Einstein Telescope: the triangle in a network and the impact of the relative orientation of detectors

Author(s)

Bruno, Giacomo, Oswald, Antonin, De Lillo, Federico

Abstract

The geometrical configuration of the Einstein Telescope (ET) gravitational-wave observatory is one the most important design choices to be made for this future scientific facility. Two baseline configurations are currently being considered, a single triangle or 2 distant L-shaped detectors tilted by about $45^{\circ}$. In this document we present a study of the scientific performance of the ET baseline configurations in both stand-alone mode and in the presence of either an L-shaped Cosmic Explorer detector with 40-km long arms located in the United States or the existing LIGO-Virgo-KAGRA network. We also include in the study an alternative ET configuration, which is currently not being considered and consists of a triangle plus a distant L-shaped detector. We find that in stand-alone mode this alternative configuration performs significantly better than the other two in both the compact binary coalescence and stochastic gravitational wave background scientific cases. The differences in performance between the ET configurations are reduced in the presence of the considered, additional non-ET detectors. We also show that the impact of possible correlated noise in co-located detectors on the stochastic gravitational-wave background performance can be addressed with the addition of extra detectors. Finally, we study the impact on the ET scientific performance of the relative orientation of the future detectors in the network. We find that, while the configurations that include a triangular ET detector are basically insensitive to this orientation, a balanced compromise for the ET configuration consisting of two L-shaped detectors could be represented by a tilt angle between the two detectors of about $30^{\circ}$.

Figures

Detector sensitivity curves adopted in this study and expressed as noise amplitude spectral density normalised to detector strain. The curves are presented for a single ET L-shaped detector with 10 km and 15 km long arms~\cite{COBASensRepository}, a CE L-shaped detector with 40 km long arms \cite{CESensRepository}, LIGO ``O5c''~\cite{ligo_projection}, Virgo ``O5 high-noise''~\cite{lvk_projection}, and KAGRA ``80 Mpc''~\cite{lvk_projection}.
Caption Detector sensitivity curves adopted in this study and expressed as noise amplitude spectral density normalised to detector strain. The curves are presented for a single ET L-shaped detector with 10 km and 15 km long arms~\cite{COBASensRepository}, a CE L-shaped detector with 40 km long arms \cite{CESensRepository}, LIGO ``O5c''~\cite{ligo_projection}, Virgo ``O5 high-noise''~\cite{lvk_projection}, and KAGRA ``80 Mpc''~\cite{lvk_projection}.
Cumulative number of BBH events detected per year as a function of SNR (top left plot) or parameter uncertainty (other plots) for the different ET configurations, with and without LVK or CE. The definition and calculation of the parameters as well as the generation and selection of the BBH events are discussed in the text.
Caption Cumulative number of BBH events detected per year as a function of SNR (top left plot) or parameter uncertainty (other plots) for the different ET configurations, with and without LVK or CE. The definition and calculation of the parameters as well as the generation and selection of the BBH events are discussed in the text.
Cumulative number of BNS events detected per year as a function of SNR (top left plot) or parameter uncertainty (other plots) for the different ET configurations, with and without LVK or CE. The definition and calculation of the parameters as well as the generation and selection of the BNS events are discussed in the text.
Caption Cumulative number of BNS events detected per year as a function of SNR (top left plot) or parameter uncertainty (other plots) for the different ET configurations, with and without LVK or CE. The definition and calculation of the parameters as well as the generation and selection of the BNS events are discussed in the text.
Cumulative number of BBH events detected per year as a function of SNR (top left plot) or parameter uncertainty (other plots) for various relative orientations of the two L-shaped detectors in the ET double-L configuration, with and without CE. The angle by which the L-shaped detector in Sardinia is rotated clockwise with respect to the one in the EMR region, which is in its default position, is indicated in the legend next to the label ``2L-''. The CE detector is rotated clockwise, starting from its default position, by the angle indicated in the legend next to the label ``CE-''. The definition and calculation of the parameters as well as the generation and selection of the BBH events are discussed in the text.
