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Astronomy meets QCD. Sergei Popov (SAI MSU). Phase diagram. The first four are related to the NS structure!. Astrophysical point of view. Astrophysical appearence of NSs is mainly determined by: Spin Magnetic field Temperature Velocity Environment. - PowerPoint PPT Presentation
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Astronomy meets QCD
Sergei Popov
(SAI MSU)
Phase diagram
Astrophysical point of viewAstrophysical appearence of NSsis mainly determined by:
• Spin• Magnetic field• Temperature• Velocity• Environment The first four are related to the NS structure!
See a recent review on astrophysical contraints on the EoS in 0808.1279.
Structure and layers
Plus an envelope and an atmosphere...
Neutron starsRadius: 10 kmMass: 1-2 solarDensity: about the nuclearStrong magnetic fields
NS interiors: resume
(Weber et al. ArXiv: 0705.2708)
R=2GM/c2
P=ρR~3GM/c2
ω=ωKR∞=R(1-2GM/Rc2)-1/2 Lattimer & Prakash (2004)
Quark stars
Quark stars can be purely quark (with and without a tiny crust) or hybrid
Proposed already in 60-s (Ivanenko and Kurdgelaidze 1965). Then the idea was developed in 70-s.
Popular since the paper by Witten (1984) Renessance in recent 10 years or so.
See a recent astrophysical review in 0809.4228.
How to recognize a quark star?
Mass-radius relation. Smaller for smaller masses.
Cooling. Probably can cool faster due to additional channels.
Surface properties. If “bare” strange star – then there is no Eddington limit.
ikikik Tc
GRgR
4
8
2
1
)( )4(
1 1
(3)
4 )2(
21
41 1 (1)
1
22
2
1
22
3
22
PP
c
P
dr
dP
cdr
d
rdr
dm
rc
Gm
mc
Pr
c
P
r
mG
dr
dP
{ Tolman (1939)Oppenheimer-Volkoff (1939)
TOV equation
EoS
EoS
(Weber et al. ArXiv: 0705.2708 )
Effective chiral model ofHanauske et al. (2000)
Relativistic mean-field modelTM1 of Sugahara & Toki (1971)
Particle fractions
Au-Au collisions
Experimental results and comparison
(Danielewicz et al. nucl-th/0208016)
1 Mev/fm3 = 1.6 1032 Pa
Astrophysical measurement Mass
Radius
Red shift (M/R)
Temperature
Moment of inertia
Gravitational vs. Baryonic mass
Extreme rotation
In binaries, especially in binaries with PSRs.In future – lensing.
In isolated cooling NS, in bursters in binaries,in binaries with QPO
Via spectral line observations
In isolated cooling NSs and in sometransient binaries (deep crustal heating)
In PSRs (in future)
In double NS binaries, if good contraintson the progenitor are available
Millisecond pulsars (both single and binary)
NS Masses
Stellar masses are directly measured only in binary systems
Accurate NS mass determination for PSRs in relativistic systems by measuring PK corrections
White
dw
arfs
Neu
tro
n s
tars
Brown dwarfs,Giant planets
Maximum-massneutronstar
Minimum-massneutron star
Maximum-masswhite dwarf
km 250~
1.0~ Sun
R
MM
km 129~
)5.25.1(~ Sun
R
MM
c
Neutron stars and white dwarfs
Minimal massIn reality, minimal mass is determined by properties of protoNSs.Being hot, lepton rich they have much higher limit: about 0.7 solar mass.
Stellar evolution does not produce NSs with barion mass less thanabout 1.4 solar mass (may be 1.3 for so-called electron-capture SN).
Fragmentation of a core due to rapid rotation potentially can lead to smallermasses, but not as small as the limit for cold NSs
Page & Reddy (2006)
BHs ?
However, now somecorrections are necessary
Compact objects and progenitors.Solar metallicity.
(Woosley et al. 2002)
There can be a range of progenitormasses in which NSs are formed,however, for smaller and larger progenitors masses BHs appear.
