%why does this not propagate from the top section to here???



The current observing plan for LIGO--Virgo--KAGRA has O5 running through the third quarter of 2029 (see \cref{schedule} and also \cite{observingDoc}). 
In 2021, the LSC organized a study group to explore and evaluate upgrades to the LIGO detectors that could be implemented after O5, and the science that could be achieved with more sensitive instruments. This `Post-O5 Study Group' issued its report\cite{T2200287}) in late 2022, and in January 2023 the LSC Council endorsed the recommendations of the report.
 

The Post-O5 report recommends a set of detector improvements\,---\,collectively known as \Asharp{}\,---\,that would produce close to a factor of 2 improved strain sensitivity over the A+ design target across the whole frequency band.
With a nominal period of 2 years for installation and commissioning, the \Asharp{} detectors would begin observing around the end of 2031, and may operate primarily in observing mode for several years.

At low frequencies (below \qty{50}{\Hz}), the improved sensitivity arises from larger test masses, upgraded test mass suspensions, and improved seismic isolation. At high frequencies (above \qty{300}{\Hz}), the strain noise reduction comes from reducing quantum noise through increased squeezing levels and higher laser power (with accompanying improvements in thermal compensation and parametric instability suppression). 
These would also decrease quantum noise at mid-frequencies (\qtyrange{50}{300}{\Hz}), but the overall strain noise reduction would be minimal without also reducing coating thermal noise, which dominates in this band. The \Asharp{} scenario thus also includes test mass coatings that have a factor of ${\sim}2$ reduction in thermal noise beyond the A+ target; better thermal noise is necessitated by strain sensitivity limitations imposed by the 4~km arm lengths of the current generation detectors. This is likely the technically riskiest aspect of \Asharp{}.

% If this or some other aspect of the \Asharp{} technology cannot be realized, then a similar strain sensitivity improvement could be pursued through the so-called ``Voyager'' technology of cryogenic silicon mirrors and \qty{2}{\um} lasers, although this technology is not as mature as the A$^\sharp$ technology and implementation would have a greater cost and downtime impact.

These broadband improvements in strain sensitivity will boost detection rates of compact binaries over those for the A+ design by factors of ${\sim}$5 and ${\sim}$2.9 for binary neutron star (BNS) and binary black hole (BBH) mergers, respectively. We would expect of order 1000 detections per year for both types of mergers with \Asharp{}. Catalogs of this size will enable detailed analyses of the astrophysical populations that can trace out mass and spin distributions with much improved accuracy.
Additionally, the loudest few signals from this population will be detected with high fidelity, enabling precision tests of compact binary dynamics and their gravitational-wave emission.
%Some of these tests which are unlikely with A+ will become more secure with \Asharp{}.
As an example, several classes of tests rely on the detection of gravitational waves in multipoles beyond the dominant $(\ell,\lvert{m}\rvert) = (2,2)$ modes.
Given LIGO's and Virgo's current estimates of the rate of binary black hole mergers, the detection of other multipoles, such as $(2,1)$ or $(3,3)$, is a risky prospect even with LIGO operating at A+ sensitivity in a network with Virgo at its O5 sensitivity.
However, as shown in \cref{fig:hom snr}, LIGO upgrades such as \Asharp{} will provide enough sensitivity enhancement to detect these weaker multipoles about once per year or better, taking an amplitude signal-to-noise ratio~$\ge$~6 as a detection threshold for each of these modes~\cite{T2200287}.

\begin{figure}[t]
    \centering
    \includegraphics[width=\textwidth]{figures/hom_snr.pdf}
    \caption{An example science target for LIGO upgrades beyond 2029: the detection of gravitational wave emission beyond the dominant $(\ell,\lvert{m}\rvert) = (2,2)$ multipoles.
    %Here, a population of mergers with total signal-to-noise ratio ${} \ge 12$ is considered.
    %
    LIGO A+ with Virgo will detect $\mathcal{O}(1000)$ binary black hole mergers annually with signal-to-noise ratio~$\ge$~12 overall, but only a small fraction of those\,---\,less than one per year\,---\,will have signal-to-noise ratio~$\ge$~6 in multipoles such as $(2,1)$ or $(3,3)$.
    Upgrades to LIGO, such as \Asharp{} or Voyager, will boost this fraction so that the detection of these other multipoles becomes a more secure observational target.
    (From P.~Schmidt, adapted from the Post-O5 Study Group Report~\cite[\S7.3]{T2200287}).
    %\edh{I took this from Patricia's presentation, which is based on the post-O5 report. We should check that this won't be duplicated in the LSC submission, and if possible ask Patricia if she can regenerate this plot. Done - ML, EH}
    \label{fig:hom snr}}
\end{figure}

