The following interactive numerical calculations are parts of my research carried out at the Interdisciplinary Center for Scientific Computing - IWR under the supervision of PD Dr. Ahmad Hujeirat within the framework of my master thesis which was submitted to the faculty of Physics and Astronomy of Heidelberg University in October 2018.
In the following we present three online calculations in which the time-independent TOV-equation is solved using different parameters and equation of states.
1. Mass-radius diagram for multiple EoS
Here, for a set of different equations of state, a combined mass-radius-diagram is
produced.
The number of points connecting each individual profile are termed as
"Neutron stars".
I use the fourth order Runge-Kutte (RK4) procedure for integrating
the TOV-equation from inside-to-outside to produce such a point. Thus increasing
the number of neutron stars results in a smoother profile for each EoS. Decreasing
the step size of the RK4 integration increases the accuracy of the mass-radius
values of the individual neutron stars.
Parameters:
2. Pressure and mass profiles with a set of tolerance values
This calculation produces pressure and mass profiles of a neutron star for a set of tolerance values. As an input parameter, the mass of the calculated neutron star can be predetermined and the algorithm tries to get as close as possible to this value within the tolerance. As algorithms the RK4 integration and a Newton method are used, which are described in detail in my masters thesis. The tolerance percentages range from 10-3 to 10-9. Like before the accuracy of the integration itself can be improved by increasing the number of steps, thus decreasing the step size of the integrations. Both methods will solve the problem repeatedly until the resulting mass of the neutron star is close enough to the given one, as a result this simulation might take a while for very large number of steps. In this case only a simple polytropic equation of state was used.
Parameters:
3. Pressure and mass profiles with a set of neutron star masses
The last calculation mirrors the second one, except that in this case the tolerance can be chosen as a parameter and a set of neutron star masses is given. This set of masses ranges from 1.4 to 2.0 solar masses in steps of 0.1.
Parameters: