Optical Flashes from Beam-Driven Light Sails with the Roman, Rubin and Euclid Observatories

Introduction

Travel time between habitable worlds by chemical rocket is long, $\sim8$–$9$ months one way for an Earth–Mars Hohmann transfer and $\sim2$ yr for the round trip once the wait for the return window is included, and the rocket equation exacts an exponential penalty in propellant mass for every increment in speed. Beam-driven light sails leave the propellant at home, with the achievable speed set by the sail area, the thermal tolerance of its material, and the power of the driving array [2, 3, 4, 32]. The required beam powers are large, terawatts for tonne-class payloads at $1$ gee ($9.8\,{\rm m\,s^{-2}}$), so the leakage of radiation past the sail is a technosignature with a well-posed physical model. In [1], hereafter GL15, we constructed that model for a microwave array conducting Earth–Mars transits, and found that the optimal frequency for a $1.5$ km aperture lies near $68$ GHz, producing transients of a few Jansky at $100$ pc lasting tens of seconds. Beams that would drive a relativistic interstellar sail have been proposed as a source of fast radio bursts [14]: the observer sits in the main beam of a planet-scale emitter, and the optimal frequency is a few GHz. That geometry is the beam itself, not the leak, and it remains a radio search.

The same matching that sets the beam frequency also sets a Fresnel-matched array diameter, and at optical wavelengths that aperture collapses from kilometers to tens of meters. The cost analysis of [3], which GL15 [1] adopted and which favored microwaves, reflected high-power microwave sources in the early 2010s. Directed-energy concepts for gram-scale to tonne-scale sails have since been developed at optical wavelengths [4, 5, 32, 6, 9], and that is the branch being prototyped on Earth [7, 8]. A civilization may well land in the optical or near-infrared because source economics no longer favor microwaves, in which case radio searches are looking in the wrong band. The same shrinkage raises the intensity at the aperture by the inverse area, and we find in § 2.2 that power handling, not Fresnel matching, is the binding constraint on the optical branch: two envelopes, $10$ km and $40$ km, bracket published emitter loadings.

Three survey facilities now cover that window. The Nancy Grace Roman Space Telescope [23, 24, 27] was launched on 2026 August 30 and is in cruise to L2 plus commissioning, with first images expected in early 2027. The Vera C. Rubin Observatory [22] began the ten-year Legacy Survey of Space and Time (LSST) on 2026 June 30. Euclid is midway through a $1.4\times10^{4}$ deg$^{2}$ survey [28, 29]; Quick Releases Q1 (2025 March) and Q2 (2026 June 24) are public, with DR1-Foundation scheduled for 2026 November. Between them these facilities cover the wavelength band of $0.3$–$2.3\,\mu{\rm m}$ and will accumulate $\sim5\times10^{14}$ star-seconds of monitoring. They have been discussed as technosignature platforms in general terms [20, 21, 19], but the specific transient of GL15 [1] has not been mapped onto them: the signal they can catch is not a directed optical-maser beam [12], not a nanosecond pulse [13], and not a narrow spectral line [17, 18], but a tens-of-seconds, spatially unresolved, single-band flash at the position of a star. The all-sky optical SETI experiment PANOSETI searches $0.35$–$1.65\,\mu{\rm m}$ at nanosecond to second cadence with a plate scale of $0.36$ deg per pixel [15]; that experiment is built for a collimated pulse, not for a tens-of-seconds PSF-shaped brightening of a star.

In § 2 we generalize the design relations of GL15 [1] to arbitrary wavelength, show that a Fresnel-matched optical aperture cannot radiate $1.5$ TW, and take the leak from two focused arrays as the signal we search for: $10$ km at $\sim20\,{\rm kW\,m^{-2}}$ and $40$ km at the published $10^{3}\,{\rm W\,m^{-2}}$ loading. § 3 describes the observable event. § 4 assesses detection prospects with the Roman, Rubin and Euclid observatories, § 5 treats backgrounds, and § 6 concludes.

Optical and near-infrared beamers

Design relations

We adopt the design relations of GL15 [1] and allow the wavelength $\lambda$ to be a free parameter. A sail accelerated by an array of diameter $D_{\rm A}$ remains in the array’s Fresnel zone, where the beam energy is delivered through a constant cross-section rather than a constant solid angle, out to the Fresnel length $d_{\rm F}=D_{\rm A}^{2}/\lambda$. The kinematic burnout distance is $d_{\rm b}=v_{\rm max}^{2}/(2a_{\rm max})$. Efficiency demands that an unfocused burn end at the Fresnel length, since beyond $d_{\rm F}$ the wasted fraction grows rapidly, and the matching condition is $d_{\rm F}=d_{\rm b}$, which fixes

which is Equation (1) of GL15 [1] solved for $D_{\rm A}$ at fixed $\lambda$ rather than for $\lambda$ at fixed $D_{\rm A}$. A focused array can end the burn at $d_{\rm b}$ deep in the near field, with $d_{\rm F}>d_{\rm b}$. Writing $\lambda_{1.06}\equiv\lambda/1.06\,\mu{\rm m}$, $v_{400}\equiv v_{\rm max}/400\,{\rm km\,s^{-1}}$ and $a_{1}\equiv a_{\rm max}/1\,{\rm gee}$, and fixing $v_{\rm max}$, $a_{\rm max}$ and $\lambda$ to those fiducials we find

Figure 1a shows that relation across twelve decades in wavelength. The $68$ GHz, $1.5$ km design of GL15 [1] lies on the $v_{\rm max}=100\,{\rm km\,s^{-1}}$ locus; the same mission executed at $1\,\mu{\rm m}$ needs a $23$ m aperture. Two horizontal lines mark the envelopes we adopt in § 2.2: $10$ km at $\sim20\,{\rm kW\,m^{-2}}$, and $40$ km, where the emitters sit near the published $10^{3}\,{\rm W\,m^{-2}}$ loading. This suggests that $20$–$100$ m optical apertures, within reach of existing terrestrial engineering as collecting areas, are the Fresnel-matched counterparts of the GL15 [1] microwave array, but that they cannot radiate $1.5$ TW.

