Abstract.
Analysis of mass-luminosity curves for different subsets of
binaries (both visual and eclipsing spectroscopic binaries) revealed the
deviation in slopes for relatively close
binaries (averaged around 3.6*10-4 light years) compare to
relatively far spaced binaries (averaged around 5.6*10-3 light
years). The slope for close binaries is larger, what means that for the same
luminosity of the main sequence stars the determined from Kepler law
gravitational mass is smaller (or gravity between stars is stronger). This
observation is opposite to the MOND idea (the far the stars the higher shift
from 1/r2 law to 1/r law for gravity) – that would be opposite
effect. The idea of dark matter seems to be confirmed once more (as if some dark
mass is hanging around the star, thus making the mass seemingly larger), but a
new concept of some kind of gravity enhancement by the mass itself may also be
relevant – the closer the binary the higher local concentration of mass and
higher value of G in the gravity law.
Introduction.
One of the unsolved problem of modern science is the observed deviations
of the galaxy rotation curves from the predicted ones. The phenomenon is
observed only on large scales and that is why it is so difficult to understand.
At the same time such phenomenon is expected to reveal itself on all scales and
all objects, including the simplest ones, where the gravity may be probed –
binary star. Indeed, the simplest atom – hydrogen atom allowed to create
quantum mechanics (including quantum electrodynamics due to Lamb shift) and
from history of science perspective it is expected that the investigation of
the simplest objects may lead to the most efficient theories. Hydrogen atom was
especially simple binary system because
both masses were quantized with high accuracy. Binary stars, of course, may
have all the possible variations of masses of both stars, but still it is a simplest model object for applications of
law of mechanics. Any deviation from simple Newton laws (Einstein modifications
for close stars would be necessary) which is visible on galactic scale (dark
matter problem) must reveal itself despite possibly in miniscule amounts on
this simple objects.
The long and unsuccessful search
for dark matter started to reveal different ideas. One of them is MOND, and at
modified Newton gravity the binaries with high deviation between stars would
start feel this deviation from Newton law and attract each other stronger [1].
Main part.
In order to
test the idea of the change of gravity law for the binaries as a function of separation between them I
decided to go the same way as for the testing of the additional gravity created
by photons [2,3]. That is, the mass-luminosity curve will have a different
slope for the different subsets for binaries (subset of binaries with close
luminosities versus subset binaries with
different luminosities would reveal any additional force connected to the
photons trapped inside the stars, for example). The comparison of subset of binaries
with relatively far separation between star versus subset of binaries with
small separation would reveal any deviation from Newton law as a function of
distance.
I manually chose several visual
binaries which are close to the Sun (the close the star, the better accuracy of
all measurements) and plotted separately relatively close binaries versus
relatively far binaries. (two eclipsing spectroscopic binaries were added to
close binaries to have points with masse between 3 and 4 Suns)
Fig 1. Mass-luminosity
relation for binaries with relatively far semi-major axis (average~ 5.6*10-3
ly) and relatively small semi-major axis (average ~ 3.6*10-4 ly).
Table 1 Distant
binaries.
|
Name of binary
|
Mass in Suns
|
Ln(Luminosity), Luminosity is
in Suns
|
|
Andromeda Groombridge 34
|
0.38
|
-3.816
|
|
0.15
|
-7.07
|
|
Eta Cassiopea
|
0.972
|
0.208
|
|
0.57
|
-2.81
|
|
24 Comae Berenices
|
4.4
|
5.155
|
|
3.3
|
3.173
|
|
61 Cygnus
|
0.7
|
-1.877
|
|
0.63
|
-2.465
|
|
Mu Cignus
|
1.31
|
1.79
|
|
0.99
|
0.34
|
|
Gamma Delphinus
|
1.57
|
1.93
|
|
1.72
|
3.034
|
|
Epsilon Lirae 1
|
2.03
|
3.18
|
|
1.61
|
2.13
|
|
Epsilon Lirae 2
|
2.11
|
3.367
|
|
2.15
|
3.466
|
|
36 Ophiuchus
|
1.7
|
-0.6
|
|
0.71
|
-2.41
|
Table 2 Close
binaries.
