Measuring MNS, RNS, MNS/RNS or R

Transcription

1 Measuring MNS, RNS, MNS/RNS or R Sebastien Guillot Advisor: Robert Rutledge Galileo Galilei Institute, Firenze March 2014

2 Some Reviews Lattimer and Prakash, 2007 Miller C., 2013 Heinke et al., 2013 Reminder Labels Optical Radio

3 Measuring MNS

4 Double neutron stars binary systems lead to precise MNS measurements Radio Double NS system PSR B Depends on MPSR and Mcomp Double-NS system PSR B Best MNS measurement MPSR = ± M (Weisberg et al. 2005) Double-Pulsar system PSRJ MPSRA = ± M MPSRB = ± M (Kramer et al. 2006)

5 Double neutron stars binary systems lead to precise MNS measurements Radio MNS (MSun) Not constraining enough!! RNS (km)

6 Neutron stars in binary systems need additional input to get MNS Radio Additional post-keplerian parameters, e.g. Shapiro delay, to break the degeneracies between mass ratio and inclination MPSR = 1.97 ± 0.04 M (Demorest et al. 2010)

7 Neutron stars in binary systems need additional input to get MNS Radio Optical Independent measure of Mcomp e.g., for WD companion to PSR J MPSR = 2.01 ± 0.04 M (Antoniadis et al. 2013)

8 Only new MNS measurements larger than previous ones improve constraints Radio on the dense matter EoS PSR J MPSR=1.97±0.04 M (Demorest et al. 2010) PSR J MPSR=2.01±0.04 M (Antoniadis et al. 2013) MNS (MSun) Mass (M ) Lattimer 2011 RNS (km)

9 Enough with MNS, Let s measure MNS and RNS

10 Two observables are necessary to measure both MNS and RNS from Type-I bursts with PRE Type-I Burst with Photospheric Radius Expansion

11 Two observables are necessary to measure both MNS and RNS from Type-I bursts Two observables model dependent with Güver et al. 2010

12 MNS and RNS measurements with known distances are very constraining... Or are they? MNS (MSun) MNS (MSun) MNS (MSun) RNS (km) RNS (km) RNS (km) EXO in globular cluster Terzan 5 (Özel et al. 2009) SAX J in globular cluster NGC 6440 (Güver & Özel, 2013) 4U in globular cluster NGC 6624 (Güver et al. 2010a)

13 MNS and RNS measurements with known distances are very constraining... Or are they? MNS (MSun) MNS (MSun) MNS (MSun) RNS (km) KS Distance estimated from distribution of surrounding stars (Özel et al. 2012) RNS (km) 4U Using surrounding red clump stars (Güver et al. 2010a) RNS (km) Rapid Buster Assuming a wide range of distances (Sala et al. 2013)

14 When the distance is unknown, an additional observable is necessary! opacities κ still depends on unknown composition Gravitational redshift measured from spectral lines in EXO z = 0.35 (Cottam et al. 2002) used to measure MNS-RNS (Ozel et al. 2006) However, those lines were not confirmed later on (Cottam et al. 2008) MNS (MSun) RNS (km)

15 Type-I bursts are controversial for MNS and RNS measurements! Composition of the atmosphere Color correction factor fc (constant or not)? Distance measurement used (and uncertainties) Analysis not self-consistent (Steiner et al. 2010) Short bursts do not match passive cooling theory (Suleimanov et al. 2011)

16 MNS-RNS contours are fixed by relaxing Rtouchdown = RNS EXO Özel et al U Güver et al. 2010a 4U Güver et al. 2010a Steiner et al. 2010

17 Different constraints are obtained when using long bursts instead of short bursts, and by fitting the entire cooling tail MNS (MSun) RNS (km) 4U (Suleimanov et al. 2012)

18 Sub-Eddington bursts can also be used to provide distance independent measurements burster GS GS , Zamfir et al. 2012

19 Now, measuring MNS/RNS

20 Analyzing the pulse profiles caused by hot spots on a rotating a neutron star can be used to measure the compactness. MNS=1.4M, RNS=10km (Bodganov et al. 2008)

21 Analyzing the pulse profiles caused by hot spots on a rotating a neutron star can be used to measure the compactness. SAX J Morsink et al, 2011 MNS (MSun) Leahy et al, 2011 MNS (MSun) RNS (km) XTE J RNS (km) Bogdanov (2013) Method described in Bogdanov et al. (2009)

22 Or placing limits on MNS and RNS

23 Extremely fast rotating neutron star can Radio place limits on MNS and RNS Because 1122 Hz not confirmed! 716 Hz Lattimer et Prakash, 2007

24 khz quasi periodic oscillations could also constrain MNS and RNS MNS (MSun) Highest frequency QPO is 1310 Hz, 4U (Barret et al. 2006) RNS (km) van der Klis 2000

25 Measuring INS directly

26 Spin-orbit coupling measurements can be used to determine the moment of inertia Radio Combining INS to known MNS can be very constraining! But, the acceleration of the centre of mass of the binary system in the gravitational potential of the Galaxy is unknown! Hypothetical INS measurement with 10% precision for double pulsar system (Lattimer & Schutz, 2005)

27 Measuring R

28 Quiescent low-mass binaries are ideal systems for R measurements. NS ~70% hydrogen ~28% helium ~2% metals

29 Quiescent low-mass binaries are ideal systems for R measurements. In quiescence, LMXBs have low mass accretion rate by deep crustal heating Surface thermal emission Thermal emission powered comes from a pure hydrogen atmosphere with LX= erg/sec Neutron star has a weak magnetic field NS ~70% hydrogen ~28% helium ~2% metals

