The Many Faces of Compact Stars - Barcelona,
September 22-26 2014
THERMAL EMISSION
FROM ISOLATED
NEUTRON STARS
R. Turolla
Dept. of Physics and Astronomy,
University of Padova, Italy
1
The Many Faces of Compact Stars - Barcelona,
September 22-26 2014
2
Outline
• Are INSs thermal emitters ?
• Observations of INSs
• Importance of thermal emission
Lecture 1
• The role of magnetic field and gravity
• The state of the NS surface
• Emission from NS atmospheres
• Non-magnetic models
• Magnetic models
• Emission from “bare” NSs
• The case of SXTs
• Models vs. observations
Lecture 2
The Many Faces of Compact Stars - Barcelona,
September 22-26 2014
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Some Like It Hot
• NSs are born very hot
Page, Geppert & Weber (2006)
(T ≈ 1011 K) and
progressively cool down
• Surface temperature
drops quickly and then
stays at ≈ 105 – 106 K
for about 1 Myr
• Thermal emission at ≈
100 eV, L ≈ 4πR2σT4 ≈
1031 – 1032 erg/s
Heating processes: magnetic dissipation, inflowing
magnetospheric currents, accretion
The Many Faces of Compact Stars - Barcelona,
September 22-26 2014
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INSs in the X-rays
• At present > 110 INSs detected in X-rays
• Large majority are “normal” (rotation powered)
radiopulsars (~ 90 sources, including HB and MPSs)
• Radio-silent (quasi), X/γ-ray bright INSs
• Anomalous X-ray pulsars and Soft γ-ray repeaters (AXPs and
•
•
•
•
SGRs, the magnetar candidates)
Central compact objects in SNRs (CCOs)
Rotating radio transients (RRaTs)
X-ray dim neutrons stars (XDINSs)
Geminga and Geminga-like objects
• “Isolated” NSs in binaries: Soft X-ray transients (SXTs)
• Thermal emission detected in about 40 sources
The Many Faces of Compact Stars - Barcelona,
September 22-26 2014
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Rotation and Magnetism
• Newborn neutron stars are
fast rotators (P0 ≈ 10-3 – 10-2
s)
• Large dipole magnetic field (B
≈ 1012 G in “normal” PSRs)
• Spin-down by magnetodipolar losses (oblique rotator
in vacuo)
(1 + sin2α) from self-consistent magnetospheric modeling (Spitkovsky 2006)
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September 22-26 2014
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Measuring P and Ṗ is crucial
Phase-coherent timing
SGR 1833 (Esposito et al. 2011)
Strictly periodic
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September 22-26 2014
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Thermally-emitting INSs (XDINSs) - I
• Soft X-ray sources, seven known (hence the
nickname “Magnificent Seven”, or M7)
• Slow rotators, P ~ 3-11 s, Ṗ  10-13 s/s
• Bp ~ 1.5-3.5x1013 G, τ ~ a few Myr, τkin ~ 5-10 times
shorter
• Faint optical counterparts
• Close-by, D  150-500 pc
• Radio-silent
• Intrinsically radio-quiet ? Misaligned PSRs ? (Kondratiev
et al. 2009)
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September 22-26 2014
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Thermally-emitting INSs (XDINSs) - II
• Thermal spectrum, T ~ 50-100 eV, RBB ~ 5-10 km
• Broad absorption features @ 300-700 eV
• Proton cyclotron/Atomic transitions ? (Turolla 2009,
Kaplan & Van Kerkwijk 2011)
• Steady, long-term spectral changes in RX J0720
• Precession (Haberl et al 2006) ? Glitch (Van Kerkwijk et al.
2007, Hohle et al. 2012) ?
