Transcript r*=13.6 km MPA1 EOS

Ya. B. Zeldovich
All-Moscow Seminar of Astrophysicists
Plamen Fiziev
LTF JINR Dubna
Models of Neutron Stars
without
Functional Relation
between
the Radius and Mass
16 December 201
Moscow
?
Tolman-Opehgeimer-Volkov
system
EOS
Does the M-R relation exist at all ?
Where is it coming from ???
In
standard
notations:
Nonrelativistic limit:
Nonrelativistic solution for:
GR
critical mass:
Integrating TOV
from
to

Realistic
(to some extend)
EOS for NS:
A two-solar-mass neutron star
2 8 O C T O B E R 2 0 1 0 | VO L 4 6 7 | N AT U R E | 1 0 8 1
arXiv:1011.4291:
THE NEUTRON STAR MASS DISTRIBUTION
R.Valentim, E. Rangel and J.E. Horvath
arXiv:1101.4872:
Mass distribution of neutron stars
B. Kızıltan, A. Kottas. S. E. Thorsett
Neutron stars in double neutron star and neutron star-white dwarf
systems show consistent respective peaks at 1.35M⊙ and 1.50M⊙.
The results strongly suggest
the existence of a bimodal
distribution of the masses,
with the first peak around 1.37M⊙,
a much wider second peak at
1.73M⊙.
2011 ApJ 742 1 (November, the 2-nd)
arXiv:1106.3131
Denis A. Leahy, Sharon M. Morsink and Yi Chou
The accreting millisecond pulsar XTE J1807-294 is studied through a
pulse-shape modeling analysis. The model includes blackbody and
Comptonized emission from the one visible hot spot and makes use of
the Oblate Schwarzschild approximation for ray-tracing. We include a
scattered light contribution, which accounts for flux scattered off an
equatorial accretion disk to the observer including time delays in the
scattered light. We give limits to mass and radius for XTE J1807-294
and compare these to limits determined for SAX J1808-3658 and
XTE J1814-334 previously determined using similar methods. The
resulting allowed region for mass-radius curves is small but consistent
with a mass-radius relation with nearly constant radius (~12 km) for
masses between 1 and 2.5 solar masse.
As long as an EOS mass-radius curve has sections that pass
through each of the star’s 3 σ allowed regions, it will be allowed by
all 3 stars’ data.
NO ONE of the EOS curves in the figure possess this property.
Excluded 10 soft EoS (arXiv:1108.2166)
ps, prak_data, schaf2, schaf1,
pclnphq, pal2, ms1506, gm3nph,
gm2nph, gm1nph
XTE J1814-338
XTE J1807-294
SAX J1808
Warning: the star rotation still not taken into account !!!
Excluded 10 stiff EoS (arXiv:1108.2166)
wff1, wff2, wff3, wff4,
MPA1, ms2, ms00, engvik,
AP1, AP2, AP3, AP4
XTE J1814-338
XTE J1807-294
SAX J1808
Warning: the star rotation still not taken into account !!!
Still remain 2 stiff EoS: AP3 and MPA1 ???
Observations versus EoS Ap3 and MPA1
AP3
MPA1
XTE J1814-338
SAX J1808
XTE J1807-294
Warning: the star rotation still not taken into account !!!
XTE J1807-294
AP3
MPA1
XTE J1814-338
SAX J1808
m*- r* relation does not exist
in the Nature!!!
Christian D. Ott, Evan P. O'Connor, Basudeb Dasgupta,
arXiv:1111.6282
The figure shows that
none of the current set of available
EOS allow for a 2-M neutron star
while at the same time being
consistent with the current massradius constraints from
observations.
The crux is that the EOS needs to
be sufficiently stiff to support 2-M
neutron stars and at the same time
sufficiently soft to make neutron
stars with moderate radii n the
canonical mass range. This
balance appears to be difficult to
realize.
The stiff set of RMF EOS produce
systematically too large neutron
stars. The soft compressible
liquid-droplet LS180 EOS agrees
well with the mass-radius
constraints, but is ruled out by its
failure to support a 2-M neutron
star.