Mass spectrum of compact objects
(Timmes et al. 1996, astro-ph/9510136)
Results of calculations(depend on the assumed modelof explosion)
A NS from a massive progenitor
(astro-ph/0611589)
Anomalous X-ray pulsar in the associationWesterlund1 most probably has a very massive progenitor, >40 MO.
So, the situation with massive progenitorsis not that clear.
NS+NS binaries
Pulsar Pulsar mass Companion mass
B1913+16 1.44 1.39B2127+11C 1.35 1.36B1534+12 1.33 1.35J0737-3039 1.34 1.25J1756-2251 1.40 1.18J1518+4904 <1.17 >1.55J1906+0746 1.25 1.35
(PSR+companion)/2
J1811-1736 1.30J1829+2456 1.25
Secondary companion in double NS binaries can give a good estimateof the initial mass (at least, in this evolutionary channel).
0808.2292
GC
Non-recycled
In NS-NS systems we can neglect all tidal effects etc.
Also there arecandidates, for examplePSR J1753-2240 arXiv:0811.2027
PSR J1518+4904
[Janssen et al. arXiv: 0808.2292]
Surprising results !!!Surprising results !!!
Mass of the recycled pulsar is <1.17 solar massesMass of its component is >1.55 solar masses
Central values are even more shocking:
0.72+0.51-0.58 and 2.00+0.58
-0.51
V~25 km/s, e~0.25The second SN was e--capture?
NS+WD binariesSome examplesSome examples
1. PSR J0437-4715. WD companion [0801.2589, 0808.1594 ]. The closest millisecond PSR. MNS=1.76+/-0.2 solar.Hopefully, this value will not be reconsidered.
2. The case of PSR J0751+1807. Initially, it was announced that it has a mass ~2.1 solar [astro-ph/0508050]. However, then in 2007 at a conference the authors announced that the
resultwas incorrect. Actually, the initial value was 2.1+/-0.2 (1 sigma error).New result: 1.24 +/- 0.14 solar[Nice et al. 2008, Proc. of the conf. “40 Years of pulsars”]
3. PSR B1516+02B in a globular cluster. M~2 solar (M>1.72 (95%)). A very light companion. Eccentric orbit. [Freire et al. arXiv: 0712.3826] Joint usage of data on several pulsars can give stronger constraints on thelower limit for NS masses.
It is expected that most massive NSs get their additional “kilos” due to
accretion from WD companions [astro-ph/0412327 ].
Pulsar masses
[Nice et al. 2008]
With WD companions With NS companions
PSR 0751+1807
(Trumper)
Massive NS: 2.1+/-0.3 solar masses – Now shown to be wrong (!) [see Nice et al. 2008]
Binary pulsars
Relativistic corrections and measurable parameters
For details seeTaylor, Weisberg 1989ApJ 345, 434
Mass measurementsPSR 1913+16
(Taylor)
Double pulsar J0737-3039
(Lyne et al. astro-ph/0401086)
Masses for PSR J0737-3039
(Kramer et al. astro-ph/0609417)
The most precise values.
Neutron stars in X-ray binariesStudy of close binary systems gives an opportunity to obtain mass estimate forprogenitors of NSs (see for example, Ergma, van den Heuvel 1998 A&A 331, L29).For example, an interesting estimate was obtained for GX 301-2. The progenitor mass is >50 solar masses.On the other hand, for several other systems with both NSs and BHsprogenitor masses a smaller: from 20 up to 50. Finally, for the BH binary LMC X-3 the progenitor mass is estimated as >60 solar.So, the situation is tricky.Most probably, in some range of masses, at least in binary systems, stars canproduce both types of compact objects: NSs and BHs.
Mass determination in binaries:mass function
mx, mv - masses of a compact object and of a normal star (in solar units), Kv – observed semi-amplitude of line of sight velocity of the normal star (in km/s),P – orbital period (in days), e – orbital eccentricity, i – orbital inclination (the angle between the prbital plane and line of sight).
One can see that the mass function is the lower limit for the mass of a compact star.
The mass of a compact object can be calculated as:
So, to derive the mass it is necessary to know (besides the line of sight velocity)independently two more parameters: mass ration q=mx/mv, and orbital inclination i.
