Gravidynamics (scalar-tensor gravitation) and the observed discrete mass spectrum of compact stellar remnants in close binary systems.

Vladimir V. SOKOLOV

(1) There are two new observational facts: the mass spectrum of neutron stars and black

hole candidates shows an evident absence of compact objects with masses within the interval 2 - 6 solar ones, and in close binary stellar systems with a low-massive optical companion the most probable mass value (a peak in the masses distribution of black hole candidates) is close to 7 masses of the Sun.

On 2-6 ʘ mass gap + a strong peak around 7 ʘ

In the long run,

the statistic of neutron stars (NSs) became equal to the statistic of the BH candidates.

At present they can be compared …

Ozel et al., ApJ, 757:55-, 2012

V. S. Petrov, A.M. Cherepaschuk, E.A. Antokhina , Astronomicheskii zhurnal, 2014, 91, No.3, p.167

Kreidberg et al. 2012 ApJ, 757:36, Fig.8

The peak in the mass distribution of relativistic objects is close to 6.7 ʘ

Ozel et al., ApJ, 757:55-, 2012

… the road test: • Finn 1994; Bailyn et al. 1998; Thorsett & Chakrabarty, 1999; Kaper et al. 2006; Nice et al. 2008; Farr et al. 2011, ¨Ozel et al. 2010, 2012; Kreidberg et al. 2012; + a new paper by the SAI team: V. S. Petrov, A.M. Cherepaschuk, E.A. Antokhina , Astronomicheskii zhurnal, 2014, 91, No.3, p.167

Ozel et al., ApJ, 757:55-, 2012

For the case of black holes, they used the exponential distribution with a low mass cut-off at Mc = 6.32M⊙ and a scale of Mscale = 1.61M⊙. The solid lines represent weighted mass distributions for each population, for which appropriate fitting formulae are given in the paper...

On 2-6 ʘ mass gap + a strong peak around 7 ʘ

Ozel et al, 2010

Ozel et al., 1006.2834

… the road test: • Finn 1994; Bailyn et al. 1998; Thorsett & Chakrabarty, 1999; Kaper et al. 2006; Nice et al. 2008; Farr et al. 2011, ¨Ozel et al. 2010, 2012; Kreidberg et al. 2012; + a new paper by the SAI team: V. S. Petrov, A.M. Cherepaschuk, E.A. Antokhina , Astronomicheskii zhurnal, 2014, 91, No.3, p.167

Fig. 6. The total probability density ζ(Mx) of distribution of compact object masses Mx in 20 X-ray binary systems. (V. S. Petrov, A.M. Cherepaschuk, E.A. Antokhina , 2014 , Astronomicheskii zhurnal, 91, No.3, p.167)

Kreidberg et al. 2012 (Particularly) on mass of compact objects In these 16 systems with a faint companion star q = Mopt / MX ≈ 0.1 For such systems the optical star is a probe body:

Kreidberg et al. 2012 ApJ, 757:36, Fig.8

The peak in the mass distribution for relativistic objects in 16 law-mass X-ray binaries is close to 6.7 ʘ

… the mass gap + a strong peak around 7 ʘ

Such a gap is puzzling in light of all theoretical studies (GR + astrophysics…)

that predict a continuous distribution

of the compact object SN remnant masses

with a smooth transition from NSs to BHs

(2) In the totally non-metric field/scalar-tensor model of gravitational interaction the total mass of a compact relativistic object with extremely strong gravitational field (an analog of black holes in GR) is approximately equal to 6.7 solar masses with radius of a region filled with matter (quark-gluon plasma) approx. 10 km.

Gravidynamics: in this model of gravitational interaction (as well as in electrodynamics) the field can be described by the energy which is quite a definite part of any gravitating object mass (like the electromagnetic mass of electron).

All known effects of the weak field are explained (as well as in GR), since in this case the field is mainly only the tensor one = the GR gravitation…

But in the strong field of a compact object the role of the scalar component – repulsion/antigravitation – increases.

Vladimir V.Sokolov, Astrophysics and Space Science, 1992, 197, p.179

Fig.1.

A half of the total mass (6.7 Mʘ) of such an object already consists only of the field – a scalar-tensor mixture…

Astrophysics and Space Science, 1993, 201, p.303, V.V.Sokolov, and S.V.Zharikov,

+ all references there…

To what density is the field energy non-localizable ?

To what the size of the gravitational field energy density itself can be considered non-localizable? (e. g., see in L.D. Landau & E.M.Lifshic, Vol. II, chapter XI, § 96)

When the contribution of this energy should be included in the mass of a field source as it is done for electron?

Where is graviton born eventually? (like photons in ED)

Fig.2.

