The Breakthrough Listen Search for Intelligent Life: Technosignature Search of 97 Nearby Galaxies

All data analyzed in this work were collected using the GBT, a 100 meter telescope in West Virginia, USA, and operated by the Green Bank Observatory. The telescope is capable of observing at frequencies between 0.2 and 116 GHz, depending on the receiver selected. We collected data for this work using four receivers spanning from 1–11 GHz: the L-band receiver from 1.10–1.90 GHz; the S-band receiver from 1.80–2.70 GHz; the C-band receiver from 4.00–7.80 GHz; and the X-band receiver from 7.80–11.20 GHz. A user-selectable notch filter blocks the L band between 1.20 and 1.34 GHz, which is used by BL observations. A permanent notch filter blocks the S band between 2.3 and 2.36 GHz. Table 1 provides band information as well as the ${\mathrm{EIRP}}_{\min }$ per receiver, calculated with each receiver's system temperature and a signal-to-noise ratio (S/N) threshold of 33 (see Section 3.1).

Table 1. Survey Parameters

Receiver	Frequency	Cadences	Hits	Events	CWTFM a	EIRP${}_{\min }$	Transmitter
	(GHz)					(1024 W) b	Limit (%) c
L	1.10–1.90	100	2186151	288	3793	2.31	3.7
S	1.80–2.70	156	853434	250	2828	2.61	3.7
C	4.00–7.80	106	1418492	650	3059	3.1	3.7
X	7.80–11.20	97	1576236	331	3686	3.46	3.7
Total	1.10–11.20	459	6034313	1519	⋯	⋯	⋯

Notes.

^a Continuous Waveform Transmitter Figure of Merit (CWTFM) is a figure of merit that describes the likelihood to find a signal above the EIRP${}_{\min }$ for that receiver. ^b Minimum Equivalent Isotropic Radiated Power (EIRP${}_{\min }$) is a measure of the minimum necessary omnidirectional power of a transmitter at each receiver to be detected. ^c The transmitter limit is the maximum percentage of galaxies in each frequency range that possess a transmitter, given that we find no signals for 97 targets (trials). This figure is discussed further in Section 3.

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The BL nearby galaxy sample, detailed by Isaacson et al. (2017), consists of 123 targets. Our sample of 97 is made up of those targets from Isaacson et al. with declinations above −20°; targets below this decl. are observed by the BL program at Parkes. Together, they compose a morphological-type-complete set of the nearest ellipticals, dwarf spheroidals, irregulars, and spiral galaxies like our own. The sky positions of the targets are shown in Figure 1.

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Distances to the 97 galaxies in the GBT sample range from 60 kpc (the Ursa Minor Dwarf galaxy) to 29.2 Mpc (NGC 5813). Therefore, even though each target is observed with approximately uniform sensitivity, the minimum equivalent isotropic radiated power (EIRP) for a transmitter in NGC 5813 to be detectable by our observations is five orders of magnitude brighter than for a transmitter in the Ursa Minor Dwarf. A histogram of minimum EIRPs for the 97 galaxies in our sample is shown in Figure 2.

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The half-power beam width of the GBT receivers is a function of frequency; the L-band receiver covers a sky area almost 40 times larger than the X-band receiver. Of the 97 galaxies in our sample, 90 are small enough in angular extent that they are entirely covered within a single L-band pointing (see Figures 1 and 3). For the remaining galaxies, we observe a single central pointing, and some of the associated stars fall outside of the half-power beam width. In future we plan to tile the outer regions of some of these galaxies with further pointings (see Figure 4). A total of 6161 pointings are needed to completely cover all of the galaxies at X band, which includes 3029 pointings dedicated to M 31 alone (the most extended galaxy in our sample), making it impractical to cover in a reasonable amount of time using our standard observation procedure on the GBT.

