Transcript Spectra of the spreading layers on the neutron star surface - Irfu

Spectra of the accreting
neutron stars boundary
layers in the spreading
layer model
V. Suleimanov1,3
in collaboration with J. Poutanen2
1- Institut fuer Astronome und Astrophysik, Tuebingen, Germany;
2 - Oulu University, Finland;
3 - Kazan State University, Russia
CEA Saclay 7 February 2008
Outlook
• Introduction. Neutron stars and X-ray binaries.
• Boundary layer – region between accretion disk
and neutron star. Two approaches.
• Spreading layer as a boundary layer. Basic
results.
• Atmospheres of the bursting neutron stars – the
base to understanding of the local spreading
layer.
• Spectra of the spreading layers. Comparison
with observations.
• Conclusions
Neutron stars – main properties and short history
M ≈ 1.4 MSun R ≈ 10 km
Eg ≈ GM2 / R ~ 5 1053 erg
ρ ≈ 7 1014 g/cc
First idea – L.Landau (1932)
Neutron stars arise due to
Supernova outbursts
W. Baade, F. Zwicky (1934)
Crab nebula (Chandra)
ESN ~ 1053 erg ~ Eg (NS)
Discovery of Pulsars - A. Hewish, J. Bell (1968)
Supernova (type II) – final of a massive star life
Massive star evolve along supergiant branch up to SNII explosion
Supernova (type II) – final of a massive star life
Massive star structure before explosion
SNII explosion calculations (T. Janka, MPE)
Reason – gravitational collapse of Fe core due to
Neutronization
Photodissociation
and
  Fe  13  4n
56
p  e  n   e
Stellar remnants
From Woosley et al. (2002)
NSs – final stages of massive (from 8-12 to 25-40 MSun) stars
Stellar remnants – White Dwarfs and Neutron Stars
Brown dwarfs,
Giant planets
Maximum
-mass
neutron
star
M ~ (1.5  2.5) M Sun
R ~ 9  12 km
Maximum-mass
white dwarf
Minimum-mass M ~ 0.1 M Sun
neutron star
R ~ 250 km
Life of a protoneutron star
Protoneutron star cooling
Due to neutrino
- optically thick (R – 200 km →12 km, kT – 50 →5 MeV , t~50 s)
- optically thin (kT – 5 → 0.12 - 0.03 MeV , t ~ 50 - 100 yr )
Due to electromagnetic radiation (t ~ 106 yr)
Neutron star structure
Main problem – inner core Equation of State (EoS)
Zoo of NS inner core EoS
Prohibited by
General
Relativity
Special family of
low-mass strange stars
Universal low-mass
curve
Solution – M and R from observations!
Many faces of NS
Masses of NS – from binaries
Radii of NSs – from thermal emission
NS in 47 Tuc (Heinke et al 2006)
XDIN RX J1856-3754
(Trümper 2005)

