Download Neutron Star Crustal Emission: a basic, unanswered question.

Neutron Star Crustal Emission:
a basic, unanswered question
Silvia Zane, MSSL, UCL
Magnetic fields & Neutron Star Surface
Cocoyoc, Mexico, February 12-14 2007
• Turolla, Zane, and Drake, 2004
• Zane, Turolla and Drake, 2004
•
•
•
•
Perez Azorin, Miralles and Pons 2005, 2006
Van Adelsberg et al. 2005
Perez Azorin, et al 2006
Ho et al. 2007
WHY?
 1970s: commonly accepted that radiation by NSs came from their
solid surface (Brinkmann 1980 and refs)
 Later, the role of the thin gaseous layer which covers the star
crust in shaping the emergent radiation spectrum was
appreciated and model atmospheres became the standard
tool for interpreting the observed emission from isolated NSs.
 However, highly magnetized NSs may be left without atmosphere if
they are cool enough. Onset of a phase transition that turns the
gaseous atmosphere into a solid when the surface T drops below
Tcrit (B) (for a given chemical composition).
 Moreover, crustal emission should be the “external boundary
condition” for any cooling model, and the “internal boundary
condition” (at the basis of the gaseous layer) for any
atmospheric model !
X-ray Pulsating Dim Isolated Neutron Star:
the largest class of thermally emitting Neutron Stars
(Treves et al, 2000, Haberl et al. 2004)
Object
kT/eV
E line/eV
P (s)
semiampl opt.
RX J0420.0-5022
44
329
3.45
12%
B>25.5
RX J0720.4-3125
85
270
8.39
11%
B=26.6
RX J0806.4-4123
96
460
11.37
6%
B>24
RBS 1223
86
290
10.31
18%
m=28.6
RBS 1556
96
493
See Frank
talk?
RX J1856.5-3754
60
7.055
m=26.8
0.07%
V=25.7
RBS 1774
100
700
9.5
4%
R>23
 Soft X-ray sources in ROSAT survey; no radio emission
 BB-like X-ray spectra, no non thermal hard emission
 Low absorption, nearby (NH ~1019-1020 cm-2)
 Constant X-ray flux over ~years: BUT 0720!
 No obvious association with SNR or binary companion
 Optically faint BUT shows a definite optical excess!
 THEIR SPECTRUM CANNOT BE REPRODUCED BY SINGLE T/SINGLE B
ATMOSPHERIC MODELS!
The striking case of RX J1856.5-3754
 500 ks DDT Chandra exposure
(i) RX J1856.5-3754 has a featureless X-ray
continuum
(ii) better fit with a simple bb than with more
sophisticated atmospheric models (Burwitz et al,
2001, Drake et al, 2002)
 Optical excess of ~6 over the Rayleigh-Jeans
tail of the X-ray best fitting bb (Walter &
Lattimer, 2002)
 Lowest measured pulsed fraction: 0.015
P ~ 7s (Tiengo and Mereghetti 2006)
 d ~170 pc (Kaplan et al, 2006)
 radiation radius of only 6-7 km!
(Drake et al, 2002)
1) Is RX J1856.5-3754 the first quark/strange star discovered ?
(Drake et al, 2002; Xu, 2002)
 Bare quark stars not covered by an atmosphere
would presumably emit a pure blackbody spectrum
 (2th component for the optical emission)
2) Other options : NS models based on a two-T surface
distribution
(Pons et al, 2002; Walter & Lattimer,
2002 )
 May account for X-ray to optical emission
 Give acceptable values for the star radius
But how to produce a featureless spectrum from a NS covered
with an optically thick atmosphere ??
How the spectrum of a quark star looks like ??
An alternative explanation: BARE NSs


Lai & Salpeter (1997), Lai (2001): NSs may be left without an
atmosphere if they are cool enough. Onset of a phase
transition
A gaseous atmosphere turns into a solid when T < Tcrit(B)
If B >> mee3c/h3 2.35 x109 G atoms and condensed matter change:
Strong magnetic confinement on e-; atoms have cylindrical shape
elongated atoms may form molecular chains by covalent bonding along B
Interactions between linear chains can then led to the formation of 3-D
condensates
4  level deviations from a bb (Burwitz et al 2003):
F ~ E B 
 = 1.28  0.30
Mimic X B , with X = absorption factor
X = 1 - x
x = reflection factor
VALUE OF Tcrit ?
Lai & Salpeter (1997), Lai (2001): still very crude expressions, although
Representing the most recent available estimetes
For H, the infinite linear chains (and metallic hydrogen) are certainly bound,
favoring the possibility of condensation for low T and/or high B
Tcrit for phase separation between condensed H and vapor:
T
H
crit