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The great distances to other galaxies pose a formidable challenge for intergalactic communication. For an isotropic beacon to be detectable from another galaxy, it would need to be transmitted with power equivalent to the output of an entire star. Even a Kardashev Type II civilization, with technology capable of capturing sufficient power, would likely still face the physical limits of conventional dish antennas. Waste heat is an inevitable byproduct of any substantial broadcasting antenna, necessitating efficient heat dissipation mechanisms to prevent structural failure. The amount of waste heat that an ideal radiator of area A and temperature T can dissipate can be calculated using the Stefan–Boltzmann law:

$$\begin{eqnarray}&&{L}_{\mathrm{waste}}={\sigma }_{\mathrm{SB}}\cdot {T}^{4}\cdot A.\end{eqnarray} \tag{ 1 }$$

For an order-of-magnitude estimate, if we assume that about half the power is dissipated within the structure as waste heat (Bonsall et al. 2019), an antenna capable of transmitting 1 L_⊙ would require a radiator capable of dissipating an equivalent quantity of waste heat:

$$\begin{eqnarray}&&{L}_{\mathrm{waste}}=74.5\,\mathrm{TW}{\left(\frac{T}{6000\,{\rm{K}}}\right)}^{4}\left(\frac{A}{1\,{\mathrm{km}}^{2}}\right).\end{eqnarray} \tag{ 2 }$$

No currently known solid material can withstand temperatures of 6000 K, so such a radiator would have to be sufficiently large to radiate 1 L_⊙ without itself melting. Because present-day Earth electronics generally function at Earth temperatures or cooler, we can assume a radiator would have to cool the antenna to temperatures around 300K. The surface area of an ideal radiator capable of emitting an equivalent power to the Sun at a temperature of 300 K would then be:

$$\begin{eqnarray}&&{A}_{\mathrm{radiator}}=\displaystyle \frac{{L}_{\mathrm{waste}}}{74.5\,\mathrm{TW}{\left(\tfrac{300}{6000}\right)}^{4}}=8.23\times {10}^{17}\,{\mathrm{km}}^{2},\end{eqnarray} \tag{ 3 }$$

similar in size to the surface area of the Sun. While such a construction would require colossal expense and effort, a Kardashev Type II civilization would require a device of comparable or greater size to collect stellar power. For a Sun-like star and Earth-like electronics, a Dyson swarm would have to be approximately the size of a sphere of radius 1 au, and a civilization capable of constructing such a system would therefore likely be able to replicate the feat. However, any construction of significant scale could face gravitational instability.

A more feasible approach involves the construction of a vast array consisting of numerous smaller transmitters operating in concert. The accumulation of coordinated, phase-aligned, weaker signals from many less powerful beacons could also produce a sufficiently bright radio signal. In the case of a system powered by a Sun-like star, the collectors themselves could serve the triple purpose of energy collection, transmission, and heat dissipation. A beacon would then take the form of a complex of transmitters, with the scale of the array varying from planetary dimensions, if highly focused, to encompassing an entire solar system, if isotropically radiating. Arrays of highly beamed laser or microwave emitters have been proposed as means of interstellar propulsion (Parkin 2018), and some propulsion signatures may be detectable from interstellar distances (Lingam & Loeb 2017).

We have based our considerations on isotropically emitting, continuous beacons, but a beamed transmitter would require far less power to achieve an equivalent EIRP. By tightly focusing the beam, the equivalent isotropic radiated power (EIRP) of a given antenna can be significantly increased, harnessing the high gain of large dish antennas. A more targeted array reduces the power requirements considerably. To encompass the region within 10 kpc of the Galactic Center from a distance of 10 Mpc, the required beam coverage (Ω) would amount to approximately 3.14 × 10⁻⁶ sr or 37 square arcminutes. Should the transmitter solely target that portion of the sky, the equivalent isotropic radiated power (EIRP) would be 4 million times brighter than its actual luminosity. Then the actual transmitting power of the array is approximately 2.5 × 10⁻⁷ times that of an isotropic beacon, or 1.9 × 10²⁰ W. The corresponding radiator (again applying Equation (2)) necessary to keep the transmitter system operating would need to have a collective surface area of 4.11 × 10¹¹ km², several times the surface area of Jupiter but much smaller than that of the Sun. Still, even a system designed to illuminate the entire Milky Way, whether simultaneously or intermittently, would be much more affordable to construct, and would represent a significantly smaller fraction of a civilization's power budget. Gray & Mooley (2017) suggest that the Milky Way's status as the second largest in the Local Group could make it a prime target for ETI attempting to communicate, and provide a detailed treatment of some lower-power possibilities.