|
Name of binary
|
Mass in Suns
|
Ln(Luminosity), Luminosity is
in Suns
|
|
Xi Bootes
|
0.9
|
-0.5
|
|
0.66
|
-2.8
|
|
Sirius
|
2.063
|
3.23
|
|
1.018
|
-2.88
|
|
Alfa Centarous
|
1.1
|
0.418
|
|
0.907
|
-0.69
|
|
Alfa Comae Berenices
|
1.237
|
0.542
|
|
1.087
|
0.56
|
|
Beta Delphinus
|
1.75
|
3.18
|
|
1.47
|
2.08
|
|
Delta Equaleus
|
1.192
|
0.81
|
|
1.187
|
0.728
|
|
Zeta Herculesis
|
1.45
|
1.879
|
|
0.98
|
-0.48
|
|
99 Herculesis
|
0.94
|
0.673
|
|
0.46
|
-1.966
|
|
Sigma Herculesis
|
2.6
|
5.44
|
|
1.5
|
2.0
|
|
Beta Leonis minor
|
2.11
|
3.58
|
|
1.35
|
1.76
|
|
Psi Centari*
|
3.114
|
4.95
|
|
1.909
|
2.89
|
|
Chi 2 Hidrae*
|
3.605
|
5.84
|
|
2.632
|
4.19
|
|
70 Ophiuchus
|
0.9
|
-0.53
|
|
0.7
|
-2.04
|
·
* - eclipsing spectroscopic binaries (obviously
close binaries)
Slopes of the curves are
different! It means that for close binaries the effective gravitational
constant would be larger. Indeed, the visual binaries gives the masses as:
M1+M2=4*π2R3/(G*T2) (1)
M1, M2 –
masses of the stars, R- semi-major axis, G – gravitational constant, T is the
period of the binary.
And similar formula for the
eclipsing spectroscopic binaries:
M1+M2=T2*(V1+V2)3/(2*π*G) (2)
Here V1, V2 –
maximum velocities of the stars
Assuming that the absolute luminosity
determines the inertial mass of the star (indeed, any deviation from
gravitation law is small and should not influence the evolution of the star), it
is possible to see, that higher slope corresponds to smaller deduced gravitational
mass for close binary compare to far binary (if the gravitational constant is
the same). Assuming the equivalence principle holds, it means that the
gravitational constant for close binaries is different from the gravitational
constant for far binaries (larger for close binaries). This observation is
exactly opposite to what is expected for MOND – in this case the far binaries
would be attracted stronger. It looks like some additional mass is present in
addition to the star masses which forces them to go closer (almost like the
dark matter is present).
However, why would the dark matter
be present only for close binaries and not for all of them (in this case on
average the slopes should be the same)? More plausible idea is that gravity
constant depends upon the mass of the star itself – the gravity enhancing field is created by ordinary matter, which is
stronger for higher concentration of the matter in the space.
What is the problem with dark
matter being considered as some kind of exotic particles being able to
gravitate but not react in any other way with usual barionic and non-barionic
(light, for example) matter? In principle such matter is possible, but all the
previous experimental evidence tells that the less particle interact with
barionic matter the less it contribute to gravity. Indeed, any ions and
molecules are easy to catch and they contribute to gravitation tremendously so
far. Electrons are less interacting with matter and also less heavy. Neutrinos
are kind of particles that are almost not interacting with barionic matter but
they are also do not have significant contribution to the gravity. It plausible
to assume that other types of particle exist which would interact with matter
even less, but they also would contribute to the gravity even less. The idea of
any type of particle which would be not interacting with ordinary matter but contribute
to the gravity even more than barionic matter is out of this sequence and seems
not obvious.
In addition the recent discovery
of ultra-diffuse galaxies with diluted
stars concentration and completely devoid of dark matter [4] poses even more
questions: how the dark matter may be separated from the ordinary matter [5] if
they interact gravitationally? Why would not dark matter be attracted back for
billions of years and completed the usual setup: dark matter halo around the visible
galaxy?
At the same time the dark matter
is absent in ultra-diffuse galaxies only – may be the concentration of ordinary
matter plays some role? The ordinary matter changes the gravity constant
through some kind of gravity enhancing field?
From the slope of the curves it is possible to roughly evaluate how
gravitational constant G changes with distance.
We have two equations:
Y=3.7978*ln(x)-0.1622 – far binaries (distance ~56.29*10-4
light years, l.y.)
Y=4.653ln(x)-0.0421 – for close binaries (distance ~3.63*10-4
l.y.)
For mass m=2 from the first equation y=2.4702. This value is
assumed to be correlated with inertial mass which determined by star evolution
and it is assumed that small change in gravity law can not influence the
luminosity (the luminosity dependence upon the heavy metal composition is neglected).
Substituting into second equation we got m=1.716 (instead of two). The
equivalence principle should not be violated for close binaries compare to far binaries, so it means
that the mass of the star is not enough for such luminosity.
It may
be simpler explanation, of course for such deviation – both stars were formed
from the same cloud, which was much denser for close binaries (that is why they
are closer) compare to very diluted cloud for far binaries. In addition to the
stars, huge amount of planets and asteroids are hanging around each star
(because the initial cloud was dense), effectively creating invisible but quite
real barionic matter (“dark matter” in the very original sense). Assuming the
observations of the brightness variation exclude such explanation (constant
dimming of the star due to interstellar objects), the other explanation is that
the gravity constant is different. From equations (1) and (2) it follows that G
would be larger for close binaries (and G=K/m law holds). For close binaries G
is 2/1.716=1.166 times larger.
Influence
of the mass to the gravity may be written in a formula similar to Coulomb law:
F=(1/[4πεεo])*q1*q2/r2 (3)
Where q1, q2 are electrostatic
charges, r is the distance between charges, ε is the permittivity of space (due to
dipole nature of the medium the force is weakened), εo is the permittivity
of free space.
