Effect of ultralight dark matter on compact binary mergers

The gist: ULDM can significantly alter merger statistics when its ambient density becomes larger than 104GeV/cm3 by affecting orbital evolution through accretion and dynamical friction, providing insight into potential observational signatures of dark matter in merger events.

Baseline Model and ULDM Incorporation

The study constructs a baseline astrophysical model of compact binary mergers and extends it by incorporating a model of ultra light dark matter which affects the orbital evolution of binaries through accretion and dynamical friction. The analysis demonstrates that compared to the baseline model, ULDM can significantly alter the merger statistics when its ambient density becomes larger than 104GeV/cm3.

Framework of ULDM Interaction

The ULDM is represented by a light scalar field satisfying the massive Klein-Gordon equation □Φ − µ2Φ = 0. Solutions for the scalar field at the rest frame of the compact object behave as plane waves at large distances. The computation of accretion and dynamical friction involves solving for the radial part of Eq. (1) in the Kerr background, matching asymptotic limits, and providing ratios of reflected and incident amplitudes to determine accretion rate and force. The dynamical friction force acting on the object in the rest frame of the DM is given by F⃗ ′ = −4πħnη2µ∆Ψ⃗ζ.

Effects on Individual Binaries

The effect of ULDM is through accretion and dynamical friction, where Eq. (6) depicts that the drag term acts universally upon any object, but the accretion term is dependent upon the nature of the surface reflectivity. The evolution of the binary separation will be different for stars and BHs because accretion is dependent on the compact object's surface reflectivity, which vanishes for a BH and will be unity for a star. The analysis shows that only if δL 0, ensuring that the binary separation never increase across the stellar endpoint.

Impact on Merger Statistics

The presence of ULDM leads to a dissipative term Pdf = F⃗ ′ · ⃗v = −4πħµnvη2∆Ψ. This dissipative term will add up to the quadrupolar radiation emitted from the binary inspiral, leading to faster energy loss from the system and hence reduces the merger time. The results for individual binaries show that in a ULDM environment with DM density ρ = 108GeV/cm3, the binary merges at z = 0.4, while in absence of DM environment it merges at z = 0.07.

Merger Rate Density and Observational Constraints

The merger rate density Rm(zm) is estimated by evolving sources using the SFR function and binning the population of merged events, leading to Rm(zm) ∼ d2Nm/dzdt dZm dVc (1 + zm). For ULDM density ρ = 104GeV/cm3, the merger rate is in tension with the LVK estimation of the merger rate, suggesting that models with DM density ρ ≤ 104GeV/cm3 can be ruled out at 90% confidence from GWTC-3 data. The ULDM model with DM density, given by ρ = 1012GeV/cm3 is the best performing and agrees with the GWTC power-law bounds for zm ≲ 2. The peak of the merger probability distribution shifts towards higher redshifts as ULDM density increases, which is an observable signature of DM density.

Conclusion

The study demonstrates that ULDM fields can indeed impact merger statistics, particularly when their density exceeds the threshold of ρ > 104GeV/cm3. The presence of ULDM leads to significantly higher proportion of mergers compared to the vacuum case for ρ > 108GeV/cm3. The peak of the merger probability distribution in redshift is another observable that can tell us a lot about the existence and nature of the DM environment in galaxies.

How it works

1. Construct a baseline astrophysical model of compact binary mergers and extend it by incorporating a model of ultra light dark matter which affects the orbital evolution through accretion and dynamical friction.

2. Represent ULDM as a light scalar field satisfying the massive Klein-Gordon equation □Φ − µ2Φ = 0.

3. Calculate the accretion rate and force due to dynamical friction using steps involving solving for the radial part of Eq. (1) in the Kerr background and matching asymptotic limits.

4. Implement these effects into binary inspiral dynamics by considering an extra dissipation force Pdf = F⃗ ′ · ⃗v.

5. Analyze the effect on merger statistics by evolving individual binaries and then considering a population of binary progenitors, showing that denser ULDM environments lead to a shift in the peak of the merger probability distribution towards higher redshifts.

How it works

The analysis shows that increasing the density of the DM medium leads to a reduction in the area under the blue-shaded region, which implies more mergers occurring at higher redshifts. Furthermore, a higher ULDM density facilitates the merging of remnants that would otherwise remain unmerged, particularly those originating from more massive progenitors. The oscillatory pattern seen in the parameter space of the unmerged population for ρ = 5 × 107 GeV/cm3 arises from similar oscillatory non-linearities present in our assumed mass-transfer function.

