Testing Dark Decays of Baryons in Neutron Stars

The observation of neutron stars with masses greater than one solar mass places severe demands on any exotic neutron decay mode that could explain the discrepancy between beam and bottle measurements of the neutron lifetime. If the neutron can decay to a stable, feebly interacting dark fermion, the maximum possible mass of a neutron star is $0.7M_{\odot }$, while all well-measured neutron star masses exceed one $M_{\odot }$. The existence of $2M_{\odot }$ neutron stars further indicates that any explanation beyond the standard model for the neutron lifetime puzzle requires dark matter to be part of a multiparticle dark sector with highly constrained interactions. Beyond the neutron lifetime puzzle, our results indicate that neutron stars provide unique and useful probes of GeV-scale dark sectors coupled to the standard model via baryon-number-violating interactions.

Figure 1

Baryon (or neutron) chemical potential (including rest mass) in MeV vs the baryon density in units of nuclear matter density, $n_0=0.16{\mathrm{fm}}^{-3}$, for the quark-hadron crossover equation of state, QHC18(0.8,1.5) [20], for the stiffer APR equation of state [21], and for noninteracting (free) neutrons. This figure shows how much more expensive it would be for a baryon to remain at high densities instead of turning into a weakly interacting dark matter particle with $m_{\chi }<{\mu }_b$.

Figure 2

Number density of dark matter fermions $\chi$ in chemical equilibrium as a function of the total number of fermions, $n_F=n_b+n_{\chi }$, in units of nuclear matter density $n_0$, for the QHC18 neutron star equation of state and for different dark matter fermion masses: $m_{\chi }=m_n$, $m_{\chi }=1.2m_n$, $m_{\chi }=1.5m_n$, and $m_{\chi }=2m_n$. The small flattening in the $m_{\chi }=m_n$ curve reflects the onset of pion condensation in the APR equation of state [21].

Figure 3

The equation of state for baryons coupled to $\chi$’s, with $m_{\chi }=m_n$, and for the QHC18(0.8,1.5), APR, and free neutron equations of state. As explained in the text, at the resolution of this graph, the corresponding curves for baryons with the QHC18 and APR equations of state in equilibrium with $\chi$’s are indistinguishable. Even though the APR equation of state is stiffer at higher densities than QHC18, in chemical equilibrium the core of the star would contain primarily dark fermions in either case. At nuclear matter density, $\epsilon \simeq 150\mathrm{MeV}/{\mathrm{fm}}^3$.

Figure 4

The QHC18(0.8,1.5) equation of state in chemical equilibrium with dark matter fermions of different masses: $m_{\chi }=m_n$, $m_{\chi }=1.2m_n$, $m_{\chi }=1.5m_n$, and $m_{\chi }=2m_n$. One sees here the dramatic softening induced by coupling to $\chi$’s. For larger $m_{\chi }$, the onset of the softening is pushed to higher $\epsilon$, where it becomes energetically favorable for a baryon to be converted to a $\chi$.

Figure 5

Neutron star masses vs central density for baryons with the QHC18(0.8,1.5) equation of state in chemical equilibrium with $\chi$’s having $m_{\chi }=m_n$ and for the QHC18(0.8,1.5), APR, and free neutron equations of state. This figure shows how coupling of baryons to weakly interacting dark matter precludes an explanation of the existence of neutron stars from $1M_{\odot }$ to $2M_{\odot }$. At the resolution of this graph, the corresponding curves for baryons with the QHC18 and APR equations of state in equilibrium with $\chi$’s are indistinguishable.

Figure 6

Neutron star mass as a function of the central energy density with baryons in chemical equilibrium with dark matter fermions for different masses: $m_{\chi }=m_n$, $m_{\chi }=1.2m_n$, and $m_{\chi }=1.5m_n$. At larger $m_{\chi }$, the conversion of baryons to dark matter is kinematically forbidden at lower densities, as shown in Fig. 2. Therefore, the neutron star mass shown here is independent of the dark matter mass for a sufficiently low central density. For $m_{\chi }=2m_n$, the neutron star mass is essentially unaffected by the small number of $\chi$’s present for this range of central densities.

Figure 7

Neutron star mass as a function of the neutron star radius for baryons with the QHC18 equation of state in chemical equilibrium with $\chi$’s of mass $m_{\chi }=m_n$, $m_{\chi }=1.2m_n$, and $m_{\chi }=1.5m_n$. Again, the QHC18 curves with no dark matter and for $m_{\chi }=2m_n$ are essentially indistinguishable for this range of central energy densities.