Research Article

A Massive Pulsar in a Compact Relativistic Binary

Science  26 Apr 2013:
Vol. 340, Issue 6131, pp.
DOI: 10.1126/science.1233232

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  1. Fig. 1

    Radial velocities and spectrum of the white dwarf companion to PSR J0348+0432. (A) Radial velocities of the WD companion to PSR J0348+0432 plotted against the orbital phase (shown twice for clarity). Overplotted is the best-fit orbit of the WD (blue line) and the mirror orbit of the pulsar (green). Error bars indicate 1-σ confidence intervals. (B) Details of the fit to the Balmer lines (Hβ to H12) in the average spectrum of the WD companion to PSR J0348+0432 created by the coherent addition of 26 individual spectra shifted to zero velocity. Lines from Hβ (bottom) to H12 are shown. The red solid lines are the best-fit atmospheric model (see text). Two models, one with Teff = 9900 K and log10g = 5.70 and one with Teff = 10,200 K and log10 g = 6.30, each ∼ 3-σ off from the best-fit central value (including systematics), are shown for comparison (dashed blue lines).

  2. Fig. 2

    Mass measurement of the white dwarf companion to PSR J0348+0432. (A) Constraints on Teff and g for the WD companion to PSR J0348+0432 compared with theoretical WD models. The shaded areas depict the χ2 − χ2min = 2.3, 6.2, and 11.8 intervals (equivalent to 1-, 2-, and 3-σ) of our fit to the average spectrum. Dashed lines show the detailed theoretical cooling models of (11). Continuous lines depict tracks with thick envelopes for masses up to ∼0.2 M that yield the most conservative constraints for the mass of the WD. (B) Finite-temperature mass-radius relations for our models together with the constraints imposed from modeling of the spectrum. Low mass–high temperature points are an extrapolation from lower temperatures.

  3. Fig. 3 System masses and orbital-inclination constraints.

    Constraints on system masses and orbital inclination from radio and optical measurements of PSR J0348+0432 and its WD companion. Each triplet of curves corresponds to the most likely value and standard deviations (68.27% confidence) of the respective parameters. Of these, two (q and MWD) are independent of specific gravity theories (in black). The contours contain the 68.27 and 95.45% of the two-dimensional probability distribution. The constraints from the measured intrinsic orbital decay (Formula, in orange) are calculated assuming that GR is the correct theory of gravity. All curves intersect in the same region, meaning that GR passes this radiative test (8). (Bottom left) cosi-MWD plane. The gray region is excluded by the condition MPSR > 0. (Bottom right) MPSR-MWD plane. The gray region is excluded by the condition sini ≤ 1. The lateral graphs depict the one-dimensional probability-distribution function for the WD mass (right), pulsar mass (top right), and inclination (top left) based on the mass function, MWD, and q.

  4. Fig. 4

    Probing strong field gravity with PSR J0348+0432. (A) Fractional gravitational binding energy as a function of the inertial mass of a NS in GR (blue curve). The dots indicate the NSs of relativistic NS-NS (in green) and NS-WD (in red) binary-pulsar systems currently used for precision gravity tests (8). (B) Effective scalar coupling as a function of the NS mass, in the “quadratic” scalar-tensor theory of (4). For the linear coupling of matter to the scalar field, we have chosen α0 = 10−4, a value well below the sensitivity of any near-future solar system experiment [e.g., GAIA (62)]. The solid curves correspond to stable NS configurations for different values of the quadratic coupling β0: −5 to −4 (top to bottom) in steps of 0.1. The yellow area indicates the parameter space allowed by the best current limit on |αPSR − α0| (23), whereas only the green area is in agreement with the limit presented here.

  5. Fig. 5 Constraints on the phase offset in gravitational wave cycles in the LIGO/VIRGO bands.

    Maximum offset in GW cycles in the LIGO/VIRGO band (20 Hz to a few kHz) between the GR template and the true phase evolution of the in-spiral in the presence of dipolar radiation as a function of the effective coupling of the massive NS for two different system configurations: a 2 M NS with a 1.25 M NS (NS-NS), and a merger of a 2 M NS with a 10 M BH (NS-BH). In the NS-NS case, the green line is for αB = α0, and the gray dotted line represents the most conservative, rather unphysical, assumption α0 = 0.004 and αB = 0 (8). In the NS-BH case, αB is set to zero (from the assumption that the no-hair theorem holds). The blue line is for α0 = 0.004 (solar system limit for scalar-tensor theories), and the purple line represents α0 = 0. The gray area to the right of the red line is excluded by PSR J0348+0432. In this plot, there is no assumption concerning the EOS.

  6. Fig. 6 Past and future orbital evolution of PSR J0348+0432.

    Formation of PSR J0348+0432 from our converging LMXB model calculation. The plot shows orbital period as a function of time (calibrated to present day). The progenitor detached from its Roche lobe about 2 Gy ago (according to the estimated cooling age of the WD) when Pb ≅ 5 hours, and since then GW damping reduced the orbital period to its present value of 2.46 hours (marked with a star). UCXB, ultracompact x-ray binary.

  7. Fig. 7 Possible formation channels and final fate of PSR J0348+0432.

    An illustration of the formation and evolution of PSR J0348+0432. The zero-age main sequence (ZAMS) mass of the NS progenitor is likely to be 20 to 25 M, whereas the WD progenitor had a mass of 1.0 to 1.6 M (LMXB) or 2.2 to 5 M (common envelope, CE), depending on its formation channel. In ∼400 My (when Pb ∼ 23 min), the WD will fill its Roche lobe, and the system becomes an UCXB, leading to the formation of a BH or a pulsar with a planet. RLO, Roche-lobe overflow; SN, supernova; IMXB, intermediate-mass x-ray binary.