Ya. B. ZeldovichAll-Moscow Seminar of Astrophysicists

Plamen FizievLTF JINR Dubna

Models of Neutron Stars without Functional Relationbetween the Radius and Mass

16 December 201Moscow

?

Tolman-Opehgeimer-Volkovsystem

EOS

Does the M-R relation exist at all ?Where is it coming from ???

In standardnotations:

Nonrelativistic limit:

Nonrelativistic solution for:

GR critical mass:

Integrating TOVfrom

to

Realistic (to some extend) EOS for NS:

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

A two-solar-mass neutron star

arXiv:1101.4872: Mass distribution of neutron stars

The results strongly suggest the existence of a bimodaldistribution of the masses, with the first peak around 1.37M , ⊙a much wider second peak at1.73M .⊙

arXiv:1011.4291: THE NEUTRON STAR MASS DISTRIBUTION

Neutron stars in double neutron star and neutron star-white dwarf systems show consistent respective peaks at 1.35M and 1.50M .⊙ ⊙

R.Valentim, E. Rangel and J.E. Horvath

B. Kızıltan, A. Kottas. S. E. Thorsett

2011 ApJ 742 1 (November, the 2-nd)

arXiv:1106.3131

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.

Denis A. Leahy, Sharon M. Morsink  and Yi Chou

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

SAX J1808

XTE J1814-338

XTE J1807-294

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

SAX J1808

XTE J1814-338

XTE J1807-294

Warning: the star rotation still not taken into account !!!

Still remain 2 stiff EoS: AP3 and MPA1 ???

AP3MPA1

Observations versus EoS Ap3 and MPA1

SAX J1808

XTE J1814-338

XTE J1807-294

Warning: the star rotation still not taken into account !!!

m*- r* relation does not exist in the Nature!!!

SAX J1808

XTE J1807-294

XTE J1814-338

MPA1AP3

Christian D. Ott, Evan P. O'Connor, Basudeb Dasgupta, arXiv:1111.6282

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.

The figure shows thatnone of the current set of available EOS allow for a 2-M neutron star while at the same time being consistent with the current mass-radius constraints from observations.

The crux is that the EOS needs to be sufficiently stiff to support 2-Mneutron 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.

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

The Number of the BH

candidates does not increase

with decreasing

of their masses.

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.

NS

HNXB + LMXB

BH candidatesExploding Star

Neutron Star Discovered Where a Neutron Star Discovered Where a Black Hole Was Expected Black Hole Was Expected

November 02, 2005,November 02, 2005, Westerlund 1Westerlund 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 Scientists found this neutron star -- a dense whirling ball of neutrons about 12 miles in diameter -- neutrons about 12 miles in diameter -- in an extremely in an extremely young star clusteryoung star cluster. Astronomers were able to use well-. Astronomers were able to use well-determined properties of other stars in the cluster to determined properties of other stars in the cluster to deduce that the progenitor of this neutron star was at least deduce that the progenitor of this neutron star was at least 40 times the mass of the Sun.40 times the mass of the Sun.

"Our discovery shows that some of "Our discovery shows that some of the most massive stars do not the most massive stars do not collapse to form black holes as collapse to form black holes as predicted, but instead form neutron predicted, but instead form neutron stars."stars."

said Michael Muno, a UCLA postdoctoral Hubble said Michael Muno, a UCLA postdoctoral Hubble Fellow and lead author of a paper to be published Fellow and lead author of a paper to be published in The Astrophysical Journal Letters.in The Astrophysical Journal Letters.

Muno and colleagues Muno and colleagues discovered discovered a pulsing neutron stara pulsing neutron star in a in a cluster of stars known as cluster of stars known as Westerlund 1Westerlund 1. . This cluster contains a hundred This cluster contains a hundred thousand or more stars in a region only 30 light thousand or more stars in a region only 30 light years across, which suggests that all the stars were years across, which suggests that all the stars were born in a single episode of star formation. Based on born in a single episode of star formation. Based on optical properties such as brightness and color optical properties such as brightness and color some of the normal stars in the cluster are known some of the normal stars in the cluster are known to have masses of about 40 suns.to have masses of about 40 suns. Since the progenitor of Since the progenitor of the neutron star has already exploded as a the neutron star has already exploded as a supernova, its mass must have been more supernova, its mass must have been more than than 40 solar masses40 solar masses..

“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?

Matt Visser, Black holes in general relativity. Do black holes “exist” ? PoS BHs,GR andS trings 2008: 001, 2008, arXiv:0901.4365

O-type supergiant

The Mass and the spin of the The Mass and the spin of the Black Black Hole(?)Hole(?)in Cygnus X-1 in Cygnus X-1 arXiv:1106.3688,arXiv:1106.3688,

1106.3689,1106.3689,1106.36901106.3690

Distnace 1.86 +0.12 −0.11 kpcKerr 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

withoutMass-Radius

Relation

An auxiliary Euclidean 3D space:

3D spherically symmetric Riemannian

space:

The area:

The radial distance:

The volume:

Some geometry

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!!!

|dl|=|ds|: dt=0, dθ=0, dϕ=0

Yes! It exists in GR!

Area blowing around the center:

Where M-R relation is coming from in the relativistic problem

R*, M*

cIn general case

If

The real situation for WD: , Springer, 2000

Theory with VERSUS Observations for 1175 WD

PF: arXiv:astro-ph/0409456 - Madej et al.: arXiv:astro-ph/0404344

TOV EOS

r*=13.6 km

rc(m*,r*)=0rc(m*,r*)>0

rc(m*,r*)>0

r*=13.6 km

Generalized TOV NS: more details

r*=13.6 km

r*=13.6 km

r*=13.6 km

r*=13.6 km

c

The domain of nonstable

NS = GRB ???

Different type of SN explosions?

or

Different type of NS ?

The new theoretical model A striking mass gap

arXiv:1110.1635

MPA1 EOSAnalytical 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

r*=13.6 km

r*=13.6 km

rc(m*,r*)>0

rc(m*,r*)>0

rc(m*,r*)>0

rc(m*,r*)>0

MPA1 EOS

r*=13.6 km

r*=13.6 km

A negative mass deffect Instability

r*=13.6 km

r*=13.6 km r*=13.6 km

MPA1 EOS

r*=13.6 km

Stronginstability

and explosionof the light

neutronstars:

m*ʘ < 0.3 r*km = 13.6

r*=13.6 km

MPA1 EOS

m min = 0.3463 ʘ

r*=13.6 km

r*=13.6 km

For r* = 13.6 km

EOS pal2

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.

NASA's WISE Mission Captures Black Hole's Wildly Flaring Jet

arXiv:1109.4064

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.

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 atthe top right corner of each plot.

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.

Thank YouThank You