R  17 km
RNS ≈ 14.5 ± 1.7 km
at M = 1.4 MSun
NS properties – from
accreting NSs in close binary systems
Bursters – luminosity near Eddington limit
(see Lewin et al. 1993, Galloway et al. 2007, …)
Problems – distance, chemical composition…
Out Attempt
Boundary Layers between accretion disc and NS in
Low Mass X-ray Binaries
X-ray Binaries
High Mass
M2 >> MSun
Young systems (Pop. I)
Accretion from wind
X-ray Pulsars
Low Mass
M2 < MSun
Old systems (Pop. II)
Secondary overfilled of the Roche lobe
Atoll- and Z-sources, Bursters,
Millisecond X-ray Pulsars
Low Mass X-ray Binaries (LMXB)
• Close binary with neutron star as a primary and a red
dwarf as a secondary.
• Galactic bulge sources (Population II). Most of them are
located near Galactic center.
• Orbital periods – few hours.
• Secondary overfilled the Roche lobe and a neutron star
accretes matter. X-ray radiation due to accretion.
• Brightest X-ray source – Sco X-1 is a LMXB.
• Neutron stars in LMXB have a relatively weak (B~108 G)
magnetic field. NO magnetosphere and accretion
column. Accretion disk exists up to the neutron star
surface.
Two types of LMXB
1) Bright (Z-sources).
Luminosities – few x1037 –
few x10 38 erg/s ~ 0.1-1 LEdd
Relatively soft two-component
spectra: relatively persistent accretion
disk spectrum with kTmax ~1 keV and
variable black body spectrum with
kT~2 keV (Mitsuda et al 1984)
Figure from Gilfanov et al (2003) (RXTE)
2) Low luminosity (atoll sources).
Luminosities – few x 1036 erg/s
~ 0.01 – 0.05 LEdd
Two spectral states: soft (look like
a Z-source) and hard (look like
an X-ray binary with a black hole
e.g. Cyg X-1)
Figure from Natalucci et al (2004) (BeppoSAX)
Horizontal branch
Normal branch
From Gilfanov et al 2003
Z source
From Done and Gerlinski 2003
Atoll source
Boundary layer (BL)
• Region between an accretion disk and a neutron star
• In BL fast rotating (with the Keplerian velocity) accretion disk matter
is decelerated to the neutron star rotation velocity.
• Luminosity of the BL comparable to the accretion disk luminosity
VK2 1 . GM NS
LBL ~ M
 M
~ LAD
2 2
RNS
.
Size of BL is smaller than the accretion disk size. Therefore, effective
temperature of BL is larger than the effective temperature of accretion
disk.
Hard black body component in the soft state of LMXB –
a boundary layer spectrum ?
Spectra of Boundary Layers
Figures from Gilfanov, Revnivtsev and Molkov (2003). They shown, that
frequency resolved (pulsed) spectra are spectra of boundary layers.
Spectra of Boundary Layers
Figures taken from Gilfanov, Revnivtsev and Molkov (2003). They shown
that shape of boundary layer spectra are independent on luminosity.
BL spectra are close to Planck spectrum with a color
temperature 2.4 ± 0.1 keV
Theory of Boundary Layers
“Classical” BL
BL as a part of the accretion
disk
NO vertical (latitude)
velocity component of
the matter
In this case
H BL  RNS BL
hBL
Figure from Inogamov and Sunyaev (1999)
CS

RNS
VK
CS2
 2 RNS
VK
hBL  RNS BL  RNS
Theory of Boundary Layers
BL as a spreading layer (SL)
Picture suggested by
Inogamov & Sunyaev (1999), below IS99
Matter has a significant latitude
velocity component, spreading above
the neutron star surface and decelerating
due to friction at the neutron star surface
(wind above the sea).
Figures from Inogamov and Sunyaev (1999)
Kley, 1989
Fisker et al. 2005
Numerical calculations confirm this picture
We slightly modified the Inogamov-Sunyaev model.
The GR effects and chemical composition were
taken into account.
Tcr4
GM NS
 e  g rad

g0  2
1/ 2
c
RNS (1  Rg / RNS )
 e  0.2(2  Y ) cm g
2
1
Pseudo-Newtonian potential

  c 1  1  Rg / RNS
2

Continuity equation

 _
    V   0
t


Euler equation
_
_
_
_
V

  V   V  P  f
t
Energy equation
Geometry of the problem
_
 1
 1

 _ _ _
2
2

  V         V    P  V   f V    q  Q
t  2

 
 2
Model suggestions


 0,
 0, Vr  0
t

We obtained the same equations as IS99
with one exception
Energy equation



1

2
2
cos V  2  S V  V   Egrav    dr   Pdr    RNS cos q




Input parameters of the model
Model distributions
M NS , RNS , M , Y
Teff ( ),  S ( ), V ( ), V ( )
Surface density and temperature distribution of the spreading layers with
luminosities L=0.1, 0.2, 04 and 0.8 LEdd along the latitude.
Scheme of the SL spectrum calculation
1. For each ring the model along height and emergent spectrum
2. SL are divided onto N rings
are calculated
3. Spectra of the each rings are summed with all relativistic corrections
2
LE  4 RNS

j
3
'
'
3


I
(cos

,

)
cos

 ij E
ij
i
ij cos  i  i  j
'
i
Basic equations
Hydrostatic equilibrium
GM NS
1 dPgas
q(r )
V 2 (r )
 2

e 
1/ 2
 dr
RNS (1  Rg / RNS )
c
RNS
Radiation transfer
 2 ( f J )
k
e
kTe  J
J

(
J

B
)

x
(

3
J

xJ
(
1

C
))




