Kilonova Distinction | Yugesh Bhoge

The Degeneracy Problem

Gravitational-wave (GW) observatories face a critical challenge: distinguishing between a high-mass ratio Binary Neutron Star (BNS) merger and a low-mass Neutron Star-Black Hole (NSBH) merger. When the primary mass falls into the range $2.5 - 5 M_\odot$, GW signals alone yield highly degenerate parameter estimations i.e. it can't distinguish between a HMNS (High Mass Neutron Star) and a LMBH (Low Mass Black Hole).

As wide-field optical surveys like the Rubin Observatory (LSST) come online, thousands of kilonovae will be discovered serendipitously without GW triggers. We demonstrate that the kilonova light curve itself, specifically its post-peak magnitude decline ($\Delta m$), acts as a definitive, distance-independent classifier.

Computational Pipeline

Population Synthesis: Simulated dense grids of $2 \times 10^4$ BNS and NSBH systems covering plausible mass, spin, and Equation of State (EoS) parameter spaces.
NR-Calibrated Fits: Extracted dynamical ($M_{dyn}$) and post-merger disk ($M_{disk}$) ejecta masses using numerical relativity formulae (Krüger & Foucart for NSBH; Nedora 2023 for BNS).

LSST Survey Strategy

Our findings establish a prioritization metric for the Vera C. Rubin Observatory. A rapid $\ge 3$ mag drop in the $u$-band within 48 hours is a smoking gun for an NSBH merger, allowing automated pipelines to immediately trigger expensive spectroscopic follow-up before the transient fades.

Physics Explorer

Adjust the physical parameters below to see how they govern the diffusion timescale ($t_d$).

Ejecta Mass ($M_{ej}$) 0.05 M⊙

Velocity ($v_{ej}$) 0.20 c

Opacity ($\kappa$) 1.0 cm²/g

Lanthanide-poorLanthanide-rich

Calculated Timescale ($t_d$)

4.2 Days

Fast diffusion: Typical of early BNS emission.

Ejecta Geometry & Composition

The observable differences in kilonovae stem from the fundamentally different ways matter is ejected during the merger, governed primarily by the electron fraction ($Y_e$) which determines lanthanide production via the r-process.

NSBH Mergers

Driven by extreme tidal disruption, NSBH mergers produce massive, highly asymmetric equatorial tidal tails. This dynamical ejecta is extremely neutron-rich (low $Y_e \le 0.1$).

Lanthanide Fraction: High ($X_{lan} \sim 10^{-1}$)
Opacity ($\kappa$): Massive ($> 10 \text{ cm}^2/\text{g}$)
Outcome: Redder, longer-lasting emission.

BNS Mergers

BNS mergers undergo violent contact, producing shock-heated polar dynamical ejecta. Neutrino irradiation raises $Y_e$ (high $Y_e \ge 0.25$).

Lanthanide Fraction: Low ($X_{lan} \sim 10^{-4}$)
Opacity ($\kappa$): Low ($< 1 \text{ cm}^2/\text{g}$)
Outcome: Early, bright blue emission that fades rapidly.

Thermodynamic Framework

The underlying physics is captured by the Arnett-Chatzopoulos-Villar (ACV) semi-analytic formulation:

$$\frac{dE}{dt} + p\frac{dV}{dt} = \dot{Q}_{decay} - L$$

$$L(t) = 2\,e^{-\left(\frac{t}{t_{\rm d}}\right)^2} \int_0^t \left(\frac{t'}{t_{\rm d}}\right) e^{\left(\frac{t'}{t_{\rm d}}\right)^2}\, \dot{E}(t')\,\frac{dt'}{t_{\rm d}}$$

$$t_d = \left( \frac{\kappa M_{ej}}{\beta c v_{ej}} \right)^{1/2}$$ (where geometric constant $\beta \approx 13.8$)

Higher opacity ($\kappa$) in NSBH ejecta leads to larger $t_d$, trapping heat and slowing the decline.

Post-Peak Photometric Decline ($\Delta m$)

Displaying magnitude evolution in the blue u-band. The absence of high-$Y_e$ polar ejecta in NSBH events leads to a rapid collapse in blue flux ($\Delta m \sim 3.38$ at day 2). BNS events sustain this emission much longer.

Displaying magnitude evolution in the red i-band. The trend reverses: massive lanthanide-rich tidal tails in NSBH mergers sustain emission longer than BNS events.

BNS Progenitor

NSBH Progenitor

Distinguishing BNS and NSBH Kilonovae via Photometric Decline Rates