Caption Cumulative number of BBH events detected per year as a function of SNR (top left plot) or parameter uncertainty (other plots) for various relative orientations of the two L-shaped detectors in the ET double-L configuration, with and without CE. The angle by which the L-shaped detector in Sardinia is rotated clockwise with respect to the one in the EMR region, which is in its default position, is indicated in the legend next to the label ``2L-''. The CE detector is rotated clockwise, starting from its default position, by the angle indicated in the legend next to the label ``CE-''. The definition and calculation of the parameters as well as the generation and selection of the BBH events are discussed in the text.
Cumulative number of BNS events detected per year as a function of SNR (top left plot) or parameter uncertainty (other plots) for various relative orientations of the two L-shaped detectors in the ET double-L configuration, with and without CE. The angle by which the L-shaped detector in Sardinia is rotated clockwise with respect to the one in the EMR region, which is in its default position, is indicated in the legend next to the label ``2L-''. The CE detector is rotated clockwise, starting from its default position, by the angle indicated in the legend next to the label ``CE-''. The definition and calculation of the parameters as well as the generation and selection of the BNS events are discussed in the text.
Caption Cumulative number of BNS events detected per year as a function of SNR (top left plot) or parameter uncertainty (other plots) for various relative orientations of the two L-shaped detectors in the ET double-L configuration, with and without CE. The angle by which the L-shaped detector in Sardinia is rotated clockwise with respect to the one in the EMR region, which is in its default position, is indicated in the legend next to the label ``2L-''. The CE detector is rotated clockwise, starting from its default position, by the angle indicated in the legend next to the label ``CE-''. The definition and calculation of the parameters as well as the generation and selection of the BNS events are discussed in the text.
Cumulative number of BBH events detected per year as a function of SNR (top left plot) or parameter uncertainty (other plots) for various relative orientations of the L-shaped and triangular detectors in the 1T+1L ET configuration, with and without CE. The L-shaped detector in Sardinia is rotated clockwise, starting from the position where its x-arm (y-arm) points North-East (North-West), by the angle indicated in the legend next to the label ``1T+1L-''. The triangular detector in the EMR region is always in its default position. The CE detector is rotated clockwise, starting from its default position, by the angle indicated in the legend next to the label ``CE-''. The definition and calculation of the parameters as well as the generation and selection of the BBH events are discussed in the text.
Caption Cumulative number of BBH events detected per year as a function of SNR (top left plot) or parameter uncertainty (other plots) for various relative orientations of the L-shaped and triangular detectors in the 1T+1L ET configuration, with and without CE. The L-shaped detector in Sardinia is rotated clockwise, starting from the position where its x-arm (y-arm) points North-East (North-West), by the angle indicated in the legend next to the label ``1T+1L-''. The triangular detector in the EMR region is always in its default position. The CE detector is rotated clockwise, starting from its default position, by the angle indicated in the legend next to the label ``CE-''. The definition and calculation of the parameters as well as the generation and selection of the BBH events are discussed in the text.
Cumulative number of BNS events detected per year as a function of SNR (top left plot) or parameter uncertainty (other plots) for various relative orientations of the L-shaped and triangular detectors in the 1T+1L ET configuration, with and without CE. The L-shaped detector in Sardinia is rotated clockwise, starting from the position where its x-arm (y-arm) points North-East (North-West), by the angle indicated in the legend next to the label ``1T+1L-''. The triangular detector in the EMR region is always in its default position. The CE detector is rotated clockwise, starting from its default position, by the angle indicated in the legend next to the label ``CE-''. The definition and calculation of the parameters as well as the generation and selection of the BNS events are discussed in the text.
Caption Cumulative number of BNS events detected per year as a function of SNR (top left plot) or parameter uncertainty (other plots) for various relative orientations of the L-shaped and triangular detectors in the 1T+1L ET configuration, with and without CE. The L-shaped detector in Sardinia is rotated clockwise, starting from the position where its x-arm (y-arm) points North-East (North-West), by the angle indicated in the legend next to the label ``1T+1L-''. The triangular detector in the EMR region is always in its default position. The CE detector is rotated clockwise, starting from its default position, by the angle indicated in the legend next to the label ``CE-''. The definition and calculation of the parameters as well as the generation and selection of the BNS events are discussed in the text.