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September 22-26 2014
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Magnetar Candidates (SGRs/AXPs) - I
• About 20 known
• Short (0.1-1 s), energetic (1039-1041 erg/s) bursts
and giant flares (up to 1047 erg/s)
• Variable (transient) persistent emission (LX 
1032-1036 erg/s)
• P ~ 2-12 s, huge Ṗ  10-10-10-13 s/s
• Bp  1013 -1015 G, τ  1-10 kyr, LX >> Ė
• Thermal + power-law spectrum (PL extends up to
200 keV), T ~ 0.5 keV, RBB < 1 km
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September 22-26 2014
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Magnetar Candidates (SGRs/AXPs) - II
• Three “low-field” magnetars recently discovered
(Rea et al. 2010, 2012, 2013)
• Bp ≤ 1013 G, τ  1 -10 Myr,
• Ultra-strong, local field measured in SGR 0418 (~ 1015
G, Tiengo et al. 2013)
• Magnetar-like activity detected in two RPPs
(Gavriil et al. 2008, Levin et al. 2010)
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September 22-26 2014
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Radio Pulsars (including HBPSRs)
• More than 2000 discovered in the radio, ~ 90 in
the X-rays
• Wide range of P ( 1ms-10 s) and Bp ( 108-1014
G)
• X-ray emission
• Thermal (~ 0.1 keV), from
• hot spots (MSPs, relatively old PSRs)
• the entire cooling surface (relatively young PSRs)
• Non-thermal, from the magnetosphere
• High-B PSRs are “normal” RPPs with a field in the
magnetar range (~ 20 with Bp > 5x1013 G) but no detected
magnetar-like activity
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September 22-26 2014
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Rotating Radio Transients (RRaTs)
• About 80 known, “normal” radio pulsars with an
exceedingly high nulling fraction (> 99%, Burke-Spolaor
2013), i.e. they emit sporadic, single radio pulses
(McLaughlin et al. 2006)
• P ~ 0.5-7 s, B ~ 1012-1014 G, τ ~ 0.1-3 Myr
• PSR J1819-1458 (P = 4.3 s, B = 5x1013 G) detected in Xrays (McLaughlin et al. 2007, Miller et al. 2013)
• Thermal spectrum (T ~ 140 eV, RBB ~ 8 km)
• One (two ?) absorption feature @ ~ 1 keV
• LX > Ė (?)
• Bright PWN (Rea et al. 2009)
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September 22-26 2014
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Central Compact Objects (CCOs)
• INS X-ray sources at the centre of SNRs, 8 found
• Young (SNR age τSNR < 104 yr)
• Radio-silent, no counterpart at other wavelengths
• Steady, thermal spectrum, quite large pulsed fraction,
absorption lines in some sources
• P and Ṗ measured (or constrained) in 3 sources (Pup A,
Kes 79, 1E 1207; Gotthelf 2010, Halpern & Gotthelf 2010, 2011)
• P ~ 0.1 -0.4 s
• B  3-10x1010 G, the “anti-magnetars”
• LX > Ė, τ >> τSNR
The Many Faces of Compact Stars - Barcelona,
September 22-26 2014
• X-ray emission ubiquitous
over the P-Ṗ diagram
• Detected from objects with
extremely different
• Ages: from young Crab-like to
old PSRs
• Magnetic fields: from low-B
ms PSRs to magnetars
Kondratiev et al. (2009)
14
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September 22-26 2014
Different mechanisms
powering X-ray emission
Rotation
SGR+AXPs
XDINSs
HBPSRs
RRaTs
Cooling
Magnetism
from Becker (2009)
15
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September 22-26 2014
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INS spectrum: thermal plus non-thermal component
(magnetospheric, if rotation-powered LNT ~ Ė ~ t-β,
β ≈ 2-4)
total
non-thermal
thermal
Young, < 1 kyr: non-thermal
component dominates (Crab,
PSR 1509-58)
Middle-aged, 10-100 kyr:
thermal emission from the
star surface (Vela, Geminga)
Old, > 1 Myr: no
magnetospheric activity
(XDINSs) + SXTs
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September 22-26 2014
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Thermal Emission from INS
• Thermal radiation from a NS first detected by
EXOSAT and Einstein (’80s)
• Many more sources found by ROSAT (’90s),
Chandra and XMM-Newton
• At present about 40 sources known: PSRs, AXPs
and SGRs, CCOs, RRaTs, XDINSs, Geminga
and Geminga-like objects
