Thermal X-rays from Millisecond Pulsars: Constraining the Fundamental Properties of Neutron Stars

Abridged) We model the X-ray properties of millisecond pulsars (MSPs) by considering hot spot emission from a weakly magnetized rotating neutron star (NS) covered by an optically-thick hydrogen atmosphere. We investigate the limitations of using the thermal X-ray pulse profiles of MSPs to constrain the mass-to-radius ($M/R$) ratio of the underlying NS. The accuracy is strongly dependent on the viewing angle and magnetic inclination. For certain systems, the accuracy is ultimately limited only by photon statistics implying that future X-ray observatories could, in principle, achieve constraints on $M/R$ and hence the NS equation of state to better than $\sim$5%. We demonstrate that valuable information regarding the basic properties of the NS can be extracted even from X-ray data of fairly limited photon statistics through modeling of archival spectroscopic and timing observations of the nearby isolated PSRs J0030+0451 and J2124--3358. The X-ray emission from these pulsars is consistent with the presence of a hydrogen atmosphere and a dipolar magnetic field configuration, in agreement with previous findings for PSR J0437--4715. For both MSPs, the favorable geometry allows us to place interesting limits on the allowed $M/R$ of NSs. Assuming 1.4 M$_{\odot}$, the stellar radius is constrained to be $R > 9.4$ km and $R > 7.8$ km (68% confidence) for PSRs J0030+0451 and J2124--3358, respectively. We explore the prospects of using future observatories such as \textit{Constellation-X} and \textit{XEUS} to conduct blind X-ray timing searches for MSPs not detectable at radio wavelengths due to unfavorable viewing geometry. Using the observational constraints on the pulsar obliquities we are also able to place strong constraints on the magnetic field evolution model proposed by Ruderman.Comment: 9 pages, 7 figures, published in the Astrophysical Journal (Volume 689, Issue 1, pp. 407-415

The Compact Central Object in Cas A: A Neutron Star with Hot Polar Caps or a Black Hole?

The central pointlike X-ray source of the Cas A supernova remnant was discovered in the Chandra First Light Observation and found later in the archival ROSAT and Einstein images. The analysis of these data does not show statistically significant variability of the source. The power-law fit yields the photon index 2.6-4.1, and luminosity (2-60)e34 erg/s, for d=3.4 kpc. The power-law index is higher, and the luminosity lower, than those observed fromvery young pulsars. One can fit the spectrum equally well with a blackbody model with T=6-8 MK, R=0.2-0.5 km, L=(1.4-1.9)e33 erg/s. The inferred radii are too small, and the temperatures too high, for the radiationcould be interpreted as emitted from the whole surface of a uniformly heated neutron star. Fits with the neutron star atmosphere models increase the radius and reduce the temperature, but these parameters are still substantially different from those expected for a young neutron star. One cannot exclude, however, that the observed emission originates from hot spots on a cooler neutron star surface. Because of strong interstellar absorption, the possible low-temperature component gives a small contribution to the observed spectrum; an upper limit on the (gravitationally redshifted) surface temperature is < 1.9-2.3 MK. Amongst several possible interpretations, we favor a model of a strongly magnetized neutron star with magnetically confined hydrogen or helium polar caps on a cooler iron surface. Alternatively, the observed radiation may be interpreted as emitted by a compact object (more likely, a black hole) accreting from a fossil disk or from a late-type dwarf in a close binary.Comment: 12 pages, 2 figures, submitted to ApJ

Light Curves of Rapidly Rotating Neutron Stars

We consider the effect of rapid rotation on the light curves of neutron stars with hot polar caps. For $P \approx 3$ms spin periods, the pulse fractions can be as much as an order of magnitude larger than with simple slowly-rotating (Schwarzschild) estimates. Doppler boosting, in particular, leads to characteristic distortion and ``soft lags'' in the pulse profiles, which are easily measurable in light curves with moderate energy resolution. With $\sim 10^5$ photons it should also be possible to isolate the more subtle distortions of light travel time variations and frame dragging. Detailed analysis of high quality millisecond pulsar data from upcoming X-ray missions must include these effects

