Challenges in the Measurement of Neutron Star Radii - PowerPoint Presentation

Slide1

Challenges in the Measurement of Neutron Star Radii

Cole MillerUniversity of Maryland

1

Collaborators:

Romain

Artigue

, Didier

Barret

,

Sudip

Bhattacharyya,

Stratos

Boutloukos

,

Novarah

Kazmi

, Fred Lamb,

Ka

Ho LoSlide2

Outline

Radii from X-ray burstsRadii from cooling neutron stars

Radii from X-ray light curvesThe promise of gravitational waves

2

NS masses are known up to 2

M

sun

. What about radii?

Key point:

all

current NS radius estimates

are dominated by systematics.

None

are

reliable. But hope exists for the future.Slide3

Measuring stellar radii

Ordinary star, like the SunToo far for angular resolutionBut can get luminosity L

If we assume blackbody, R2=L/(4ps

T

4

)

But for NS, usually gives ~5 km!

Why? Spectral shape is ~Planck, but inefficient emissionNeed good spectral modelsBut data usually insufficient to test3Slide4

M and R from X-ray Bursts

van Paradijs

(1979) methodXRB: thermonuclear explosions on accreting NSAssume known spectrum, emission over whole surf.

Only with RXTE (1995-2011) is there enough data

http://cococubed.asu.edu/images/binaries/images/xray_burst3_web.jpg

4Slide5

4U 1820 Bursts: Soft EOS?

Fits of good spectral models to hours-long bursts

show that fraction of emitting area changes!

Guver et al. 2010; known dist (globular)

Uses most optimistic

assumption: no systematics,

only statistical uncertainties

But small errors are

misleading; only ~10

-8

of prior prob. space gives

M, R in real numbers!

(

Guver

et al., Steiner et al.)

S

pectral model is

terrible

fit to best data!

5Slide6

6

Inferred relative emitting areas,

for

102 16-s segments near

the peak

of the 1820

superburst

: Miller et al., in prepSlide7

Emission from Cooling NS

Old, transiently accreting NSDeep crustal heating (e.g., e capture)

If know average accretion rate, emission provides probe of cooling; can we use to fit radius?

Predictions of simple model:

Minimum level of emission Spectrum should be

thermal

No

variability: steady, slow decay7Slide8

Cooling NS Observations

Oops!All the predictions fail

L sometimes below minimum

Large

power law component

Significant

variability

Excuses exist, but failure of basic model means we can’t use these observations to get RAlso: is surface mainly H? He? C? Makes 10s of percent difference to R

Magnetic field can also alter spectrum

Again, wide variety of models fit data, thus can’t use data to say which model is correct

8Slide9

RXJ

1856.5–3754

Specific isolated NS

Argument: BB most efficient emitter, thus R>=R

BB

True for bolometric but

not

for given band

Example: Ho et al. condensed surface fit

Different R constraints for different models

9

Klähn

et al. 2006Slide10

RXJ

1856.5–3754

Specific isolated NS

Argument: BB most efficient emitter, thus R>=R

BB

True for bolometric but

not

for given band

Example: Ho et al. condensed surface fit

Different R constraints for different models

10

Klähn

et al. 2006Slide11

Baryonic vs. Grav. Mass

Pulsar B in the double pulsar systemMgrav

=1.249+-0.001 MsunIf this came from e capture on Mg and Ne,

M

bary

=1.366-1.375

M

sun for coreBut what about fallback?Or could mass be lost after collapse?11Slide12

Ray Tracing and Light Curves

Rapidly rotating star 300-600 Hz v

surf~0.1-0.2c

SR+GR effects

Light curve informative about M, R

Bogdanov

2012; MSP Must deal carefully with degeneraciesLo et al., arXiv:1304.2330 (synth data); no systematic that gives good fit, tight constraints, and large bias

Weinberg, Miller, and Lamb 2001

12Slide13

Phase Accumulation from GWs

aLIGO/Virgo: >=2015

Deviation from point mass in NS-NS inspiral: accumulated tidal effectsFor

a

LIGO

,

can measure tidal

param (Del Pozzo+ 2013: distinguish R~11, 13 km?)Recent analytics confirmed by numerical relativity (

Bernuzzi

et al. 2012)

High-

freq

sensitivity key

Damour

et al., arXiv:1203.4352

13

High-

freq

modeling, tooSlide14

Conclusions

Current radius estimates are all dominated by systematics

Light curve fitting shows promise:

No deviations we have tried from our models produce significant biases while fitting well and also giving apparently strong constraints.

LOFT, AXTAR, NICER

Future measurements of M and R using gravitational waves

may be competitive in their precision with X-ray based

estimates, and will have very different systematics

Open question: how can we best combine astronomical

information with laboratory measurements (e.g.,

208

Pb skin

thickness)?Slide15

Ray Tracing from MSP

S.

Bogdanov

2012

Binary millisecond pulsar J0437-4715

Two spots, H

atm

Multitemp

plus

Comptonized

spect

Qs about beaming, spectrum; intriguing results, though!

15

Bogdanov

2012Slide16

High inclinations allow tight constraints on M and R

Spot and observer inclinations = 90°, high background

16Slide17

Low inclinations produce looser constraints

Amplitude similar to the previous slide, but low spot and

observer inclinations, low background

17Slide18

Independent knowledge of the

observer

’

s

inclination can increase the precision

Observer inclination unknown

spot and observer inclinations = 90°, high background

18Slide19

Observer inclination known to be 90°

Independent knowledge of the

observer

’

s

inclination can increase the precision

spot and observer inclinations = 90°, high background

19Slide20

Incorrect modeling of the spot shape

increases the uncertainties

Actual spot elongated E-W by 45°

spot and observer inclinations = 90°, medium background

20Slide21

21

Fits Using New Models

64-second segment at peak

temperature

This model has F=0.95F

Edd

Best fit:



2

/

dof

=42.3/48

Best B-E fit:



2

/

dof

=55.6/

50

For full 102-segment data set,

best fit has



2/dof=5238/5098B-E best: 2/dof=5770/4998Fits are spectacularly good!Much better than B-E, so further info can be derived

Pure He, log g = 14.3, F=0.95F

Edd

Model from Suleimanov et al. 2010

Yes! New models from

Suleimanov

et al. 2010 do seem

to fit the data quite well. Slide22

Keplerian Constraints

Suppose we observe periodic variations in the

radial velocity of star 1, with period P

b

and

amplitude v

rad

. Then we can construct themass function

This is a lower limit to the mass of star 2, but

depends on the unknown inclination i and the

unknown mass m

1

of the observed star.

22Slide23

Post-Keplerian Parameters

With high-precision timing, can break degeneracies:

If both objects are pulsars, also get mass ratio.

Allows mass measurements, GR tests

23Slide24

Artigue

et al. 2013

24

c

2

/

dof

for all five bursts combined: 1859/1850 (44%)

c

2

/

dof

for far left burst only: 401.8/372 (14%)

Hot spot model fits very well

Analysis of bursts from 4U 1636-536; previously

claimed

to contradict rotating spot model