constraining neutron star radii and equations of state josh grindlay harvard (collaboration with...
TRANSCRIPT
Constraining Neutron Star Radii
and Equations of State
Josh GrindlayHarvard
(collaboration with Slavko Bogdanov McGill Univ.)
Outline of talk
Radii from X-ray bursts (BB fits)
Radii from quiescent LMXBs (BB fits)
Radii of isolated NSs (e.g. RXJ1856-3754)(J. Truemper’s talk…)
Radii from MSPs (M/R from light bending)
NS Radii from X-ray bursts
Type I x-ray bursts are thermonuclear flashes on NSs in low mass X-ray binaries (LMXBs)
Some are Eddington limited (flat-topped Lx) with BB radii determined from Lx ~ R2 T4 and measured T at “touchdown” when emission from (entire) NS surface
Best done with LMXB in globular cluster, at well measured distance
Radius Expansion X-ray burst from M15
M15 burst seen from X2127+119 by RXTE from M15 (d = 10 ±0.5 kpc) by Smale (2001):
Derived NS parameters: R* = 8.6 ±1km (but uncertain by Comptonizing atmosphere model) 1 + z = 1.28 ±0.06 and mass of NS = 2.38 ±0.18 Msun
vs. Spectral line shifts in X-ray burst
Cottam et al (2002, Nature) observed and stacked 28 bursts from EXO 0748-676
Candidate Fe XXVI lines seen at redshift z = 0.35
Atmospheric radii of quiescent LMXBs
Heinke et al (2006, ApJ) derive constraints on luminous quiescent LMXB X7 in 47Tuc, using NS-atmosphere model of Rybicki et al
Derived RNS = 14.5 ±1.7 km
for M = 1.4Msun
1 + z = 1.26 ±0.12
or if R = 10 km M = 2.20 ±0.1Msun
• ~50 MSPs detected in X-rays to date (mostly in globular clusters)
• Very faint X-ray sources - LX
1033 ergs s–1 (0.1-10 keV) - typical: LX 1030–31 ergs s–1
• Many exhibit (pulsed) soft, thermal X-ray emission from magnetic polar caps
Rotation-powered (“recycled”) millisecond pulsars
Bogdanov et al. (2006)
MSPs are “ideal”: Constant, noise free Binary companions
(allow mass meas.)
R
Y
19 MSPs in 47 TucChandra ACIS-S
0.3-6 keV
e+
e+
X-rays
Thermal X-ray emission due to polar cap heating by a return current of relativistic particles from pulsar magnetosphere
X-rays
The surface radiation can serve as a valuable probe of neutron star properties (compactness, magnetic field geometry, surface composition,…)
Modeling thermal X-ray emission from MSPs
Ingredients: - rotating neutron star
- two X-rayemitting hot spots
- General & special relativity * Schwarzschild metric
(good for 300 Hz)* Doppler boosting/aberration
* propagation time delays
- optically-thick hydrogen atmosphere
Viironen & Poutanen (2004)
= pulsar obliquity
= b/w line of sight & pulsar spin axis
(t) = rotational phase
= photon w.r.t surface normal
= photon at infinity
b = photon impact parameter at infinity
Viironen & Poutanen (2004)
Bogdanov, Grindlay, & Rybicki (2008)
Synthetic MSP X-ray pulse profiles - R = 10 km, M = 1.4 M
- Teff = 2 106 K (H atmosphere)
- 2 antipodal, point-like polar caps
Nollert et al. (1989)
FlatSchwarzschild
Gravitational redshift & bending of photon trajectories
For M = 1.4 M, R = 10 km ~80% of the entire neutron star surface is visible at a given instant.
Bogdanov et al. (2007, 2008)
9 km12 km16 km
for M = 1.4 M
* Fits to X-ray pulse profiles of MSPs can be used to infer NS compactness
1 + zg = (1 – 2GM/c2R)–1/2 (Pavlov & Zavlin 1997;Zavlin & Pavlov 1998)
* Independent mass measurement for binary MSPs (e.g. PSR J04374715, M=1.76 0.2 M)
constrain R separately
tight constraint on NS EOS
}=10°, =30°
=30°, =60°
=60°, =80°
=20°, =80°
Model MSP X-ray pulse profiles: Constraints on the NS EOS
Neutron Star Hydrogen Atmosphere Model
Courtesy of G.B. Rybicki
BB
H atm.
