How Much SETI Has Been Done? Finding Needles in the *n*-Dimensional Cosmic Haystack

The Fermi Paradox highlights the apparent contradiction between optimistic estimates of extraterrestrial intelligence (ETI) from the Drake Equation and the lack of observed evidence. A common interpretation of the paradox centers on the "Great Silence" or "Eerie Silence," suggesting a thorough search has yielded no results. This paper refutes this interpretation by quantitatively assessing the extent of SETI searches. The authors argue that the search effort to date is minuscule compared to the vastness of the search space, similar to searching a single glass of seawater for evidence of fish in the entire ocean. This analogy is extended into a more robust, mathematical model of the search space. The central research question is: How much of the potential search space for extraterrestrial radio signals has actually been explored? The study aims to quantify the incompleteness of SETI searches to date and provide a framework for evaluating future search efforts. This is important because the perceived lack of success of SETI has been used to argue against further investment in the field, or to suggest fundamental flaws in the assumptions underlying the search for ETI. Demonstrating the minuscule portion of the search space already explored strengthens the rationale for continued, and expanded, SETI efforts.

The paper reviews existing attempts to quantify SETI search efforts. Early work by Wolfe et al. (1981) and Papagiannis (1985) visualized the search space as a multi-dimensional "Cosmic Haystack," highlighting the challenge of finding rare signals. Tarter et al. (2010) used a nine-dimensional haystack analogy to emphasize the vastness of the search space and the small fraction explored. The paper also discusses various figures of merit proposed for comparing the efficiency of different SETI surveys. Drake et al. (1984) and Enriquez et al. (2017a) discussed challenges in creating a universally applicable metric due to differences in survey strategies and assumptions. The paper analyzes existing figures of merit, such as that of Drake et al. (1984), Dreher & Cullers (1997), and Enriquez et al. (2017a), highlighting their strengths and limitations in capturing the multidimensional nature of the search space. The paper notes the inherent difficulties in comparing search speeds across different surveys using these simpler metrics because of their different search methodologies and assumptions. These limitations highlight the need for a more comprehensive approach to measuring search completeness.

The core methodology involves developing a quantitative, eight-dimensional model of the radio SETI haystack. The eight dimensions considered are: sensitivity (to transmitted or received power), transmission central frequency, distance and position (three spatial dimensions), transmission bandwidth, time/repetition rate, polarization, and modulation. The authors define the boundaries of the haystack based on observable parameters and technological limitations. For instance, the upper limit on distance is set to 10 kpc, encompassing a significant portion of the Galaxy. The sensitivity dimension is defined using the equivalent isotropically radiated power (EIRP) of a hypothetical transmitter. The boundaries in this dimension are set by the minimum detectable EIRP. Transmission bandwidth is also incorporated, acknowledging that sensitivity decreases with increasing bandwidth. Time/repetition rate is considered, recognizing that searches for continuous signals differ from searches for pulsed signals. Polarization is simplified to a single parameter representing the fraction of polarizations that a given survey can detect. Lastly, modulation is treated as a complex catch-all dimension that accounts for various signal encoding schemes. The volume of this eight-dimensional haystack is calculated using an analytic integral, with details provided in the appendices. The authors apply this model to analyze several large radio SETI programs, including Breakthrough Listen, Project Phoenix, and surveys using the Murchison Widefield Array (MWA). For each program, relevant parameters like sensitivity, bandwidth, sky coverage, and observation time are plugged into the model to compute the fraction of the haystack searched. The calculations are presented in Table 1. A Python script is provided for calculating the haystack volumes for future searches, allowing for adaptations to different search parameters.

The primary finding is that the total fraction of the eight-dimensional radio SETI haystack explored to date is extremely small, estimated to be on the order of 6.0 × 10^-18. This signifies that the cumulative efforts of various large SETI programs have searched only a minuscule fraction of the potential search space. The authors use the analogy of searching a small volume of water (approximately 8000 liters) in the Earth's oceans to illustrate the scale of the unexplored search space. While the specific numbers are highly dependent on the choice of haystack boundaries, this quantitative analysis strongly supports the notion that our search for ETI is still in its early stages. Table 1 details the calculated haystack fractions for individual SETI programs. The analysis shows that, even with the different search strategies, the fraction of the eight-dimensional haystack searched remains incredibly small for the different surveys. The MWA surveys of Tingay et al. (2016, 2018) are identified as the largest surveys in terms of the haystack metric, highlighting the efficiency of wide-field surveys. The paper emphasizes the sensitivity of the results to the chosen haystack definition and boundaries, recognizing that focusing on a smaller, more specific portion of the search space (such as nearby stars) could yield much higher completeness.

The findings directly address the central question of how much of the SETI search space has been explored. The extremely small fraction of the haystack searched refutes the common misconception that SETI has already conducted a thorough search, demonstrating the premature nature of drawing conclusions about the absence of ETI based on current observations. The result highlights the need for continued and expanded SETI research, justifying further investment in larger and more comprehensive surveys that cover wider frequency ranges and larger portions of the sky. The study acknowledges that the definition of a "complete" survey is inherently subjective, as one can always search for rarer or more subtle signals. However, the order-of-magnitude estimates provided in the paper provide a valuable benchmark for future efforts and for evaluating the significance of future null results. The paper concludes that a large number of needles (detectable ETI signals) might be present in the haystack, and even a small fraction of the haystack searched could potentially uncover evidence of ETI, emphasizing the need for continued exploration.

This paper provides a quantitative framework for assessing the completeness of SETI searches, using an eight-dimensional model of the "Cosmic Haystack." The analysis demonstrates that a minuscule portion of the search space has been explored to date, challenging the notion that SETI has "failed." The authors provide a Python script to facilitate similar calculations for future surveys. Future research should focus on refining the haystack model, incorporating additional dimensions, improving the accuracy of sensitivity calculations, and applying the model to searches for technosignatures beyond radio signals.

The primary limitation is the sensitivity of the results to the chosen haystack definition and boundaries. Different choices of boundaries can significantly alter the calculated haystack volume and search fraction. The simplifying assumptions made in the calculations, such as uniform sensitivity across instrumental bandpasses and uniform sensitivity to narrow and broadband transmissions, might also slightly overestimate the fraction of the haystack searched. The model's treatment of modulation as a single, multifaceted dimension is another simplification. While the authors incorporate some elements of modulation, the complexity and diversity of potential signal modulations mean that some signals might not be detected even within the defined haystack. The model also assumes that any signal detected would be properly identified as an artificial signal, ignoring any misidentification issues. Finally, the paper focuses solely on radio SETI; the method needs adaptation for other technosignature searches. Despite these limitations, the order-of-magnitude estimates still convincingly highlight the incompleteness of current SETI searches.