Sterigoulas for clarifications on the RNS code, Polychronis koligiannis for his help in checking the results, Mr. In the following paper, observations are made of how the rotation of neutron stars changes their maximum mass, radius and other characteristic variables. The last sections present a description of the RNS code and its functions, as well as a new user-friendly environment for the RNS code.
Under those conditions, by observing the mass as well as the radius of neutron stars, we can draw useful conclusions about the equation of state of nuclear matter, and observing rapidly rotating neutron stars can give us even more clues about the composition of nuclear matter at high densities on these point should be mentioned that neutron stars are the only place where we can extract all that information, since we cannot observe how matter behaves inside a black hole.
Historical Background
Characteristics
- Mass of neutron star
- Radius of neutron star
- Temperature of neutron stars
- magnetic field
- interesting observed neutron stars
Besides temperature, the composition of the star's atmosphere and its magnetic field are important factors. Further analysis of the temperature of the neutron stars escapes the theme of this work. The observations of magnetic fields coming from the atmosphere of neutron stars is a demanding procedure.
The evolution of magnetic fields is more complicated as it depends on more parameters while closely related to the hot evolution of the star.
Neutron star structure
The mass and frequency are mentioned as benchmarks for the comparison of the calculated (theoretical) models of neutron stars. When integrating the TOV equations, it is valuable to define a generalization of the Newtonian specific enthalpy. To integrate the equations, a value for the enthalpy at the center of the starηcm must be chosen and the initial conditions r(ηc) = 0 and m(ηc) = 0 must also be set.
Due to the structure of the star (outer shell, inner shell, outer core, inner core) it is impossible to construct an equation for the whole star.
Equations of state
Cold equations of state
Hot equations of state
Stiff-Soft equations of state
Static model
This means that the maximum mass that a neutron star can hold is smaller than the rotation of a rotating neutron star. This also means that the total baryonic number (A) which depends on the mass M, remains stable. That state precedes the rise of the mass M of the neutron star, so that the gravitational force will bring the star to its initial state.
Kepler frequency
- Introduction
- Lense-Thirring effect
- Kepler frequency definition
- RNS code
- RNS code inputs and tasks
- RNS code output and examples of single models
- RNS sequenced model calculations and command ex-
The fact that more mass can be built up changes the space-time metric in correlation with the rotational frequency of the star. Due to the Lens-Thirring phenomenon, a free-falling particle does not fall in a straight line to the center of the star, on the contrary, the free-falling particle follows a curved orbit following the rotation of the neutron star. Where ω is the angular velocity of the neutron star and ω is the angular frame drag velocity.
The relative angular velocity is inversely proportional to r3 and is correlated with the radius, polar angle and the angular velocity of the neutron star. Ωk represents the Kepler angular velocity, referred to in the bibliography as Kepler frequency. Frequencies higher than ΩK lead to fluid diffusion from the equator of the neutron star into outer space.
It should be mentioned at this point that the Kepler frequency defined earlier can only describe Newtonian systems and not relativistic systems, which means that it is not appropriate to describe a neutron star. To find an equation expressing the relativistic Kepler frequency, we set dr = dθ = 0 in the space-time metric as it is mentioned in the Kepler frequency. Using the new space-time metric and calculating the neutron star's angular momentum, we attempt to produce an equation for ΩK.
The parameters should be the central energy density in gr/cm3 and depending on the ratio of the duty axes, mass, rest mass, angular velocity, angular momentum. All seven tasks require setting the energy density as a parameter, while four of the tasks also require setting a second parameter.
User-friendly environment
- System requirements
- Code summary
- Running the RNS program from python
- RNS output data filtering
- Errors
The developed program receives input from the user in a friendly environment, compiles the command needed to run RNS, runs (rns.exe) (rns1.1c) while the RNS code is running, the program saves the output values and saves them to an output file or creates diagrams . The above section presents the python code responsible for the execution (rns.exe). The code above includes a time trigger in case (rns.exe) is unable to calculate the models for the parameters set by the user.
When the time runs out, a function will be called to stop the execution of (rns.exe) and python will continue with the next model or produce an empty graph, the time of the above actions will vary based on the number of computation . At this point, it should be mentioned that it is not possible to set a standard time trigger for all computers simply because not all computers have the same computing power, that is why the time trigger has higher values. The code directly stores the output of the RNS code while it is still running.
