Examining the Probability of an Electron Capture Supernova of the Crab Nebula Using a Non-constant Acceleration Model to Derive an Equation of State

Undergraduate #329
Discipline: Physics
Subcategory: Astronomy and Astrophysics

Luis Rivera - Lake-Sumter State College
Co-Author(s): William Newton, Texas A&M University, Commerce, TX

Observations suggest the Crab nebula was formed in an electron-capture supernova, and that the nebula’s expansion is accelerating. One possible source of energy to power this acceleration is the Crab pulsar’s rotational kinetic energy which is lost through the coupling between the Crab pulsar’s magnetic field and the nebula. Using this model, we derive a new lower limit on the moment of inertia of the Crab pulsar and use that limit to derive constraints on the neutron star equation of state (EoS). We also compare the limit on the moment of inertia with that derived assuming the Crab pulsar was formed in an electron-capture supernova. We find the electron-capture supernova scenario is broadly consistent with the acceleration implied by the observational data.

Funder Acknowledgement(s): National Science Foundation; Texas A&M University Commerce.

Faculty Advisor: William Newton, William.Newton@tamuc.edu

Role: Graphed modified skyrme models for pressure as a function of density. I used the three previously derived PNM constraints and averaged them, using the lowest values as a lower constraint for our skyrme models. The highest for the highest constraint. I graphed them to nuclear saturation density. I used dimensionless comparison graphs of the moment of inertia vs the compactness parameters. I also derived our own analytical formula. I calculated the moment of inertia for neutron stars of 1.25 (electron capture) 1.4 as an average and 1.6 solar masses for all skyrme models. Graphed them dimensionless as well. I used our analytical formula to set constraints on the values of the needed moment of inertia to power a given mass nebula. Recalculated nebula mass, radius, acceleration rate.