Stellar-mass binary black holes (BBHs) may merge in the vicinity of a
supermassive black hole (SMBH). It is suggested that the gravitational-wave
(GW) emitted by a BBH has a high probability to be lensed by the SMBH if the
BBH’s orbit around the SMBH (i.e., the outer orbit) has a period of less than a
year and is less than the duration of observation of the BBH by a space-borne
GW observatory. For such a BBH + SMBH triple system, the de Sitter precession
of the BBH’s orbital plane is also significant. In this work, we thus study GW
waveforms emitted by the BBH and then modulated by the SMBH due to effects
including Doppler shift, de Sitter precession, and gravitational lensing. We
show specifically that for an outer orbital period of 0.1 yr and an SMBH mass
of $10^7 M_odot$, there is a 3%-10% chance for the standard, strong lensing
signatures to be detectable by space-borne GW detectors such as LISA and/or
TianGO. For more massive lenses ($gtrsim 10^8 M_odot$) and more compact outer
orbits with periods <0.1 yr, retro-lensing of the SMBH might also have a
1%-level chance of detection. Furthermore, by combining the lensing effects and
the dynamics of the outer orbit, we find the mass of the central SMBH can be
accurately determined with a fraction error of $sim 10^{-4}$. This is much
better than the case of static lensing because the degeneracy between the lens’
mass and the source’s angular position is lifted by the outer orbital motion.
Including lensing effects also allows the de Sitter precession to be detectable
at a precession period 3 times longer than the case without lensing. Lastly, we
demonstrate that one can check the consistency between the SMBH’s mass
determined from the orbital dynamics and the one inferred from gravitational
lensing, which serves as a test on theories behind both phenomena. The
statistical error on the deviation can be constrained to a 1% level.
Examining the Conclusions
In this study, the authors investigate the gravitational-wave (GW) emissions of binary black holes (BBHs) merging near a supermassive black hole (SMBH). They suggest that the GWs emitted by the BBHs have a high probability of being lensed by the SMBH if the outer orbit of the BBH around the SMBH has a period of less than a year and is shorter than the duration of observation by a space-borne GW observatory. Additionally, they find that the de Sitter precession of the BBH’s orbital plane is significant in this triple system.
By analyzing the effects of Doppler shift, de Sitter precession, and gravitational lensing, the authors show that there is a 3%-10% chance for standard lensing signatures to be detectable by space-borne GW detectors like LISA and/or TianGO, when the outer orbital period is 0.1 year and the SMBH mass is ^7 M_odot$. They also suggest that for more massive lenses ($gtrsim 10^8 M_odot$) and more compact outer orbits with periods <0.1 year, retro-lensing of the SMBH could have a 1% chance of detection.
The authors further reveal that combining the lensing effects and dynamics of the outer orbit can accurately determine the mass of the central SMBH with a fractional error of about ^{-4}$. This improved accuracy is attributed to lifting the degeneracy between the lens’ mass and the source’s angular position through outer orbital motion. Additionally, considering lensing effects enables the detection of de Sitter precession at a period three times longer compared to cases without lensing. Lastly, they demonstrate that comparing the SMBH mass determined from orbital dynamics with the mass inferred from gravitational lensing can serve as a test for theories behind both phenomena.
Future Roadmap
Based on the conclusions of this study, there are several potential challenges and opportunities on the horizon:
1. Detection of Lensing Signatures
There is a 3%-10% chance of detecting lensing signatures by space-borne GW detectors, such as LISA and TianGO, when considering BBH + SMBH triple systems with specific parameters. The main challenge in this regard would be accurately identifying and distinguishing these lensing signatures from other sources of noise and gravitational wave signals. Further research and developments are needed to improve the sensitivity and reliability of detectors to increase the chances of detection.
2. Retro-lensing of More Massive Lenses
For more massive lenses (masses $gtrsim 10^8 M_odot$) and compact outer orbits with periods less than 0.1 year, retro-lensing of the SMBH might have a 1% chance of detection. This presents an opportunity to further investigate the gravitational lensing phenomenon and its dynamics. However, the challenge lies in developing observational strategies and techniques to differentiate retro-lensing signals from other astrophysical phenomena.
3. Accurate Determination of SMBH Mass
Combining lensing effects with outer orbital dynamics can lead to an accurate determination of the central SMBH mass with a fractional error of about ^{-4}$. This opens possibilities for refining our understanding of SMBHs and their formation mechanisms. However, precise measurements require advanced data analysis techniques, improved modeling of orbital dynamics, and more extensive observational data.
4. Detecting De Sitter Precession
Including lensing effects allows the detection of de Sitter precession at a longer precession period compared to cases without lensing. By observing this precession, we can gain insights into the general relativistic effects on BBH systems near supermassive black holes. However, detecting such precession requires more extended observation periods and enhanced sensitivity in space-borne GW detectors.
5. Consistency Test for SMBH Mass Determination
The authors propose using the consistency between the SMBH mass determined from orbital dynamics and the mass inferred from gravitational lensing as a test for theories behind both phenomena. This offers an opportunity to validate the theoretical models and frameworks used in studying SMBHs and gravitational lensing. However, achieving accurate measurements and better understanding the systematic uncertainties associated with these methods are essential challenges in performing such consistency tests.
In conclusion, this study provides valuable insights into the interplay between binary black holes, supermassive black holes, and gravitational lensing. It highlights potential avenues for further research, while also emphasizing the challenges that need to be overcome in order to fully explore and exploit the opportunities presented by these phenomena.