How it works

The merger rate density Rm(zm) is computed by evolving sources at a given z using Eq. (15) and then binning the population of all the merged events according to their merger redshifts, resulting in Rm(zm) ∼ d2Nm/dzdt dZm dVc (1 + zm). This rate is then compared to the inferred rate Rinfm (zm) from LIGO-Virgo observations. The results show that for ρ > 108GeV/cm3, almost 80% of the original progenitor binary configurations have merged.

How it works

The merger probability pmerg(zm) is determined by the time integral of the quantity (d2Nm/dzdt) defined above, where pmerg(zm) ∼ Z dt d2Nm/dzdt. The findings in Fig. 5 are consistent with previous results, indicating that denser ULDM environments tend to reduce merger timescales and make individual binaries merge faster.

How it works

The peak of the merger probability distribution in redshift is another observable that can tell us a lot about the existence and nature of the DM environment in galaxies. The results highlight the potential role of ULDM in shaping the observable characteristics of compact binary mergers and hence provides a novel perspective on how DM may influence astrophysical merger events.

How it works

The study concludes that increasing the density of the DM medium leads to a shift in the peak of the merger probability distribution towards higher redshifts. This is expected, as the DM density increases the dynamical friction also increases, leading to an enhanced loss of orbital energy for the dipole. As a consequence, most of the binaries lose energy faster and hence merges at a higher redshift, i.e., earlier than expected from a vacuum environment.

How it works

The paper provides an illustrative tool to study how the surrounding dark matter environment can shape merger statistics by exploring the key qualitative effects that arise when compact binaries evolve within a ULDM background.

1. textbfFundamental Modification of Merger Rate Density Modeling: Incorporating ULDM Effects in Population Synthesis Tools. This allows AI systems to predict how the astrophysical merger rate density is altered by dark matter environments, moving beyond baseline models that ignore DM.

2. textbfEnhanced Constraint Derivation from Gravitational Wave Data: Utilizing Merger Redshift Distribution for Dark Matter Density Limits. The paper shows that increasing the density of the DM medium leads to a shift in the peak of the merger probability distribution towards higher redshifts, enabling AI to use observed merger redshift peaks as a probe for ULDM density, especially when the peak of the merger probability distribution in redshift is another observable that can tell us a lot about the existence and nature of the DM environment.

3. textbfDevelopment of Environment-Aware Binary Evolution Simulators: Creating Models That Differentiate Binary Outcomes Based on DM Density. The AI system can now evolve individual binaries by incorporating the extra dissipation force, which in the scalar’s rest field gives rise to an additional loss of power, given by Pdf, allowing it to predict faster merger timescales and/or smaller remnant separation compared to vacuum evolution.

4. textbfImproved Merger Probability Prediction for Population Statistics: Quantifying Mergers Across Redshift Bins Based on ULDM Density. By calculating the merger probability, pmerg(zm) ∼ Z dt d 2Nm/dzmdt, the AI can predict significantly higher proportion of mergers compared to the vacuum case when ULDM density exceeds a threshold, providing specific merger fraction predictions for different densities like nearly 80% of configurations merging for densities ∼ 108GeV/cm3.

5. textbfExtrapolation Capability for Future Detector Sensitivity: Modeling Merger Rates Across Redshift Ranges Using Inferred Power-Law Exponents. The AI can use the inferred relation Rinf m (zm) ≃ R0 (1 + zm)κ to extrapolate merger rates beyond current detector sensitivity, allowing for predictions of merger probability distribution of GW events at higher redshifts, contingent on parameter fitting from existing data.

6. textbfModel Comparison and Degeneracy Analysis: Identifying ULDM Signatures Against Astrophysical Uncertainties. The AI system can perform a systematic check against the baseline model, noting that for densities ρ ≤ 104GeV/cm3 the merger rate is in tension with the LVK estimation of the merger rate, which helps in distinguishing DM effects from various astrophysical considerations like Roche overflow or stellar winds.

The growing catalogue of gravitational wave events enables a statistical analysis of compact binary mergers, typically quantified by the binary merger rate density. This quantity can be influenced by ambient factors, following which, in this work we have investigated the impact of dark matter environment on the merger statistics. We construct a baseline astrophysical model of eccentric and quasi-circular compact binary mergers and extend it by incorporating a model of ultra light dark matter, which affects the orbital evolution of binaries through accretion and dynamical friction. Our analysis of the merged population of binary progenitors demonstrates that, compared to the baseline model, ULDM can potentially alter the merger statistics around an optimal combination of ambient density 10 4 GeV/cm cubed and eccentricity about 0.5. A comparison with the gravitational wave data from the GWTC-3 catalogue provides crucial insight into potential observational signatures of the ULDM in merger events, leading to possible constraints on the existence and density of dark matter distribution in galaxies.