Research ArticleASTRONOMY

Magnetar formation through a convective dynamo in protoneutron stars

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Science Advances  13 Mar 2020:
Vol. 6, no. 11, eaay2732
DOI: 10.1126/sciadv.aay2732
  • Fig. 1 Time series of the densities of kinetic energy in the rotating frame (blue) and magnetic energy (red) for a fast-rotating model with rotation period P = 2.1 ms and Pm = 2.

    The orange line represents the energy of the dipole component (l = 1 mode of the poloidal potential). The dashed gray horizontal lines show the fiducial range from 1014 to 1015 G for the intensity of the dipole field constrained by magnetar timing parameters. The insets show slices of the azimuthal magnetic field Bϕ at times t ∼ 2 s and 10 s indicated by vertical dotted lines. The upper x axis is labeled in units of magnetic diffusion time.

  • Fig. 2 Three-dimensional rendering of the weak and strong field solutions.

    Snapshots (A) and (B) correspond to the left and right insets in Fig. 1, respectively. Left-right snapshots correspond to the left-right insets in Fig. 1. Magnetic field linesare colored by the total field strength and the inner boundary by the entropy. Blue (red) isosurfaces of the radial velocity materializes the downflows (outflows). Radial velocities are of order 108 cm/s.

  • Fig. 3 Ratio of the magnetic to the kinetic energy densities as a function of the inverse Rossby number.

    The thick line shows the strong field best-fit scaling EBEK=0.5Ro1, and the thin horizontal line corresponds to the equipartition scaling. Symbol color indicates fOhm, the ratio of ohmic to total dissipation. The ohmic (resp. viscous) heating appears to be the dominant dissipation mechanism on the strong (resp. weak) field branch. The green banner indicates approximate rotation periods. The symbol shape indicates the type of the outer magnetic boundary condition (b. c.).

  • Fig. 4 RMS values of the magnetic field as a function of the PNS rotation period.

    (A) Intensity of the total dipole component. (B) Intensity of the toroidal axisymmetric component. The vertical dashed line shows the breakup rotation period Pc=2π(GMr<ro/ro3)1/21.75ms. For a given rotation period, the vertical scatter is due to different Pm values.

Supplementary Materials

  • Supplementary material for this article is available at http://advances.sciencemag.org/cgi/content/full/6/11/eaay2732/DC1

    Fig. S1. Entropy per baryon and density profile inside the PNS 0.2 s after bounce.

    Fig. S2. Normalized diffusivity profiles as a function of radius.

    Fig. S3. Ratio of the poloidal and toroidal magnetic energy.

    Fig. S4. Time evolution of the magnetic helicity for a run that saturates on the strong field branch with P = 2.1 s and Pm = 2.

    Fig. S5. Kinetic (blue) and magnetic (red) energy spectra.

    Table S1. Overview of the numerical simulations carried out.

  • Supplementary Materials

    This PDF file includes:

    • Fig. S1. Entropy per baryon and density profile inside the PNS 0.2 s after bounce.
    • Fig. S2. Normalized diffusivity profiles as a function of radius.
    • Fig. S3. Ratio of the poloidal and toroidal magnetic energy.
    • Fig. S4. Time evolution of the magnetic helicity for a run that saturates on the strong field branch with P = 2.1 s and Pm = 2.
    • Fig. S5. Kinetic (blue) and magnetic (red) energy spectra.
    • Table S1. Overview of the numerical simulations carried out.

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