As in other BL searches, we focus on continuous, narrowband Doppler-drifting beacon signals. The turboSETI pipeline searches for linearly chirped signals in time-frequency spectra using an incoherent Taylor "tree deDoppler" algorithm as described by Siemion et al. (2013). The tree summation method is computationally advantageous and allows fast analysis of large data volumes, but, as it is an incoherent method, the detection efficiency for complex or high-drift signals is influenced by the time-frequency resolution of the data products. Signals with drift rates higher than the "unit drift rate," defined as ${\dot{\nu }}_{\mathrm{unit}}=\tfrac{{\rm{\Delta }}f}{{\rm{\Delta }}t}$, where Δf is the fine-frequency-channel bandwidth and Δt is the length of a single time integration, will smear across multiple frequency channels in the same time integration, resulting in a reduced intensity in the Doppler-corrected integrated spectrum. For the BL fine-frequency-resolution data products, ${\dot{\nu }}_{\mathrm{unit}}\sim 0.153$ Hz s⁻¹.

Recent work has detailed resolution-dependent limitations of the turboSETI algorithm. Margot et al. (2021) conducted a signal injection and recovery analysis quantifying turboSETI performance in noise-free constant-power synthetic spectra, confirming that turboSETI reaches peak efficiency at drift rates $\dot{\nu }\leqslant {\dot{\nu }}_{\mathrm{unit}}$, and decreases as 1/N with increasing drift rate, where N is the number of frequency channels a drifting signal spreads in Δt. Modifications to our search algorithms to compensate for these effects are ongoing. To inform these efforts, we conducted signal injection and recovery tests to investigate turboSETI's performance in real data as a function of signal intensity and drift rate and its response to detailed simulated technosignatures.

3.1.1. Signal Generation and Injection

3.1.2. Coarse Channel Response and Noise Calculations

We first measured the pipeline's efficiency at detecting signals at or near the S/N value, ρ_tseti, specified by the user when running turboSETI, which revealed discrepancies between injected and recovered signal-to-noise ratios. The disagreement on S/N value between turboSETI and setigen arises because of the different methods of noise calculation utilized by the two software packages, as well as bias in injection and noise calculation stages due to the coarse channel response.

The roll-off in sensitivity due to the coarse channelization process is well known, but its impact on turboSETI noise calculation has not been fully appreciated. Figure 5 shows a histogram of counts across a coarse channel, which displays a bimodal profile. One peak corresponds to the data distribution in the channel plateau, while the lower-intensity peak corresponds to the data distribution of the coarse channel roll-off. After summing the spectrogram along the time axis with no dedrifting (integrating across a full observation), the overlap of the two distributions creates a long low-intensity "tail," while the Gaussian representing the data distribution in the channel plateau narrows. turboSETI version 2.3.2 searches a coarse channel at a time and calculates the S/N of a signal by time-summing the data array, discarding the dimmest and brightest 5% of pixels, and then calculating the median and standard deviation directly from the remaining distribution using numpy (Harris et al. 2020) methods. In contrast, setigen applies a sigma-clipping function, which iterates five times at a 3σ level to remove outliers and arrive at a single-mode noise mean. Figure 6 shows the application of each method to one low-RFI coarse channel, with trimmed data overlaid on the untrimmed histogram. The 5% method discards only a small fraction of the tail, as well as a portion of samples within 1σ of the mean of the remaining data, whereas the sigma-clipping approach eliminates most if not all of the tail and returns a mean centered on the higher noise peak and a significantly smaller standard deviation. The factor of difference in the standard deviations produced by the two methods varies according to the noise and RFI present in a given frame, but for 1280 coarse channels across a full X-band observing bandwidth from 7500 to 11250 MHz has a mode of 3.25.

