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Strong neutrino cooling by cycles of electron capture and β− decay in neutron star crusts

Nature volume 505, pages 62–65 (2014)Cite this article

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Abstract

The temperature in the crust of an accreting neutron star, which comprises its outermost kilometre, is set by heating from nuclear reactions at large densities1,2,3,4, neutrino cooling5,6 and heat transport from the interior7,8,9,10,11. The heated crust has been thought to affect observable phenomena at shallower depths, such as thermonuclear bursts in the accreted envelope10,11. Here we report that cycles of electron capture and its inverse, β− decay, involving neutron-rich nuclei at a typical depth of about 150 metres, cool the outer neutron star crust by emitting neutrinos while also thermally decoupling the surface layers from the deeper crust. This ‘Urca’ mechanism12 has been studied in the context of white dwarfs13 and type Ia supernovae14,15, but hitherto was not considered in neutron stars, because previous models1,2 computed the crust reactions using a zero-temperature approximation and assumed that only a single nuclear species was present at any given depth. The thermal decoupling means that X-ray bursts and other surface phenomena are largely independent of the strength of deep crustal heating. The unexpectedly short recurrence times, of the order of years, observed for very energetic thermonuclear superbursts16 are therefore not an indicator of a hot crust, but may point instead to an unknown local heating mechanism near the neutron star surface.

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Figure 1: Schematic nuclear energy-level diagrams for an electron-capture/β−-decay pair.
Figure 2: Electron-capture/β−-decay pairs on a chart of the nuclides.
Figure 3: Neutrino luminosities in the accreted neutron star crust.

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Acknowledgements

This project was funded by NSF grants PHY 08-22648 (Joint Institute for Nuclear Astrophysics) and PHY 06-06007. A.W.S. was supported by INT DOE grant DE-FG02-00ER41132. E.F.B. was supported by NSF grant AST 11-09176. P.M. was supported by the National Nuclear Security Administration of the US Department of Energy at Los Alamos National Laboratory under contract no. DE-AC52-06NA25396. We thank D.M. Yakovlev, P. Shternin and S. Reddy for discussions and comments on the manuscript.

Author information

Authors and Affiliations

  1. National Superconducting Cyclotron Laboratory, Michigan State University, 640 South Shaw Lane, East Lansing, Michigan 48824, USA ,

    H. Schatz, E. F. Brown, L. Keek & R. Lau

  2. Joint Institute for Nuclear Astrophysics, 225 Nieuwland Science Hall, University of Notre Dame, Notre Dame, 46556, Indiana, USA

    H. Schatz, P. Möller, M. Beard, E. F. Brown, A. T. Deibel, L. Keek, R. Lau, A. W. Steiner & M. Wiescher

  3. Department of Physics and Astronomy, Michigan State University, 567 Wilson Road, East Lansing, Michigan 48824, USA,

    H. Schatz, E. F. Brown, A. T. Deibel, L. Keek & R. Lau

  4. Indian Institute of Technology Ropar, Nangal Road, Rupnagar (Ropar), Punjab 140 001, India ,

    S. Gupta

  5. Theoretical Division, MS B214, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA,

    P. Möller

  6. Department of Physics, 225 Nieuwland Science Hall, University of Notre Dame, Notre Dame, 46556, Indiana, USA

    M. Beard & M. Wiescher

  7. Departamento de Física Nuclear, Instituto de Física da Universidade de São Paulo, Caixa Postal 66318, 05315-970 São Paulo, Brazil,

    L. R. Gasques

  8. Physics Division, Oak Ridge National Laboratory, PO Box 2008, Oak Ridge, Tennessee 37831-6354, USA,

    W. R. Hix

  9. Department of Physics and Astronomy, University of Tennessee, 401 Nielsen Physics Building, 1408 Circle Drive, Knoxville, Tennessee 37996-1200, USA,

    W. R. Hix

  10. Institute for Nuclear Theory, University of Washington, Physics and Astronomy Building, Box 351550, Seattle, Washington 98195-1550, USA ,

    A. W. Steiner

Authors
  1. H. Schatz
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Contributions

H.S. calculated crust models, analysed data and prepared the manuscript. S.G. developed and implemented the phase space calculation. S.G. and P.M. calculated the weak transition rates. E.F.B. calculated crust temperature profiles and assisted with writing the manuscript. A.T.D. computed the temperature scaling of the neutrino emission. L.K. calculated superburst models. M.B., W.R.H. and R.L. wrote model code. All authors contributed to the interpretation of the results, and contributed to or commented on the manuscript.

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Correspondence to H. Schatz.

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Extended data figures and tables

Extended Data Figure 1 Calculated proton and neutron single-particle energy levels in 105Zr as functions of nuclear deformation.

Left panel, proton levels; right panel, neutron levels. The 40 protons and 65 neutrons in 105Zr fill all levels up to the Fermi levels corresponding to these nucleon numbers in the two diagrams (red dots). Levels corresponding to even parity are shown as solid lines, those corresponding to odd parity as dashed lines. Shell gaps are characterized by a particularly large separation in energy between two adjacent single-particle levels. The numbers of protons or neutrons that occupy levels up to the shell gap are indicated by circled numbers. The single-particle levels are shown for a spherical nucleus in spectroscopic standard notation (left side of each panel), and for a deformation near the calculated ground-state shape of 105Zr with quadrupole and hexadecapole shape-parameter values ε2 = 0.333 and ε4 = 0.06, respectively23 (right side of each panel). The middle section of each panel shows the change in level energies as ε2 and ε4 change from spherical values ε2 = ε4 = 0 to deformed values28. The well-known “magic numbers” 50 and 82 corresponding to particularly large gaps stand out at zero deformation29. When the nuclear shape becomes deformed, the spherical shell gaps disappear resulting in a large density of levels in the vicinity of the Fermi level. This gives rise to a large number of states at low excitation in 105Zr. Some of these states can be populated by strong β− decay transitions from the ground state of 105Y. The situation is similar for the electron capture on 105Zr into deformed 105Y.

Extended Data Figure 2 Temperature as a function of depth in the accreted neutron star crust for different Urca shell cooling strengths.

Here we use as a proxy for depth, where P is the pressure, g the local gravitational acceleration, ρ the mass density and z the spatial depth coordinate. As a baseline model, we fix the temperature to be T = 0.42 GK at P/g = 109 g cm−2 and T = 0.35 GK at the crust–core transition. In the absence of Urca shell cooling, the peak local temperature reaches 0.73 GK (solid curve) with the temperature at the superburst ignition depth (P/g ≈ 1012 g cm−2) being 0.66 GK. With the addition of cooling using the HFB-21 mass model and a superburst ash composition (blue dotted line), a local temperature minimum, T = 0.33 GK, appears at the location of the Urca shell. Indeed, for these conditions the temperature at the Urca shell is lower than that at the upper boundary, so that a temperature inversion develops. Even for the much lower Urca shell emissivity of the FRDM mass model (blue dashed line), the temperature at the depth of the superburst ignition is ≲, which is inconsistent with typical superburst ignition conditions10. For both mass models, the temperature has a local minimum at the location of the Urca shell. The steady-state cooling luminosity from the shell is 2 × 1035 erg s−1 for the HFB-21 mass model and 1.4 × 1035 erg s−1 for the FRDM mass model. As a result, the Urca shell thermally decouples the envelope of light elements from the heating in the deeper crust.

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Schatz, H., Gupta, S., Möller, P. et al. Strong neutrino cooling by cycles of electron capture and β− decay in neutron star crusts. Nature 505, 62–65 (2014). https://doi.org/10.1038/nature12757

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