1st Doha International Astronomy Conference, 10-13 Feb 2013

Complying with Tully–Fisher

Y SoboutiInstitute for Advanced Studies in Basic

Sciences – Zanjan (IASBS), Iran,<sobouti@iasbs.ac.ir>

Tully-Fisher relation, an empirical rule, states :a. Rotation curves of spiral galaxies have flat asymptotes.

b. Asymptotic speeds are proportional to the fourth root of the mass of the galaxy .

Both features are utterly non Newtonian and non Einsteinian .

They indicate insufficient gravitational force of the observed mass to keep stars in galactic orbit .

The followings from Sanders and McGaugh show the observed flat asymptote and the insufficient contributions from baryonic matter .

To explain observations:Since Zwicky, 1933, many scientists have turned

to dark matters .Since Milgrom, 1983, many others have proposed modified and alternative

gravities .To this date, however, neither any dark matter scenario nor any alternative gravity has found wide enough acceptance to call it

consensus .

To Author's knowledge, however, one possibility is not tapped to date :

To entertain time varying spacetime metrics around galaxies, and to pump energy to an outlying star from the gravitational radiation of the galaxy or from the radiation of any other field , such as Brans-Dicke scalar or

others .

Tully –Fisher relation requires a force field

A wave-like perturbation in the gravitational field has such features. For instance ,

where

Astronomical time spans, for instance

are long enough to allow minute effects to accumulate over times and become noticeable.

They are also long enough not to be noticeable in human time scales and not raise alarm that periodic time changes are not reported by observers.

As an example, let us look at Brans-Dicke scalar in its linear approximation:

A wave solution of the latter in the weak field approximation is

The B term of Schwarzschild’s metric becomes

A brute solution for the speed of an orbiting star is

This solution has the desired r- independent asymptote. Its amplitude has the square root dependence on the mass of the host galaxy. It is, however, time periodic of the order of the

dynamical times of the galaxies .

Time dependence can be suppressed by invoking absorption of energy by a star from the wave emanating from the galaxy. There are long enough times for small effect to

accumulate over astronomical times .There, however, is another drawback. Energies absorbed from a wave (absorption cross

sections) are not proportional to frequencies .In the case gravitational waves (quadrupole radiation), cross section is . For dipole radiation,

one has . For a scalar, I suspect . ,

Conclusion: This is not finished piece of work. It is simply an idea among many .