• “Isolated” NSs in binaries: Soft X-ray Transients
(SXTs)
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September 22-26 2014
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Tapping the NS surface - I
Comparison of observations with theoretical
models can provide Ts, Bs, chemical composition,
R (and M)
Consider a simple, idealized case: the NS surface
emits a blackbody at TBB (≈ 100 eV) and neglect GR
Fitting the observed X-ray spectrum with a BB
2
−2 2
0.01(𝑅𝐵𝐵 1 km) (𝐷 1 kpc) 𝐸
𝐵𝐵 𝐸 =
exp( 𝐸 𝑘𝑇𝐵𝐵 ) − 1
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September 22-26 2014
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provides Ts and (RBB/D)2, and, if distance is known,
RBB
Beware that RBB is the linear
size of the emitting region
(projected onto the sky) and
not necessary coincides with
the NS radius
RBB
R
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September 22-26 2014
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Tapping the NS Surface - II
• Real life is a trifle more complicated…
• Isolated NSs are highly magnetized (B ≈ 1011-1015
G) and very compact (R ≈ 10-15 km ≈ 3 RS)
• The strong B field affects
• Photon propagation
• Surface temperature distribution
• Local emission
• Gravity effects are important
• Ray bending
• Gravitational redshift
The Many Faces of Compact Stars - Barcelona,
September 22-26 2014
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Photons in a Magnetized Medium
• Magnetized plasma is anisotropic and
birefringent, radiative processes sensitive to
polarization state
• Two normal, elliptically polarized modes in the
magnetized “vacuum+cold plasma”
The extraordinary (X) and ordinary (O) modes
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September 22-26 2014
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B
EO
EX
k
O mode: electric field in the k-B plane
X mode: electric field perpendicular to
the k-B plane
The opacities of the O mode are
little affected by B, those of the X mode
are substantially reduced at E << Ec
Scattering cross section for the
X and O modes (Ventura 1979)
The Many Faces of Compact Stars - Barcelona,
September 22-26 2014
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NS Thermal Maps
• Electrons move much more easily along B than
across B
• Thermal conduction
is highly anisotropic inside a
Greenstein & Hartke (1983)
NS: Kpar >> Kperp until EF >> hνc or ρ >>
104(B/1012 G)3/2 g/cm3
• Envelope scaleheight L ≈ 10 m << R, B ~ const
and heat transport locally 1D
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September 22-26 2014

TS  cos   K perp / K par sin 
2
2

1/ 4
24
Tpole
K perp / K par  1
TS  cos 
1/ 2
Tpole
Core centered dipole
Core centered quadrupole
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September 22-26 2014
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Gravity Effects - I
• NSs are highly relativistic objects
• GM/Rc2 ~ 0.15 (M/M)(R/10 km)-1
• (J/Mc)/(GM/c2) ~ 4x10-4 (P/1 s)-1 (M/M)-1(R/10 km)2 (the Kerr solution
does not describe spacetime outside a rotating star though)
• Schwarzschild spacetime
𝑑𝑠 2
=− 1
2𝐺𝑀
− 2
𝑟𝑐
𝑐𝑑𝑡
2
+ 1−
2𝐺𝑀 −1
2
𝑑𝑟
𝑟𝑐 2
+ 𝑟 2 𝑑Ω2
• Radiation emitted at frequency ν at the NS surface (r = R) is
redshifted
𝜈∞
𝜈
=
1−
2𝐺𝑀
𝑅𝑐 2
(Δν/ν ≈ 0.2)
2𝐺𝑀
• For BB radiation 𝑇∞ = 𝑇 1 − 2 (uniform T on the surface)
𝑅𝑐
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September 22-26 2014
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Gravity Effects - II
• R is the circumferential radius (i.e. Lcirc = 2πR for a local
observer at rest). An observer at infinity measures a
radius 𝑅∞ = 𝑅/ 1 −
2𝐺𝑀
𝑅𝑐 2
• The luminosity at infinity is lower
2𝐺𝑀 −1
2𝐺𝑀 −1
𝐿 = 4𝜋𝑅 𝜎𝑇 = 4𝜋𝑅∞ 𝜎𝑇∞ (1 −
) = 𝐿∞ (1 −
)
2
2
𝑅𝑐
𝑅𝑐
• For a non-uniform surface temperature compute the
(monochromatic) flux from dS = R2sinθdθdφ (remember
that there is a single ray which leaves dS and reach the
observer)
𝑑𝑆
𝑑𝐹𝜈 = 𝐼𝜈 cos 𝜃 2
𝐷
2
4
2
4
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September 22-26 2014
More Than Meets the Eye
• Oops, light rays are not straight lines !