PQ = 1/3 (ε - 4B)

In GR (in Vacuum around the same bag with PQ = 1/3 (ε - 4B) the gravitational field energy nonlocalizable and nonmetering in the total mass of any compact object (e.g. NSs).

And in gravidynamics the contribution of the field energy to the total mass of a stellar collapsar should be also taken into consideration…

Eventually, the key is to predict new observational consequences in the strong field...

A collapsar in gravidynamicsA half of the total mass (6.7 Mʘ) of such an object already consists only of the field – a scalar-tensor mixture…(See more in Astrophysics and Space Science, 1993, 201, p.303, V.V.Sokolov, and S.V.Zharikov,

+ all references there…)

The gauge invarianceThe consistent dynamic interpretation of the field equations consists in the fact that the potentials of the field Ψik (just as in ED) must be understood absolutely independently of the chosen metrics ηik.

Like a vector 4-potential in ED, Ψik can be of any value by virtue of the indeterminacy of

This transformation for Ψik is the gauge transformation

with an auxiliary 4-vector Ai and a 4-scalar Λ.

(1)

Basic equationsCorresponding field equations which are relativistically and

gauge invariant (1), will be of the form:

a is determined by the choice of unit for Ψik . Tik is the EMT of point particles as was mentioned above, and

Basic equations

In the same linear approximation, if we base it on the interaction f ΨikTik, which one can write down in symbolic form

consistently adhering to the dynamical interpretation of the field Ψik we can also obtain the equations of particle motion in a given field Ψik just as it is done for an electron moving in a given ED-field.

f ΨikTik => (4)

The universality f is the same for any field -- the universality of the gravitational interaction. So, the interaction of the electromagnetic field with the given gravitational one Ψik must be in the form

This ultimately gives the correct description of the light interaction effects in a gravitational field, such as the light deflection and radio signal lag in the field of the Sun. For the correct description of the redshift effect one must add to the interaction (5) the interaction with the spinor (e-e+) field constructed by the same rule, i.e., with the same f [Mosinsky 1950, Okun 1999].

f Ψik tik(el) =>

(5)

No vector source

The gauge invariance leads to a demand for sources following the strong conservation law (Neuther's identity):

i.e. to the absence of a vector source.

Since there is no vector Tik,k , the direct use of the gauge invariance

allows excluding a vector field (corresponding to this source) contained in the symmetric tensor Ψik

( ) in the general case.

The second rank symmetric tensor Ψik can be decomposed into corresponding spin parts:

In general, the tensor Tik is the source of fields with four spins also:

The Hilbert-Lorentz gauge condition

It means that if the gauge is chosen in such a way that in the theory there is no vector

constructed of two possible 4-vectors

then “long” equations are transformed to the short form:

The condition Вi = 0 in the conservation of the current Tik,k = 0,

retains in the theory the gravitons with two spins. So, for real gravitons there remains:

And the source of purely scalar gravitons is a nonzero trace of the EMT of point particles:

One can divide the field Ψik and the source Tik into two components corresponding to

by the representation of equations (10) as an equivalent system of equations for every component separately - pure scalar and tensor ones. For this it is necessary to represent the potential in such an invariant form separating explicitly the scalar and the tensor:

Ψik ≡ Фik + 1/4 ηik Ψ (14)

where Фik ηik ≡ 0. Here Фik describes only the tensor part of the

field Ψik and the invariant tensor 1/4 ηik Ψ describes the purely scalar

component of the same field. In exactly the same way one may manipulate Tik:

where Tik(2)ηik ≡ 0.

The Nonlinear GD: In accordance with the universality of gravitational interaction one must consider the field itself to be the source of gravitation (which lacks in ED). It means that in the Lagrangian, besides the term f ΨikTik , terms arise of the type:

fΨikθik => (6)

Perturbation theory -> including nonlinearities, smallness of G – the gravitational interaction constant, nonlinear corrections in Lagrangian

The higher is probability,the higher is the energy density of gravitational field

The correct the field energy including itself = the correct nonlinear processes including.

Localizability (locality) and the energy sign

gravitons

the local process, the field in the first approximation m > 0

the local process, the second approximation

θ00 > 0

To what the size of the gravitational field energy density itself can be considered non-localizable? (e. g., see in L.D. Landau & E.M.Lifshic, Vol. II, chapter XI, § 96)

When the contribution of this energy should be included in the mass of a field source

as it is done for electron?

Where is graviton born eventually?

(like photons in ED)

fΨikθik => f(Фik + 1/4 ηik Ψ) => fФik

fФik + fФik

Localizability = locality in GraviDynamics

source-points and “test” particles

eventually: only two types of real gravitons

only(!) two nonlinear processes

+ energy equipartition

for field of a collapsar

And at which field energy density such process become essential !?

How and where it can be tested ?

