# Quark matter with strong magnetic field and possibility of the third family of compact stars

## TL;DR

This paper explores the potential existence of a third family of compact stars influenced by strong magnetic fields, showing that such stars could be stable even with soft equations of state and high magnetic fields, offering insights into the hyperon puzzle.

## Contribution

It demonstrates the possibility of a third family of compact stars under strong magnetic fields, expanding understanding of stellar stability and composition.

## Key findings

- Strong magnetic fields can stabilize a third family of compact stars.
- Even soft hadronic equations of state can produce two-solar-mass stars with magnetic fields.
- The results may help resolve the hyperon puzzle in nuclear physics.

## Abstract

We consider the possibility for the existence of the third family of compact objects, considering the effect of strong magnetic fields inside the hybrid stars. As a result, we demonstrate such new sequences of stable equilibrium configurations for some hadronic equations of state. Through the analysis of the adiabatic index inside stars, we find the conditions for appearing the third family of compact objects, i.e., for hadronic stars without quarks, that the maximum mass should be small, the central density for the maximum mass should be also small, and the radius for the the maximum mass should be large. Even for soft hadronic equations of state, the two solar-mass stars might survive as the third family of compact objects, once quark matter with strong magnetic field, such as $\sim {\cal O}(10^{19} {\rm G})$, is taken into account. It might give a hint to solve the so-called hyperon puzzle in nuclear physics.