The beam power required to drive a perfectly reflecting sail is $P_{\rm A}=m_{\rm s}a_{\rm max}c/2$, i.e. $1.5$ TW for a tonne at $1$ gee, unchanged from GL15 [1] and roughly $10$% of worldwide primary energy consumption. The diffraction scale of that aperture is

At the fiducials that is $2.9$ mas, and the corresponding beam solid angle is $\Omega_{\rm A}=\pi\theta_{\rm A}^{2}$. With the GL15 [1] ratio $D_{\rm s}\simeq5D_{\rm A}$ the sail covers the beam core at burnout.

The $93$ m aperture that Fresnel matching requires must still radiate $1.5$ TW, so the intensity leaving the aperture is $P_{\rm A}/A_{\rm A}=2.2\times10^{8}\,{\rm W\,m^{-2}}$, five orders above published directed-energy loadings, a level that greatly exceeds the physical capabilities of any known optical beam design.

Four ways out of that loading present themselves: (i) Oversizing the aperture until $I_{\rm A}$ is tolerable puts $d_{\rm F}$ beyond an Earth–Mars burnout, so the sail stays in the near field, where an unfocused beam is a tube of width $D_{\rm A}\gg D_{\rm s}$ and the sail intercepts only $(D_{\rm s}/D_{\rm A})^{2}$. (ii) Lowering $a_{\rm max}$ until $I_{\rm A}\sim10^{3}\,{\rm W\,m^{-2}}$ requires $a_{\rm max}\sim2\times10^{-3}$ gee, pushes $D_{\rm A}$ back to $2$ km and $d_{\rm F}$ to $25$ AU, and again leaves a planetary transfer inside the near field. (iii) Sparse fill runs the wrong way. At fixed $P_{\rm A}$ and fixed envelope $D_{\rm A}$, reducing the fill factor $\phi$ shrinks the emitting area to $\phi A_{\rm A}$ and raises the intensity on the emitters to $I_{\rm A}/\phi$, which at $\phi=10^{-5}$ is $2\times10^{13}\,{\rm W\,m^{-2}}$, ten orders of magnitude above the [43] value rather than comparable to it. (iv) Holding the emitters at $10^{3}\,{\rm W\,m^{-2}}$ instead demands $1.5\times10^{9}\,{\rm m^{2}}$ of emitting area, and at $\phi=10^{-5}$ an envelope of $1.4\times10^{4}$ km, for which $d_{\rm F}=D_{\rm A}^{2}/\lambda$ is $10^{9}$ AU and the sail never leaves the near field.

Changing the fill does not put that unfocused tube onto the sail. What remains is to spread $P_{\rm A}$ over the area the loading demands and to apply phase curvature, so that the tube focuses on the sail instead of illuminating a volume around it.

The physical solution: a beam-formed emitter

The intensity problem is an area problem. [3] costed the reusable launcher as source plus aperture, $C_{C}=aA+c_{P}P$, and minimized that capital at fixed sail speed by cutting the beam when the far-field spot first exceeded the sail; at the minimum the two terms are equal, so $A=(c_{P}/a)P$. Two things in the focused optical machine break that algebra. (i) The mission power is pinned at $P_{\rm A}=1.5$ TW by a tonne at a gee, independent of $\lambda$ and $D_{\rm A}$. (ii) Focusing puts the sail in the near field of a large envelope, so that envelope can still fill the sail at $0.055$ AU. What remains of $C_{C}=aA+c_{P}P$ at fixed power is an envelope that shrinks until something else sets the size; there is no interior cost minimum. The stop we adopt is emitter loading. A free-flying orbital array, or an array laid on an airless surface such as the Moon, has no atmosphere and so no thermal blooming. We adopt $\sim20\,{\rm kW\,m^{-2}}$ as the loading the emitters themselves will bear, and at $1.5$ TW that is $D_{\rm A}\simeq10$ km ($I_{\rm A}=19\,{\rm kW\,m^{-2}}$), twenty times the published directed-energy loading. We use the same scale, without a separate blooming calculation, for an Earth-like ground site. The published loading of [43, 4] is a benchmark, $I_{\rm A}=10^{3}\,{\rm W\,m^{-2}}$, not a Benford output; holding the emitters there requires $D_{\rm A}=44$ km. We adopt $40$ km ($I_{\rm A}=1.2\,{\rm kW\,m^{-2}}$). The optical coefficients of [32] ($a=500$–$10^{4}\,{\rm \$\,m^{-2}}$, $c_{P}=0.01$–$1\,{\rm \$\,W^{-1}}$) span $c_{P}/a$ from $10^{-6}$ to $2\times10^{-3}$, i.e. $D_{\rm A}=1.4$–$62$ km if one still wrote $A=(c_{P}/a)P_{\rm A}$. We treat $10$ km and $40$ km as two emitter-loading choices that bracket the plausible range, the first near the emitters’ thermal limit and the second aperture-heavy, at $1.2\,{\rm kW\,m^{-2}}$.

