The promise of multi-band gravitational wave astronomy

Abstract: We show that the black hole binary (BHB) coalescence rates inferred from the advanced LIGO (aLIGO) detection of GW150914 imply an unexpectedly loud GW sky at milli-Hz frequencies accessible to the evolving Laser Interferometer Space Antenna (eLISA), with several outstanding consequences. First, up to thousands of BHB will be individually resolvable by eLISA; second, millions of non resolvable BHBs will build a confusion noise detectable with signal-to-noise ratio of few to hundreds; third -- and perhaps most importantly -- up to hundreds of BHBs individually resolvable by eLISA will coalesce in the aLIGO band within ten years. eLISA observations will tell aLIGO and all electromagnetic probes weeks in advance when and where these BHB coalescences are going to occur, with uncertainties of <10s and <1deg^2. This will allow the pre-pointing of telescopes to realize coincident GW and multi-wavelength electromagnetic observations of BHB mergers. Time coincidence is critical because prompt emission associated to a BHB merger will likely have a duration comparable to the dynamical time-scale of the systems, and is only possible with low frequency GW alerts.

• The paper presents a multi-band strategy where eLISA forecasts thousands of binary black hole signals that later enter the aLIGO band.
• The paper develops binary black hole population models based on GW150914 data, predicting both resolvable and confusion noise signals.
• The paper demonstrates that precise parameter estimation with eLISA enables coordinated electromagnetic follow-ups of transient coalescences.

The Promise of Multi-Band Gravitational Wave Astronomy Post-GW150914

The detection of GW150914 by the Advanced LIGO (aLIGO) marked a pivotal moment in gravitational wave (GW) astronomy, revealing a promising horizon in multi-band GW studies. Alberto Sesana's paper explores the implications of this event and elaborates on the critical role the evolving Laser Interferometer Space Antenna (eLISA) could play at milli-Hz frequencies. Key topics discussed include the potential for a significant number of resolvable black hole binaries (BHBs) and the opportunity for coincident electromagnetic (EM) observations informed by eLISA.

Gravitational Wave Astronomy: From Detection to Prediction

The study begins by contextualizing the BHB coalescence rates inferred from GW150914, projecting a prolific presence of GW signals at milli-Hz, the frequency range eLISA would be operational. It posits three main predictions:

1. Thousands of BHBs will be individually detectable by eLISA.
2. Millions of unresolved BHBs will contribute to a detectable confusion noise.
3. Up to hundreds of eLISA-resolvable BHBs will coalesce within the aLIGO frequency band over a decade.

These predictions carry significant implications for real-time astrophysical data processing. Notably, eLISA could forecast BHB coalescences, allowing for synchronized GW and EM observations. With accuracy down to tens of seconds and a small degree of sky localization, eLISA could enable precision pre-pointing of telescopes, maximizing observational coincidence and the potential capture of transient post-merger emissions.

Binary Black Hole Population Models

The paper creates BHB population models grounded in the observed data of GW150914, exploring two mass distribution models: a log-flat model and a Salpeter-like distribution. These models are integral to calculating the probabilistic distribution of mergers across the universe, facilitating the projection of signals that would populate the eLISA frequency domain. These population models entail different assumptions about mass, frequency, and redshift, which directly influence number and detectability predictions.

Signal and Parameter Estimation

The robustness of eLISA's predicted detection capability hinges on its system design. An analysis of various configurations of eLISA shows that between tens to over a thousand BHB systems could be resolvable, with a non-negligible fraction progressing to aLIGO bands. Signal-to-noise ratio (S/N) computations are validated through analytical estimates, emphasizing eLISA’s ability to locate coalescences with precision, thus enhancing detection confidence.

Parameter precision is scrutinized through a Fisher Matrix approach, showing that eLISA could predict coalescence times with impressive granularity, guiding follow-up aLIGO observations and EM counterparts. The capability to characterize chirp mass and other parameters with high accuracy opens pathways for nuanced physical investigations.

Implications and Future Directions

The possible simultaneous observations bring to light several avenues in GW and EM astronomy:

• Multi-Messenger Astronomy: eLISA can drive preemptive observational strategies for aLIGO, facilitating multimodal data richness and enhanced source characterization.
• Fundamental Physics and Cosmology: Enhanced mass precision and system characterization from eLISA findings could inform gravitational theories and serve as standard sirens for cosmological measurements.
• Cross-Validation and Calibration: Consistency checks across eLISA and aLIGO offer mutual calibration opportunities, ensuring data integrity across bands.

The paper emphasizes that the design and operational parameters of eLISA will deeply influence the scientific yield of these efforts. A well-configured eLISA could unlock major scientific gains, ranging from high-confidence source detections to the probing of deep cosmological questions. To capitalize on the multi-band prospective synergy, it calls for a reflective re-analysis of design considerations, especially concerning sensitivity attributes critical at high signaling frequencies.

In conclusion, Sesana’s paper underscores the transformative potential of a finely tuned eLISA in conjunction with aLIGO. As gravitational wave astronomy evolves, this multi-band strategy could serve as a foundational framework for understanding BHB systems and leveraging cosmic signals to decode the fundamental laws governing the universe.