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When full coarse channels are used for injection, the overlap of the data distributions in the dynamic spectra causes an initial overestimation of the standard deviation, which results in an S/N greater than requested in setigen frames. setigen calculates the intensity of a signal for injection by multiplying a requested S/N by the standard deviation of the full 2D array, then dividing by ${N}_{t}^{1/2}$ to counteract the corresponding reduction in background noise and increase in variance of the data set when N_t time integrations are summed. Because of the overlap of the peaks in Figure 5, the sigma-clipping process overestimates the standard deviation in the nonintegrated data (see Figure 7). As the noise of the full array is used for signal injection, this results in injected signals with greater power than intended. When the final spectrogram is time-summed, the sigma-clipping process then correctly calculates the standard deviation of the distribution, and the result is an inflated S/N after normalization.

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3.1.3. Spectral Leakage

To observe systematic turboSETI behavior in regions of sparse or dim RFI, we selected the fine-frequency spectrum of a single node (N_coarse = 64) from an X-band observation of UGCA 127 taken on 2021 July 16. Because of reduced RFI density at higher frequencies, turboSETI detected no signals above a ρ_tseti = 10 threshold preinjection. All signals returned could therefore be clearly identified as resulting from the injection process. We ran several injection tests at high constant S/N and a drift rate of 0 Hz s⁻¹ to investigate the frequency dependence of signal injection and assess noise floor levels. We selected central frequencies uniformly spaced across the coarse channel bandwidth in even numbers to avoid interference from the central DC (direct current) spike, injecting 10 signals per coarse channel for a total of 640 injected signals. Again, signals were injected with a sinc²(f) frequency profile to simulate the effects of our pipeline's FFT and reproduce the subsequent fine channelization response.

Small variations in recovered power did occur across the bandwidth because of nonuniform noise, but two more significant effects led to the loss of injected signal power. First, turboSETI version 2.3.2 does not search for 0 drift rate signals; signals inserted with a drift rate of 0 are instead reported with the smallest drift rate turboSETI searches. The first dedrifting iteration shifts the bottom half of the spectrum by one pixel and results in a factor of two reduction for signals contained within a single frequency bin. Second, the fine channelization process of our data products leads to a variation in recovered intensity at the fine-frequency scale. In our data, the fine channel response is defined by a sinc²(f) distribution around the central frequency of the signal. The detected intensity of a nondrifting signal will therefore be attenuated depending on its central frequency with respect to channel edges and the bandwidth of the signal, as

$$\begin{eqnarray}&&{I}_{d}=I\cdot {\mathrm{sinc}}^{2}\left(\displaystyle \frac{| \delta f| }{{\rm{\Delta }}f}\right),\end{eqnarray} \tag{ 5 }$$

where I is the total power of the signal, δ f is the frequency offset of the signal's central frequency from the central frequency of the nearest fine channel, Δf is the frequency resolution, and I_d is the power that results in data.

For a linearly drifting signal, power is spread continuously across frequencies, and the apparent recorded intensity becomes an integral of the response across the range of frequencies that a signal occupies during a time integration. Figure 8 details the power reduction experienced by a signal with intensity both constant in time and bandpass profile that occurs as a result of the sinc(f)² response in spectral data, depending on whether the signal is centered on a fine channel or its edge. Figure 9 displays the integrated power recovered as a function of offset and the interaction of offset with signal bandwidth. As we have no a priori knowledge of the power with which a signal is sent, understanding these effects and how they present in the power recorded in our data will allow us to more accurately determine the characteristics of a signal and its transmitter in the event of a successful detection, as well as to place more accurate constraints on transmitter populations in the event that no technosignatures are detected.

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3.1.4. Doppler Smearing

To confirm and quantify turboSETI's behavior in real data as a function of drift rate, we again selected 10 uniformly spaced central frequencies across each coarse channel bandwidth, aligned with fine channel central frequencies to avoid offset attenuation, for a total of 640 signals. We chose an S/N value of 1000 to capture any sensitivity loss, and varied drift rates across a range of ±5 Hz s⁻¹, wider than our search range, to further test turboSETI performance with signals that are outside the user-inputted bounds. Signals were injected with a frequency profile bandwidth of ∼5.6 Hz, equivalent to the width of two fine channels. The setigen Doppler_smearing routine reproduces the effect of Doppler smearing by averaging a given number of copies of a signal between t and t + 1, spaced evenly between center frequencies. The resulting "dechirping loss" causes attenuation of a signal proportional to its drift, spreading the total power of the signal across adjacent frequency bins in a given integration.