An unfocused beam of either diameter is a $10$ km or $40$ km tube, and the sail intercepts only $(D_{\rm s}/D_{\rm A})^{2}$ of it, far short of what $1$ gee requires. This suggests building that envelope as a phased array: $N$ small emitters (tiles) laid on a regular lattice of pitch $p$ (the distance between tiles), each able to take an independent delay. A uniform extra delay of one tile, a piston of physical length $\sigma_{z}$, is a phase $\sigma_{\phi}=2\pi\sigma_{z}/\lambda$ on that tile alone. A linear gradient of those phases across the aperture steers the interference peak; a quadratic curvature, the thin-lens phase of focal length $d$, focuses it, concentrating the tube onto the sail and shaping it to a $D_{\rm s}$-diameter flat-top. We take $D_{\rm s}$ from the sail’s thermal tolerance: spreading $1.5$ TW over $8.7\times10^{6}\,{\rm W\,m^{-2}}$ at absorptivity $\alpha=10^{-4}$ (§ 2.4) gives $D_{\rm s}=465$ m and $T\simeq300$ K, coincidentally $5D_{\rm A}$ of the Fresnel-matched $93$ m aperture. An unshaped diffraction-limited focus at $d_{\rm b}$ would instead put $1.5$ TW into an Airy core of first-null radius $1.22\lambda d_{\rm b}/D_{\rm A}$, $26$ cm at $40$ km and $1.1$ m at $10$ km, at $7\times10^{12}\,{\rm W\,m^{-2}}$ and $4\times10^{11}\,{\rm W\,m^{-2}}$ respectively, which no sail survives. In that unshaped geometry the sail edge sits $880$ spot radii out at $40$ km and $220$ at $10$ km, and the missed fraction is $f_{\rm miss}=1.9\times10^{-4}$ ($7.5\times10^{-4}$). That Airy tail is a floor on core spill, not the lock of Table tab:surveys: a synthesized flat-top has edge spill set by the achievable roll-off. The survey halo is set by piston statistics, not by that core.

The far field of a tiled array is the product of two diffraction patterns, the array factor (the interference of the $N$ tiles treated as points, an interference peak whose width is set by the full envelope, $\lambda/D_{\rm A}$) and the element pattern (what one tile radiates by itself, $\theta_{\rm el}=1.22\lambda/p$, set by the tile size and independent of how the tiles are phased). A regular lattice also produces grating lobes, extra copies of the array-factor peak at multiples of $\lambda/p$, the Fourier comb of the grid. Locked phases put the central peak on the sail. Uncorrelated piston does not steer that peak: it reduces the fraction of power that remains in the locked core, the Strehl $S=e^{-\sigma_{\phi}^{2}}$, exact for Gaussian phase statistics rather than the Maréchal approximation, and dumps the residual $1-S$ into the element pattern, a halo of width $\theta_{\rm el}$. The element pattern is an envelope: the array factor can redistribute power within it but cannot synthesize a footprint wider than $\theta_{\rm el}$. Covering a $D_{\rm s}$ sail therefore requires $1.22\lambda d_{\rm b}/p\gtrsim D_{\rm s}/2$, i.e. $p\lesssim45$ m at the fiducials. We adopt $p=40$ m, a round pitch just inside that coverage limit. Relative to the $45.4$ m intercept match, encircled energy and $f_{\rm leak}$ barely move, while $\theta_{\rm el}$ and the umbra in units of $\theta_{\rm el}$ do. Violate it and the footprint shrinks below the sail: $N=100$ on the $40$ km envelope is $p\simeq3.5$ km ($0.89$ km on $10$ km) and a $\sim3$ m spot at burnout, $\sim2\times10^{11}\,{\rm W\,m^{-2}}$, four orders above the $8.7\times10^{6}\,{\rm W\,m^{-2}}$ flat-top and two above the dust-seeded hot-spot failure of [11]. The sail does not survive. Tiles individually steered, or laid on a curved surface so that different tiles illuminate different parts of the sail, would beat the envelope only by giving up coherent gain; we do not take that architecture. Smaller pitches leak more at the same lock and at fixed $D_{\rm s}$, so the $\lambda/10$ value $f_{\rm leak}=0.054$ is a floor over thermally viable pitches. Meter-class modules, the published-concept end of that range, leak a third of $P_{\rm A}$ because the sail encircles only $0.18$% of a halo of first-zero radius $10.6$ km; that is a tens-of-minutes $m\sim23$ bump, and Table tab:surveys does not constrain it. Filling $10$ km at $p=40$ m gives $N=(\pi/4)(D_{\rm A}/p)^{2}=4.9\times10^{4}$ tiles, and $40$ km gives $N=7.9\times10^{5}$.

For an intercept-matched pitch $p=2.44\lambda d_{\rm b}/D_{\rm s}$, the element scale is $\theta_{\rm el}=D_{\rm s}/(2d_{\rm b})$ exactly, the sail’s angular radius as seen from the array, and $\tau_{\rm el}=D_{\rm s}/(2 v_{\perp})$, with $\lambda$, $p$ and $D_{\rm A}$ all cancelling. The first-ring isotropic-equivalent luminosity scales as $L_{\rm iso}\propto I_{\rm pk}(1-S)P_{\rm A}(d_{\rm b}/D_{\rm s})^{2}$, again independent of $\lambda$ and $D_{\rm A}$. The observable set $\{\theta_{\rm el},\tau_{\rm eff},L_{\rm iso}\}$ depends only on $(P_{\rm A},D_{\rm s},d_{\rm b},\sigma_{z}/\lambda,v_{\perp})$, and either envelope drops out of the survey prediction. That is why $\tau_{\rm eff}$ is identical in every row of Table tab:surveys, why the row-to-row $m_{\rm pk}$ differences are instrumental, and why the $10$ km and $40$ km arrays overlie in Figure 1b and Figure 4. We use $p=40$ m rather than $45.4$ m, so this cancellation is approximate. A higher tolerable loading $I_{\rm A}$ shrinks $D_{\rm A}\propto I_{\rm A}^{-1/2}$ without changing the halo observables of this section; $10^{3}\,{\rm W\,m^{-2}}$ is a technological choice, not a physical one. Smaller payloads lower $P_{\rm A}$, and longer burns at lower $a_{\rm max}$ (with the array still focused) and staged launches are still sized to the same intensity limit.

