ANTIGRAVITY MATTER AND BOK GLOBULES

 

 

 

 

 

Tim E Simmons

Preston, UK

tim@preston.u-net.com

 

ABSTRACT

A hypothetical type of matter is proposed that is affected by a repulsive force that acts as the reverse of gravity.  This type of matter is referred to as antigravity matter.  Its hypothetical behaviour is investigated and some effects it would have on normal matter objects are predicted.  Bok globules are then shown to demonstrate the predicted normal matter behaviour.

Key words: (Cosmology:) Dark Matter, Gravitation, ISM: clouds, zodiacal dust

1. INTRODUCTION

Gravitationally attractive dark matter was first suggested by Zwicky, 1933 to explain unexpected gravitational phenomena in space.  This paper explores a competing explanation for those gravitational phenomena.  This is that they are caused by a previously unrecognised form of matter that is affected by a force that operates as the reverse of gravity.  This matter is referred to as antigravity matter.  According to this explanation antigravity matter is spread out fairly evenly throughout most of space.  The unexpected gravitational phenomena are caused by a local reduction in the density of antigravity matter, not by the local presence of dark matter.  This concept is shown in Fig 1. 

 Figure 1 - Dark matter and antigravity matter concepts

 

Bok globules were first described by Bok, 1933.  Bok globules are small molecular clouds.  They are typically a few light years in diameter and contain a few solar masses of gas and dust.  They are particularly dense and have particularly clearly defined surfaces.  They are not associated with any theory of dark matter.

The theory of antigravity matter is being developed via a website at www.preston.u-net.com/AGMatter/Index.htm.  The purpose of this paper is to formally publish a part of the content of that website in order to establish the scientific validity of the theory and stimulate academic debate.

2. ASSUMPTIONS

The following assumptions are made in this paper relating to antigravity matter:-

2.1       Antigravity matter consists of particles that have positive mass.

2.2       Antigravity matter particles are repelled from normal matter objects by antigravity.  This repulsive force follows the equation:-

(1)       

where:-

Gna is the gravitational constant for normal matter to antigravity matter repulsion. 

m1 and m2 are the masses of the normal matter object and the antigravity matter particle that are affected by the force.

r is the distance between the objects.

2.3       Antigravity matter particles do not interact with photons except by gravity.

2.4       Antigravity matter particles are not attracted to other antigravity matter particles by gravity or any other force.  They may even be repelled from each other by antigravity.  However for the purposes of this paper any antigravity matter to antigravity matter repulsion is assumed to be small and insignificant.

2.5       The universe contains a large amount of antigravity matter.  Antigravity matter particles have spread out throughout deep space with approximately constant density except where they are affected by normal matter objects.  They form an atmosphere in deep space which has the bulk properties of density, temperature, and pressure.

2.6       Most antigravity matter has existed for most of the life of the universe.  Because of the expansion of the universe the density, temperature, and pressure of the deep space atmosphere of antigravity matter are all low but non-zero.

2.7       Antigravity matter expands adiabatically as a monatomic gas.

3. ANALYSIS

With reference to Figure 2, consider a universe containing antigravity matter particles and a single normal matter object of mass M.  The antigravity matter particles have spread out throughout most of space to form a thin, cold atmosphere.  Any affect on the distribution of the antigravity matter caused by M is rotationally symmetrical around M.  The antigravity matter atmosphere and mass M are at equilibrium and there are no other factors influencing the distribution of antigravity matter.

The objective of this analysis is to derive an equation that describes how the distribution of antigravity matter is affected by mass M.

Figure 2 Universe containing mass M and an atmosphere of antigravity matter

 

The background density of antigravity matter in deep space = Dab

The background pressure of antigravity matter in deep space = Pab

The antigravity matter density at radius r from M  =

The antigravity matter pressure at radius r from M = p

Consider a thin spherical shell of antigravity matter concentric with M of thickness .  The shell is in equilibrium.  It is repelled from M by antigravity but pushed towards M by a force caused by the change of antigravity matter pressure across the thickness of the shell, referred to as.

(2)       

The equation for adiabatic expansion of antigravity matter as pressure decreases is

(3)        where k is a constant

Therefore

(4)       

and

(5)       

But

(6)       

Integrate

(7)       

When r =  p = Pab

(8)       

and therefore

(9)       

Equation (9) gives the pressure of antigravity matter at any radius from M.  The relationship between pressure and radius has the form shown in Figure 3.

Figure 3 Form of the relationship between antigravity matter pressure and radius from M

 

From Figure 3 it can be seen that antigravity matter is pushed away from M.  At close range the pressure of antigravity matter is reduced to zero, and from equation (3) the density of antigravity matter is also reduced to zero.  The repulsion from M clears antigravity matter out of a spherical region of space around M.  The surface of that sphere is referred to as the AGM Boundary.

