Improved Bounds on Nonluminous Matter in Solar Orbit

Abstract

We improve, using a larger set of observations including Voyager 2 Neptune flyby data, previous bounds on the amount of dark matter (DM) trapped in a spherically symmetric distribution about the sun. We bound DM by noting that such a distribution would increase the effective mass of the sun as seen by the outer planets and by finding the uncertainty in that effective mass for Uranus and Neptune in fits to the JPL Developmental Ephermeris residuals, including optical data and those two planets' Voyager 2 flybys. We extend our previous procedure by fitting more parameters of the developmental ephemerides. Additionally, we present here the values for Pioneer 10 and 11 and Voyager 1 and 2 Jupiter ranging normal points (and incorporate these data as well). Our principal result is to limit DM in spherically symmetric distributions in orbit about the sun interior to Neptune's orbit to less than an earth mass and interior to Uranus' orbit to about 1/6 of an earth's mass.

Indication, from Pioneer 10/11, Galileo, and Ulysses Data, of an Apparent Anomalous, Weak, Long-Range Acceleration

“…The only parameter that could possibly mask the spacecraft-determined a R is (GM ⊙ ). But a large error here would cause inconsistencies with the overall planetary ephemeris [11,17]. We conclude that the Viking ranging data limit any unmodelled radial acceleration acting on Earth and Mars to no more than 0.1 × 10 −8 cm/s 2 .…”

“…For this to cause a P , even only out to 50 AU, would require the total dark matter to be > 3×10 −4 M ⊙ . But this is in conflict with the accuracy of the ephemeris, which allows only of order a few times 10 −6 M ⊙ of dark matter even within the orbit of Uranus [11]. (A 3-cloud neutrino model also did not solve the problem [12].)…”

Can the Pioneer Anomaly be of Gravitational Origin? A Phenomenological Answer

“…In regard to the outer planets, Pitjeva was able to determine the extra-advances of perihelion for Jupiter, Saturn and Uranus (see Table 1 for their relevant orbital parameters) because the temporal extension of the used data set covered at least one full orbital revolution just for such planets: indeed, the orbital periods of Neptune and Pluto amount to about 164 and 248 years, respectively. For the external regions of the Solar System only optical observations were used, apart from Jupiter (Pitjeva 2005a); they are, undoubtedly, of poorer accuracy with respect to those used for the inner planets which also benefit of radar-ranging measurements, but we will show that they are accurate 1 The perihelia, as the other Keplerian orbital elements, are not directly observable. 2 Only the general relativistic, gravitomegnetic Lense-Thirring effect and the Newtonian force due to the Kuiper belt objects (in the case of the inner planets) were not modelled.…”

“…In (Anderson et al 1995) the ranging data of the Voyager 2 encounter with Neptune were used yielding a unique ranging measurement of a (Julian Date JD=2447763.67); eq. (28) …”

Constraints on dark matter in the solar system

“…The effect will depend on the density of dark matter, on its distribution in space, etc. Let us assume, as is usually done (Anderson et al 1989(Anderson et al , 1995 the Sun, planets, asteroids, and trans-Neptunian objects (TNOs), any planet at distance r from the Sun can then be assumed to undergo an additional acceleration from dark matter:…”