We take a residual piston $\sigma_{z}=\lambda/10$ ($100$ nm), the leftover error of a feedback loop that holds each tile rather than the laboratory lock of [10], and find $S=e^{-\sigma_{\phi}^{2}}=0.67$. The sail encircles $0.83$ of the element Airy, so $f_{\rm leak}=(1-S)(1-0.83)\simeq0.054$, a floor at this lock and fixed $D_{\rm s}$, $80$ GW missing the sail (Figure 2d). Unlocking the loop sets $S=0$ and $f_{\rm leak}$ saturates at $0.17$. At $\lambda/90$ the extra halo is $0.08$%. A $4$ cm sideways placement of the outer tiles is another $\lambda/10$ of path to the sail and raises $f_{\rm leak}$ to $0.074$. A common pointing error of $\sim3$ nrad, about a tenth of $\theta_{\rm el}$, slides the locked core by $25$ m, $\sim10$% of the sail radius, and leaves $f_{\rm leak}$ unchanged; $30$ nrad would dump the core off the sail entirely ($245$ m at $d_{\rm b}$). Holding the pointing to that tenth of $\theta_{\rm el}$ is as demanding as the $\lambda/10$ piston lock. We model only that uncorrelated piston, which we treat as the single free parameter. Intra-tile figure error on a $40$ m aperture would broaden $\theta_{\rm el}$ and cut the fluence as $\theta^{-1}$; correlated (common-mode) piston scatters into the core rather than the halo and reduces $f_{\rm leak}$. Both omitted terms push the same way on the observable, so the predicted flash is an upper envelope on this lock. At the fiducial $p=40$ m the first grating lobe falls at $\lambda d_{\rm b}/p\simeq217$ m, inside the $232$ m sail radius, so it lands on the sail and is not a feature of this leak. Grating lobes and a speckle of $N$ random phasors appear in the leak only when the pitch is small enough that those features miss the sail and $N$ is still modest; that is a laboratory tiled pupil [10], not this array.

The leaked field of one tile is the Fraunhofer transform of the tile’s sail-plane Airy truncated by the sail disk [42], smoothing scale $\lambda/D_{\rm s}\simeq2.3$ nrad ($0.07\,\theta_{\rm el}$). $I$ is in units of the unocculted tile peak, which carries scattered power $(1-S)P_{\rm A}$, so the first-ring $L_{\rm iso}=I_{\rm pk}\,4\pi(1-S)P_{\rm A}A_{\rm el}/\lambda^{2}=0.38\,L_{\odot}$ at $I_{\rm pk}=0.022$. A central observer sees two first-ring peaks $\sim30$ s across and $87$ s apart (the intensity-ring peak at $b\simeq1.33$, not the $W$ peak), with the on-axis intensity $0.58$ of the peak rather than a dark umbra; a $30$% band fills that dip to $0.90$ of the peak, so the doublet contrast is a narrowband discriminant (Figure 2b). Chords with $b\lesssim1.2$ cross the first ring twice. On axis the intensity between the peaks is $0.58$ of the peak; off axis, through the umbra, the dip is nearly dark. The two peaks merge at $b\simeq1.33$. Against $b_{\rm max}\simeq4.9$ that is about one detection in four; the geometric umbra, $0.88\,\theta_{\rm el}$, is the dark core of that region, not the edge of the doublet. The rest are a single first-ring transit. The tangential chord at $b=1.25$, where $W$ peaks at $0.040$, is that single peak, $m_{\rm AB}\simeq19.4$ in F146 at $8$ kpc, which a matched filter over $\tau_{\rm eff}$ records at ${\rm S/N}\simeq1.5\times10^{3}$; the central chord has about half that fluence, $W(0)/W(1.25)=0.54$, at ${\rm S/N}\simeq810$ (Figure 2a–c), and that is the halo of Table tab:surveys and Figure 1b and Figure 4. We adopt the $10$ km and $40$ km focused arrays as the practical optical designs, and the halo of this section is the leak a Galactic survey would catch.

The leaked field of Figure 2a is an ensemble average. A single realization is a speckle pattern with grain $\lambda/D_{\rm A}$, set by the array envelope, and the pistons are the residual of a live loop, so that pattern boils on the loop timescale. An observer sweeping a few $\theta_{\rm el}$ would then see excess variance on top of the $60$ s envelope. The sail boundary sets the pattern’s envelope and the umbra depth, not the grain. We do not develop that discriminant here: the loop bandwidth is unmodeled and the contrast depends on it.

From $10$ GW to $10$ TW

The leaked fraction is set by the lock and the intercept, not by the radiated power. What $P_{\rm A}$ sets is the payload. Varying the mass at $1$ gee, $P_{\rm A}=m_{\rm s}a_{\rm max}c/2$ runs from $10$ GW at $7$ kg to $10$ TW at $7$ tonnes, with the tonne of GL15 [1] at $1.5$ TW. High-power sites on Earth have entered the lower decade of that range. Data-center campuses built to train large models are now specified at gigawatts [49], and the Stargate program has committed $10$ GW of dedicated capacity in the United States [50], about ten large nuclear plants and a tenth of the $0.1$ TW Saturn V that GL15 [1] compared to a tonne. A $10$ GW beamer is a megaproject, but it is a megaproject of a kind already being assembled, if for computation rather than propulsion. It accelerates $7$ kg at $1$ gee. The tonne still requires $1.5$ TW, $150$ such $10$ GW campuses, and remains $\sim10$% of worldwide primary energy consumption.

At the $\lambda/10$ intercept-matched lock that is $0.54$ GW leaking at the low end and $540$ GW at the high end, a straight line through the $80$ GW of a tonne (Figure 3a). Unlocking the loop multiplies the leak by three ($f_{\rm leak}=0.17$). If instead the $40$ m pitch is frozen and the sail is grown with the thermal loading, $D_{\rm s}\propto P_{\rm A}^{1/2}$, a $10$ GW payload is a $38$ m sail that encircles only $0.019$ of the element Airy and leaks $0.32$ of $P_{\rm A}$, while a $10$ TW cargo is a $1.2$ km sail that swallows the halo down to $f_{\rm leak}=0.023$. The two $\lambda/10$ curves meet at the fiducial, where $p=40$ m is close to the intercept match.