• Unmagnetized (B108 G ~ 0), Optically-Thick Hydrogen Atmosphere:
- 100% pure hydrogen due to gravitational sedimentation
- harder than blackbody for same effective temperature
- energy-dependent limb darkening
}Zavlin et al. (1996)
cos=0
cos=103
- P = 4 ms, R = 10 km, M = 1.4 M
- Teff = 2 106 K (H atmosphere)
- 2 antipodal, point-like polar caps
Blackbody
Blackbody + Doppler
H atmosphere
H atmospere + Doppler
Due to limb-darkening,
H atmosphere pulse profiles
differ substantially from
Blackbody and are required
=10°, =30°
=30°, =60°
=60°, =80°
=20°, =80°
Model MSP X-ray pulse profiles: H atmosphere vs blackbody
(see Pavlov & Zavlin 1997;
Zavlin & Pavlov 1998;
Bogdanov et al. 2007, 2008)Bogdanov et al. (2007)
PSR J0437–4715 (nearest and brightest MSP)
P = 5.757451924362137(99) ms D = 156.3 1.3 pc LX = 3 1030 ergs s–1
M = 1.76 0.2 M NH = 2 1019 cm–2
Bogdanov, Rybicki, & Grindlay (2007)
XMM–Newton EPIC-pnfast timing mode
0.3–2 keV69 ks Black body
H-atmos
Two-temperature H atmosphere
T1 2 × 106 K T2 0.5 × 106 K
R1 300 m R2 2 km
Inconsistent with blackbody
H atmosphere + centered dipole
Offset dipole required (~1 km)
R = 8.5–17.6 km (95% confidence)
R measured since
R > 8.5 km (99.9% confidence)
for M = 1.76 MBogdanov, Rybicki, & Grindlay (2007)
69 ks
PSR J0437–4715
Bogdanov & Grindlay in prep.
PSR J0030+0451
R > 10.6 km (95% conf.)
R > 10.4 km (99.9% conf.)
Lower limits since angles α, ζ not fixed
for M = 1.4 M
Two-temperature H atmosphere
T1 1.5 × 106 K T2 0.7 × 106 K
R1 400 m R2 1.5 km
Inconsistent with blackbody
H atmosphere required
Evidence for offset dipole
Nearby (D 300 pc) isolated MSP
XMM–Newton EPIC pn
130 ks
Constraints on M/R for MSP J0030+0451
95% conf. limits:
For M ≥1.4Msun
R ≥ 10.6km
Rules out Quark
Star models
SQM1, SQM3
(Bogdanov &
Grindlay 2009)
Modeling Thermal X-ray Emission from MSPs
• Most (?) Promising method for constraints on NS EOS:
Extraordinary rotational stability (P =5.757451924362137(99) for J04374715)
Non-transient (always “on”) and non-variable
“Weak” magnetic fields (Bsurf~108–9 G) B-field does not affect radiative properties of atmosphere
Dominant thermal emission (95% of total counts @ 0.1–2 keV)
Radiation from small fraction of NS surface(Reff 2 km) emission region size and shape only important at 1%
level
High precision distances (0.8% for PSR J04374715; Deller et al. 2008) uncertainty in (Reff/D)2 greatly reduced
Independent, accurate mass measurements possible from radio timing unique constraint on R
Conclusions
Bursts involve time-variable phenomena; not ideal but provide interesting constraints on M/R
qLMXBs in “purely thermal” state (without complications of hard-emission components found from PWN and/or propeller effect contributions) give more reliable M/R
MSPs with thermal polar cap emission offer best M/R constraints
MSP J0437-4715 is a clean (WD-NS) binary. Shapiro delay timing will give M; angles α, ζ can be measured. Actual values of M and R can/will be obtained !