• Because of light bending, the ray which
hits your eye leaves dS at an angle α ≠ θ
2𝐺𝑀
𝑑 cos 𝛼 𝑑𝑆
𝑑𝐹𝜈 = (1 − 2 )𝐼𝜈 cos 𝜃
2
𝑅𝑐
𝑑 cos 𝜃 𝐷
More than half the surface is visible
• The total flux is obtained by integrating
over the visible part of the emitting region
• Dependence of α on θ somehow
complicated. Simple, accurate
approximation (Beloborodov 2002)
1 − cos 𝛼 = (1 − cos 𝜃)(1 −
2𝐺𝑀
)
𝑅𝑐 2
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September 22-26 2014
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The terminator is at
α = π/2, cos θF = (1-2GM/Rc2)-1
R = 15 km
M = 1.4 M
No gravity
112°
LOS
90°
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September 22-26 2014
LOS
Hot spot
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The Many Faces of Compact Stars - Barcelona,
September 22-26 2014
STEP 1
Specify viewing geometry
and B-field topology;
compute the surface
temperature distribution
STEP 2
Compute emission from
each surface patch
STEP 4
Predict lightcurve and
phase-resolved spectrum
Compare with observations
30
STEP 3
GR ray-tracing to obtain
the spectrum at infinity
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September 22-26 2014
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What is the correct model for
surface thermal emission ?
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September 22-26 2014
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A “Hard” Surface ?
• NS surface composition: either H (accreted from ISM or
from fallback of SN material) or heavy elements (C, Ne,
adapted from Turolla et al (2004)
Fe H
Fe)
condensation
• Under typical conditions surface layers are in gaseous
(Lai 2001)
state: NS atmosphere
• For sufficiently low T and large B (and depending on
C He
composition) the surface can be in a condensed Fe
state:
condensation
H
“bare” NS
(Medin & Lai
Fe
2006, 2007)
Whatever the state of the surface, the emitted
thermal radiation is NOT a blackbody
The Many Faces of Compact Stars - Barcelona,
September 22-26 2014
NS Atmospheres
Very different from atmospheres around
normal stars
• For a NS: M ~ 1.4 M, R ~ 10 km
• Huge surface gravity, g = GM/R2 ≈ 1014 cm/s2
• Pressure scale-height, H ~ kTs/mpg ≈ 1 cm
• Large densities, ρ ≈ 0.01 – 10 g/cm3
In NSs 108 G < B < 1015 G
Magnetic effects important if
Ece > kT, Eion → B > 1010 (T/106 K) G
33
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September 22-26 2014
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Low-B Atmospheres
• H << R → plane-parallel approximation
• Isotropic medium: P=P(z), T=T(z),…
• Radiation field: monochromatic intensity Iν(z,μ) (μ=cosθ)
z
n
Iν(z,μ)
θ
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September 22-26 2014
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Radiative transfer equation
I

   ( I  S )
z
1
1
1
S  ( J   B ) , J   I d
2 1
     total opacity (absorption plus scattering)
Hydrostatic equilibrium
dP
  g
dz
Radiative energy equilibrium

aT    J d  0
4
0
+ EOS, ionization balance,…
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September 22-26 2014
Opacity depends on density,
temperature and chemical
composition
Free-free, free-bound,
bound-bound transitions
Thomson scattering (σν = σT)
κν ~ ν-3
Zavlin & Pavlov (2002)
36
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September 22-26 2014