The improved low frequency sensitivity would bring additional science benefits. For example, the lead time for early-warning BNS alerts would more than double compared to the A+ design, enabling detection of signals six minutes or more before merger. An important caveat making comparisons in this band must contend with the large discrepancy that historically and currently exists between actual interferometer performance and the design noise spectrum at very low frequencies: the LIGO interferometers are currently about an order of magnitude above their design strain noise at \qtyrange{10}{20}{\Hz}. \Asharp{}'s heavier test masses and improved suspensions and seismic isolation will be critical to reducing this performance gap and finally achieving design sensitivity at low frequencies. 

The sensitivity improvement at higher frequencies (above \qty{300}{\Hz}) will provide insights into neutron star physics. Higher SNR in the merger phase of a BNS coalescence detected by \Asharp{} would improve the precision measurements of neutron star tidal deformability by almost a factor of 2 over A+. Studying the post-merger phase would provide valuable information about the equation of state of hot, dense nuclear matter. The post-merger signal lies above \qty{1000}{\Hz}, and the sensitivity at these frequencies could be further improved by operating the interferometers in a wideband configuration\footnote[3]{This would be achieved by using a more highly reflective signal recycling mirror, an optic which is relatively easy to change.}, which would reduce the strain noise at several kiloHertz by a further factor of ${\sim}2$, while sacrificing some sensitivity at mid-frequencies. 
Current estimates are that a BNS post-merger signal with such a wideband \Asharp{} configuration could be detected at a signal-to-noise ratio of up to 5.6 at a luminosity distance of \qty{100}{Mpc}~\cite{T2200287}; this compares to a maximum SNR of 2 for A+, or 2.6 with A+ in a similar wideband configuration.

\section{LIGO as a Technology Pathfinder for the Next Generation of Detectors}
%\Lazz{Someone created this section as part of the \Asharp{} section...??? It does not appear in the main.tex file. I think this and the next section could be combined. Happy to do that if folks agree.}

In addition to delivering the science outcomes described in the previous section, the \Asharp{} upgrade is a significant step towards developing the detector technologies needed for CE. Both \Asharp{} and CE are based on the current LIGO interferometer design: a dual-recycled Michelson interferometer with Fabry--Perot arm cavities and frequency-dependent squeezing, \qty{1}{\um} laser light, and fused silica test masses operating at room temperature. The \Asharp{} upgrade pushes several of the key technologies beyond the A+ levels: higher laser power and more squeezing; heavier test masses and improved suspensions; and seismic isolation. Cosmic Explorer starts from these technical advances\,--\,and a further increase in test mass size\,--\,and lengthens the arms by an order of magnitude. 
% The one area where the overlap between \Asharp{} and CE technology requirements is less is in low-noise test mass coatings: 
%the CE design is based on the coating thermal noise level targeted for A+ (scaled for CE's larger beam size). But the overlap is not zero: while the A+ level of coating thermal noise would be adequate for the CE \qty{40}{\km} interferometer, lower noise coatings would be beneficial for the \qty{20}{\km} interferometer.
%dhs proposed rewording:
%the CE design is based on the coating thermal noise level targeted for A+ (scaled for CE's larger beam size), not the more demanding \Asharp{} design (required by the shorter 4~km arm length). On the other hand, while the A+ level of coating thermal noise would be adequate for the CE 40~km interferometer, lower noise coatings would improve sensitivity in the band of frequencies where the detector is most sensitive; this is especially so for the shorter 20~km interferometer.
The improvements in coatings planned for \Asharp{} could also be beneficial for the CE 20~km interferometer, although the great arm length relaxes the requirements on coating thermal noise significantly. The 40~km CE interferometer could use A+ coatings. The larger coating surface of the CE optics will require a separate development effort.