Mass-radius relations for 10 publically available finite temperature EOS along with several constraints. Ozel et al. analyzed
three accreting and bursting neutron star systems and derived mass-radius regions shown in green. Steiner et al.
performed a combined anaylsis of six accreting neutron star systems, shown are 1- and 2- results in blue.
An old problem:
Comparizon of the interior and exterior mass – radius relations
Ap&SS.234...39L, 1995
A more recent results:
? What is the situation now ?
A.M.Cherepashchuk, talk at 15th Lomonosov Conference,
18 of August, 2011, Moscow State University
HNXB + LMXB
NS
BH candidates
It seems to be strange because the number of stars in
the Galaxy – progenitors of BHs (M > 30 M) is strongly
increasing with decreasing of their masses: N ~ M - 5.
Exploding Star
The Number
of the BH
candidates
does not
increase
with
decreasing
of their
masses.
Neutron Star Discovered Where a
Black Hole Was Expected
November 02, 2005, Westerlund 1
A very massive star collapsed to form a neutron star and not a
black hole as expected, according to new results from NASA's
Chandra X-ray Observatory. This discovery shows that nature
has a harder time making black holes than previously thought.


Scientists found this neutron star -- a dense whirling ball of
neutrons about 12 miles in diameter -- in an extremely
young star cluster. Astronomers were able to use welldetermined properties of other stars in the cluster to
deduce that the progenitor of this neutron star was at least
40 times the mass of the Sun.
"Our discovery shows that some of
the most massive stars do not
collapse to form black holes as
predicted, but instead form neutron
stars."
said Michael Muno, a UCLA postdoctoral Hubble
Fellow and lead author of a paper to be published
in The Astrophysical Journal Letters.
Muno and colleagues discovered
a pulsing neutron star in a cluster of
stars known as Westerlund 1.
This cluster contains a hundred thousand or
more stars in a region only 30 light years across,
which suggests that all the stars were born in a
single episode of star formation. Based on optical
properties such as brightness and color some of
the normal stars in the cluster are known to have
masses of about 40 suns.
Since the progenitor of the neutron star
has already exploded as a supernova, its
mass must have been more than
40 solar masses.
Matt Visser, Black holes in general relativity. Do black holes “exist” ?
PoS BHs,GR andS trings 2008: 001, 2008, arXiv:0901.4365
“This innocent question is more subtle than one might expect, and the answer depends
very much on whether one is thinking as an observational astronomer, a classical
general relativist, or a theoretical physicist.”
Astronomers have certainly seen things that are small, dark, and heavy.
Classical general relativist:
Eternal black holes certainly exist mathematically.
Theoretical physicist:
We have not seen direct observational evidence of the event horizon.
The mathematical solutions suffer essential physical shortcomings !
Visser M, Barcelo C, Liberati S, Sonego S: gr-qc/0902.0346
Small, dark, and heavy: But is it a black hole?
The Mass and the spin of the Black
Hole(?)in Cygnus X-1 arXiv:1106.3688,
1106.3689,1106.3690
O-type supergiant
Distnace
1.86 +0.12 −0.11 kpc
Kerr black hole (?)
with a spin parameter
a∗ > 0.97 (3 σ)
News: arXiv:1110.4374:
A weak compact jet in a soft state of Cygnus X-1
New Models of
Neutron Stars
without
Mass-Radius
Relation
Some geometry
An auxiliary Euclidean 3D space:
3D spherically symmetric Riemannian space:
The area:
The radial distance:
The volume:
Familiar case:
Unusual case:
The spherically symmetric 3D geometry in terms of area radius
(Hilbert gauge 1917):
The original Schwarzschild solution
(1916)
tt
The center is at the metric singularity !
How it could be ?!?
A point with a finite surface!!!
Yes! It exists in GR!