The results of this experiment are shown in Figure 10. Powers are normalized as described in subsection 3.1.2. We find that 100% of injected signals were recovered with greatly attenuated S/N at high drift rates, reproducing the expected detection efficiency loss as a function of drift rate. We note that, for a signal that is sufficiently smeared, turboSETI recovers signals with real drift rates greater than its search bounds with inaccurate drift rates and central frequencies. Provided that the power of the signal is sufficient to overcome its attenuation as a result of drift or frequency offset, turboSETI successfully recovers narrowband, constant-power signals, including those with drift rates outside its drift bounds. Though we search only a small fraction of drift rate parameter space, this effect demonstrates that the turboSETI pipeline is capable of detecting some hits outside its bounds.

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3.1.5. Limitations and Countermeasures

We ran turboSETI on 459 cadences, finding a total of 6,034,313 hits and 1519 events across the four observing bands, distributed as shown in Table 1. The hit and event frequency distributions are shown in Figure 11. Histograms of the hit distribution as functions of drift rate and S/N are shown in the right and left columns of Figure 12. Although L-band observations accounted for only 21.7% of the sample, the largest share of hits were found in the L band, at 36.2%. The C and X bands had similar numbers of hits, at 23.5% and 26.1%, respectively, followed by the S band at 14.1%. Though the S band comprised the largest proportion of cadences and has a historically cluttered RFI environment (see Figure 13), S-band observations contributed the least fraction of both hits and events, with 16.5% of the total events. The largest fraction of events (42.8%) was recorded at the C band, double that at the X band (21.8%) and L band (19.0%). For all bands, the number of hits falls with S/N, though peaks appear at higher S/Ns, which likely indicate populations of RFI transmitters that are either nearby to the telescope or intrinsically bright. While the statistics in Table 1 do not include any zero-drift hits, a strong peak still appears at drift rates near zero, as turboSETI still can recover a signal with bandwidth sufficiently greater than a single fine channel if the intensity is nonuniform.

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If we assume that all the hits found by turboSETI are from human-created RFI, the spectral occupancy can be used to assess the quality of the data as a function of frequency. We compute spectral occupancy as the fraction of observations that contain at least one hit in a given 1 MHz-wide frequency bin. This quantity is calculated using a large ensemble of observations from the BL back end at GBT beginning in 2016, all of which have been passed through turboSETI. A bin with a spectral occupancy of one means that every observation recorded has at least one hit (and in many cases more than one hit) in that range, and a spectral occupancy of zero would mean that no observation recorded a hit in that range.

The targets used for the spectral occupancy analysis include some of the observations of the galaxy sample presented in Section 1.2, but also archival observations of other targets in order to obtain more precise spectral occupancy statistics. The observations cover the L, S, C, and X bands, with 2368, 5017, 3818, and 7863 observations, respectively. Each file corresponds to a single 5-minute observation spanning the band's observing frequency range as defined in Table 1. The full-sky spectral occupancy plots for the L, S, C, and X bands are shown in Figure 13. These plots are similar to plots of received power as a function of frequency that are often used to determine how badly observations may be affected by RFI, but are subtly different given that we are using many observations to calculate the fraction of observations in which signals are detected as a function of frequency.

The observation data were grouped by various parameters to qualitatively search for patterns in the hit counts, including grouping by telescope altitude and azimuth and the local time of observation at the GBT. The most apparent differences appeared when splitting the azimuth angle into northern and southern halves of the sky. The southern sky exhibited higher hit counts in the C-band frequency ranges of 4000–4200 MHz, caused by the top of the C-band geostationary satellite downlink range (see Figure 14), and X-band frequency ranges of 8100–8300 MHz and 10,700–11,200 MHz (see Figure 15). In all three cases, the increased hit counts appear in bands with known satellite transmissions, given in Table 2.

