Madeline Cross-Parkin is a first year PhD student at the University of Queensland working on cosmological parameter estimation using gravitational waves. Outside of research, she loves playing the piano, going to classical music concerts, and running.
Title:Impact of weak lensing on bright standard siren analyses
Authors: Charlie T. Mpetha, Giuseppe Congedo, Andy Taylor, Martin A. Hendry
First Author’s Institution: Institute for Astronomy, School of Physics and Astronomy, University of Edinburgh
Status: Published to Physical Review D (2 July 2024) [open access]
Gravitational waves are ripples in spacetime caused by massive accelerating bodies, first predicted by Albert Einstein in 1916 as a consequence of his general theory of relativity. Nearly a century later, on September 14th, 2015, scientists detected these waves for the first time. This faint signal, created by the merger of two black holes, was captured by the Laser Interferometer Gravitational Wave Observatory (LIGO). LIGO operates with two detectors located in Louisiana and Washington State, which work in tandem to measure the tiny ripples in space-time caused by the mergers of stellar-mass black holes and neutron stars.Today, there are four gravitational wave observatories spread around the globe, with plans in the works for a network of third generation (3G) ground-based detectors. These Earth-based detectors are sensitive to high-frequency waves produced by relatively small compact objects like stellar-mass black holes and neutron stars. However, their sensitivity range limits them from detecting gravitational waves from supermassive black hole (SMBH) binaries, which are thought to reside at the centre of nearly every galaxy.
To bridge this gap, the European Space Agency (ESA) has begun developing the Laser Interferometer Space Antenna (LISA), a space-based gravitational wave observatory specifically designed to detect the low-frequency waves emitted by SMBHs.
As gravitational waves move through space, they ride a cosmic roller coaster of over- and under-densities. Over-densities are regions in the Universe where the matter density can be several times higher than the average, often hosting structures like galaxy clusters. In contrast, under-densities, such as voids, are areas where the density falls to less than one-tenth of the average density of the Universe. When gravitational waves pass through dense regions, their paths bend slightly, altering the signal we detect (this signal, known as a strain, is shown in Figure 1). This effect is known as weak gravitational lensing and makes the signal appear slightly stronger (magnified) or weaker (de-magnified) than it would without lensing.
Figure 1: Diagram illustrating the gravitational wave strain (signal) produced as two compact objects in a binary system merge. [Credit: Cervantes-Cota 2016]
Why is this an issue?
A unique feature of gravitational waves is that they act as absolute distance indicators, sometimes called ‘standard sirens’. This means that we can determine the distance to the gravitational wave event just from the signal itself–a remarkable feature, since measuring cosmic distances is one of the biggest challenges in cosmology. However, if the signal is magnified or de-magnified by weak lensing, our calculated distance will be off. This can become a problem when we use gravitational waves in cosmology, especially in measuring parameters like the expansion rate of the Universe, the Hubble constant (H0). This paper investigates the impact of weak lensing on our estimates of H0 from gravitational wave signals.
The Hubble tension and gravitational waves
Before getting into the details of what this paper explored, why is measuring the Hubble constant so important to cosmologists? One of the most significant issues in cosmology today is the Hubble tension; the disagreement in the value of H0 measured using early Universe probes (like the cosmic microwave background radiation) versus the measurements found using late Universe probes (such as galaxy distances measurements). Despite both methods achieving precision below 2%, their results differ at the 5-sigma level. This level of tension corresponds to only a 1 in 3.5 million probability of arising by random chance.
Gravitational waves provide a promising new method for measuring the Hubble constant by using the distance information encoded directly in the wave signal. Currently, the number of gravitational-wave detections is too low to produce a precise H0 measurement. However, as the number of detections grows, the uncertainty in the gravitational-wave-based H0 measurement will decrease, potentially offering new insights into the Hubble tension.
Overview of the paper
Due to the sensitivity limits of existing detectors, none of the gravitational wave events observed to date have been significantly affected by lensing. However, as gravitational waves travel across greater distances, the effect of lensing becomes more pronounced. Events that occur further away have to travel through more “clumpy” regions in space, meaning that there is an increased likelihood that the gravitational wave will be lensed. The authors explored the potential impact of lensing in future gravitational wave observations with both the upcoming 3G network of ground-based detectors and the space-based LISA, both of which will be detecting events from much further away. Their aim was to evaluate the probability that lensing would introduce a bias in measured cosmological parameters, such as H0.
To achieve this, the authors generated a population of supermassive black hole mergers (which could be detected by LISA), as well as neutron star mergers (which would be observable by the future 3G ground-based network). For each simulated merger, the authors duplicated the signal and applied a random magnification or de-magnification to the duplicate, simulating the effects of weak lensing. This allowed them to model the same population of gravitational wave events both with and without lensing distortions. For both the lensed and unlensed populations, the researchers calculated the expected value of the Hubble constant.
The researchers repeated the process or 300 trials, recalculating H0 for both the lensed and unlensed populations in each trial. Finally, they averaged the Hubble constant values across all trials and compared the lensed and unlensed measurements to identify any potential bias.
Key findings
This study shows that the more sensitive 3G ground-based detectors will detect neutron star mergers that have experienced lensing effects. Specifically, the authors find that for neutron star merger events weak lensing could introduce a small bias of ΔH0=-0.1 km s-1 Mpc-1. This means if the true value of the Hubble constant is H0=70 km s-1 Mpc-1, weak lensing would shift the measured value slightly to H0=69.9 km s-1 Mpc-1. This bias is minimal and would not have a significant impact on the Hubble tension, as the discrepancy between the Hubble constant measurements fuelling the tension is much larger, at approximately 5 km s-1 Mpc-1.
For supermassive black hole binaries, however, the authors find a much larger spread of potential biases: ΔH0=±5 km s-1 Mpc-1. This means that depending on the gravitational wave’s path and the amount of matter it encounters, the observed value of H0 could be shifted up or down by as much as 5 km s-1 Mpc-1. Such a significant bias would definitely affect the Hubble tension. Fortunately, with LISA’s launch planned for 2035 there is still time to improve our weak gravitational lensing models, which will enable us to better account for these effects on gravitational wave measurements of H0 and other cosmological parameters.
Astrobite edited by Lindsey Gordon
Featured image credit: Cervantes-Cota 2016