Using gravitational-wave standard sirens

TL;DR

This paper proposes using gravitational-wave standard sirens from massive BBH inspirals detected by LISA to probe the distance–redshift relation and dark energy. It explains how $D_L$ is extracted from inspiral waveforms, the role of LISA's orbital modulation for sky localization, and the necessity of an electromagnetic counterpart to obtain redshift and sub-percent distance accuracy. The authors quantify measurement precisions with Monte-Carlo simulations, show how lensing degrades constraints, and discuss strategies to identify counterparts within LISA error boxes. Overall, GW standard sirens could provide a powerful, complementary cosmological probe to Type Ia supernovae, contingent on the identification of EM counterparts and careful treatment of lensing effects.

Abstract

Gravitational waves (GWs) from supermassive binary black hole (BBH) inspirals are potentially powerful standard sirens (the GW analog to standard candles) (Schutz 1986, 2002). Because these systems are well-modeled, the space-based GW observatory LISA will be able to measure the luminosity distance (but not the redshift) to some distant massive BBH systems with 1-10% accuracy. This accuracy is largely limited by pointing error: GW sources generally are poorly localized on the sky. Localizing the binary independently (e.g., through association with an electromagnetic counterpart) greatly reduces this positional error. An electromagnetic counterpart may also allow determination of the event's redshift. In this case, BBH coalescence would constitute an extremely precise (better than 1%) standard candle visible to high redshift. In practice, gravitational lensing degrades this precision, though the candle remains precise enough to provide useful information about the distance-redshift relation. Even if very rare, these GW standard sirens would complement, and increase confidence in, other standard candles.

Figures (8)

• Figure 1: Illustration of the LISA antenna's orbit. The constellation "rolls" as its centroid orbits the sun, completing one full revolution for each orbit.
• Figure 2: Pointing and distance error distributions for measurements at $z = 1$ of a binary of masses $m_1 = 10^5\,M_\odot$, $m_2 = 6\times10^5\,M_\odot$. These distributions were made by Monte-Carlo simulations of 10,000 LISA BBH measurements, randomly distributing the binaries' positions, orientations, and merger times; see hughes2002 for details. The top distribution shows that the most likely position error boxes have sides $\delta\theta\lesssim 10\,\hbox{arcminutes}$, spreading out to $\delta\theta\gtrsim 3^\circ$. The distance distribution peaks at $\delta D_L/D_L \lesssim 1\%$, with most of the distribution confined to $\delta D_L/D_L\lesssim 5\%$.
• Figure 3: Pointing and distance error distributions for measurements at $z = 3$ of a binary of masses $m_1 = 10^5\,M_\odot$, $m_2 = 6\times10^5\,M_\odot$. The distribution for position error is so broad that we cannot really identify a "most likely" position error; however, most of the distribution lies at $\delta\theta\lesssim 10^\circ$. The distance distribution peaks at $\delta D_L/D_L \lesssim 10\%$, with most of the distribution confined to $\delta D_L/D_L\lesssim 30\%$.
• Figure 4: Distance errors for BBH measurements at $z = 1$ with $m_1 = 10^5\,M_\odot$, $m_2 = 6\times10^5\,M_\odot$, assuming that an electromagnetic counterpart allows precise sky position determination. The peak error is at $\delta D_L/D_L \sim 0.1\%$, and is almost entirely confined to $\delta D_L/D_L\lesssim 0.5\%$.
• Figure 5: Distance errors for BBH measurements at $z = 3$ with $m_1 = 10^5\,M_\odot$, $m_2 = 6\times10^5\,M_\odot$, assuming that an electromagnetic counterpart allows precise sky position determination. The peak error is at $\delta D_L/D_L \sim 0.5\%$, and is almost entirely confined to $\delta D_L/D_L\lesssim 2\%$.