What a survey records is not that wattage but the first-ring $L_{\rm iso}$. Holding $D_{\rm s}=465$ m and turning the array up or down, $L_{\rm iso}$ tracks $P_{\rm A}$ and Roman’s $8\sigma$ floor at $8$ kpc sits at $8$ GW, so the left edge of Figure 3b is where a tonne-class sail driven at reduced power drops through threshold. Growing the sail and re-matching the pitch, the halo solid angle grows with the power, $L_{\rm iso}$ is independent of $P_{\rm A}$, and the flash stays at $m_{\rm AB}\simeq19.4$; the matched-filter S/N still rises, from $160$ at $10$ GW to $2.9\times10^{3}$ at $10$ TW, because $\tau_{\rm eff}\propto D_{\rm s}$. At fixed loading the envelope scales as $D_{\rm A}\propto P_{\rm A}^{1/2}$, $0.8$–$26$ km at $19\,{\rm kW\,m^{-2}}$ and $3.6$–$113$ km at $10^{3}\,{\rm W\,m^{-2}}$ over the same range, and the halo observables of § 2.2 do not depend on that envelope. We retain $P_{\rm A}=1.5$ TW as the fiducial because it is a tonne at a gee.

Survival of the sail and its reflection

Naively one might spread $P_{\rm A}$ over the full sail and find $I_{\rm s}=4P_{\rm A}/\pi D_{\rm s}^{2}=8.7\times10^{6}\,{\rm W\,m^{-2}}$ and $T\simeq300$ K. For the unfocused $93$ m aperture the beam cross-section is $\sim D_{\rm A}$, not $D_{\rm s}=5D_{\rm A}$, for most of the burn; the sail is oversized to catch the beam only near $d_{\rm F}$. The illuminated spot therefore carries $2.2\times10^{8}\,{\rm W\,m^{-2}}$ early and $\sim5\times10^{7}\,{\rm W\,m^{-2}}$ at burnout. With absorptivity $\alpha=10^{-4}$ at $1\,\mu{\rm m}$ and two-sided radiation at infrared emissivity of order unity, the sail equilibrates at $T\simeq660$ K at the start and $T\simeq460$ K at burnout. The focused $10$ km and $40$ km arrays of § 2.2 shape a $D_{\rm s}$-diameter flat-top onto the sail at every $d$, so that $8.7\times10^{6}\,{\rm W\,m^{-2}}$ and $T\simeq300$ K hold for the whole burn rather than only near $d_{\rm F}$; the $\lambda/10$ lock leaves $S=0.67$ of $P_{\rm A}$ in that core and the sail still encircles $0.83$ of the element Airy, and the on-axis intensity at burnout is $\simeq1.4\times10^{7}\,{\rm W\,m^{-2}}$ ($T\simeq330$ K). A factor-of-sixteen peak on that flat-top, $(600/300)^{4}$, would still be only $T\simeq600$ K. The $300$–$660$ K range is a factor of two to five below the $\sim1600$ K vacuum-decomposition threshold of silicon nitride [9], and sits at the cool end of the $500$–$1500$ K window already assumed for Starshot thermal design [5, 6]. The failure mode at $1\,{\rm GW\,m^{-2}}$ is a dust-seeded hot spot [11], two orders above the focused flat-top and a factor of a few above the unfocused spot. Lower accelerations relieve the thermal load (the sail intensity scales as $a_{\rm max}$, the aperture intensity as $a_{\rm max}^{2}$) at the cost of a larger array. The fiducial sail is $465$ m across, area $1.7\times10^{5}\,{\rm m^{2}}$, at a total system mass of $10^{3}$ kg. A $0.2$–$1\,{\rm g\,m^{-2}}$ film in the Starshot range [5, 32] is then $34$–$170$ kg of sail, leaving $830$–$966$ kg for payload, structure and thermal control. The system areal density, $10^{3}\,{\rm kg}/1.7\times10^{5}\,{\rm m^{2}}\simeq6\,{\rm g\,m^{-2}}$ under $1$ gee, is aggressive even by Starshot standards.

The sail is a near-perfect mirror and returns essentially the intercepted power, $\simeq0.95\,P_{\rm A}$ at the $\lambda/10$ lock. The array focuses a converging beam onto the sail, so a flat mirror at normal incidence sends that return back as a diverging beam. The return refills roughly the whole aperture, at about the array’s own emission loading, whether the array is a free-flyer or is laid on an airless surface (§ 2.2). On the $10$ km envelope that loading is already $\sim20\,{\rm kW\,m^{-2}}$, near the emitters’ thermal limit, so a return at the same intensity is intolerable unless it is steered off the aperture. The $40$ km array, at $1.2\,{\rm kW\,m^{-2}}$, could absorb its return. Deflection is a requirement for the $10$ km envelope, not an optional geometry. Two ways remain to keep the return off the array: metasurface beam-riding sails [9] deflect rather than retro-reflect, sending the return along a third axis, or that deflected beam is aimed at a recapture site, a solar collector that recovers a fraction of $P_{\rm A}$. Recapture points at a fixed collector and paints no strip on the sky. Deflection alone is a fixed angle off the array–sail line, so the strip sweeps with that line through the full burn, and $L_{\rm iso}^{\rm (refl)}=4P_{\rm A}/\theta_{\rm refl}^{2}$ is independent of $d$, so $\Delta\phi_{\rm eff}$ is the whole $\sim1.1$ rad rather than $5.1\times10^{-5}$. For a flat sail the diffraction half-angle is $\theta_{\rm refl}=1.22\lambda/D_{\rm s}=2.8$ nrad, which gives $L_{\rm iso}^{\rm (refl)}\simeq2\times10^{3}\,L_{\odot}$. The return’s full width $2\theta_{\rm refl}$ is about $60$ times narrower than the leak strip ($2b_{\rm max}\theta_{\rm el}=3.2\times10^{-7}$ rad) and, because the sweep is the full $\sim1.1$ rad, a few hundred times larger in solid angle. What kills it is duration: $\tau=\theta_{\rm refl}\,d_{\rm b}/v_{\perp}\simeq2.8$ s at burnout and shorter earlier, a single-read spike, exactly the regime where the persistence cut of § 5 is unavailable and the $10^{7}$ snowballs come back. We take deflection off the array, with or without recapture. The array loading does not by itself say what an observer sees. For completeness, and because a partially retro-reflecting sail is the naive design, we check whether its return could supply a second flash. If the sail still retro-reflects, a sag $\sigma$ (a cone or spherical cap, the geometry assumed for beam-riding stability before those designs) spreads that return over $8\sigma/D_{\rm s}$. Attitude wander $\delta$ during the arrival burn smears the same beam by $2\delta$. Holding a $465$ m membrane to microradians for eleven hours is the binding requirement, tighter than the figure tolerance $\sigma/D_{\rm s}$. Then $\theta_{\rm refl}$ is the quadrature of $1.22\lambda/D_{\rm s}$, $8\sigma/D_{\rm s}$ and $2\delta$, $L_{\rm iso}^{\rm (refl)}=4P_{\rm A}/\theta_{\rm refl}^{2}$, and the duration is $\theta_{\rm refl}/\dot\phi$.