Recent mass estimates
ArXiv: 0707.2802
Massive NSs
We know several candidates to NS with high masses (M>1.8 Msun) in X-ray binaries:
Vela X-1, M=1.88±0.13 or 2.27±0.17 Msun (Quaintrell et al., 2003)
4U 1700-37, M=2.4±0.3 Msun (Clark et al., 2002)
2S 0921-630/V395 Car, M=2.0-4.3 Msun [1] (Shahbaz et al., 2004)
We will discuss formation of very massive NS due to accretion processes in binary systems.
What is «Very Massive NS» ?1.8 Msun < Very Massive NS < 3.5 Msun
• 1.8Msun: (or ~2Msun) Upper limit of Fe-core/young NS according to modeling of Supernova explosions (Woosley et al. 2002).
• ~3.5Msun: Upper limit of rapidly rotating NS with Skyrme EOS (Ouyed 2004).
Evolution
For our calculations we use the “Scenario Machine’’ code developed at the SAI. Description of most of parameters of the code can be found in (Lipunov,Postnov,Prokhorov 1996)
Results
1 000 000 binaries was calculated in every Population Synthesis set
104 very massive NS in the Galaxy (formation rate ~6.7 10-7 1/yr) in the model with kick
[6 104 stars and the corresponding formation rate ~4 10-6 1/yr for the zero kick].
State of NS with kick
zero kick
Ejector 32% 39%
Propeller+Georotator 2% 8%
Accretor 66% 53%astro-ph/0412327
Results II
Mass distribution of very massive NS
Dashed line: Zero natal kick of NS ( just for illustration).Solid line: Bimodal kick similar to (Arzoumanian et al. 2002).
Luminosity distribution of accreting very massive
NS
Outside of the star
RrRR
MMMM
g
b
/1/
2.0~ sun
r
r
drdrr
rdtc
r
rds
c
GMr
r
r
rc
GM
MrmRr
gr
gg
gg
1
1 1
2 ,1
21e
(1) и (3) изconst )( При
222
1
222
222
Bounding energy
Apparent radius
redshift
Baryonic vs. Gravitational massPodsiadlowski et al. [astro-ph/0506566] proposed that in the double pulsarJ0737-3039 it is possible to have a very good estimate of the initial massof one of the NSs (Pulsar B). The idea was that for e--capture SN baryonic massof a newborn NS can be well fixed.
[Bisnovatyi-Kogan et al. In press]
However, in reality it is necessaryto know the baryonic mass with1% precision. Which is not easy.
Equator and radiusds2=c2dt2e2Φ-e2λdr2-r2[dθ2+sin2θdφ2]
In flat space Φ(r) and λ(r) are equal to zero.
• t=const, r= const, θ=π/2, 0<Φ<2π l=2πr
• t=const, θ=const, φ=const, 0<r<r0 dl=eλdr l=∫eλdr≠r0
0
r0
Gravitational redshift
)( e
0
e ,e
r
dt
dNr
dt
dN
d
dNdtd
r
r
rcGm
2
2
21
1e
It is useful to use m(r) – gravitational mass inside r –instead of λ(r)
Frequency emitted at r
Frequency detected byan observer at infinity
This function determinesgravitational redshift
NS Radii
A NS with homogeneous surface temperature and local blackbody emission
42 4 TRL
42
2 /
4TDR
D
LF
From X-rayspectroscopy
From dispersion measure
Limits from RX J1856
(Trumper)
Radius determination in bursters
See, for example,Joss, Rappaport 1984,Haberl, Titarchuk 1995
Explosion with a ~ Eddington liminosity.
Modeling of the burst spectrumand its evolution.
Burst oscillations
[Bhattacharyya et al. astro-ph/0402534]
Fitting light curves of X-ray bursts.Rc2/GM > 4.2 for the neutron star in XTE J1814-338
Fe K lines from accretion discs
[Cackett et al. arXiv: 0708.3615]
Measurements of the inner disc radius provide upper limits on the NS radius.
Ser X-1 <15.9+/-14U 1820-30 <13.8+2.9-1.4GX 349+2 <16.5+/-0.8(all estimates for 1.4 solar mass NS)
Suzaku observations
Mass-radius diagram and constraints
(astro-ph/0608345, 0608360)
Unfortunately, there are nogood data on independentmeasurements of massesand radii of NSs.