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Intermittent RFI can lead to false positive events when it appears, by random chance, in three consecutive "on" observations and is absent in the intervening "off" observations. To estimate how often this occurs as a function of frequency, we bootstrapped the individual observations used in the Transiting Exoplanet Survey Satellite  target search of Traas et al. (2021), and reran FindEvent to create artificial events. This was done by randomly selecting six files (three on and three off targets) without replacement. In general, the observation cadence is now ABCDEF, instead of the usual ABACAD, and unlike for the standard ABACAD cadences, the targets were not necessarily observed consecutively in time. The list of files is then passed into turboSETI's find event pipeline with modified timestamps to appear as if the files all came from a single observation cadence. As we do not expect a technosignature candidate to be made up of hits coming from different positions in the sky at different times, we can be confident that any events found are false positives because of intermittent RFI. We performed 100,000 random draws for each observing band. Additionally, the event occupancy was also calculated. The process for calculating the event occupancy is identical to that of spectral occupancy, with the key difference being that only events are counted, as opposed to all hits detected during an observation. The histogram showing the event distributions can be found in Figure 16 and the event occupancy in Figure 17. It can be seen that C and X bands had the fewest events resulting from chance, with 1033 and 216 events in 100,000 simulated observations. L and S bands had a much higher number of events: 407,636 and 32,547, respectively.

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The frequency of chance events at L and S band is higher than what is predicted by Equation (6)–37% of observations record an event in the 1626 MHz bin and 8.8% of observations record an event in the 2595 MHz bin. These can be attributed to the high density of radio transmissions at these frequencies, which is smoothed over during the spectral occupancy calculation. The spectral occupancy calculation treats any number of hits greater than zero exactly the same, whether there is one narrowband signal in the bin or many narrowband signals packed densely, as seen in the examples shown in Figures 21 and 22 (Appendix D). With the higher number of hits per bin, the detection of a higher number of events can be expected, resulting in an increased event occupancy.

The spectral occupancy gives us the probability of observing a hit in a given frequency bin. Thus for an event in an ABACAD cadence, we multiply the probability of observing a hit in the "on" targets with the probability of not observing a hit in the "off" targets. We find that the probability of an event is given by

$$\begin{eqnarray}&&{P}_{\mathrm{event}}{(o{(f))=o(f)}^{3}(1-o(f))}^{3}\end{eqnarray} \tag{ 6 }$$

where o(f) is the spectral occupancy for a given frequency bin. As a result, we find that we are most likely to find events at frequencies with a spectral occupancy of 50%, at which a predicted maximum of 1.56% of observations yield events at that frequency. As the spectral occupancy moves away from 50%, the likelihood of an event decreases, with events being least likely at frequencies with spectral occupancies near 100% or 0%.

With the prevalence of RFI and the frequency with which it gets flagged as a potential extraterrestrial technosignature (Enriquez et al. 2017; Price et al. 2020; Traas et al. 2021; Franz et al. 2022), we want a way to tell us which events to inspect first. Equation (6) allows us to use the spectral occupancy to quantify the likelihood of detecting an event, but given the number of events that are detected, it would be useful to have a way to quantify which events should be looked at first. One method is to look at the events that are least likely to occur, specifically at frequencies that have a low spectral occupancy. This can be achieved by adding a bias term to Equation (6) to give a higher weight to frequencies with low spectral occupancy and a lower weight to those with higher spectral occupancy. Here we divide Equation (6) by a cubic bias term, resulting in

$$\begin{eqnarray}&&{P}_{\mathrm{weighted}}{(o(f))=(1-o(f))}^{3}\end{eqnarray} \tag{ 7 }$$

where o(f) is the spectral occupancy for a given frequency bin. This can be interpreted as the uniqueness of the candidate based on the likelihood of a signal not appearing in the "off" observations. For example, an event appearing in a frequency bin with a spectral occupancy of zero would be weighted as most interesting, while an event appearing in a bin with a spectral occupancy of one would be weighted as least interesting.