Area blowing
around the center:
|dl|=|ds|: dt=0, dθ=0, dϕ=0
Where M-R relation is coming
from in the relativistic problem
R*, M*
In general case
If
c
The real situation for WD:
, Springer, 2000
Theory with
VERSUS
PF: arXiv:astro-ph/0409456 -
Observations
for 1175 WD
Madej et al.: arXiv:astro-ph/0404344
TOV EOS
r*=13.6 km
rc(m*,r*)>0
rc(m*,r*)=0
r*=13.6 km
rc(m*,r*)>0
Generalized TOV NS: more details
r*=13.6 km
r*=13.6 km
r*=13.6 km
r*=13.6 km
c
The new theoretical model
A striking mass gap
arXiv:1110.1635
The domain of
nonstable
NS = GRB ???
Different type of SN
explosions?
or
Different type of NS ?
MPA1 EOS
Analytical EOS for NS
Haensel, P., & Potekhin, A. Y. 2004, A&A, 428, 191.
C. Gungor, K. Y. EksiarXiv:1108.2166
MPA1 EOS
r*=13.6 km
r*=13.6 km
rc(m*,r*)>0
rc(m*,r*)>0
r*=13.6 km
rc(m*,r*)>0
r*=13.6 km
rc(m*,r*)>0
MPA1 EOS
r*=13.6 km
r*=13.6 km
r*=13.6 km
r*=13.6 km
r*=13.6 km
A negative mass
deffect
Instability
MPA1
EOS
Strong
instability
and
explosion
of the light
neutron
stars:
m*ʘ < 0.3
r*km = 13.6
r*=13.6 km
r*=13.6 km
r*=13.6 km
MPA1 EOS
For r* = 13.6 km
m min = 0.3463 ʘ
r*=13.6 km
EOS pal2
NASA's WISE Mission Captures Black Hole's Wildly Flaring Jet
WISE images showing strong bursts
and dimming of infrared light in the
”black hole”
GX 339-4. The data cover a period
of approximately 1 day, speeded up.
arXiv:1109.4064
Temporal analysis of long and short
GRB light curves carried out here
supports the 83 general observation
that the short bursts are temporally
similar to long ones but compressed
384 in time, which could be related to
the nature of the central engine of
the respective bursts.
A
A sample pulse fit to one long burst GRB080723D (upper
plot) and one short burst GRB090227B (lower plot). The
histogram in black is the GRB light curve and the fitted
background is shown as black dashed line. The pulses
shown in green are the lognormal pulses fitted to those in
the light curves. The sum of the background model and
the fitted pulses is shown as purple continuous line. The
goodness of fit parameter, n, is indicated at
the top right corner of each plot.
Sample pulse fits to the lowest 6
energy channels of NaI and the full
energy range light curve from BGO
detector of a long GRB 090626A.
Thank You
Some suspected to be BH objects:
astro-ph/0808.0435
arXiv:0911.5408v1 [astro-ph.HE]
The Schwarzschild radii
and
the geometrical radii
of some
astrophysical objects
Moon
0.018
cm
1,737
km
Earth
Sun
SgrA Galaxy
1.5 cm
3 km
1.3x107 5.4x1011
6,378
km
7x105
km
km
km
5 x 1014
km
Dr. Neil Gehrels of NASA Goddard
Space Flight Center, Greenbelt, Md.,
Swift principal investigator.
"None of this was realized before simply
because we couldn't get to the scene of
the explosion fast enough."
"Swift has the unique ability to detect
bursts and turn its X-ray and ultravioletoptical telescopes to the explosion's
embers within minutes. As such, Swift is
detecting new burst details that might
rewrite theory."
A new 2008 result:
astro-ph/0804-1856
The mass of the progenators of long duration GRB
(Witnessing the real death of massive stars)



For star population ~ 5 Myr > 50 Solar masses
For star population ~ 8 Myr > 25 Solar masses
For star population < 7 Myr > 20 Solar masses
Nevertheless,
in the collapse which leads to long duration GRB
BH do not form at least in the “classical” way.
astro-ph/0805.014
arXiv:
1110.4758
GRBs
from
INTEGRAL
arXiv:1108.0638
The longest
observed
GRB110328
arXiv:1109.3018