0.37
2
2
2
 0.1194.1B12  4.4ln B12  6.05   p , p   B , p   p , p
2


1/ 2
1

  B , p  eV
2

Situation more uncertain for heavy elements (as Fe). It is likely that,
unless B12>>100, the linear chains are unbound for Z>6.
Lai 2001: The cohesive energy is only a tiny fraction of the atomic
binding energy. But, even such weak cohesion of the Fe condensate can
give rise to a phase transition at sufficiently low T.
QS  0.05 Eatom ~ Z 9 / 5 B12 eV
2/5
Cohesive energy of
the 3D condensate
Tcrit  0.1QS  27 B12 eV
Fe
2/5
By equating ion density of the condensed
phase near zero pressure to the gas
density in the vapor
The coolest thermally emitting NSs
with available B + RX J1856.5-3754
Source
Tcol (eV)
RX J1856.5-3754 61.1  0.3
RX J0720.4-3125 86.0  0.6
RBS 1223
90.6  1.6
Vela
128.4  7
Geminga
48.3 +6.1-9.5
PSR 0656+14
69.0  2.5
PSR 1055-52
68.1 +10.2 –17.2
B (1012 G)
-24.
34.
3.3
1.5
4.7
1.1
Refs
1,2
3,4
5
6,7
8,9
10,7
11,7
[1] Burwitz et al, 2001; [2] Drake et al, 2002; [3] Paerels et al, 2001;
[4]Zane et al, 2002; [5} Kaplan et al; [6] Pavlov et al, 2001; [7]
Taylor et al, 1993; [8] Halpern & Wang, 1997; [9] Bignami & Caraveo,
1996; [10] Marshall & Schulz 2002; [11] Greivendilger et al, 1996.
Critical T for H and Fe. Condensation is possible in
the shaded region for Fe and in the cross-hatched
region for H. Filled circles are the NSs listed in the
table. The horizontal line is the color temperature of
RX J1856.5-3754
Most Isolated Neutron Stars have T well in excess of THcrit :
 if surface layers are H-dominated an atmosphere is unavoidable.
But: if some objects have not accreted much gas:
 we may detect thermal emission directly from the iron surface layers
 depending on B the outer layers of RX J1856.5-3754 might be in form
of condensed matter !
SPECTRUM?
Turolla, SZ & Drake, 2004 (see also Brinkmann 1980)
 dA = 2 R2sin  d = surface element at magnetic co-latitude 
 i,  = angle of incidence and azimuth of the incident wave vector k
  = total surface reflectivity for incident unpolarized radiation
  = (1 - ) = absorption coefficient
 j =B (T) = emissivity (Kirchoff’s law)
Total flux:


2
 /2
0
0
0
 /2
F   dF   B (T ) sin  d  d
  (i,  , ) sin idi
Anisotropy of the medium response properties
  strongly depends on the direction of the refracted ray
• Pure
vacuum outside the star (neglect vacuum birefringence)
• EM wave incident at the surface with (E,k) is partly reflected (E’,k’) and partly
refracted
• Birefringence of the medium: the refracted wave is sum on an ordinary (E’’1,k’’1)
and an extraordinary (E’’2,k’’2) mode.
First: write down the dielectric tensor ij

ij
| 
= k’i k’j - |k|2ij +(2/c2)ij = Maxwell tensor
ij
| = 0 = dispersion relation  refractive index nm , m=1,2
Once nm, m=1,2 are known:
 solve the wave equation for the two refracted modes:  ij (nm)E’m,j =0
 obtain the ratios E’m,x / E’m,z and E’m,y / E’m,z
 put these ratios into the BCs at the interface between the two media
(Fresnel equations)
 obtain the E-field of the reflected wave in terms of the E-field of the
incident wave
E||” = f1 E + f2 E||
E” = f3 E + f4 E||
 = ||, + , = reflected/incident wave amplitude
|| = |f2|2 + |f4 | 2
, = |f1|2 + |f3| 2
A) dielectric tensor ij for a cold electron plasma
(unrealistic but instructive!)
- No contribution from the ion lattice,
- No damping of free electrons due to collisions
 S cos 2   P sin 2 

 
iD cos 
 sin  cos  ( P  S )