Still, it is possible to putimportant constraints.Most of recent observationsfavour stiff EoS.
Rotation!
Most rapidly rotating PSR716-Hz eclipsing binary radio pulsar in the globular cluster Terzan 5
(Jason W.T. Hessels et al. astro-ph/0601337)
Previous record (642-Hz pulsar B1937+21)survived for more than 20 years.
Interesting calculationsfor rotating NS have beenperformed recently by Krastev et al.arXiv: 0709.3621
Rotation starts to be important from periods ~3 msec.
QPO and rapid rotationXTE J1739-285 1122 HzP. Kaaret et al.astro-ph/0611716
(Miller astro-ph/0312449)
1330 Hz – one of thehighest QPO frequency
The line corresponds tothe interpretation, thatthe frequency is thatof the last stable orbit,6GM/c2
Rotation and composition
(Weber et al. arXiv: 0705.2708)
Computed for a particular model:density dependent relativistic Brueckner-Hartree-Fock (DD-RBHF)
(equatorial) (polar)
Rotation and composition
(Weber et al. arXiv: 0705.2708) 1.4 solar mass NS (when non-rotating)
hyperonhyperon quark-hybridquark-hybrid quark-hybridquark-hybrid(quarks in CFL)(quarks in CFL)
Mass-radius relation Main features
• Max. mass• Diff. branches (quark and normal)• Stiff and soft EoS• Small differences for realistic parameters• Softening of an EoS with growing mass
Rotation is neglected here. Obviously, rotation results in:• larger max. mass• larger equatorial radius
Spin-down can result in phase transition.Haensel, Zdunikastro-ph/0610549
Gravitational redshift• Gravitational redshift may provide M/R in
NSs by detecting a known spectral line, E∞ = E(1-2GM/Rc2)1/2
• Fe and O lines in EXO 0748-676, M/R ~ 0.22 (Cottam et al 2002)
Combination of different methods
(Ozel astro-ph/0605106)
EXO 0748-676
Limits on the EoS from EXO 0748-676
(Ozel astro-ph/0605106)
Stiff EoS are better.Many EoS for strangematter are rejected.But no all! (see discussionin Nature).
X- hydrogene fractionin the accreted material
However, redshift measurements forEXO 0748-676are strongly critisized now.
Limits on the moment of inertia
Spin-orbital interaction
PSR J0737-3039(see Lattimer, Schutzastro-ph/0411470)
The band refers to ahypothetical 10% error.This limit, hopefully,can be reached in several years of observ.
NS Cooling
NSs are born very hot, T > 1010 K At early stages neutrino cooling dominates The core is isothermal
LLdt
dTC
dt
dEV
th
1)( , 4 2/142 TTTRL ss
Neutrino luminosity
Photon luminosity
Cooling depends on:
(see Yakovlev & Pethick 2004)
1. Rate of neutrino emission from NS interiors2. Heat capacity of internal parts of a star3. Superfluidity4. Thermal conductivity in the outer layers5. Possible heating
Depend on the EoSand composition
Neutrinocooling stage
Photoncooling stage
Main neutrino processes
(Yakovlev & Pethick astro-ph/0402143)
Questions
• Additional heating
• Heating in magnetars (and probably in the M7)
• For example, PSR J0108-1431 [0805.2586] Old (166 Myr) close by (130 pc) PSR with possibly thermal (90 000K) emission)
Cooling curvesCooling curves for hadron (ie. normal) stars.
There are many-many models.