2
2
3
k   e
k   e mec x x
x

h
kTe
Radiation equilibrium
x
kTe
CJ
1 dq
 k ( J  B )dx   m c 2 (4J  xJ (1  x3 ))dx    dr
e
k
- true-absorption coefficient (mainly free-free transitions)
e
- Thomson electron scattering coefficient
X-ray bursting neutron star model
atmospheres
• X-ray bursting NSs – LMXBs with nuclear explosions at
the neutron star surface
• Close to Eddington limit during the burst
• Burst duration ~10 sec, time between bursts ~1 day
Figure from Pavlinsky et al (2001)
Compton scattering is very important!
h
k   T at x 
 0.1  1
kTe
Photons which we observe are emitted at the depth
 eff   ff  T  1
- thermalization depth
At this depth, electron scattering optical depth  T  1
In the case of Thomson scattering, the radiation and the gas are weakly
coupled in the surface layers of atmosphere → low surface temperature.
If Compton scattering is taken into account, hard photons heat electrons at
the surface up to T>Teff. This results in the emergent spectrum close to the
diluted black body.
Surface density which correspond to thermalization depth ~ 10 g/cm2
Diluted blackbody spectrum
1
F  4 B ( f c Teff )
fc
Bν – Planck function
fc – color correction (hardness factor)
Tc= fcTeff - color temperature
fc ~(1.3 – 1.9) mainly depend on L / LEdd
fc  0.15 ln C1  0.59 4 / 5 C12 / 15 l 3 / 20
C1  (8  5Y ) /(1  l ) l  L / LEdd  g rad / g0
Pavlov et al. 1991
X-ray bursting NS model atmosphere spectra and temperature structures
SL structure along height
1) dV  dq  0
dr dr
IS99, X-ray bursting NS
dV
dq
A


2)
dm dm
S  m
A  2.5 b1/ 2 ,  b  0.001
dm   dr
parameter of IS99 model
Analogy with classical hydrodynamic
boundary layers
dV
dz
3)
dV
dq
1


dm dm
S

dq 1

dz z
Temperature structure of the local SL models
X-ray bursting NS (IS99)
Second case ΣS=630 g/cm2
Second case ΣS=63 g/cm2
Third case
Spectra of local SL models from previous figure
fc  0.15 ln C1  0.59 4 / 5 C12 / 15 l 3 / 20
C1  (8  5Y ) /(1  l ), l  g rad / geff , geff  g 
Pavlov et al. (1991)
V2
R
SL spectra slightly depend on the luminosity and the inclination
angle to line of sight
Spectra of Boundary Layers
Figures taken from Gilfanov, Revnivtsev and Molkov (2003). They shown
that shape of boundary layer spectra are independent on luminosity.
BL spectra are close to Planck spectrum with a color
temperature 2.4 ± 0.1 keV
Comparison of the observed spectra of the BLs and the model spectra of
the SL. Black circles – GX 340+0 in the normal branch, green circles – 5 Z
and atoll sources in horizontal branch (Suleimanov & Poutanen 2006).
Main Idea

Tc
 1  rg / R f cTeff ( M , R)
fc
fc , T
Teff
Tc=fcTeff
Latitude, θ
No dependence on distance!
On chemical composition only (H or solar)
Allowed areas (shaded) for the NS mass and radii, which can have SLs with
color temperatures 2.4 +/- 0.1 keV. Various theoretical mass-radius relations for
neutron and strange stars are shown for comparison. Red dashed curve
corresponds to the NS with the apparent radius 16.5 km
(Suleimanov & Poutanen 2006).
1.6 m s
3RS
1.6 m s
3RS
X7
R=14.5 +/1.7 km
(1.4 M_sun)
R ap = 17 k m
1.6 m s
3RS
Our
Result
R=14.9 +/1.5 km
(1.4 M_sun)
Contours at 68% (dotted curves), 90% (dashed curves), and 99% (long-dashed
curves) confidence in the mass-radius plane derived for X7 (NS in 47 Tuc) by
spectral fitting (Heinke et al. 06). Allowed area from our model and limitations from
the apparent radius of RX J1856 and from the rotation period of B1937 are added.
Conclusions
• Local spectra of the optically thick (ΣS > 100 g/cm2)
spreading layers weakly depend on details of SL
structure along height and close to X-ray bursting NS
spectra with the same Teff , log g and Y.
• Integral spectra of the high luminosity spreading layers
(LSL > 0.2 LEdd ) are close to diluted Planck spectra.
• Radiation spectra of the spreading layers on the surface
of the neutron stars with stiff equations of state are
compatible with the observed spectra of boundary layers
in LMXBs.
Future work …
2D radiation hydrodynamic modeling
- transition region between accretion disk and SL
- vertical structure effects on global structure of SL
- non-axisymmetric models
- instabilities (QPO in LMXBs ?!)
The same accretion rate !