In this paper, we study the impact of anisotropy on neutron stars with
different equations of state, which have been modeled by a piecewise polytropic
function with continuous sound speed. Anisotropic pressure in neutron stars is
often attributed to interior magnetic fields, rotation, and the presence of
exotic matter or condensates. We quantify the presence of anisotropy within the
star by assuming a quasi-local relationship. We find that the radial and
tangential sound velocities constrain the range of anisotropy allowed within
the star. As expected, the anisotropy affects the macroscopic properties of
stars, and it can be introduced to reconcile them with astrophysical
observations. For instance, the maximum mass of anisotropic neutron stars can
be increased by up to 15% compared to the maximum mass of the corresponding
isotropic configuration. This allows neutron stars to reach masses greater than
$2.5M_odot$, which may explain the secondary compact object of the GW190814
event. Additionally, we propose a universal relation for the binding energy of
an anisotropic neutron star as a function of the star’s compactness and the
degree of anisotropy.
The Impact of Anisotropy on Neutron Stars
In this study, we explore the effects of anisotropy on neutron stars with different equations of state. Neutron stars are modeled using a piecewise polytropic function with continuous sound speed, and anisotropic pressure in these stars can arise from various factors such as magnetic fields, rotation, or exotic matter.
Quantifying Anisotropy and its Constraints
To measure the level of anisotropy within the neutron star, we assume a quasi-local relationship. Through our analysis, we have discovered that the radial and tangential sound velocities play a critical role in determining the allowable range of anisotropy within the star.
Influence on Macroscopic Properties
Unsurprisingly, the presence of anisotropy has a significant impact on the overall macroscopic properties of neutron stars. By introducing anisotropy, we are able to reconcile these properties with astrophysical observations. Notably, we have found that anisotropic neutron stars can have a maximum mass up to 15% greater than that of their isotropic counterparts.
Implications for Observations
The ability for neutron stars to reach masses greater than 2.5 times the mass of our sun is of particular interest. This increased maximum mass could potentially explain the presence of the secondary compact object observed in the GW190814 event.
Universal Relation for Binding Energy
In addition to our findings regarding mass, we also propose a universal relation for the binding energy of an anisotropic neutron star. This relation considers both the compactness of the star and the degree of anisotropy, providing valuable insights into the energy required to keep the star bound together.
Roadmap for the Future
- Further exploration of anisotropy in neutron stars with a wider range of equations of state.
- Refinement and validation of the quasi-local relationship used to quantify anisotropy.
- Investigation of the physical mechanisms responsible for anisotropic pressure in neutron stars (e.g., magnetic fields, rotation, exotic matter).
- Extension of the study to consider the impact of anisotropy on other macroscopic properties of neutron stars.
- Experimental verification of the proposed universal relation for binding energy through observations and simulations.
Challenges and Opportunities
- Challenges: Further research is needed to fully understand the mechanisms behind anisotropic pressure in neutron stars and to accurately model these states. Additionally, obtaining observational data to validate theoretical findings presents a considerable challenge.
- Opportunities: Exploring the effects of anisotropy on neutron stars offers exciting opportunities to deepen our understanding of these celestial objects and their behaviors. The ability to explain observed phenomena and potentially uncover new ones provides avenues for further scientific exploration.
Note: This analysis is based on current knowledge and may be subject to revision as additional data and insights become available.