The X-ray Spectrum of the Vela Pulsar Resolved with Chandra

We report the results of the spectral analysis of two observations of the Vela pulsar with the Chandra X-ray observatory. The spectrum of the pulsar does not show statistically significant spectral lines in the observed 0.25-8.0 keV band. Similar to middle-aged pulsars with detected thermal emission, the spectrum consists of two distinct components. The softer component can be modeled as a magnetic hydrogen atmosphere spectrum - for the pulsar magnetic field $B=3\times 10^{12}$ G and neutron star mass $M=1.4 M_\odot$ and radius $R^\infty =13$ km, we obtain \tef^\infty =0.68\pm 0.03 MK, $L_{\rm bol}^\infty = (2.6\pm 0.2)\times 10^{32}$ erg s$^{-1}$, $d=210\pm 20$ pc (the effective temperature, bolometric luminosity, and radius are as measured by a distant observer). The effective temperature is lower than that predicted by standard neutron star cooling models. A standard blackbody fit gives $T^\infty =1.49\pm 0.04$ MK, $L_{\rm bol}^\infty=(1.5\pm 0.4)\times 10^{32} d_{250}^2$ erg s$^{-1}$ ($d_{250}$ is the distance in units of 250 pc); the blackbody temperature corresponds to a radius, $R^\infty =(2.1\pm 0.2) d_{250}$ km, much smaller than realistic neutron star radii. The harder component can be modeled as a power-law spectrum, with parameters depending on the model adopted for the soft component - $\gamma=1.5\pm 0.3$, $L_x=(1.5\pm 0.4)\times 10^{31} d_{250}^2$ erg s$^{-1}$ and $\gamma=2.7\pm 0.4$, $L_x=(4.2\pm 0.6)\times 10^{31} d_{250}^2$ erg s$^{-1}$ for the hydrogen atmosphere and blackbody soft component, respectively ($\gamma$ is the photon index, $L_x$ is the luminosity in the 0.2--8 keV band). The extrapolation of the power-law component of the former fit towards lower energies matches the optical flux at $\gamma\simeq 1.35$--1.45.Comment: Submitted to ApJ, three figures; color figure 1 can be found at http://www.xray.mpe.mpg.de/~zavlin/pub_list.htm

A Hydrogen Atmosphere Spectral Model Applied to the Neutron Star X7 in the Globular Cluster 47 Tucanae

Current X-ray missions are providing high-quality X-ray spectra from neutron stars (NSs) in quiescent low-mass X-ray binaries (qLMXBs). This has motivated us to calculate new hydrogen-atmosphere models, including opacity due to free-free absorption and Thomson scattering, thermal electron conduction, and self-irradiation by photons from the compact object. We have constructed a self-consistent grid of neutron star models covering a wide range of surface gravities as well as effective temperatures, which we make available to the scientific community. We present multi-epoch Chandra X-ray observations of the qLMXB X7 in the globular cluster 47 Tuc, which is remarkably nonvariable on timescales from minutes to years. Its high-quality X-ray spectrum is adequately fit by our hydrogen-atmosphere model without any hard power-law component or narrow spectral features. If a mass of 1.4 Msol is assumed, our spectral fits require that its radius be in the range R=14.5^{+1.8}_{-1.6} km (90% confidence), larger than expected from currently preferred models of NS interiors. If its radius is assumed to be 10 km, then a mass of M=2.20^{+0.03}_{-0.16} Msol is required. Using models with the appropriate surface gravity for each value of the mass and radius becomes important for interpretation of the highest quality data.Comment: 14 pages, 6 figures, ApJ in press (replaced with accepted version

High energy neutrinos from magnetars

Magnetars can accelerate cosmic rays to high energies through the unipolar effect, and are also copious soft photon emitters. We show that young, fast-rotating magnetars whose spin and magnetic moment point in opposite directions emit high energy neutrinos from their polar caps through photomeson interactions. We identify a neutrino cut-off band in the magnetar period-magnetic field strength phase diagram, corresponding to the photomeson interaction threshold. Within uncertainties, we point out four possible neutrino emission candidates among the currently known magnetars, the brightest of which may be detectable for a chance on-beam alignment. Young magnetars in the universe would also contribute to a weak diffuse neutrino background, whose detectability is marginal, depending on the typical neutrino energy.Comment: emulateapj style, 6 pages, 1 figure, ApJ, v595, in press. Important contributions from Dr. Harding added. Major revisions made. More conservative and realistic estimates about the neutrino threshold condition and emission efficiency performed. More realistic typical beaming angle and magnetar birth rate adopte

Gamma-Ray Emissions from Pulsars: Spectra of the TEV Fluxes from Outer-Gap Accelerators

We study the gamma-ray emissions from an outer-magnetospheric potential gap around a rotating neutron star. Migratory electrons and positrons are accelerated by the electric field in the gap to radiate copious gamma-rays via curvature process. Some of these gamma-rays materialize as pairs by colliding with the X-rays in the gap, leading to a pair production cascade. Imposing the closure condition that a single pair produces one pair in the gap on average, we explicitly solve the strength of the acceleration field and demonstrate how the peak energy and the luminosity of the curvature-radiated, GeV photons depend on the strength of the surface blackbody and the power-law emissions. Some predictions on the GeV emission from twelve rotation-powered pulsars are presented. We further demonstrate that the expected pulsed TeV fluxes are consistent with their observational upper limits. An implication of high-energy pulse phase width versus pulsar age, spin, and magnetic moment is discussed.Comment: Revised to compute absolute TeV spectra (22 pages, 9 figures