With the qualitative difference in the hit distributions based on position in the sky such as those seen in Figures 14 and 15, we divided the sky into three altitude bins and four azimuthal bins, corresponding to widths of 30° and 90°, respectively, and calculated the spectral occupancy for each region independently. This has the advantage of grouping hits that are nearby on the sky, increasing their influence on the ranking of nearby events and reducing their impact on events in a different region. These grouped spectral occupancies have been applied to the 1519 events detected in the nearby galaxy survey. The distribution of events can be seen plotted against frequency and their ranking under Equation (7) in Figure 18.

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The large and complex parameter space of SETI searches makes it difficult to quantify the comprehensiveness of a study. Efforts to examine the rigor of large surveys with respect to certain parameters or subsets of parameters have resulted in the development of various "figures of merit." Here, we calculate the most widely used figures of merit, comment on their caveats, and provide values from other similar surveys to facilitate comparison.

The Drake Figure of Merit (DFM; Drake et al. 1984) is a well-known metric that endeavors to allow comparisons of physical survey characteristics. It is given by

$$\begin{eqnarray}&&\mathrm{DFM}=\displaystyle \frac{n\,{\rm{\Delta }}{\nu }_{\mathrm{tot}}\,{\rm{\Omega }}}{{F}_{\min }^{3/2}},\end{eqnarray} \tag{ 8 }$$

where n is the number of sky pointings, Δν_tot is the total observing bandwidth, Ω is the FWHM of the receiver, and ${F}_{\min }$ is the minimum detectable flux density. As the DFM depends on antenna characteristics, it must be calculated separately for different receivers; surveys using multiple detectors may compute a combined figure as the sum of the DFM at each. All else being equal, larger figures indicate more comprehensive surveys. For our survey, we found the DFM to be ∼1.71 × 10³² for signals with drift rates ≤ 0.16 Hz s⁻¹, and ∼1.46 × 10³⁰ for the highest drift rates we searched.

The DFM is a useful heuristic for comparing the breadth of searches in frequency and geometric space, but as discussed by Price et al. (2020) and Margot et al. (2021), its focus on sky coverage and minimum detectable flux density neglects potential nuances of ETI transmitter distributions and stellar density as well as other dimensions of survey sensitivity. Enriquez et al. (2017) define one approach to an improved heuristic: the Continuous Waveform Transmitter Rate Figure of Merit (CWTFM), defined as

$$\begin{eqnarray}&&\mathrm{CWTFM}={\zeta }_{\mathrm{AO}}\,\displaystyle \frac{{\mathrm{EIRP}}_{\min }}{{N}_{\mathrm{stars}}\,{\nu }_{\mathrm{rel}}}\end{eqnarray} \tag{ 9 }$$

where ν_rel is the fractional bandwidth, N_stars is the number of pointings times the number of stars per pointing, and the ${\mathrm{EIRP}}_{\min }$ is the minimum detectable EIRP in units of Watts. ζ_AO is a normalization constant such that the CWTFM is 1 for an EIRP equal to that of Arecibo. ${{EIRP}}_{\min }$ depends on the distance to the target as well as the minimum detectable flux density, and denotes the power requirements on a putative transmitter located in the most distant source in our sample.

Figure 19 shows the EIRP plotted against the transmitter rate (defined as 1/N_stars ν_rel) alongside values from other surveys for comparison. Figures of merit were calculated using only unique pointings, that is, counting each galaxy once. Estimates (see Table 5, Appendix B) for the number of stars observed (to determine the transmitter rate) were derived from K-band luminosities collated by Isaacson et al. (2017), assuming the average mass of a star is 1M_⊙, and calculating the percentage of each galaxy covered by a GBT pointing at each band assuming a uniform stellar density across the galaxy's area. Technosignature searches are compromises between sensitivity (higher sensitivity toward the left-hand side of the figure) and sky and bandwidth coverage (more stars, and/or wider fractional bandwidth coverage, toward the bottom of the figure).