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Specify model parameters: M, R (or g) and L (or
Teff = [L/4πR2σB]1/4); chemical composition
Solve transfer equation, hydrostatic and energy balance;
dz → dτ = -σρdz (0 < τ < τmax » 1)
RTE integro-differential: moment methods, Λ-iteration
Obtain Iν(τ,μ), T(τ), ρ(τ)
Compute emergent flux F (0)  2
1

1
dI (0,  )
Model atmospheres investigated e.g. in Romani (1987),
Zavlin et al. (1996), Rajagopal & Romani (1996), Gänsicke,
Braje & Romani (2002), Pons et al. (2002)
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Non-magnetic Spectra
g = 2.4x1014 cm s-2
g = 2.4x1014 cm s-2
Zavlin & Pavlov (2002)
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H, He spectra are typically broader (harder) than
the blackbody at Teff
Fe spectra are closer to a blackbody but show
many lines and edges
Because of the frequency-dependent opacity
(κν ~ ν-3) higher-energy photons decouple in the
deep layers which are hotter
Emerging spectrum like the superposition of
blackbodies at different temperatures
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September 22-26 2014
Magnetized Atmospheres
• Magnetized plasma is anisotropic and birefringent,
radiative processes sensitive to polarization state
• Two normal, elliptically polarized modes in the
magnetized “vacuum+cold plasma”: ordinary and
extraordinary
• Radiative transfer for both modes
• Heat transfer in the crust mainly along B → surface
temperature inhomogeneous
40
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Opacities are different for the two modes and depend
on n·B/B
Assume B along the z-axis (n·B/B = μ)
Radiative transfer equations
2
 (i ) (i )

I( i )
( i ) B
( j)
(i, j )

    I  
   d I (  ) (  ,  )
z
2 j 1


i  1,2
Hydrostatic and radiative energy equilibrium
Fix g, Teff, chemical composition, B and obtain
1
F (0)  2  d[ I(1) (0,  )  I( 2) (0,  )]
1
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September 22-26 2014
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Magnetic Spectra
Ionized
H
Not too different from
non-magnetic
models. Magnetic
opacities higher:
spectra more BB-like
Proton cyclotron line
 B 
Ecp  0.63 14  keV
 10 G 
Zavlin & Pavlov (2002)
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September 22-26 2014
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• Ionized, H atmospheres investigated e.g. in Shibanov et
al. (1992), Pavlov et al. (1994; 1995), Zavlin et al.
(1995), Zane et al. (2001), Ho & Lai (2001)
• Ionization affected by B: at 𝐵 > 𝐵0 =
𝑚2 𝑐𝑒 3
~2.3 ×
ℏ3
109 𝐺 the atoms binding energy increases and their size
along B decreases. Light elements which are fully
ionized at low B are not in NS atmospheres
• H (e.g. Ho et al. 2003; 2008) and heavier elements (Z < 10)
(Mori & Hailey 2006; Mori & Ho 2007) models with partial
ionization
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hydrogen
Ho et al (2008)
Mori & Ho (2007)
• For B > 1013 G models need to account for vacuum
polarization and mode switching
• Magnetized models are “local”: B and T change on
the surface
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September 22-26 2014
Condensed Surface
𝜐𝑝𝑒 =
45
4𝜋𝑒 2 𝑛𝑒
𝑚∗
Commonplace: the surface of a body at temperature T
always emits The
a blackbody
at T mirror works !
