Transcript Vladimir_Sokolov

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 Xray 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 gravidynamics
A 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 invariance
The 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
(1 )
This transformation for Ψik is the gauge transformation
with an auxiliary 4-vector Ai and a 4-scalar Λ.
Basic equations
Corresponding 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
f ΨikTik =>
(4)
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 EDfield.
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
f Ψik
tik
(el)
=>
(5)
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].
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
gravitons
The correct the field energy including itself =
the correct nonlinear processes including.
Localizability (locality) and the energy sign
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.
.
GD
GM
1 r*
  f  00 (r )  
(1 
)
r
2r
PQ = 1/3 (ε - 4B)
½ MQc^2 (the bag with R = RQGP) + ½ MQc^2 (the 'coat' in vacuum) = MQc^2
 2  nucl 

2 
4
B
/
c


1/ 2
M Q  6.64 M
ʘ
PQ = 1/3 (ε - 4B)
B = 67 MeV fm-3. PQ = 0,
ρQGP ≈ 1.7 ρnucl
(ρnucl = 2.8x1014 g cm-3).
1/ 2
 67MeVfm 3 
M max (C )  1.85 

B


M
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
 2  nucl 

2 
4
B
/
c


1/ 2
M Q  6.64 M
ʘ
In conclusion:
Gravitational collapse as the source
of
gamma-ray
bursts
V.V.Sokolov
Special Astrophysical Observatory of RAS, Nizhnij Arkhyz, Russia
Email: [email protected]
Gamma-ray bursts (GRBs) are the brief
(~0.01-100s), intense flashes of γ-rays (mostly subMeV) 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.
zGRB = 2.140
A cyclotron
feature
Erest = 21.7
(+1.9/-1.6)keV
zrest = 0.318
for magnetic field
~1012 Gauss
ApJ. 616 (2004) 1078-1085
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 nonspherical 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.
The shock
breaks out
through the wind
The wind
envelope
= ?
56Ni
synthesized
behind the
shock wave
astro-ph/0603297
Leonard, 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 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!