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Given our lack of a technosignature detection, we can calculate the transmitter limit, or the maximum percentage of nearby galaxies that possess a transmitter detectable with our system and search parameters. Price et al. (2020) and Traas et al. (2021) calculate this limit using a one-sided 95% Poisson confidence interval with a 50% probability of actually observing a signal if the transmitter is present (Gehrels 1986), interpreted as a 97% Poisson confidence interval. Calculated in the same manner for comparison, using the tables of Gehrels (1986), we find an upper limit of 3.8% at all four bands. However, we offer an alternative method for determining upper limits on transmitter rates that we believe to be more faithful to a frequentist interpretation. For a Poissonian model, the cumulative distribution function gives the probability of detecting N_d = n events or fewer, assuming some underlying model is true. To find the upper limit on the transmitting fraction ${{\rm{f}}}_{{tr}}$, we must exclude all models such that

$$\begin{eqnarray}&&\mathrm{CDF}(n;{{\rm{f}}}_{{tr}})\leqslant 1-p\end{eqnarray} \tag{ 10 }$$

where p is the desired confidence level.

For our analysis, we choose a one-sided 95% confidence interval, corresponding to a p value of 0.95. Because we detected n = 0 events, Equation (10) gives an N_d value of 3 for a Poisson distribution (Gehrels 1986). We count each galaxy once for a total of 97 targets, so the maximum fraction of galaxies in our sample that could possess a transmitter of sufficient power is ${f}_{{tr}}=3/97\,=\,3.1 \%$. With the caveats discussed in Sections 3 and 4, we report that a lack of a successful detection at any of 97 distinct targets results in an upper limit of 3.09% of targets at all four bands (L, S, C, X), for narrowband, 100% duty cycle transmitters with equivalent isotropic radiated power on the order of 10²⁴ Watts.

Radio emission phenomena traveling significant distances in intergalactic and interstellar space are necessarily subject to the effects of scattering and the fluctuating density of free electrons along their paths. Scattering can produce a number of observable phenomena, but most significant to a narrowband search are spectral broadening, which can spread signal power across adjacent frequency bins, and intensity scintillations, which can help or hinder detection on characteristic timescales. In the interstellar medium (ISM), the degree of broadening and the timescale of scattering modulations are both dependent on line of sight (LOS) relative to the Galactic plane, distance traversed toward the Galactic Center (GC), and total amount of scattering material along the LOS. Though some of our LOS cut close to the Galactic plane, the GC lies below the cutoff for our GBT sample (−20° decl.). However, our search targets the centers of nearby galaxies, and therefore a signal would have to pass through the densest portion of the host galaxy's ISM for us to detect it. Still, even in the worst-case scenario of ∼1 Hz scatter broadening for the Milky Way (Cordes & Lazio 1991), tests show turboSETI successfully detects signals with the correct modulation and sufficient brightness. Therefore, scatter broadening can still be neglected for our purposes.

The greater obstacle to a narrowband microwave SETI search is intermittency. Cordes & Lazio (1991) demonstrate that scintillation due to the ISM can modulate a signal above the detection threshold or attenuate it below. The scintillated intensities follow an exponential distribution such that the signal is attenuated most of the time. Scintillation occurs on longer timescales farther from, and for shorter paths through, the Galactic plane. Taking observations many characteristic timescales apart can lead to nonrepeatability of signal detections if amplitude modulations are significant enough, but the likelihood of detection for a strongly scattered signal can be increased by taking many repeated observations of the same location, separated by periods of time longer than a characteristic scintillation timescale (Cordes et al. 1997). Work is ongoing to better understand the impact of scintillation on narrowband radio SETI surveys and develop strategies for the detection of scintillating signals (Brzycki et al. 2023). SETI surveys of the GC have applied the method of repeated observations (Gajjar et al. 2021), but the observing overhead and storage requirements for this sample prevented its application to our survey. Nevertheless, we do have repeat data for a number of targets in our sample.

Because our search deals with nearby galaxies, the intergalactic medium (IGM) and the ISMs of other galaxies also contribute to scattering in our sample. Intergalactic scattering has been comparatively less studied; studies of extragalactic phenomena such as pulsars and fast radio bursts consider the effects of the ISM of the host galaxy as well as passage through intervening galaxies (Ocker et al. 2022). As our sample consists of only the nearest galaxies and the beam of the GBT is sufficiently narrow, we avoid the problem of overlapping galaxies, but we note the possibility of further modulation and a shortening of the scintillation timescale as a result of scattering in the ISM of the host galaxy and the IGM between us and each galaxy.