Those two limits do not overlap as a second flash. A flat sail, $\theta_{\rm refl}=2.8$ nrad, is about $60$ times narrower than the halo strip half-width $b_{\rm max}\theta_{\rm el}\simeq160$ nrad at the bulge, so an observer who sees the launch leak has probability $\sim2\times10^{-2}$ of also lying in the reflection, and that assumes the reflection axis coincides with the leak axis. A surface sag that produces $\theta_{\rm refl}=1^{\prime\prime}$ ($\sigma\simeq0.3$ mm) covers every leak-observer and is detected at $8$ kpc ($34\sigma$ in a matched filter), but it sweeps past in $\theta_{\rm refl}/\dot\phi\simeq5\times10^{3}$ s, an hour-scale brightening, not a second entry in a tens-of-seconds ramp search. The region of $(\sigma,\delta)$ in which the reflection is both geometrically probable and a tens-of-seconds flash is empty: a $10$–$100$ s reflection has overlap $0.01$–$0.1$ with the leak strip, and covering that strip forces the duration to hours. The reflection is not a second Galactic yield channel, and it is not a pair of flashes. The pair that does survive is internal to the leak, the two first-ring crossings on either side of the sail’s shadow (§ 3).

The observable event

Duration

Because the sail must be tracked, the beam sweeps, and GL15 [1] found of order a radian of azimuthal motion during a three-hour burn (their $100\,{\rm km\,s^{-1}}$ case; the fiducial here lasts $11.3$ h), with the sweep fastest early (when the sail is near the array) and slowest at burnout, where the isotropic-equivalent luminosity peaks (their Figure 3). The 2015 trajectory is specified completely: the sail starts in low orbit about the origin world, and the array beams along the world–sail line, so the force is radial and the specific angular momentum $L=v_{\rm LEO}R_{\rm LEO}$ is conserved about that world. We take a $400$ km circular orbit, $R_{\rm LEO}=6.77\times10^{6}$ m and $v_{\rm LEO}=7.67\,{\rm km\,s^{-1}}$, so $L=5.20\times10^{10}\,{\rm m^{2}\,s^{-1}}$. In closed form, the residual transverse speed at the end of the burn from that angular momentum alone is

and the time for a diffraction scale $\theta$ to sweep past a fixed observer is $\tau=\theta/\dot\phi=\theta\,d_{\rm b}/v_{\perp}(d_{\rm b})$. Integrating the same three-body trajectory as GL15 [1] gives a full-burn sweep $\Delta\phi\simeq1.1$ rad. Equation (4) gives $v_{\perp}(d_{\rm b})=6.4\,{\rm m\,s^{-1}}$. The start-from-rest integral $\Delta\phi=(4L/3a_{\rm max}^{2})(t_{1}^{-3}-t_{\rm F}^{-3})$ with $d=\tfrac12a_{\rm max}t^{2}$ from $d_{1}=R_{\rm LEO}$ gives $0.44$ rad; the factor $2.5$ is the initial orbital velocity and the non-zero starting radius. The Sun and the destination contribute a few meters per second at $d_{\rm b}$, a $30$–$50$% correction to that residual; we add $5\,{\rm m\,s^{-1}}$ in quadrature and use $v_{\perp}(d_{\rm b})=8.1\,{\rm m\,s^{-1}}$. Equation (4) applied to the GL15 [1] microwave design gives $v_{\perp}=0.10\,{\rm km\,s^{-1}}$ and a duration $\theta_{\rm A}d_{\rm b}/v_{\perp}=18$ s. For the halo of § 2.2 the scale is the element pattern, $\theta_{\rm el}=1.22\lambda/p=32$ nrad at $p=40$ m, and $\tau_{\rm el}=\theta_{\rm el}/\dot\phi=33$ s.