At the AGM Boundary p = 0

(10)      = Constant

Equation (10) shows that the radius of the AGM Boundary is proportional to M.

Thus far M has been treated as a point mass of normal matter.  However M could BE a diffuse object.  For example M could be spread out evenly throughout the spherical volume inside its own AGM Boundary.   In that case its gravity field outside the AGM Boundary would be unchanged from the point mass case, and the distribution of antigravity matter would also be unchanged.  M’s density would be given by M’s mass divided by the volume within its AGM Boundary.  This density is referred to as the AGM Exclusion Density because it is the average density of a normal matter object that will completely exclude antigravity matter from within its volume.  The AGM Exclusion Density is also referred to by the abbreviation Dnx.

(11)      AGM Exclusion Density = Dnx =

and therefore at the AGM Boundary

(12)     

Equation (12) shows that the radius of the AGM Boundary is inversely proportional to the square root of AGM Exclusion Density.

Consider the case where M is a cloud of gas and dust whose mass is arranged in a rotationally symmetrical manner around the centre point.  If the extremities of the cloud extend a little beyond the AGM Boundary some of its gas and dust will mix with the anti-gravity matter.  This situation is shown in Figure 4.

Figure 4 – Mass M as a diffuse cloud extending a little beyond its AGM Boundary

 

The antigravity matter is cold, and the gas and dust is cooled by it.  The cooled gas and dust is transported inwards within the cloud by convection currents.  Heat energy within the core of the cloud is transported outwards.  The heat lost by the cloud diffuses away through the antigravity matter in nearby space.  Over time the cloud is cooled and shrinks until it retreats within its AGM Boundary.  At that point the cooling effect substantially stops.  The cloud’s average density stabilises at about the AGM Exclusion Density.

If several such clouds existed of varying masses and well separated from each other we would expect the radii of the clouds to be inversely proportional to the square root of their average densities as predicted by equation (12).

4. BOK GLOBULES

Data relating to several Bok Globules have been published by Kandori et al 2005.  This includes an estimate of the mass of the Bok globules measured by absorption of radiation from background stars.  Data extracted from that publication are shown in Table 1 along with a calculation of the radius and average density of the Bok globules. Angular radius is taken from Table 4 of that publication.  Other data are taken from the second lines of Table 5 which have been corrected using a Bonner-Ebert model.  Data have only been used for the 11 Bok globules for which such a correction has been provided.

.  Name

Angular

Radius

(arcsecs)

Distance

(pc)

Mass

(sols)

Radius

(m)

Average

Density

(kg m-3)

CB 87

87.5

304

2.72

3.69E+15

2.58E-17

BC 110

61.1

561

7.21

4.76E+15

3.19E-17

CB 131

103

323

7.83

4.62E+15

3.79E-17

CB 134

59.6

264

1.91

2.19E+15

8.74E-17

CB 161

62.5

357

2.79

3.10E+15

4.48E-17

CB 184

112

332

5.76

5.16E+15

2.00E-17

CB 188

127

317

7.19

5.59E+15

1.96E-17

FeSt 1-457

144

73

1.12

1.46E+15

1.72E-16

Lynds 495

75

315

2.95

3.28E+15

3.99E-17

Lynds 498

75

200

1.42

2.08E+15

7.50E-17

Barnard 68

100

85

0.9

1.27E+15

2.09E-16

 

Table 1 – Data from Kandori et al 2005 with a calculation of Bok globule radius and density

 

A graph of Bok globule average density against radius is shown in Figure 5 below.  More massive Bok globules are less dense.  The correlation coefficient for log(radius) against log(density) is -0.951.  The probability of such a correlation occuring by chance is less than 0.0001.

The solid line has a gradient of -0.5 on this log/log graph.  Bok globule radius appears to be approximately inversely proportional to the square root of Bok globule average density.  This is the relationship that was predicted by equation (12) for a normal matter cloud within an atmosphere of antigravity matter.  This relationship is not predicted by any theory of dark matter.

Figure 5 - Bok globule radius vs average density with a prediction of gradient from equation (12)

 

If this relationship is caused by antigravity matter we can make the following estimates:-

(13)      = 2.1 ×107 kg0.5 m-0.5

If antigravity matter behaves as a monatomic ideal gas and  then:-

(14)      = 1.4 ×10-15 m kg-1

5. CONCLUSION

The relationship between Bok globule radius and average density appears to be consistent with the proposal that the universe contains a thin atmosphere of antigravity matter.  This relationship is not explained by any theory of dark matter.

REFERENCES

Bok, B., Reilly, E., 1947, Astrophysical Journal 105

Kandori, R., Nakajima, Y., Tamura, M., Tatematsu, K., Aikawa, Y.,Naoi, T., Sugitani, K., Nakaya, H., Nagayama, T., Nagata, T., 2005 The Astronomical Journal 130

Zwicky F., 1933, Helv. Phys. Acta, 6, 110.