Left panel: PI curves, as defined in the text, for different configurations of an ET-only network, with or without the LVK detector network at design sensitivity. The angle between the two L-shaped detector is indicated after ``2L-'' in the legend. Maximum alignment for this option corresponds to $2.51^\circ$. The 1T+1L \textit{reduced} configuration only uses cross-correlation data from the three pairs of distant detectors, as discussed in the text. Right panel: PI curves for different ET configurations when including an additional CE detector in the network. The ``best'' (``worst'') labels correspond to the configurations providing the lowest (highest) minimum of the PI curve in Fig.~\ref{fig:PI_curve_min}.
Caption Left panel: PI curves, as defined in the text, for different configurations of an ET-only network, with or without the LVK detector network at design sensitivity. The angle between the two L-shaped detector is indicated after ``2L-'' in the legend. Maximum alignment for this option corresponds to $2.51^\circ$. The 1T+1L \textit{reduced} configuration only uses cross-correlation data from the three pairs of distant detectors, as discussed in the text. Right panel: PI curves for different ET configurations when including an additional CE detector in the network. The ``best'' (``worst'') labels correspond to the configurations providing the lowest (highest) minimum of the PI curve in Fig.~\ref{fig:PI_curve_min}.
Left panel: PI curves, as defined in the text, for different configurations of an ET-only network, with or without the LVK detector network at design sensitivity. The angle between the two L-shaped detector is indicated after ``2L-'' in the legend. Maximum alignment for this option corresponds to $2.51^\circ$. The 1T+1L \textit{reduced} configuration only uses cross-correlation data from the three pairs of distant detectors, as discussed in the text. Right panel: PI curves for different ET configurations when including an additional CE detector in the network. The ``best'' (``worst'') labels correspond to the configurations providing the lowest (highest) minimum of the PI curve in Fig.~\ref{fig:PI_curve_min}.
Caption Left panel: PI curves, as defined in the text, for different configurations of an ET-only network, with or without the LVK detector network at design sensitivity. The angle between the two L-shaped detector is indicated after ``2L-'' in the legend. Maximum alignment for this option corresponds to $2.51^\circ$. The 1T+1L \textit{reduced} configuration only uses cross-correlation data from the three pairs of distant detectors, as discussed in the text. Right panel: PI curves for different ET configurations when including an additional CE detector in the network. The ``best'' (``worst'') labels correspond to the configurations providing the lowest (highest) minimum of the PI curve in Fig.~\ref{fig:PI_curve_min}.
Minimum of PI sensitivity curve for different orientations of the ET and CE detectors. Top left panel: The ET L-shaped detector in the EMR region is kept fixed with the x-arm (y-arm) pointing the local East (North). The ET L-shaped detector in Sardinia and the CE in Idaho are rotated counterclockwise by angles $\alpha_{\rm ET_{S}}$ and $\alpha_{\rm CE}$, respectively, starting from the same local position as the ET L-shaped detector in the EMR region. The angles are in the $[0°, 90°]$ interval, with a spacing of $0.25°$. Top right panel: Same as in the top left panel, but with the ET L-shaped detector in EMR replaced by a triangle with a side parallel to the West-East local direction and the opposite vertex pointing North. Bottom panel: the three ET stand-alone ET configurations. Starting from the same initial positions defined above, the triangle for the 1T and the ET L-shaped detector in Sardinia, for the 2L and 1T+1L, are rotated clockwise by an angle $\alpha$. The blue star corresponds to the 2L configuration with an angle of $45^\circ$ between the two detectors.
Caption Minimum of PI sensitivity curve for different orientations of the ET and CE detectors. Top left panel: The ET L-shaped detector in the EMR region is kept fixed with the x-arm (y-arm) pointing the local East (North). The ET L-shaped detector in Sardinia and the CE in Idaho are rotated counterclockwise by angles $\alpha_{\rm ET_{S}}$ and $\alpha_{\rm CE}$, respectively, starting from the same local position as the ET L-shaped detector in the EMR region. The angles are in the $[0°, 90°]$ interval, with a spacing of $0.25°$. Top right panel: Same as in the top left panel, but with the ET L-shaped detector in EMR replaced by a triangle with a side parallel to the West-East local direction and the opposite vertex pointing North. Bottom panel: the three ET stand-alone ET configurations. Starting from the same initial positions defined above, the triangle for the 1T and the ET L-shaped detector in Sardinia, for the 2L and 1T+1L, are rotated clockwise by an angle $\alpha$. The blue star corresponds to the 2L configuration with an angle of $45^\circ$ between the two detectors.
