Thermodynamically Consistent Equation of State for an Accreted Neutron Star Crust

Area of Science:

• Astrophysics
• Nuclear Physics
• Condensed Matter Physics

Background:

• Accreting neutron stars possess crusts with complex equations of state (EOS).
• Existing EOS models often implicitly assume co-movement of free neutrons and nuclei in the inner crust.
• This assumption violates the hydrostatic equilibrium condition for unbound neutrons (μn∞ = const).

Purpose of the Study:

• To construct a novel EOS for accreting neutron star crusts that respects hydrostatic equilibrium conditions.
• To investigate the implications of this new EOS on crust properties and stability.
• To compare the new EOS with existing models for accreted crusts.

Main Methods:

• Application of the compressible liquid-drop approximation.
• Incorporation of the condition μn∞ = const for unbound neutrons.
• Analysis of pressure at the outer-inner crust interface and crustal instabilities.

Main Results:

• The new EOS closely resembles the catalyzed EOS throughout most of the inner crust.
• It significantly differs from previously discussed accreted crust EOSs.
• Pressure at the outer-inner crust interface is determined by equilibrium conditions, not neutron drip pressure.
• An instability is identified at the base of the accreted crust, promoting transformation to homogeneous nuclear matter.

Conclusions:

• The derived EOS provides a more accurate description of accreting neutron star crusts by enforcing hydrostatic equilibrium.
• The findings challenge conventional models and highlight the importance of equilibrium conditions in crust formation.
• The identified instability ensures self-similar crust structure during accretion.