 R

   1  p2
   B
 L
2
plasma frequency ħ p
 iD cos 
S
iD cos 
 p2
P  1 2

0.7
Z1/5
B12
sin  cos  ( P  S ) 

 iD cos 

P cos 2   S sin 2  
S  RL
  
2
 D
3/5
(/s) keV
ħ p,0
s  560 AZ-3/5 B12 6/5 g/cm3, ion density near zero pressure (Lai,
2001)
The Spectrum by a Bare NSs is not necessarily a bb
 Strong (angle-dependent) absorption for photons with energy comparable
or lower than the plasma frequency.
 Strong absorption around the e- cyclotron frequency.
 Below the plasma freq (and close to the resonant frequency -, one of the
two modes may be non-propagating: a whistler. Whistlers have very
large, divergent refractive index (Melrose, 1986).
 Appearance of cut-off energies (n0) and evanescent modes which can not
propagate into the medium.
 If the refractive index has large imaginary part : highly damped modes.
They can not penetrate much below the surface (Jackson, 1975).

OSS: the existence of these damped waves is not in contradiction
with having neglected collisional damping.
 The “conductivity” sigma plij of a cold plasma can be computed from
the dielectric tensor as:  ij =  ij + i (4 /) pl ij and is therefore
purely imaginary (see Jackson ’75, Meszaros ‘92).
 Quotation marks are placed on “conductivity” because there is no
resistive loss of energy in this case.
 Yet, depending on their frequency and grazing angle, electromagnetic
waves may be exponentially damped even in the cold electron
plasma.
RESULTS: absorption features may or may not appear in the X-ray
spectrum, depending on the model parameters (mainly on B).
Monochromatic absorption
coefficient vs energy for a
given surface element. Plots
are for B=1012 G and
different values of the
magnetic field angle. From
top to bottom: 2/=0.05,
0.2, 0.4, 0.6, 0.8, 0.9, 0.95.
Total absorption coefficient
averaged over the star surface,
for different values of B.
Bp=5e12 G (full), 1e13 G
(dotted), 2e13G (dashed), 5e13
G (dash-dotted).
The “reference” plasma
frequency ħp0 has been used.
Spectra and a few numbers
• Teff = 75 eV , B = 3e13 G
• Left : T=cost
• Right : T() as given by
Greenstein & Hartke ‘83
For B  5 x 1013 G:
•Dashed line: bb at Teff
•Dashed-dotted line: best
fitting bb in the 0.1-2 keV
range
•Solid lines: spectra
•Upper/lower curves: po and
2.5 po
No features whatsoever in the 0.1-2 keV band
The Spectrum is within  4% from the best-fitting bb, no
hardening
The total power radiated by the surface in the 0.1-2 keV
band is  30-50% of the bb power, slightly larger for
the meridional temperature variation models
Correcting the Angular Size RX J1856.5-3754
R /(d/100 pc) = 4.12  0.68 km (Drake et al, 2002)
Ratio of the emitted to the bb
power in the 0.1-2 keV range for
different values of the plasma
frequency.
Circles: B =3 x1013 G.
Diamonds: B =5x1013 G
Filled: T=constant. Open: T().
SINCE d~ 170 pc, IF THE CORRECTION IS AS LOW AS 0.3-0.5,
THEN R  ~10-12 Km COMPATIBLE WITH THE PREDICTIONS OF EOS
of NSs (Lattimer & Prakash, 2001)
B) A (slightly) more realistic case:
accounting for e-/phonon interactions

In the solid crust e- are strongly degenerate. If ~s quantum effects
due to the B-field are not negligible.

In the degenerate surface layers charge (and heat) is transported
primarily by electrons.  needs an accurate determination of the
electrical conductivity  (Potekhin ’99 and refs therein)

Above the crystallization temperature of ions  is dominated by
scattering off ions, but below the crystal melting point the dominant
process is scattering by crystal lattice vibrations (phonons) through
Umklapp processes. Eventually, if T decreases further, impurities in the
crystal structure and scattering off lattice defects are important.

B-fields in the NS crust complicate e- transport making it anisotropic.
e- move freely parallel to B, but their motion perpendicular to the field
is quantized.
THE B-FIELD STRENGHT AFFECTS THE CHARGE TRANSPORT
(Potekhin et a. 2003)
1) T>>TB =ħe B / (me c): Non-quantizing (classical) regime.
A non-quantizing B-field essentially does not affect the
thermodynamic properties of matter, BUT hampers
transverse motion and produces Hall currents.
2) T << TB
weakly quantizing. When e- populate several
Landau levels
strongly quantizing regime. When the B-field
confines most e- in the ground Landau level.
Transition to strongly quantizing regime: < B 7x103(A/Z) B123/2 g/cm3
Note that the zero pressure density S is << B for B >> 1010 G.
The electrical conductivity tensor is computed from the transport
tensor (Hernquist ’84, Potekhin ’99)
N B  
 f 0 
 ij   e
 ij   
d
2
 /c
  