(Kaminker et al. 2001)
Data on cooling
Page, Geppertastro-ph/0508056
Two tests
Age – Temperature
&
Log N – Log S
Standard test: temperature vs. age
Kaminker et al. (2001)
Log N – Log S
Log of flux (or number counts)
Lo
g o
f th
e n
um
ber
of
sou
rces
bri
gh
ter
than
th
e g
iven
flu
x
-3/2 sphere: number ~ r3
flux ~ r-2
-1 disc: number ~ r2
flux ~ r-2
calculations
Log N – Log S as an additional test Standard test: Age – Temperature
Sensitive to ages <105 yearsUncertain age and temperatureNon-uniform sample
Log N – Log SSensitive to ages >105 years (when applied to close-by NSs)Definite N (number) and S (flux)Uniform sample
Two test are perfect together!!!
astro-ph/0411618
List of models (Blaschke et al. 2004)
Model I. Yes C A Model II. No D B Model III. Yes C B Model IV. No C B Model V. Yes D B Model VI. No E B Model VII. Yes C B’ Model VIII.Yes C B’’ Model IX. No C A
Blaschke et al. used 16 sets of cooling curves.
They were different in three main respects:
1. Absence or presence of pion condensate
2. Different gaps for superfluid protons and neutrons
3. Different Ts-Tin
Pions Crust Gaps
Model I Pions. Gaps from Takatsuka &
Tamagaki (2004) Ts-Tin from Blaschke, Grigorian,
Voskresenky (2004)
Can reproduce observed Log N – Log S
Model II
No Pions Gaps from Yakovlev et al.
(2004), 3P2 neutron gap suppressed by 0.1
Ts-Tin from Tsuruta (1979)
Cannot reproduce observed Log N – Log S
Model III
Pions Gaps from Yakovlev et al.
(2004), 3P2 neutron gap suppressed by 0.1
Ts-Tin from Blaschke, Grigorian, Voskresenky (2004)
Cannot reproduce observed Log N – Log S
Model IV
No Pions Gaps from Yakovlev et al.
(2004), 3P2 neutron gap suppressed by 0.1
Ts-Tin from Blaschke, Grigorian, Voskresenky (2004)
Cannot reproduce observed Log N – Log S
Model V
Pions Gaps from Yakovlev et al.
(2004), 3P2 neutron gap suppressed by 0.1
Ts-Tin from Tsuruta (1979)
Cannot reproduce observed Log N – Log S
Model VI
No Pions Gaps from Yakovlev et al.
(2004), 3P2 neutron gap suppressed by 0.1
Ts-Tin from Yakovlev et al. (2004)
Cannot reproduce observed Log N – Log S
Model VII
Pions Gaps from Yakovlev et al. (2004),
3P2 neutron gap suppressed by 0.1.
1P0 proton gap suppressed by 0.5
Ts-Tin from Blaschke, Grigorian, Voskresenky (2004)
Cannot reproduce observed Log N – Log S
Model VIII
Pions Gaps from Yakovlev et al.
(2004), 3P2 neutron gap suppressed by 0.1. 1P0 proton gap suppressed by 0.2 and 1P0 neutron gap suppressed by 0.5.
Ts-Tin from Blaschke, Grigorian, Voskresenky (2004)
Can reproduce observed Log N – Log S
Model IX
No Pions Gaps from Takatsuka
& Tamagaki (2004) Ts-Tin from Blaschke,
Grigorian, Voskresenky (2004)
Can reproduce observed Log N – Log S
HOORAY!!!!
Log N – Log S can select models!!!!!Only three (or even one!) passed the second test!
…….still………… is it possible just to update the temperature-age test???
May be Log N – Log S is not necessary?Let’s try!!!!
Different sensitivities of two tests Effects of the
crust (envelope) Fitting the crust it
is possible to fulfill the T-t test …
…but not the second test: Log N – Log S !!!
(H. Grigorian astro-ph/0507052)
Sensitivity of Log N – Log S
Log N – Log S is very sensitive to gaps Log N – Log S is not sensitive to the crust if it is applied to
relatively old objects (>104-5 yrs) Log N – Log S is not very sensitive to presence or absence of
pions
We conclude that the two test complement each other
Model I (YCA) Model II (NDB) Model III (YCB) Model IV (NCB) Model V (YDB) Model VI (NEB)Model VII(YCB’) Model VIII (YCB’’) Model IX (NCA)
Mass constraint• Mass spectrum has to be taken into account when discussing data on cooling• Rare masses should not be used to explain the cooling data• Most of data points on T-t plot should be explained by masses <1.4 Msun
In particular:• Vela and Geminga should not be very massive
Subm. to Phys. Rev .Cnucl-th/0512098(published as a JINR [Dubna] preprint)
Hybrid starsWe use models of HySsintroduced by Grigorian et al. (2005)Phys. Rev. C 71, 045801astro-ph/0511619
2SC phase
μc = 330 MeV
Mass spectrum
Model I
Model II
Model III
Model IV
Resume for HySs
One model among four was able to pass all tests.