30 The thermal emission from qlmxb is powered by Deep Crustal Heating. Brown et al. 1998

31 The atmosphere of the neutron star in a qlmxb is composed of pure hydrogen. H-atmosphere thermal spectrum seen by observer H Photosphere ~ 10 cm Gravity H Helium

32 Flux The thermal emission from a NS surface is modelled with atmosphere models. Models by Zavlin et al. (1996), Heinke et al. (2006), Haakonsen et al. (2012) Spectral fitting of the thermal emission gives us Teff and (R /D) 2 Log(Energy) (kev) NSA, NSAGRAV models Zavlin et al 1996, A&A 315 NS H-atmosphere model parameters are: Effective temperature kteff Mass MNS (M ) Radius RNS (km) Distance D (kpc)

33 Absorption increases kteff increases Neutron stars properties are extracted from the spectra. Radius increases Mass increases

34 Globular clusters host an overabundance of LMXB systems... EINSTEIN Observatory 1980s ROSAT 1990s Chandra Obs. 2000s Optical Image...and they have wellmeasured distances.

35 29 quiescent LMXBs are known within globular clusters of the Milky Way. Host Globular Cluster Distance (kpc) Proxy for Absorption NH (10 22 cm -2 ) Number of qlmxbs Useful Observational Difficulties Need Chandra ωcen NO M NO M Moderate pile-up YES NGC YES NGC YES NGC NEEDS TO BE CONFIRMED YES 47 Tuc (+3?) Important pile-up YES M Large distance YES M Large distance YES NGC Large distance YES NGC Large distance and NH YES NGC Very Large NH NO NGC Large distance and NH YES Unconstrained R measurements Terzan Large distance and NH YES

36 qlmxbs inside globular clusters are observed with Chandra, and sometimes with XMM-Newton. Chandra X-Ray Observatory XMM-Newton 6 angular resolution 1 angular resolution 4x effective area of Chandra In spectral imaging mode, photons are time-tagged with ~0.1 3sec resolution, and energy resolution of about 150eV at 1keV

37 Quiescent LMXBs are routinely used for MNS-RNS measurements, but only place weak constraints on the dense matter EoS. Servillat et al qlmxb in M28 ~ R Webb & Barret Tuc X7 ω Cen M13 MNS (MSun) Servillat et al RNS (km) Energy (kev)

38 In Guillot et al (2013), we follow a simplified parametrization for the EoS. Equations of state consistent with ~ 2Msun are those described by a constant radius for a wide range of masses. MNS (MSun) PSR J MPSR=2.01±0.04 M PSR J MPSR=1.97±0.04 M RNS (km) We assume that all neutron stars have the same radius

39 We simultaneously fit the spectra of 5 qlmxbs with H-atmosphere model XMM-Newton Chandra X-Ray Observatory One radius to fit them all! Five parameters per target: Teff, MNS, NH, distance, power-law component Residuals Cts/sec/keV /dof = 0.98/628(p. = 0.64) Energy (kev) Guillot et al. 2013

40 Targeted Globular Clusters M13 ωcen NGC6304 M28 NGC6397

41 Our most conservative radius measurement relies on the least number of assumptions. Most conservative NS radius measurement is 90% conf. level Guillot et al. 2013

42 Our most conservative RNS measurement includes most sources of uncertainty We included the uncertainties linked to: - Galactic absorption - Distances of the host clusters - Possible power-law component - Calibration of detectors

43 There are analysis assumptions NS surface emits isotropically Negligible magnetic field Composition MNS (MSun) H MNS (MSun) He Guillot et al RNS (km) Servillat et al (2012) RNS (km)

44 Our most conservative radius measurement places important constraints on the dense matter equation of state. MNS (MSun) RNS (km) RNS in the 7-11 km range at the 99%-confidence level Guillot et al. 2013

45 What about thermally-cooling isolated neutron stars? Only RX J is remotely useful for this Problems: What is the distance? d = pc What is the composition? What are the effects of the magnetic field? Pons et al. 2002

46 Combining previous results...

47 MNS-RNS contours can be combined to parametrize the EoS. Type I bursts Steiner et al 2010, 2012 Quiescent LMXBs MNS (MSun) RNS (km) + MNS (MSun) RNS (km) + M-R contour of burst KS Özel et al M-R contour of qlmxb in NGC6397 from Guillot et al. 2011

48 MNS-RNS contours can be combined to parametrize the EoS. RNS is roughly constrained between 10 and 13 km for a wide range of masses, RNS mostly insensitive to the exclusion of extremum contours (like M13, or 47Tuc), or to the exclusion of type-i burst sources MNS (MSun) Steiner et al 2012 RNS (km)

49 Summary of methods Measurement Type of neutron star Limitations MNS Radio timing of pulsars Only higher than before MNS are useful MNS and RNS Type-I bursts Modelling issues Limits on MNS and RNS Millisecond radio pulsars khz QPOs () Only higher than before fspin are useful Model assumptions INS Radio timing of double NS systems Difficult measurement RNS and MNS/RNS R Pulse-profile analysis () Quiescent low-mass binaries Isolated neutron stars () Need high S/N pulse profiles and several assumptions Need high S/N spectra Not useful individually Distance? Magnetic fields? See talks during conference March 24-28, by: C. Heinke: "Probing the neutron star equation of state through spectroscopy" D. Chakrabarty: "Probing the neutron star equation of state through timing" Z. Arzoumanian: "The Neutron Star Interior Composition Explorer: An Astrophysics Facility Dedicated to Neutron Star Science" M. Chakraborty: " Bursts from Accreting Neutron star LMXBs" H. Stiele: "Millihertz Quasi-periodic Oscillations in 4U : Pulse Profile and Energy Spectrum"

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