass of the two body system and µ the

 

> gravitational force

 

>

 

> Substituting a = 6500 AU and e = 0.98801923 into Equation (2), we have,

 

> b = a(1 - e^2)^1/2

 

> b = 6500(1 - 0.98801923^2)^1/2

 

> b = 6500(1 - 0.976182)^1/2

 

> b = 1003.15028 AU

 

> b = 1.500712819 * 10^11 km

 

> b = 1.500712819 * 10^14 m

 

>

 

> Substituting G = 6.672 * 10^-11 Nm^2/kg^2, Msun = 1.989 * 10^30 kg and Mbd

 

> = 3.23 * 10^28 kg into Equation (3), we have, k = (6.672 * 10^-11) * (1.989

 

> * 10^30) * (3.23 * 10^28)

 

> k = 4.286406384 * 10^48

 

>

 

> Substituting Msun = 1.989 * 10^30 kg and Mbd = 3.23 * 10^28 kg into

 

> Equation (4), we have, µ = (Msun * Mbd)/(Msun + Mbd)

 

> µ = [(1.989 * 10^30) * (3.23 * 10^28)]/[(1.989 * 10^30) + (3.23 * 10^28)]

 

> µ = 6.42447 * 10^58/2.0213 * 10^30

 

> µ = 3.178385198 * 10^28

 

>

 

>

 

> J = (b/a^1/2)(µk)^1/2

 

> Substituting b = 1.500712819 * 10^14 m, a = 9.724 * 10^14 m, µ =

 

> 3.178385198 * 10^28 and k = 4.286406384 * 10^48 into Equation (1), we have,

 

> J = [1.500712819 * 10^14/(9.724 * 10^14)^1/2] * [(3.178385198 *

 

> 10^28)(4.286406384 * 10^48)]^1/2 J = [1.500712819 * 10^14/31183328.88] *

 

> [(3.178385198 * 10^28)(4.286406384 * 10^48)]^1/2 J = 4812548.477 *

 

> [1.36238506 * 10^77]^1/2

 

> Therefore J = 1.776335738 * 10^45 kg.m^2/s

 

>

 

> For a two-body system, h = sqrt(G * M * a(1-e^2))

 

> ----------------------------------- Equation (5) where M is the sum of the

 

> mass of the central object (the Sun, in this case) and the BD Substituting

 

> G = 6.672 * 10^-11 Nm^2/kg^2, Msun = 1.989 * 10^30 kg, Mbd = 3.23 * 10^28

 

> kg, a = 1.933149899 * 10^12 km and e = 0.98801923 into Equation (5), we

 

> have, h = sqrt[6.672 * 10^-11 * [1.989 * 10^30 + 3.23 * 10^28 kg] *

 

> 1.933149899 * 10^12(1 - 0.98801923^2) h = sqrt[6.672 * 10^-11 * [1.989 *

 

> 10^30 + 3.23 * 10^28 kg] * (1.933149899 * 10^12 - 1.887106133 * 10^12)] h =

 

> sqrt[6.672 * 10^-11 * [1.989 * 10^30 + 3.23 * 10^28 kg] * (4.604376628 *

 

> 10^10)] h = sqrt[(6.672 * 10^-11)(2.0213 * 10^30)(4.604376628 * 10^10)]

 

> h = sqrt[6.209514626 * 10^30]

 

> h = 2.49188977 * 10^15 m^2/s

 

>

 

> Are my computed values for (J) and (h) correct? What good is it for us to

 

> compute and know the values to (J) and (h)? i.e. How would knowledge of J

 

> and h afford us a better understanding of this hypothetical BD companion?

 

>

 

The above is all unnecessarily complicated, but mostly correct. Your

 

expression for J can be written

 

 

 

J = Msun * Mbd * sqrt{G*a*(1 - e^2)/(Msun + Mbd)}

 

 

 

This can be simplified using Kepler's Third Law to

 

 

 

J = (Msun * Mbd * G * P * sqrt (1 - e^2)) / (2 * pi * a)

 

 

 

And h = J/mu where mu is the reduced mass, defined as you have it. I agree

 

quite well with your value of J, but not with your value of h. The difference

 

seems to be your value of a (1.933 * 10^12 km). Where did you get that from?

 

Finally, J and h are derived quantities, and wouldn't tell you much that you

 

hadn't discovered already by determining the quantities from which they are

 

derived.

 

 

 

> Q6.

 

> Suppose this BD companion itself is orbited by a planet with a mass = 6.221

 

> * 10^24 kg (i.e. 1.040 Mearth) at 0.011531 AU from the BD, what are the

 

> changes we'll have to make to the above equations (e.g. V1 = 2 * pi * a/(P

 

> sqrt (1 - e^2)), V2 = e * V1, Radial Velocity (RV) = V2 sin x, Tangential

 

> Velocity (Vt) = V1 + V2 cos x and µ = Vt/d) if like before, we want to

 

> "see" this planet from the comfort of Earth?

 

>

 

You would simply have to add orbital velocities, much as you would do to find

 

the velocity of a Galilean satellite of Jupiter. First find the speed of

 

Jupiter with respect to the sun, and resolve it into radial and tangential

 

components, adding or subtracting the relevant components of the earth-s

 

velocity. Then find the velocity of the satellite relative to Jupiter, and

 

again add components.

 

 

===========================================================

 

Prof. Scott Tremaine of Peyton Hall, Princeton has verified that there is NOTHING and NOBODY in the astronomical/astrophysical community able to RULE OUT a BD just as yet. In fact the anomalous cometary fluxes observed by Matese et al and investigated by Horner and Evans shows an UNMISTABLE trend.

 

I shall quote you what Prof. Scott Tremaine has shared with me:

 

"Yes; the hypothetical brown dwarf you are suggesting is not ruled out by any

dynamical arguments that I know of.

 

Regards,

[Astrobuff]

Quotes from some other astronomers I have had the privilege of corresponding or pestering LOL in the past.

 

Prof Kim Griest:

"You clearly have thought a lot about this subject so I may not have too

much to offer you. I misjudged your level of sophistication and knowledge!"

 

Prof. Basri:

"I wouldn't normally have the time or inclination to respond to such an

extensive interrogation. But your questions were pretty good, and indicated

a seriousness on your part."

 

From: Michael Rich <rmr@astro.UCLA.EDU>

"You have some excellent points, I cannot help you much further. in fact, you know more than I do. You might want to go for a Ph.D."

 

From: "Howard E. Bond" <bond@stsci.edu>

"well, it looks like you are better acquainted with the literature on the KB than I am!"

[Ophiolite]

Astrobuff, you make much of the orbital peculiarities of Sedna etc. However alternative, potentially viable and certainly plausible alternative explanations exist. For example Morbidelli, et al, considered five explanations:

"(1) the passage of Neptune through a high-eccentricity phase,

(2) the past existence of massive planetary embryos in the Kuiper belt or the scattered disk,

(3) the presence of a massive trans-Neptunian disk at early epochs that perturbed highly inclined scattered-disk objects,

(4) encounters with other stars that perturbed the orbits of some of the solar system's trans-Neptunian planetesimals, and

(5) the capture of extrasolar planetesimals from low-mass stars or brown dwarfs encountering the Sun."

 

They favoured "mechanism 4, since it produces an orbital element distribution that is more consistent with the observations....."

 

What is your view of their interpretation?

 

Morbidelli, A. et al Scenarios for the Origin of the Orbits of the Trans-Neptunian Objects 2000 CR105 and 2003 VB12 (Sedna) The Astronomical Journal, Volume 128, Issue 5, pp. 2564-2576 2004