Minimum of PI sensitivity curve for different orientations of the ET and CE detectors. Top left panel: The ET L-shaped detector in the EMR region is kept fixed with the x-arm (y-arm) pointing the local East (North). The ET L-shaped detector in Sardinia and the CE in Idaho are rotated counterclockwise by angles $\alpha_{\rm ET_{S}}$ and $\alpha_{\rm CE}$, respectively, starting from the same local position as the ET L-shaped detector in the EMR region. The angles are in the $[0°, 90°]$ interval, with a spacing of $0.25°$. Top right panel: Same as in the top left panel, but with the ET L-shaped detector in EMR replaced by a triangle with a side parallel to the West-East local direction and the opposite vertex pointing North. Bottom panel: the three ET stand-alone ET configurations. Starting from the same initial positions defined above, the triangle for the 1T and the ET L-shaped detector in Sardinia, for the 2L and 1T+1L, are rotated clockwise by an angle $\alpha$. The blue star corresponds to the 2L configuration with an angle of $45^\circ$ between the two detectors.
Caption Minimum of PI sensitivity curve for different orientations of the ET and CE detectors. Top left panel: The ET L-shaped detector in the EMR region is kept fixed with the x-arm (y-arm) pointing the local East (North). The ET L-shaped detector in Sardinia and the CE in Idaho are rotated counterclockwise by angles $\alpha_{\rm ET_{S}}$ and $\alpha_{\rm CE}$, respectively, starting from the same local position as the ET L-shaped detector in the EMR region. The angles are in the $[0°, 90°]$ interval, with a spacing of $0.25°$. Top right panel: Same as in the top left panel, but with the ET L-shaped detector in EMR replaced by a triangle with a side parallel to the West-East local direction and the opposite vertex pointing North. Bottom panel: the three ET stand-alone ET configurations. Starting from the same initial positions defined above, the triangle for the 1T and the ET L-shaped detector in Sardinia, for the 2L and 1T+1L, are rotated clockwise by an angle $\alpha$. The blue star corresponds to the 2L configuration with an angle of $45^\circ$ between the two detectors.
Minimum of PI sensitivity curve for different orientations of the ET and CE detectors. Top left panel: The ET L-shaped detector in the EMR region is kept fixed with the x-arm (y-arm) pointing the local East (North). The ET L-shaped detector in Sardinia and the CE in Idaho are rotated counterclockwise by angles $\alpha_{\rm ET_{S}}$ and $\alpha_{\rm CE}$, respectively, starting from the same local position as the ET L-shaped detector in the EMR region. The angles are in the $[0°, 90°]$ interval, with a spacing of $0.25°$. Top right panel: Same as in the top left panel, but with the ET L-shaped detector in EMR replaced by a triangle with a side parallel to the West-East local direction and the opposite vertex pointing North. Bottom panel: the three ET stand-alone ET configurations. Starting from the same initial positions defined above, the triangle for the 1T and the ET L-shaped detector in Sardinia, for the 2L and 1T+1L, are rotated clockwise by an angle $\alpha$. The blue star corresponds to the 2L configuration with an angle of $45^\circ$ between the two detectors.
Caption Minimum of PI sensitivity curve for different orientations of the ET and CE detectors. Top left panel: The ET L-shaped detector in the EMR region is kept fixed with the x-arm (y-arm) pointing the local East (North). The ET L-shaped detector in Sardinia and the CE in Idaho are rotated counterclockwise by angles $\alpha_{\rm ET_{S}}$ and $\alpha_{\rm CE}$, respectively, starting from the same local position as the ET L-shaped detector in the EMR region. The angles are in the $[0°, 90°]$ interval, with a spacing of $0.25°$. Top right panel: Same as in the top left panel, but with the ET L-shaped detector in EMR replaced by a triangle with a side parallel to the West-East local direction and the opposite vertex pointing North. Bottom panel: the three ET stand-alone ET configurations. Starting from the same initial positions defined above, the triangle for the 1T and the ET L-shaped detector in Sardinia, for the 2L and 1T+1L, are rotated clockwise by an angle $\alpha$. The blue star corresponds to the 2L configuration with an angle of $45^\circ$ between the two detectors.
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