Dark matter vs. modifications of the gravitational inverse-square law. Results from planetary motion in the solar system

In this morning's astro-ph, we read about a topic of occasional
interest in this group. I find the second sentence and the last
sentence of particular interest.



astro-ph/0606197
Title: Dark matter vs. modifications of the gravitational
inverse-square law. Results from planetary motion in the solar
system
Authors: M. Sereno (Univ. Zuerich), Ph. Jetzer (Univ. Zuerich)
Comments: 7 pages, 4 figures, accepted for publication in MNRAS

Dark matter or modifications of the Newtonian inverse-square law in
the solar-system are studied with accurate planetary astrometric
data. From extra-perihelion precession and possible changes in the
third Kepler's law, we get an upper limit on the local dark matter
density, rho_{DM} 3*10^{-16} kg/m^3 at the 2-sigma confidence
level. Variations in the 1/r^2 behavior are considered in the form of
either a possible Yukawa-like interaction or a modification of gravity
of MOND type. Up to scales of 10^{11} m, scale-dependent deviations in
the gravitational acceleration are really small. We examined the MOND
interpolating function mu in the regime of strong gravity. Gradually
varying mu suggested by fits of rotation curves are excluded, whereas
the standard form mu(x)= x/(1+x^2)^{1/2} is still compatible with
data. In combination with constraints from galactic rotation curves
and theoretical considerations on the external field effect, the
absence of any significant deviation from inverse square attraction in
the solar system makes the range of acceptable interpolating functions
significantly narrow. Future radio ranging observations of outer
planets with an accuracy of few tenths of a meter could either give
positive evidence of dark matter or disprove modifications of gravity.


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"Joseph Lazio" wrote in message
...

astro-ph/0606197
Title: Dark matter vs. modifications of the gravitational
inverse-square law. Results from planetary motion in the solar
system
Authors: M. Sereno (Univ. Zuerich), Ph. Jetzer (Univ. Zuerich)
Comments: 7 pages, 4 figures, accepted for publication in MNRAS

Dark matter or modifications of the Newtonian inverse-square law in
the solar-system are studied with accurate planetary astrometric
data. From extra-perihelion precession and possible changes in the
third Kepler's law, we get an upper limit on the local dark matter
density, rho_{DM} 3*10^{-16} kg/m^3 at the 2-sigma confidence
level. ...

Fascinating, that is 3*10^{-19} g/cm^3, exactly the same
as the upper bound found from the Pioneer anomaly:

http://www.arxiv.org/abs/astro-ph/0501626

The direction of the Pioneer anomaly also implies DM dust
at that density would need to be at rest wrt the Solar
system since both craft are accelerated towards the Sun.

The mean density suggested from the Milky Way's rotation
curve is given as 2*10^{-25} g/cm^3 so the Solar system
interplanetary density would then be 6 orders higher than
the local interstellar mean yet it would need to be nearly
constant with heliocentric range.

George

In article ,
"George Dishman" wrote:

"Joseph Lazio" wrote in message
...

astro-ph/0606197
Title: Dark matter vs. modifications of the gravitational
inverse-square law. Results from planetary motion in the solar
system
Authors: M. Sereno (Univ. Zuerich), Ph. Jetzer (Univ. Zuerich)
Comments: 7 pages, 4 figures, accepted for publication in MNRAS

Dark matter or modifications of the Newtonian inverse-square law in
the solar-system are studied with accurate planetary astrometric
data. From extra-perihelion precession and possible changes in the
third Kepler's law, we get an upper limit on the local dark matter
density, rho_{DM} 3*10^{-16} kg/m^3 at the 2-sigma confidence
level. ...

Fascinating, that is 3*10^{-19} g/cm^3, exactly the same
as the upper bound found from the Pioneer anomaly:

http://www.arxiv.org/abs/astro-ph/0501626

The direction of the Pioneer anomaly also implies DM dust
at that density would need to be at rest wrt the Solar
system since both craft are accelerated towards the Sun.

The mean density suggested from the Milky Way's rotation
curve is given as 2*10^{-25} g/cm^3 so the Solar system
interplanetary density would then be 6 orders higher than
the local interstellar mean yet it would need to be nearly
constant with heliocentric range.

*At most* six orders of magnitude; if all we have is an "upper
limit/bound" we can't even be sure that the DM density is greater around
here than in interstellar space. Absent a lower bound or other
refinement of the estimate, AFAICT it says more about the insensitivity
of our methods WRT this application than it does about the actual
quantity in question.

--
Odysseus

"Odysseus" wrote in message
news
In article ,
"George Dishman" wrote:

"Joseph Lazio" wrote in message
...

astro-ph/0606197
Title: Dark matter vs. modifications of the gravitational
inverse-square law. Results from planetary motion in the solar
system
Authors: M. Sereno (Univ. Zuerich), Ph. Jetzer (Univ. Zuerich)
Comments: 7 pages, 4 figures, accepted for publication in MNRAS

Dark matter or modifications of the Newtonian inverse-square law in
the solar-system are studied with accurate planetary astrometric
data. From extra-perihelion precession and possible changes in the
third Kepler's law, we get an upper limit on the local dark matter
density, rho_{DM} 3*10^{-16} kg/m^3 at the 2-sigma confidence
level. ...

Fascinating, that is 3*10^{-19} g/cm^3, exactly the same
as the upper bound found from the Pioneer anomaly:

http://www.arxiv.org/abs/astro-ph/0501626

The direction of the Pioneer anomaly also implies DM dust
at that density would need to be at rest wrt the Solar
system since both craft are accelerated towards the Sun.

The mean density suggested from the Milky Way's rotation
curve is given as 2*10^{-25} g/cm^3 so the Solar system
interplanetary density would then be 6 orders higher than
the local interstellar mean yet it would need to be nearly
constant with heliocentric range.

*At most* six orders of magnitude; if all we have is an "upper
limit/bound" we can't even be sure that the DM density is greater around
here than in interstellar space.

Not even that. The calculation of drag includes a
coefficient shown as K in the paper. It is 0 for
transmission, 1 for absorption and 2 for reflection.
The assumption made in deriving the limit is that it
is close to 1 which is reasonable for normal matter.
We know dark matter doesn't interact through EM so
the possibility is that K might be very small, the
particles passing through the craft like neutrinos.
For an arbitrarily small value of K, you can have
an arbitrarily high density so Pioneer doesn't even
set an upper limit via drag (though it might through
the limit on gravitational mass).

The point was that if (big if!) dark matter produced
a drag by being swept up by the craft then it would
take a density of at least 3*10^{-19} g/cc (K=1) to
explain the Pioneer anomaly, which coincidentally
happens to be the upper limit set by entirely
different means. This would mitigate the problem
of the absence of an effect on larger bodies since
the force would be proportional to surface area, not
the mass of the object. Asteroids etc. might still
rule it out of course.

Absent a lower bound or other
refinement of the estimate, AFAICT it says more about the insensitivity
of our methods WRT this application than it does about the actual
quantity in question.

Agreed, it isn't an easy quantity to measure even
for normal matter and especially for something that
doesn't interact with EM in any way.

George