For gravity it
would be:
F=(εg/[4πεgo])*m1*m2/r2 (4)
Where m1,m2 are
masses, r is the distance between masses, εg is the gravitoelectric
permittivity of space (due to the absence of antigravitation it always enhances
the force) and εgo is the gravitoelectric permittivity of free space
(the notations would be suitable for gravitoelectromagnetism [6,7]).
In this equation εg moved
up to numerator compare to formula (3) because the gravity is enhanced, not
weakened as in the case of electricity.
With loose similarity to Debye length
[8] the dependence of such field may be written in a way like this:
εg=1+δ*{ΣMi*exp(-ri/ξ)}/{ΣMi} (5)
Here Mi are masses around
the point (actually all masses in Universe, but due to exponential decay only
closest masses are necessary), ri are distances to the point of
interest, ξ is the decay length, δ is some empirical constant (how strongly
gravitational constant is enhanced). Formula (5) would drop to 1 in infinity
(no influence of mass) and to some enhanced value near the star.
Simplifying even further to evaluate
the value of the effect in the Solar system:
G=Go*exp(-r/ξ) (6)
And 1.166=[exp(-3.6*10-4/ξ)]/[exp(-5.6*10-3/ξ)]
The decay length would be 0.034 l.y. (3.2*1014 m) and
for the Pluto orbit (5.9*1012 meters) change of gravitational
constant of 2% is expected (G=0.98Go).
This is quite
large a change and should be easily noticeable if the Cavendish experiment is
performed on Pluto orbit or on the Pluto surface (because the planets are small
compare to Sun, the only real player in Solar system is Sun). For example, the
Cavendish experiment performed on Moon surface would lead to only around 4*10-8
relative change – not enough with modern accuracy of Cavendish experiment. The
previously published idea of Cavendish experiment near the surface of the Sun
would be helpful in the case the accuracy will be good enough.
It is
interesting to note, that the idea of quantum vacuum being influenced by different
fields with corresponding change of gravity constant or electric field
constants is not new and was already discussed [6,9]. In [6] the weakness of
gravity is hypothesized to be due to the existence of Higgs boson “gravitational
antiparticle” (second quantization is predicted), so that virtual pairs
particle-gravitational antiparticle would weaken the field in exactly the same
way as virtual electron-positron pairs are weakening the electric field in
quantum vacuum explanation of speed of light value. If there is no gravitational
antiparticle in nature, the presence of the mass is expected to polarize the
quantum vacuum in such a way, that popping out of quantum vacuum particles are
all bosons with the same positive sign of mass (all attracting each other). In
this case if the boson condensation of all of them is avoided (collapsing the
mass into the black hole as described in [6,9]), the virtual particles would be
increasing the strength of the gravitational filed, not weakening it as in the
case of electromagnetism. This would be exactly what is observed in this
article. The enhancement length seems to be enormous – but this is in the range
what is expected for dark matter (actually the real length may be higher,
because more accurate experiments are necessary.
Conclusion.
The discovered deviation in the
mass-luminosity curves is a hint, that the gravity constant is not valid
for the free space and becomes stronger in the presence of classical barionic
matter. Such behavior is exactly opposite for what is expected by MOND and
formally in line with dark matter hypothesis (the non-barionic unseparable and mass
induced field is in broad sense would be “dark matter”). However, such
observation is more consistent with old definition of field, not matter. To
confirm or reject the observation made here the more accurate data on numerous
binaries would be necessary (because the “googled” data can not be considered
accurate in modern science). The article may be of some interested for visual
binaries specialists who are trying to decrease the scattering in the
mass-luminosity curve (the idea is that the scattering is not really the
experimental error, which would be much smaller in the time of space-based
telescopes, but rather some underlying physical mechanism, which may give
different slopes for different subsets of binaries). To my best knowledge, nobody
so far analyzed mass-luminosity curves from this perspective.
References.
1. McCulloch, M.E., Lucio, J.H. Testing
Newton/GR, MoND and quantised inertia on wide binaries. Astrophys Space Sci 364, 121
(2019). https://doi.org/10.1007/s10509-019-3615-z
https://link.springer.com/article/10.1007/s10509-019-3615-z
2. https://vixra.org/pdf/2005.0250v1.pdf
3. https://vixra.org/pdf/2007.0195v1.pdf
4. https://www.discovermagazine.com/the-sciences/hubble-reveals-new-evidence-for-controversial-galaxies-without-dark-matter
5. https://astronomy.com/news/2019/03/ghostly-galaxy-without-dark-matter-confirmed
6. https://en.wikipedia.org/wiki/Gravitoelectromagnetism
7. https://tipikin.blogspot.com/2019/12/quantum-vacuum-application-to-gravity.html
8. https://en.wikipedia.org/wiki/Debye_length
9. https://tipikin.blogspot.com/2020/03/unification-of-gravitational-and.html