way a metallic
In general the emissivity is j (n)   (n) B (T ) or
j (n)  [1   (n)]B (T ) where α (ρ) are the absorbitivity
(reflectivity)
In a metal conduction electrons are unable to oscillate in
response to an incident wave with ν > νpe: the wave is
absorbed, α = 1 and blackbody emission
The opposite occurs below νpe: the wave is reflected,
ρ ~ 1, α ~ 0 and no emission
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• The condensed surface works much in the same way
(after all it is made of iron )
• Zero-pressure density of the condensate: ρs ≈
560 AZ3/5B126/5 g/cm3
• Plasma frequency in the surface layers: hνpe ≈
0.7Z1/5B123/5(ρ/ρs)1/2 keV
• Emissivity strongly suppressed at ν ≲ νpe (Lenzen &
Trümper 1978, Brinkmann 1980)
• NSs with condensed surface are cold: hν ≈ kT ≈ 100
eV, soft X-ray/UV-optical spectrum depressed wrt a
blackbody
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Spectra from a Condensed Surface
Compute the emissivity in a highly magnetized medium
(Turolla et al. 2004; Pons et al. 2005; Van Adelsberg et al. 2005)
Potekhin (2014)
Free ions
Fixed ions
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Bare NS spectra - fixed ions (Turolla, Zane & Drake 2004)
X-ray spectra (0.1 – 2 keV) close to a blackbody in shape
but depressed by a factor of ~ 3
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Absorption Features - I
• Detection of spectral “lines” is crucial: information on
chemical composition, B, …
• And M/R ! If the physical process responsible for the line
is known, the line energy (in the lab) is known and the
ratio Eline,∞/Eline = (1-2GM/Rc2)1/2 gives M/R
• Broad absorption features observed in the thermal
spectrum of several INSs (XDINSs, with the exception of
RX J1853.5-3754, the RRAT PSR J1819-1458, SGR
0418+5729, the CCO 1E 1207.4-5209 and PSR
J1740+1000)
• Multiple lines and (phase/long-term) line variability
reported in a few sources
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Absorption Features - II
• No convincing explanation
for &the
exists (and
Van Kerkwijk
Kaplan features
(2007)
their origin is likely different in different INS classes…)
• Consider the XDINSs (and possibly the RRAT PSR
J1819-1458)
• proton cyclotron lines (e.g. Zane et al. 2001)
• Ec,p → B in fair agreement with the spin-down measure
• need an atmosphere
• cannot work for multiple lines: higher harmonics strongly suppressed
• Atomic transitions in light (H, He) elements (e.g. Van Kerkwijk & Kaplan
2007)
• Etrans → B in fair agreement with the spin-down measure
• need an atmosphere
• cannot work forRXsources
with larger Eline
J0720.4-3125 (Haberl et al 2004)
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Absorption Features - III
• Features (edges) in the spectrum emitted from a bare surface
(Pèrez-Azorìn et al. 2006)
• Resonances in the free-free opacity in a quantizing magnetic field
(Suleimanov, Pavlov & Werner 2010)
• The features are not there ! What we observe is a deformation of
the continuum due to the superposition of surface patches at
different T (Viganò et al. 2014)
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September 22-26 2014
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The Optical Excess
• Bulk of the emission is in (soft) X-rays for T ≈ 100 eV
• Can we observe thermal emission in the optical ?
• Fairly faint… FX/Fopt ≈
5.5+log 𝑘𝑇 100 eV
𝐹𝑋 /𝐹
3
𝑜𝑝𝑡 ~10
(EX/Eopt) ≈ (100 eV/1 eV)3 ≈ 106
a 50 W bulb at the distance of the moon
!