These durations assume an array whose transverse velocity $u$ relative to the origin world’s center is small compared with $v_{\perp}(d_{\rm b})$. An equatorial ground site has $u\simeq465\,{\rm m\,s^{-1}}$, a geostationary platform $u\simeq3.1\,{\rm km\,s^{-1}}$, and a low-orbit array $u\simeq7.8\,{\rm km\,s^{-1}}$, which would shorten $\tau_{\rm el}$ by factors of $58$, $390$ and $10^{3}$. The fiducial burn lasts $v_{\rm max}/a_{\rm max}=11.3$ hours, longer than a target stays above the horizon at a single ground site, so a ground array would also have to hand off between sites and the sweep would not be the smooth $L/d^{2}$ used here. This suggests a free-flying array co-orbital with the origin world, the architecture assumed by most large-aperture directed-energy concepts [4, 32]. Holding that array to $u\ll8\,{\rm m\,s^{-1}}$ over an $11$ hour burn is a station-keeping requirement we do not solve; we instead recompute $N_{\rm det}$ and $\tau_{\rm eff}$ as functions of $v_{\perp}(d_{\rm b})$ from $1$ to $10^{3}\,{\rm m\,s^{-1}}$ (Figure 4d). Because $\tau_{\rm eff}$ and $\Delta\phi_{\rm eff}$ trade, $N_{\rm det}/f_{\rm b}$ runs from $0.016$ at $1\,{\rm m\,s^{-1}}$ to $0.33$ at $100\,{\rm m\,s^{-1}}$, of order the Table tab:surveys value near the fiducial $8\,{\rm m\,s^{-1}}$. A ground site at $465\,{\rm m\,s^{-1}}$ is a $1$ s flash: $r_{\rm max}=17$ kpc still exceeds the bulge (${\rm S/N}=35$ at $8$ kpc) and the integrated yield is $0.42\,f_{\rm b}$, but the event is a single-read spike rather than a $60$ s ramp, and a ground array must still hand off between sites.

A distant observer whose line of sight passes at impact parameter $b$ from the pattern center records a chord through the leaked far-field. Integrating along that chord gives the event fluence, which we write as $\tau_{\rm eff}(b)=(W(b)/I_{\rm pk})\,\tau_{\rm el}$ with

with $u$ and $b$ in units of $\theta_{\rm el}$, so $x=\pi p\theta/\lambda$ is the standard Airy argument [42], and $I$ the leaked far-field of the truncated tile Airy in units of the unocculted tile peak. $W$ peaks at $0.040$ for $b=1.25$ (Figure 2c), the leaked first-ring peak is $I_{\rm pk}=0.022$, and $\tau_{\rm eff}\simeq60$ s. At the bulge $b_{\rm max}\simeq4.9$ in units of $\theta_{\rm el}$, so the events that make up the Roman yield are chords through the first ring and its inner Airy wings, not a broad $b^{-2}$ sidelobe tail.

The durations above are the ones at burnout. Earlier in the burn the sail covers more of the element Airy, $f_{\rm leak}$ is smaller, and the first ring has not yet cleared the occulter. For a bulge star the end-of-burn halo fluence exceeds the Roman threshold by a factor $(r_{\rm max}/8\,{\rm kpc})^{2}\simeq190$, which with the computed $d$-scaling of the occulted element pattern corresponds to $d_{\rm min}/d_{\rm b}\simeq0.31$ and $\Delta\phi_{\rm eff}=5.1\times10^{-5}$ rad. The full $1.1$ rad of the GL15 [1] trajectory is accumulated almost entirely in the first minutes, when the leak is suppressed. Naively using the full-burn sweep overestimates the geometric probability by four to five orders of magnitude. The start-from-rest integral agrees with the three-body trajectory once $d_{1}/d_{\rm b}\gtrsim0.05$, because then $d_{1}\gg R_{\rm LEO}$. The bulge window opens at $d_{\rm min}/d_{\rm b}\simeq0.31$, inside that range, so the integral is adequate here. We use $\Delta\phi_{\rm eff}$ in the yield.

Appearance in an imaging survey

Figure 2 shows the halo and two representative light curves for a system at $8$ kpc. At peak the flash reaches $m_{\rm AB}\simeq19.4$ in the F146 photon-rate zeropoint, a factor $\sim17$ above the Roman $8\sigma$ single-read line, and lasts $\tau_{\rm eff}\simeq60$ s. Four properties follow, and together they define the search.

(i) The event is short compared with a visit and long compared with a cosmic ray [39]. The first-ring pair of Figure 2b is not resolved as a spatial ring; the survey measures its fluence. On Roman, $\tau_{\rm eff}\simeq60$ s spans $\sim\!20$ reads of $3.04$ s, so that fluence is a short ramp transient rather than a single-sample jump [26]. A central chord is two peaks of duration $\sim30$ s separated by $87$ s, so Roman’s ramp records a doublet in one visit; a tangential chord is a single peak, and that single peak is the typical detection, the umbra being missed off axis. Rubin’s $30$ s visits (Table tab:surveys; [22]) and Euclid’s $87$ s NISP integrations [31] generally do not resolve that doublet; $2\times15$ s snap mode is a recommended option (§ 4.4), not the as-executed baseline. The search we advocate is a matched filter over the flash window, Equation (6). For a fixed-fluence transient the background noise is $\sqrt{B\tau_{\rm eff}}$, independent of $t_{\rm samp}$; read noise worsens as $t_{\rm samp}$ shrinks if reads are combined incoherently. The argument for short sampling is instead localization of the flash window, which matters when $\tau_{\rm eff}$ is much shorter than the exposure (the Euclid VIS case, $t_{\rm samp}=566$ s; [30]). Figure 2b shows both the matched-filter threshold and the harder cut a single $3.04$ s sample would need; the ranking of the three facilities is set by collecting area and by how well $t_{\rm samp}$ matches $\tau_{\rm eff}$.

(ii) The flash is single-band, not necessarily a spectral line. For the focused array the relevant chromaticity is whether the focus and the tile lock are true time delay, which is achromatic, or phase, for which $\sigma_{\phi}=2\pi\sigma_{z}/\lambda$ varies by $\sim30$% across a $30$% band [10]. Either way a $10$–$30$% fractional bandwidth still lands all of the flash energy in one filter. Figure 2 is monochromatic at the Nd:YAG line $\lambda=1.06\,\mu{\rm m}$ [4, 32]; a $30$% band broadens $\theta_{\rm el}$ by that fraction and fills the far-field dip from $0.58$ of the peak to $0.90$, so the doublet contrast is a narrowband discriminant and does not restore a core. That is the basis of a color veto on a single flash: astrophysical variability is achromatic or smoothly chromatic [37]. An unresolved feature on a stellar trace in NISP grism data at $R\sim450$ [31] would require $\Delta\lambda/\lambda\lesssim2\times10^{-3}$, two orders of magnitude tighter than a $30$% band, and we do not assume it [17, 18].