Cooling of X-ray transients“Many neutron stars in close X-ray binaries are transient accretors (transients);They exhibit X-ray bursts separated by long periods (months or evenyears) of quiescence. It is believed that the quiescence corresponds to a lowlevel,or even halted, accretion onto the neutron star. During high-state accretionepisodes, the heat is deposited by nonequilibrium processes in the deep layers(1012 -1013 g cm-3) of the crust. This deep crustal heating can maintain thetemperature of the neutron star interior at a sufficiently high level to explain apersistent thermal X-ray radiation in quiescence (Brown et al., 1998).”
(quotation from the book by Haensel, Potekhin, Yakovlev)
Cooling in soft X-ray transients
[Wijnands et al. 2004]
MXB 1659-29~2.5 years outburst
~1 month
~ 1 year
~1.5 year
Aql X-1 transient
A NS with a K star.The NS is the hottestamong SXTs.
Deep crustal heating and cooling
ν
γ
γ
γγ
γ
Accretion leads to deep crustal heating due to non-equilibrium nuclear reactions.After accretion is off:• heat is transported inside and emitted by neutrinos• heat is slowly transported out and emitted by photons
See, for example, Haensel, Zdunik arxiv:0708.3996
New calculations appeared very recently 0811.1791 Gupta et al.
Time scale of cooling(to reach thermal equilibrium of the crust and the core) is ~1-100 years.
To reach the state “before”takes ~103-104 yrs
ρ~1012-1013 g/cm3
Pycnonuclear reactionsLet us give an example from Haensel, Zdunik (1990)
We start with 56FeDensity starts to increase
56Fe→56Cr56Fe + e- → 56Mn + νe
56Mn + e- → 56Cr + νe
At 56Ar: neutron drip56Ar + e- → 56Cl + νe
56Cl → 55Cl +n55Cl + e- → 55S + νe
55S → 54S +n54S → 52S +2n
Then from 52S we have a chain:52S → 46Si + 6n - 2e- + 2νe
As Z becomes smallerthe Coulomb barrier decreases.Separation betweennuclei decreases, vibrations grow.40Mg → 34Ne + 6n -2e- + 2νe
At Z=10 (Ne) pycnonuclear reactions start.
34Ne + 34Ne → 68Ca36Ne + 36Ne → 72Ca
Then a heavy nuclei can react again:72Ca → 66Ar + 6n - 2e- + 2νe
48Mg + 48Mg → 96Cr96Cr → 88Ti + 8n - 2e- + 2νe
A simple model
[Colpi et al. 2001]
trec – time interval between outburststout – duration of an outburstLq – quiescent luminosityLout – luminosity during an outburst
Dashed lines corresponds to the casewhen all energy is emitted from a surface by photons.
Deep crustal heating~1.9 Mev per accreted nucleonCrust is not in thermal equilibrium with the core.After accretion is off the crust cools down andfinally reach equilibrium with the core.
[Shternin et al. 2007]
KS 1731-260
Testing models with SXT
[from a presentation by Haensel, figures by Yakovlev and Levenfish]
SXTs can be very important in confronting theoretical cooling models with data.
Theory vs. Observations: SXT and isolated cooling NSs
[Yakovlev et al. astro-ph/0501653]
Conclusions Mass
Radius
Red shift (M/R)
Temperature
Moment of inertia
Gravitational vs. Baryonic mass
Extreme rotation
In binaries, especially in binaries with PSRs.In future – lensing.
In isolated cooling NS, in bursters in binaries,in binaries with QPO
Via spectral line observations
In isolated cooling NSs and in sometransient binaries (deep crustal heating)
In PSRs (in future)
In double NS binaries, if good contraintson the progenitor are available
Millisecond pulsars (both single and binary)