That way if the timer stops the (rns.exe) all the output up to that point will be saved. In this part of the code, the data collected from the (rns.exe) is filtered for each model being calculated. If one model of the row has errors in one of the variables executed in this part of the code, it is deleted while the rest of the models are kept.
The code may not work when calculating series of ten or fewer models or when the starting price of energy density is very low. I haven't thoroughly checked the code for more bugs, so I'll rely on emails from users for that.
Influence of rotation in maximum mass
Kepler vs Static
Having completed the theoretical content and the references to the codes, we now proceed to the calculation part. It should be mentioned that the following presented diagrams are mass-radius diagrams with the mass on the vertical axes and radius on the horizontal axis. In the graphs presented above, two curves can be distinguished, one closer to the beginning of the axis with a shorter radius the static model curve and one curve with a larger radius representing the neutron star rotating in Kepler frequency.
As expected, the maximum mass of a rotating star will be greater than that of a static one.
Influence of rotation in maximum mass
However, it is observed that the maximum mass of the static as well as the slowly rotating neutron star curves in all the constitutions is negligible compared to the maximum mass of the Kepler rotating neutron star. This is especially true because only a few Hz-rotating stars have been observed so far, with the fastest neutron-rotating star ever observed at a rotation speed of 716 Hz (PSRU1748-24463d). However, the Kepler angular velocity is a theoretical calculation and it is strange that such stars have not yet been observed in the universe.
Influence of the equation of state in maximum mass
In the above (mass radius) diagram, eleven equations of state have been calculated for the axle ratio (0.75). The energy density bounds differ for the equations, but are of the same magnitude. From the models created for static-Kepler equations, the effect of rotation on neutron stars is immediately apparent. Let us first assume that as the energy density at the center of the neutron star increases, matter concentrates on a smaller scale at a point where it becomes hyperdense.
Furthermore, it is very important that while the equations of state have different initial conditions or a different function in general, the characteristic curve has the same shape in all constitutive equations studied and in all types of rotation. It is also noticeable that for the given conditions there is a large gap in the maximum masses of the equations of state, with eosL having the largest mass of all equations of state and eosFPS having the minimum-maximum mass.
Energy plateau in (energy density - gravitational mass) dia-
Finally, the graph of the eosC Kepler model appears at a higher mass value as mentioned above, the star can withstand a larger increase in matter than a slowly rotating neutron star. In the diagram above, there is a comparison of the gravitational mass with the energy density for various equations of state for their Kepler frequencies. It is clear that the equation of state is a critical factor for the definition of the maximum allowable mass in a neutron star.
Comparing the above diagrams, it can be safely assumed that the equation of state is the main parameter that determines the maximum mass of a neutron star. Summarizing, through all the theoretical and computational studies, I reached some very important conclusions about the functions of neutron stars and confirmed my perception of the behavior of the maximum mass with respect to the rotation frequency. It is theoretically plausible that there could be much larger neutron stars, with much higher frequencies.
Nevertheless, the observed neutron stars have a significantly lower frequency, so it is not currently possible to study stars with a maximum mass greater than the observed mass. If rapidly spinning neutron stars do indeed exist, it is strange that they have not yet been observed. This may be due to the fact that their rapid rotation is slowed relatively quickly by electromagnetic radiation, or that such an object cannot exist due to instability. So physics is needed to answer these questions over time, for a deeper understanding of these remarkable objects. and the documentation of neutron star theories.
Although the program developed in python is a handy tool for running the (rns1.1c) code and harvesting the data it prints as output, there is an even better way to make it happen, so with the help of Dimitris Kaitatzidis we started developing a code based in Reactive and Nodejs. The new program will allow the user to operate it from any device that has a browser, even from a smartphone with minor changes. 9] Upper limits set by causality on the rotation and mass of uniformly rotating relativistic stars, Scott Koranda, Nikolaos Stergioulas and John L.
10] Comparison of models of rapidly rotating relativistic stars constructed by two numerical methods, Stergioulas Nikolaos, Friedman John L., Astrophysical Journal, part 1 (ISSN 0004-637X), vol.