The sophistication of our discussion improves with new observations and interpretations, both subjected to vigilance toward biases in the data and in ourselves. - gm
David Black - - - Sky & Telescope, Aug 1996, Vol.92,No.2,
1. There is no way to bias star selection toward extreme face-on orbits, especially for unseen companions. The target stars are located all over the sky, and they are selected with no prior knowledge about the existence of any low-mass companions. Thus no information about orbital inclinations exists. Stellar and brown dwarf companions reside in randomly oriented orbits.
2. There are too few orbiting brown dwarfs and stars from which to draw the face-on orbits. Suppose hypothetically that a selection bias does exist that favors face-on orbits. How many brown dwarf companions, N, must reside in a reservoir, from which 25 face-on orbits could be drawn, to masquerade as planets?
To fix ideas, suppose that the N brown dwarfs have a typical mass of, M = 45 Mjup (Jupiter-masses), and suppose that 25 of them exhibit Msin(i) < 2 Mjup (faking as planets because of their nearly face-on orbits). The orbits of the 25 "fake-planets" must be face-on within an angle: i < 2.5 deg (sini < 2/45). The fraction of orbits that are face-on within 2.5 deg is:
Fraction = 1 - cos(2.5 deg) = 1 / 1000
Thus, the brown dwarf reservoir from which the "fake planets" were drawn must contain:
N = 25 * 1000 = 25000 brown dwarf companions.
Conclusion: If 25 extrasolar planets are merely brown dwarfs in face-on orbits, a reservoir of 25000 brown dwarf companions must exist somewhere, out of which the face-on orbits were selected.
This conclusion is not plausible, as less than 10 brown dwarf companions are known, not the required 25000. The required reservoir of 25000 brown dwarf companions does not exist from which the 25 face-on orbits could be drawn. Even a purposeful selection of face-on orbits cannot explain the planets, by a factor of over 1000.
Corollary: It is further implausible that stellar companions in face-on orbits could serve as the explanation for the "planets". A reservoir of 125000 orbiting M dwarf companions (M = 0.1 solar-mass) is required in order to yield 25 face-on orbits having Msini < 2 Mjup. No catalog of 125000 M dwarf companions exists. Even if such a catalog of binaries existed, we would still need a way to select orbits that were face-on within 1 degree, for which the probability is 0.0002 .
3. No "selection effect" is possible: the target stars include of all solar-type stars within 30 pc. All main sequence stars having spectral type G and K, and brighter than magnitude V=7.5 (some 1000 stars), are included in our planet search. (We only exclude known binary stars with separations less than 2 arcsec, to avoid light from two stars entering the spectrometer slit). Thus for such a nearly complete sample of target stars, it is impossible for the orbital inclinations to be extremely face-on (or even systematically face-on).
4. The histogram of Msini is peaked at below 1 Jupiter mass.This peak at low masses can only occur if the true mass distribution is peaked similarly at below 1 Jupiter mass. Doppler techniques easily detect the more massive companions, Msini = 10-80 Mjup. Despite this ease of detection, all Doppler surveys show that such massive companions are rare.
If companions of 10-100 Jupiter masses (brown dwarfs) were common, we would easily detect them with their randomly oriented orbital inclinations. But such values of Msini (10-100 jupiters) simply are rarely found in Doppler surveys. Instead, the distribution of Msini is peaked below 1 Jupiter mass, with a dearth of Msini between 10-100 Jupiter masses.
5. The transiting planet orbiting HD209458, definitely resides in an edge-on orbit, not face-on. Its mass is also known unambiguously: M = 0.63 Jupiter masses. The occurrence of one transiting planet among the 10 known close-in jupiters is consistent with the hypothesis that the orbits are randomly oriented. If the orbits were preferentially face-on, the probability of finding a transiting planet would be small.
6. If the companions were stars instead of planets we could detect the infrared luminosity from them, both as IR excess luminosity and as resolved point sources with adaptive optics. However, while most of the 50 extrasolar planets have been carefully examined with adaptive optics in the infrared, none has revealed a stellar companion.
7. Astrometry from the Hipparcos satellite can just barely reveal angular wobbles of 2 milliarcsec (2 sigma). Such detectable wobbles would occur for the following benchmark case: a companion of 40 Jupiter masses, orbiting at 1 AU around a target star that is 20 pc away.
The Hipparcos research team has spent 8 years studying the subtle nature of the uncertainties from Hipparcos measurements They have examined the Hipparcos astrometry of planet-bearing stars and found no such wobbles, i.e., (Perryman et al. 1996). The lack of astrometric wobbles provides secure upper limits of 40 Jupiter masses for planets orbiting at least 1 AU from a typical star surveyed.
The probability that the orbital plane is inclined so much that its mass is greater than 4.6-Jupiter is 0.5%.
51 Peg b could have a mass of, say, 45 Jupiter masses, making it
truly a brown dwarf. However, the probability that 51 Peg B has over 45
an extreme orbital inclination) is less than 1 in 10,000.
Moreover, if 51 Peg's companion were as massive as, say, 45 Jupiter masses, the companion would tidally spin up the star. This is clearly not the case, because 51 Peg is a chromospherically quiet stars and has low coronal xrays. 51 Peg is not spinning rapidly and therefore its companion is not a massive brown dwarf (Pravdo et al. 1996).
Clearly, the probability that most of the orbits of the 50 extrasolar planets are viewed nearly face-on is negligible. Indeed, there is a bias toward detecting orbits that are nearly edge-on, because the Doppler variations are greater for such orientations.
In general, the extrasolar planets must have masses predominantly under a few Jupiter-masses. The histogram of Msini rises steeply toward the lowest detectable masses. This rise can only occur if most of the companions have masses near or below that of Jupiter, rather than 10x the mass of Jupiter. All biases favor the detection of the high--mass companions. Such massive companions (50 Mjup) are rare compared to the Jupiter-mass planets.
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