For one point particle with mass M resting at the origin of coordinates (ra = rM = 0 and v = 0) this tensor has the form:

Tik = Mc2δ(r) diag(1,0,0,0). (3)

As a mutter of fact, for a massive gravitating centre it fixes an inertial reference frame, in which we may investigate the field of such a source.

*00

1( ) (1 )

2GD

rGMf r

r r

.

PQ = 1/3 (ε - 4B)

½ MQc^2 (the bag with R = RQGP) + ½ MQc^2 (the 'coat' in vacuum) = MQc^2

1/ 2

2

26.64

4 /nucl

QM MB c

ʘ

PQ = 1/3 (ε - 4B)

B = 67 MeV fm-3. PQ = 0, ρQGP ≈ 1.7 ρnucl (ρnucl = 2.8x1014 g cm-3).

1/ 23

max

67MeV( ) 1.85

fmM C M

B

Mʘ

PQ = 1/3 (ε - 4B)

PQ = 1/3 (ε - 4B)

½ MQc^2 (the bag with R = RQGP) + ½ MQc^2 (the 'coat' in vacuum) = MQc^2

1/ 2

2

26.64

4 /nucl

QM MB c

ʘ

Gravitational collapse as the source of

gamma-ray burstsV.V.Sokolov

Special Astrophysical Observatory of RAS, Nizhnij Arkhyz, Russia

Email: sokolov@sao.ru

In conclusion:

Gamma-ray bursts (GRBs) are the brief (~0.01-100s), intense flashes of γ-rays (mostly sub-MeV) with enormous electromagnetic energy release up to ~1051-1054 ergs. The rapid temporal variability, δT <10 msec, observed in GRBs implies compact sources with a size smaller than

cδT < 3000 km.~

~

(3) Polarized emission of gamma-ray bursts, a black-body component in their spectrum and other observed properties could be explained by the direct manifestation of surface of these collapsars.

Astro-ph/0408436 F.Frontera et al. ApJ. 616 (2004) 1078-1085

zGRB = 2.140

A cyclotron

feature

Erest = 21.7

(+1.9/-1.6)keV zrest = 0.318for magnetic field

~1012 Gauss

The emission anisotropy may be related to

radiation transfer in a medium with the strong (regular ~1014 - 1016 Gauss) magnetic field on or near the surface of a compact object.

Then absorption of photons polarized across the magnetic field (the extraordinary wave) turns out to be very small (B. Paczyński, 1992; V.G. Bezchastnov, G.G. Pavlov, Yu.A. Shibanov, V.E. Zavlin,1996).

Then the observation of strong linear polarization of GRB prompt emission must be another consequence of the compact model namely.

The model of an asymmetric explosion of a GRB/SN progenitor

= ?…a strongly non-spherical explosion may be a generic feature of core-collapse supernovae of all types.

…Though while it is not clear that the same mechanism that generates the GRB is also responsible for exploding the star.astro-ph/0603297Leonard, Filippenko et al.

Fig. from Astro-ph/0604131, Woosley and Heger

Though the phenomenon itself is unusual, the source-object is not too unique !/? The closer is a GRB, the more are SN signs .

The windenvelope

The shock breaks outthrough the wind

56Ni synthesizedbehind the shock wave

the mass gap + SNe & GRBs

GRB is the beginning of CC-SNe explosion

Ozel et al., ApJ, 757:55-, 2012

MISSING BLACK HOLES UNVEIL THE SUPERNOVA EXPLOSION MECHANISM

Belczynski et al, arXiv:1110.1635v2

The main conclusions

On 2-6 ʘ mass gap + a strong peak around 7 ʘ

.

These compact objects (BH candidates) CAN have their own equation of state and their own evolution in close binary systems… (Though then these are not black holes).

GR is not the Holy Scripture. Here everything should be tested!

For discussion

Before speaking about cosmological black holes (+ dark matter and so on) first one should make certain that the stellar black holes exist indeed.

The science of stellar evolution is much more understandable that that of cosmological one!

What do the words “Black holes are discovered” mean? Are they discovered indeed?

TAFN ( that’s all for now )

arXiv: 1308.5733

1309.5257

The black body radiation with kT ~ 100 keV

for the time-resolved GRB spectra

arXiv:0705.1061v1, M. Battelino, F. Ryde, N. Omodei and F. Longo – On the Black-body component and GeV(?)

On 2-6 ʘ mass gap + a strong peak around 7 ʘ

Ozel et al., 1006.2834

The mass spread (double and triple peaks in distribution ) of the BH candidates CAN be treated just in the same way as for NSs.

So, these compact objects (BH candidates) CAN have their own equation of state and their own evolution in close binary systems… (Though then these are not black holes).

GR is not the Holy Scripture. Here everything should be tested!