Radio sirens: inferring $H_0$ with binary black holes and neutral hydrogen in the era of the Einstein Telescope and the SKA Observatory

Author(s)

Dupletsa, Ulyana, Mastrogiovanni, Simone, Spinelli, Marta, Ronconi, Tommaso, Schulz, Matteo, Murgia, Riccardo, Harms, Jan, Baker, Tessa, Calabrese, Matteo, Carbone, Carmelita, Cunnington, Steven, Harrison, Ian, Leyde, Konstantin, Nanadoumgar-Lacroze, Dounia

Abstract

A new synergy between gravitational waves (GWs) and the study of the large-scale structure of the Universe is now emerging. Along this line of research, we combine simulated observations of stellar-origin black hole mergers and neutral hydrogen 21 cm line intensity mapping to probe the expansion rate of the Universe through the distance-redshift relation. GW signals from binary black holes provide direct distance information, while neutral hydrogen intensity maps offer a tomographic view of the large-scale structure of the Universe. Using the 3-dimensional density fields of hydrogen as a redshift prior for GW events, we explore a novel dark-sirens-like approach, here termed radio sirens, to measure the late-time expansion history of the Universe. We study the performance of the next-generation GW observatories, such as the Einstein Telescope, to ensure enough statistics and access to high-redshift data. On the other hand, future spectroscopic intensity mapping surveys with the SKA-Mid telescope are expected to trace the underlying dark matter distribution at large scales up to redshift $z\sim 3$. This combined methodology allows us to constrain the Hubble constant to $\sim 8\%$ precision, using around 3,000 GW events with signal-to-noise ratios greater than 150. This corresponds to an improvement of around $90\%$ compared to not considering the information from the neutral hydrogen maps.

Figures

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Horizon plots (\textit{in magenta}) for the \ac{et} observations compared to the \ac{skao} reach in redshift. The horizon represents the maximum redshift for \ac{cbc} equal-mass and optimally oriented \ac{gw} sources observed with a threshold \ac{snr}. Here we compare the standard SNR = 8 threshold (\textit{dashed line}), with the one we use throughout this work, i.e. SNR = 150 (\textit{solid line}). On the \textit{x-axis} is the total source-frame mass of the binary, while on \textit{y-axis} is the redshift of the merger. We used the triangular configuration for \ac{et} with the full cryogenic sensitivity curve available \href{https://apps.et-gw.eu/tds/?r=18213}{here}. The \ac{skao} redshift ranges are highlighted horizontally in \textit{purple}: there are the two bands of SKA-Mid, band 2 ($950-1760$\,MHz) and band 1 ($350-1050$\,MHz), and the high-redshift SKA-Low band ($50-350$\,MHz). The intersection region of the two SKA-Mid bands is marked with two different hatches. In this work, we focus on both bands of SKA-Mid.

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Sky maps of the \hi\ density contrast and simulated \ac{gw} event distributions at two representative redshifts. \textit{Top panels}: Mollweide projections of the \hi\ density contrast at $z\simeq 0.04$ (left) and $z\simeq 0.2$ (right). The yellow boxes indicate the sky region shown in the zoomed-in panels below. Color bars denote the amplitude of the density contrast. \textit{Bottom panels}: Zoom-in of the boxed regions, comparing clustered \ac{gw} events (left subpanels), which trace the underlying \hi\ distribution, with isotropically distributed \ac{gw} events (right subpanels). We increased the number of \ac{gw} sources to 10k per map and the resolution of the map (using \texttt{nside}=128) for visualization purposes. While at low $z$ the difference between clustered and isotropically distributed \ac{gw} events is more pronounced, this distinction progressively diminishes at higher redshifts, where the two distributions become increasingly similar, according to the variation of the \ac{dm} density contrast as shown in Fig.~\ref{fig:los_profile}.

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Sky maps of the \hi\ density contrast and simulated \ac{gw} event distributions at two representative redshifts. \textit{Top panels}: Mollweide projections of the \hi\ density contrast at $z\simeq 0.04$ (left) and $z\simeq 0.2$ (right). The yellow boxes indicate the sky region shown in the zoomed-in panels below. Color bars denote the amplitude of the density contrast. \textit{Bottom panels}: Zoom-in of the boxed regions, comparing clustered \ac{gw} events (left subpanels), which trace the underlying \hi\ distribution, with isotropically distributed \ac{gw} events (right subpanels). We increased the number of \ac{gw} sources to 10k per map and the resolution of the map (using \texttt{nside}=128) for visualization purposes. While at low $z$ the difference between clustered and isotropically distributed \ac{gw} events is more pronounced, this distinction progressively diminishes at higher redshifts, where the two distributions become increasingly similar, according to the variation of the \ac{dm} density contrast as shown in Fig.~\ref{fig:los_profile}.

Caption

Sky maps of the \hi\ density contrast and simulated \ac{gw} event distributions at two representative redshifts. \textit{Top panels}: Mollweide projections of the \hi\ density contrast at $z\simeq 0.04$ (left) and $z\simeq 0.2$ (right). The yellow boxes indicate the sky region shown in the zoomed-in panels below. Color bars denote the amplitude of the density contrast. \textit{Bottom panels}: Zoom-in of the boxed regions, comparing clustered \ac{gw} events (left subpanels), which trace the underlying \hi\ distribution, with isotropically distributed \ac{gw} events (right subpanels). We increased the number of \ac{gw} sources to 10k per map and the resolution of the map (using \texttt{nside}=128) for visualization purposes. While at low $z$ the difference between clustered and isotropically distributed \ac{gw} events is more pronounced, this distinction progressively diminishes at higher redshifts, where the two distributions become increasingly similar, according to the variation of the \ac{dm} density contrast as shown in Fig.~\ref{fig:los_profile}.