• May be feasible for close-by sources: the XDINSs
• An optical counterpart discovered for all the seven
sources (mV > 25; Kaplan et al. 2011)
• Optical SED is a power-law λ-p (?); however
• p is often different from 4 (the Rayleigh-Jeans exponent)
• the optical flux is higher than the extrapolation of the X-ray BB at lower
energies by a factor ≈ 5-50
Kaplan et al. 2011
RX J1856.5-3754
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53
Soft X-ray Transients
• SXTs: a subset of the low-mass X-ray binaries (LMXBs,
compact object+low mass star); many found in globular
clusters
• Large X-ray outbursts (weeks, LX ≈ 1036 - 1037 erg/s)
followed by quiescent phases (LX ≈ 1031 – 1033 erg/s)
• Outbursts driven by accretion instabilities
• Accretion switched off in quiescence
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September 22-26 2014
54
Quiescent Emission
Thermal + power-law spectra, kT ~ 0.1-0.3 keV, Γ ~ 1-2,
Lpl/Ltot < 0.1 for Ltot ~ 1033 erg/s (PL may be absent)
NSs inAql
SXTs
too old
to retain formation heat
X-1 (Campana
et al. 1998)
Accretion heats them up !
Heat is deposited in the crust by nuclear reactions and
then transferred to the (cold) core
Stationary state attained in ~ 104 yr (Haensel & Zdunik 1990;
Bildstein & Rutledge 2000)
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September 22-26 2014
55
Measuring NS Radii in SXTs
• In quiescence SXTs behave much like isolated cooling
NSs
• There are advantages, however:
• The magnetic field is low (it has been “buried” by accretion),
B ≈ 108-109 G
• The surface layers are nearly pure H (metals settle below the
photosphere because of gravity, Bildstein 1990)
• The surface is at same T
• Being in GCs the distance is fairly well known
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One can use unmagnetized, H, constant T atmosphere
models to fit the thermal component
Source
omega Cen
(Chandra)
R∞
(km/D)
D
(kpc)
kTeff,∞
(eV)
13.5 ± 2.1
5.36 ±6%
66+4-5
Rutledge et
al (2002)
Ref.
omega Cen
(XMM)
13.6 ± 0.3
5.36 ±6%
67 ± 2
Gendre et
al (2003)
M13
12.8 ± 0.4
7.80 ±2%
76 ± 3
Gendre et al
(2003)
47 Tuc X7
14.5-1.6+1.8
4.85 ±4%
105 ± 6
Heinke et al
(2006)
M28
14.5-3.8+6.9
5.5 ±10%
+30
Becker et al
(2003)
90-10
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September 22-26 2014
57
Models and Observations
H atmosphere models work for youngish
PSRs (10-30 kyr, T > 106 K): Vela,
J0538+2817, B1706-44...
Do not work for older, cooler PSRs:
Geminga, 0656+14, 1055-52...
H atmosphere models work for SXTs in
quiescence: Aql X-1, omega Cen, …
Do not work for the XDINSs
Models of emission from a condensed
surface work for the XDINSs
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September 22-26 2014
58
Further Readings
• Becker, W. 2009, “X-ray Emission from Pulsars and Neutron
•
•
•
•
•
•
•
Stars”, Ap&SS Library, 357, 91
Harding, A.K., Lai, D. 2006, “Physics of Strongly Magnetized
Neutron Stars”, RPPh, 69, 2631 (arXiv:astro-ph/0606674)
Harding, A.K. 2013, “The Neutron Star Zoo”, Frontiers of Physics,
8, 679 (arXiv:1302.0869)
Kaspi, V.M. 2010, “Grand Unification of Neutron Stars”,
PNAS,107, 7147 (arXiv:1005.0876)
Özel, F. 2013, “Surface Emission from Neutron Stars and
Implications for the Physics of Their Interiors”, RPPh, 76, 6901
(arXiv:1210.0916)
Potekhin, A.Y. 2014, “Atmospheres and Radiating Surfaces of
Neutron Stars”, arXiv:1403.0074
Turolla, R. 2009, “Isolated Neutrons Stars: the Challenge of
Simplicity”, Ap&SS Library, 357, 141
Zavlin, V.E. 2009, “Theory of Radiative Transfer in Neutron Star
Atmospheres and Its Applications”, Ap&SS Library, 357, 181