relaxation times
2
For strongly degenerate e- and not too close to
the Landau thresholds:
 ij  e nec /  F  ij  F 
2
Fermi energy.
2
 3 independent components: parallel to the field ( zz = ||),
transverse ( xx =  yy =  ), and one off-diagonal (Hall)
component (xy = H ), which is non-dissipative.
 In rotating coordinates only  || and   are needed
Potekhin ’99: most complete expressions for 
Accounts for correlation effects in the strongly coupled Coulomb
liquid and multi-phonon scattering in the Coulomb crystal.
 in a weakly quantizing field:
the conductivity in the
longitudinal and transverse
direction oscillates around
their classical values.
 for
strong quantization:
oscillations are quite
prominent and may reach
several orders of
magnitudes  transport
properties of matter much
different from the
classical regime.
Electrical and thermal
conductivities for two values of
log T. Dashed lines: classical limit.
From P99.
1) We write down the “conductivity” of the cold electron plasma
and that related to e-/phonon scattering
2) We define the corresponding relaxations times
3) We sum the effective frequencies of the two processes
tot
 rotat
.coord
 p2
 R tot 

 tot   1  2
D
L 





i

B



Damping
frequencies
In the two
directions

D
|| 
4||
2
p
 S tot
 tot
  iD
 0

 iD tot
S tot
0
0 

0 
P tot 
2


p
P tot  1  2
   i||D
 S tot  R tot  Ltot
 tot  
D 
2





1
D
2  4 

 
1  1  4 B
 2
2 4  
p


2
p




2




e-/phonon damping seriously affects the emission properties of the
surface. Below ~1keV the emissivity declines quite rapidly with
decreasing photon energy. Suppression mainly due e-phonon damping
in the transverse plane, more pronounced at lower B.
No damping
Total absorption coefficient
averaged over the star surface,
for different values of B.
Bp=5e12 G (full), 1e13 G
(dotted), 2e13G (dashed), 5e13
G (dash-dotted).
The “reference” plasma
frequency ħp0 has been used.
Damping
Spectra and a few numbers
• Teff = 75 eV
• B = 3e13 G and 5e13 G
• Left : T=cost
• Right : T() as given by
Greenstein & Hartke ‘83
•Dashed line: bb at Teff
•Dashed-dotted line: best
fitting bb in the 0.1-2 keV
range
•Solid lines: spectra
Fit with a bb in the 0.1-2 keV range still acceptable: max deviations
below 20% (4% in the cold e- case)
Larger suppression: only 35% of the bb power radiated for B=2e13G
 solve the “small radius problem”? (but feature at 300 eV)
At low fields B<<5e12 G virtually no emission is expected below
~0.5keV. For B~5e13G the surface can radiate down to a few
tens of eV's, but for B<<5e12G the star surface behaves as a
perfect reflector below ~100 eV.
The basic, unanswered question:
How the crust emits at low energies?
Can crustal emission be responsible for the
enhanced optical excess (possible with some
reprocessing from a low density gaseous
layer)?
What is the role of ions?
Our original “mistake”:
In a preliminary version of our work, we attempted to account for the
ion contribution by including free protons in the dielectric tensor.
Zane et al. (Cospar symp., 2002)
e- only
e- and p (no damping)
 By including protons as free particles gives a “flat” enhanced
emissivity at low E (and a proton cycl. feature in absorption).
 However, this treatment of protons is obviously incorrect.
 Ions form a lattice and cannot be considered as free particles
(as well as those e- which are bounds to ions).
 The simplistic treatment of the dielectric tensor as an e-/ion
plasma is unrealistic and not applicable.
More recent works and applications
• Turolla, Zane, and Drake, 2004: e- and phonon damping
• Zane, Turolla and Drake, 2004 : e- and phonon damping + gaseous
layer (see also Motch et al. 2003)
• Perez Azorin, Miralles and Pons 2005, A&A, 433, 275: similar to
TZD 2002 + models with free ions
• Van Adelsberg et al. 2005 : include free ions !
• Perez Azorin, Miralles and Pons, 2006, A&A 451, 1009 2006:
effects of toroidal fields on heat transport, crustal
mission as boundary condition
•Perez Azorin et al. 2006, A&A, 459, 175: explain the excess in
RXJ0720. Need free ions ? (no clear)
• Ho, et al. 2007, MNRAS: explain the excess in RXJ1856 with
free ions