Caption

Sky maps of the \hi\ density contrast and simulated \ac{gw} event distributions at two representative redshifts. \textit{Top panels}: Mollweide projections of the \hi\ density contrast at $z\simeq 0.04$ (left) and $z\simeq 0.2$ (right). The yellow boxes indicate the sky region shown in the zoomed-in panels below. Color bars denote the amplitude of the density contrast. \textit{Bottom panels}: Zoom-in of the boxed regions, comparing clustered \ac{gw} events (left subpanels), which trace the underlying \hi\ distribution, with isotropically distributed \ac{gw} events (right subpanels). We increased the number of \ac{gw} sources to 10k per map and the resolution of the map (using \texttt{nside}=128) for visualization purposes. While at low $z$ the difference between clustered and isotropically distributed \ac{gw} events is more pronounced, this distinction progressively diminishes at higher redshifts, where the two distributions become increasingly similar, according to the variation of the \ac{dm} density contrast as shown in Fig.~\ref{fig:los_profile}.

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Distribution of $\rho_{\rm BH} / \bar{\rho}_{\rm BH}$ along three different lines of sight identified by their right ascension RA and declination Dec (specified in the legend). The variation is more pronounced at low redshift and becomes increasingly uniform toward higher redshift, approaching homogeneity by $z\sim 3$, the maximum redshift covered by the \hi\ maps. The apparent flattening at low redshift is a binning artifact: the input redshift grid is sparse at low $z$.

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Corner plot showing the marginalized posterior distributions and the $1\sigma$ and $2\sigma$ 2D confidence regions for the cosmological and rate parameters $H_0$, $\Omega_{m,0}$, $\gamma$, $\kappa$, and $z_p$, inferred from clustered \ac{gw} events. The dark purple contours correspond to the analysis including \hi\ information (Clustered GWs - \hi), while the light purple contours show the case without \hi\ information (Clustered GWs - No \hi). The injected fiducial values are indicated by magenta lines. The panels on the diagonal display the one-dimensional marginalized posteriors, with quoted median values and 68\% credible intervals, highlighting the improvement in parameter constraints when \hi\ data are included.

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Posterior probability distributions for $H_0$ inferred from both clustered (Clustered GWs) and isotropically distributed (Isotropic GWs) \ac{gw} events under two scenarios: with \hi\ information included (\hi\,) and without \hi\ information (No \hi\,). The vertical line indicates the injected value of $H_0$.

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Results for the headline results with Clustered GWs - \hi\ including the two parameters entering the bias parametrization: $b_{\rm GW}$ and $\alpha_{\rm GW}$. The injected fiducial values are indicated with magenta lines.

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\Ac{los} evolution of the \ac{bh} mass density contrast, $\rho_{\rm BH}/\bar{\rho}_{\rm BH}$, as a function of redshift for a fixed sky direction (RA = $150^\circ$, Dec = $30^\circ$), under different assumptions for the \ac{gw} bias parameters. The baseline case ($b_{\rm GW} = 1$, $\alpha_{\rm GW} = 0$) corresponds to \ac{gw} sources tracing the underlying matter field without additional redshift dependence. Increasing the bias amplitude ($b_{\rm GW} = 2$) enhances the contrast of overdense and underdense regions, while introducing a redshift-dependent bias ($\alpha_{\rm GW} = 2$) further amplifies fluctuations at higher redshift.

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Posterior predictive constraints on $H(z)/(1+z)$ as a function of redshift $z$. The shaded bands show the $68\%$ (darker shade) and $95\%$ (lighter shade) credible intervals for Clustered GWs - \hi\, (in \textit{purple}) and for Clustered GWs - No \hi\, (in \textit{pink}). The solid magenta line indicates the injected cosmological model. For comparison, the black lines represent the prior predictive distribution ($68\%$--$95\%$ credible intervals).

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Posterior probability distributions for $H_0$ inferred from isotropically distributed (Isotropic GWs) \ac{gw} events under two with \hi\ information included (\hi\ ) at the analysis stage. We show the results with perfectly measured \acp{gw} and including \ac{pe} errors. The vertical line indicates the injected value of $H_0$.

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Posterior probability distributions for $H_0$ inferred from clustered \ac{gw} events with \hi\ information included, under different \ac{gw} events distribution realizations. The vertical line indicates the injected value of $H_0$.

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Luminosity distance versus sky localization area for the $\sim 3100$ detected \ac{gw} events in the clustered \acp{gw} case. Each point represents a detected event, plotted as a function of luminosity distance (bottom axis) and corresponding redshift (top axis). The vertical axis shows the 90\% credible sky localization area, $\Delta \Omega_{90\%}$, in deg$^2$. Horizontal lines indicate the pixel area of the map ($\sim 13$\,deg$^2$) and multiples thereof (10\,$\times$ and 100\,$\times$) for reference. The plot illustrates the general trend of increasing localization uncertainty with distance (and redshift).

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Posterior probability distributions for $H_0$ inferred from clustered \ac{gw} events with \hi\ information included (\hi\ ), under two different numerical stability checks: $N_{\rm eff, PE}$ and $N_{\rm eff, inj}$. The vertical line indicates the injected (true) value of $H_0$.