Thermal Emission from Isolated Neutron Stars

The Many Faces of Compact Stars - Barcelona, September 22-26 2014

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THERMAL EMISSION FROM ISOLATED NEUTRON STARSR. Turolla

Dept. of Physics and Astronomy,

University of Padova, Italy


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Outline• Are INSs thermal emitters ?• Observations of INSs• Importance of thermal emission• 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 1

Lecture 2


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Some Like It Hot• NSs are born very hot

(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

Page, Geppert & Weber (2006)

Heating processes: magnetic dissipation, inflowing magnetospheric currents, accretion

Dima Yako

vlev’s

lectu

res


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

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The Neutro

n Star Z

oo


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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 magneto-dipolar losses (oblique rotator in vacuo)

(1 + sin2α) from self-consistent magnetospheric modeling (Spitkovsky 2006)


6

Measuring P and Ṗ is crucial

Phase-coherent timing Strictly periodic

SGR 1833 (Esposito et al. 2011)


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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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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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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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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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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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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 X-

rays (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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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


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• 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)


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L X = Ė ro

t

from Becker (2009)

SGR+AXPs

XDINSs

HBPSRs

RRaTs

Different mechanisms powering X-ray emission

Rotation

Cooling

Magnetism


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INS spectrum: thermal plus non-thermal component

(magnetospheric, if rotation-powered LNT ~ Ė ~ t-β, β ≈ 2-4)

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)

thermal

non-thermal

total

+ SXTs


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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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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 surfaceemits a blackbody at TBB (≈ 100 eV) and neglect GR

Fitting the observed X-ray spectrum with a BB


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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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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


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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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Scattering cross section for the X and O modes (Ventura 1979)

B

kEX

EO

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 modeare substantially reduced at E << Ec


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NS Thermal Maps

• Electrons move much more easily along B than across B

• Thermal conduction is highly anisotropic inside a 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

Greenstein & Hartke (1983)


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poleS

parperp

poleparperpS

TT

KK

TKKT

2/1

4/122

cos

1/

sin/cos

Core centered dipole Core centered quadrupole


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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

• Radiation emitted at frequency ν at the NS surface (r = R) is redshifted (Δν/ν ≈ 0.2)

• For BB radiation (uniform T on the surface)


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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

• The luminosity at infinity is lower

• 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)

2 4


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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

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)


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LOS

112°

90°

R = 15 kmM = 1.4 M

No gravity

The terminator is atα = π/2, cos θF = (1-2GM/Rc2)-1


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LOS

Hot spot


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STEP 1Specify viewing geometry and B-field topology;compute the surface temperature distribution

STEP 2Compute emission fromeach surface patch

STEP 3GR ray-tracing to obtainthe spectrum at infinity

STEP 4Predict lightcurve andphase-resolved spectrumCompare with observations


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What is the correct model for surface thermal emission ?


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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, Fe)

• Under typical conditions surface layers are in gaseous state: NS atmosphere

• For sufficiently low T and large B (and depending on composition) the surface can be in a condensed state: “bare” NS

Fe Hcondensation(Lai 2001)

Fe C Hecondensation (Medin & Lai 2006, 2007)Fe

H

Whatever the state of the surface, the emitted thermal radiation is NOT a blackbody

adapted from Turolla et al (2004)


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NS Atmospheres

• 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

Very different from atmospheres around normal stars

In NSs 108 G < B < 1015 GMagnetic effects important if Ece > kT, Eion → B > 1010 (T/106 K) G


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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

θ

Iν(z,μ)n


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Radiative transfer equation

total opacity (absorption plus scattering)

Hydrostatic equilibrium

gdz

dP

Radiative energy equilibrium

1

1

1

2

1 ,)( dIJBJS

00

4

dJaT

)( SIz

I

+ EOS, ionization balance,…


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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)


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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

Model atmospheres investigated e.g. in Romani (1987), Zavlin et al. (1996), Rajagopal & Romani (1996), Gänsicke, Braje & Romani (2002), Pons et al. (2002)

1

1),0(2)0( IdF


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Non-magnetic Spectra


g = 2.4x1014 cm s-2

g = 2.4x1014 cm s-2


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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 thedeep layers which are hotter

Emerging spectrum like the superposition of blackbodies at different temperatures


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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


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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

Hydrostatic and radiative energy equilibrium

Fix g, Teff, chemical composition, B and obtain

2,1

),()(2

2

1

),()()()()()(

i

IdB

Iz

I

j

jijiiii

]),0(),0([2)0(1

1

)2()1( IIdF


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Magnetic Spectra

Not too different fromnon-magneticmodels. Magnetic opacities higher: spectra more BB-like

Ionized H

Proton cyclotron line

keV G 10

63.014

B

Ecp



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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 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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• 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

Mori & Ho (2007)Ho et al (2008)

hydrogen


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)()](1[)( TBj nn )()()( TBj nn

Commonplace: the surface of a body at temperature T always emits a blackbody at T

In general the emissivity is or 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

The way a metallic mirror works !

Condensed Surface


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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 AZ3/5B12

6/5 g/cm3

• Plasma frequency in the surface layers: hνpe ≈ 0.7Z1/5B12

3/5(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)

Free ions

Fixed ions

Potekhin (2014)


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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 features exists (and

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 for sources with larger ElineRX J0720.4-3125 (Haberl et al 2004)

Van Kerkwijk & Kaplan (2007)


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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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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 ≈ (EX/Eopt)3 ≈ (100 eV/1 eV)3 ≈ 106 !

• 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

a 50 W bulb at the distance of the moon

Kaplan et al. 2011RX J1856.5-3754


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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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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)

Aql X-1 (Campana et al. 1998) M13 Ga (Gendre, Barret & Webb 2003)NSs in SXTs too old to retain formation heat

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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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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SourceR∞

(km/D)

D

(kpc)

kTeff,∞

(eV)Ref.

omega Cen(Chandra)

13.5 ± 2.1 5.36 ±6% 66+4-5

Rutledge et al (2002)

omega Cen(XMM)

13.6 ± 0.3 5.36 ±6% 67 ± 2Gendre et al (2003)

M13 12.8 ± 0.4 7.80 ±2% 76 ± 3Gendre 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% 90-10 +30

Becker et al (2003)

One can use unmagnetized, H, constant T atmosphere

models to fit the thermal component


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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 inquiescence: Aql X-1, omega Cen, …Do not work for the XDINSsModels of emission from a condensed surface work for the XDINSs


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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

Documents

Thermal Emission from Isolated Neutron Stars