Hydrogen Phases on the Surface of a Strongly Magnetized Neutron Star

The outermost layers of some neutron stars are likely to be dominated by hydrogen, as a result of fast gravitational settling of heavier elements. These layers directly mediate thermal radiation from the stars, and determine the characteristics of X-ray/EUV spectra. For a neutron star with surface temperature T\lo 10^6 K and magnetic field B\go 10^{12} G, various forms of hydrogen can be present in the envelope, including atom, poly-molecules, and condensed metal. We study the physical properties of different hydrogen phases on the surface of a strongly magnetized neutron star for a wide range of field strength $B$ and surface temperature $T$. Depending on the values of $B$ and $T$, the outer envelope can be either in a nondegenerate gaseous phase or in a degenerate metallic phase. For T\go 10^5 K and moderately strong magnetic field, B\lo 10^{13} G, the envelope is nondegenerate and the surface material gradually transforms into a degenerate Coulomb plasma as density increases. For higher field strength, $B>> 10^{13}$ G, there exists a first-order phase transition from the nondegenerate gaseous phase to the condensed metallic phase. The column density of saturated vapor above the metallic hydrogen decreases rapidly as the magnetic field increases or/and temperature decreases. Thus the thermal radiation can directly emerge from the degenerate metallic hydrogen surface. The characteristics of surface X-ray/EUV emission for different phases are discussed. A separate study concerning the possibility of magnetic field induced nuclear fusion of hydrogen on the neutron star surface is also presented.Comment: TeX, 35 pages including 6 postscript figures. To be published in Ap

X-ray Spectrum and Pulsations of the Vela Pulsar

We report the results of the spectral and timing analysis of observations of the Vela pulsar with the Chandra X-ray Observatory. The spectrum shows no statistically significant spectral lines in the observed 0.25--8.0 keV band. It consists of two distinct continuum components. The softer component can be modeled as either a magnetic hydrogen atmosphere spectrum with kT = 59 +- 3 eV, R = 15.5 +- 1.5 km, or a standard blackbody with kT = 129 +- 4 eV, R = 2.1 +- 0.2 km (the radii are for a distance of 250 pc). The harder component, modeled as a power-law spectrum, gives photon indices depending on the model adopted for the soft component: gamma = 1.5 +- 0.3 for the magnetic atmosphere soft component, and gamma = 2.7 +- 0.4 for the blackbody soft component. Timing analysis shows three peaks in the pulse profile, separated by about 0.3 in phase. Energy-resolved timing provides evidence for pulse profile variation with energy. The higher energy (E > 1.8 keV) profile shows significantly higher pulsed fraction.Comment: 4 pages, 2 figures, To appear in "Neutron Stars in Supernova Remnants" (ASP Conference Proceedings), eds P. O. Slane and B. M. Gaensler Corrected TYPO

The very soft X-ray spectrum of the Double Pulsar System J0737-3039

We present the results of an 80 ks Chandra ACIS-S observation of the double pulsar system J0737-3039. Furthermore, we report on spectral, spatial and timing analysis of the combined X-ray observations performed so far for this system. Fitting a total of ~1100 photons, we show that the X-ray spectrum of the J0737-3039 system is very soft, and not satisfactorily modeled by a simple blackbody or an atmospheric model. However, it is not possible yet to discriminate between a predominantly non-thermal and a predominantly thermal origin for the X-ray emission. Adopting a simple power-law emission model, the photon index (Gamma=3.7) and the implied conversion efficiency of the rotational energy of PSR J0737-3039A into X-ray emission (4.1x10^-4, for a distance to the source of 500 pc) are compatible with the X-ray photons being emitted in the magnetosphere of PSR J0737-3039A. This hypothesis is also supported by the absence of detectable X-ray orbital modulation (up to ~20%) or any X-ray nebular emission and it is in agreement with the high (~75%) X-ray pulsed fraction of PSR J0737-3039A. A two blackbody or a Comptonized blackbody model also reproduce the data, and the upper limit to the value of the hydrogen column density N_H <10^20 cm^-2, is in better agreement (with respect to the power-law model) with the Galactic N_H in that direction and at that distance. For the two blackbody model the implied emission radii and temperatures are also compatible with those seen in other recycled pulsars, calling for the bulk of the X-ray photons being originated from heated regions at the surface of pulsar A. On the other hand, in the Comptonized blackbody model, the electron temperature seems to be significantly smaller than in other similar objects.Comment: 12 pages. Accepted for publication in Ap