(iii) The source is unresolved and coincident with a star. At $8$ kpc the fiducial $d_{\rm b}=8.2\times10^{9}$ m ($0.055$ AU) subtends $7\,\mu$as. The flash is therefore a perfect point source at the stellar position, which is what permits the background rejection of § 5.

(iv) Launch and arrival leaks are antiparallel. If both worlds host arrays, so that the cargo can be decelerated [2], there are two beams. At launch, $A$ beams along $A\to B$ and the leaked radiation continues toward $B$ and beyond. At arrival, $B$ beams head-on at the incoming sail, along $B\to A$, and its leak continues toward $A$ and beyond. The two leaked strips are antiparallel, so an observer beyond $B$ sees the launch flash and is not illuminated at arrival; the geometric factor of $2$ in Equation (8) counts those disjoint strips, one flash per transfer per observer. The reflected beam restores a pair only in a thin corner of sail figure and attitude (§ 2.4). The pair that does survive is internal to one burn: a line of sight that clips the axis crosses the first ring on both sides of the shadow, and Roman’s ramp records two peaks $87$ s apart (Figure 2b). As in § 2.2, about one detection in four is such a doublet, and the rest are single first-ring transits.

A second flash from a later transfer is a much weaker prospect. One burn paints a strip $\Delta\phi_{\rm eff}=5.1\times10^{-5}$ rad long and $2b_{\rm max}\theta_{\rm el}=3.2\times10^{-7}$ rad wide, and the strip lies along the line joining the two worlds, which turns at $\sim\!10^{-7}\,{\rm rad\,s^{-1}}$ as they orbit and so moves $\sim\!2\times10^{-3}$ rad between transfers six hours apart, some forty strip lengths. Later transfers lay their strips elsewhere along the band that rotating line sweeps, and an observer already in the band is caught again with probability $\Delta\phi_{\rm eff}/2\pi=8\times10^{-6}$ per transfer. Over the $157$ transfers a GBTDS star is watched through at one per $6$ h, the expected number of repeats is $1\times10^{-3}$, and a repeat inside the survey would need a launch every $\sim\!30$ s. A single flash is therefore a photometric candidate; the typical detection is a single first-ring peak, and the doublet, about one chord in four, is the confirmation test. The statistical cut of § 5 is what a single flash has to survive. Because the laser wavelength sets the intercept-matched pitch, the four rows of Table tab:surveys are four distinct beamers on either envelope; a Roman candidate is characterized in F146 (host photometry), not by asking Rubin or Euclid to catch the same flash in $r$ or $H_E$.

Detectability with Roman, Rubin and Euclid

Detection statistic

Point (i) above implies that the search should not be conducted on stacked light curves. For the near-infrared detectors of Roman and Euclid/NISP, exposures are sampled up the ramp and the pipelines already compute, for every pixel and every read, the jump between successive samples in order to identify cosmic rays [26]. A tens-of-seconds flash appears in this data product as a run of consecutive jumps that is (a) confined to $\sim\!\tau_{\rm eff}$, (b) distributed across the pixels of the stellar point-spread function (PSF) in proportion to the PSF, and (c) centered on a cataloged star. We therefore advocate a PSF-matched ramp search: fit each ramp segment with the PSF at the position of each cataloged source and record the amplitude and its $\chi^{2}$. For Rubin the analog is a search of individual $15$ s snaps or single visits against the deep template [22], retaining PSF-consistent positive residuals. In each case the matched-filter significance over the flash window is

where $E_{\gamma}=hc/\lambda$ is the photon energy, $S_{\rm peak}$ is the flash flux at the telescope, $\dot N_{\rm src}$ is the host stellar photon rate in the aperture, $A_{\rm eff}$ is the effective collecting area (Table tab:surveys caption), $n_{\rm pix}$ is the number of pixels in that aperture, and $\sigma_{\rm read}$ is the read noise per pixel. The denominator is the null: sky, host, and read noise, without the flash’s own shot noise. The numerator does not depend on the host’s intrinsic luminosity: it is set by the beamer alone and only the noise knows about the star. The factor of two on the read noise is the difference of two ramp segments. Faint hosts are therefore better targets, until the sky and read-noise floor is reached. In GBTDS fields the noise is dominated by crowding, which correlates with position rather than host magnitude, and bright-star masking removes some of the footprint. We adopt a filling factor of $0.7$, so $N_{\star}$ in Equation (9) is $1.5\times10^{8}$, the bright-star-masked faint column, rather than the raw $W149<25$ prediction of $2.1\times10^{8}$ [25]. That masked column is the primary search. A giant-host cut is a secondary sample, the unmasked $W149\simeq14$–$17$ stars, and host shot noise in Equation (6) then sets its range (below). The background cut of § 5 is stricter. It asks for coincidence with a resolved, cataloged source. In the bulge those two populations are almost the same, the mean separation $0.33^{\prime\prime}$ at $1.22\times10^{8}$ deg$^{-2}$ being comparable to the Roman PSF [25], so the discriminant is weak exactly where the star-seconds are. At high latitude the cataloged column is the right $N_{\star}$ for both the yield and the cut, and the discriminant is strong, but that is not where the harvest is. The faint-host search is limited by distance, not by host magnitude, and its reach is

with $L_{\rm iso}$ the isotropic-equivalent luminosity of the leaked first-ring halo, $Q$ the adopted threshold and $\sigma$ the matched-filter noise in the faint-host limit. Relative to a single-sample denominator the matched statistic is the conservative one for Roman’s numbers ($B\simeq50$ e$^{-}$ s$^{-1}$, $\sigma_{\rm read}\sqrt{n_{\rm pix}}=41.6$ e$^{-}$, $\tau_{\rm eff}=60$ s): a bulge flash of $2.0\times10^{3}$ e$^{-}$ s$^{-1}$ then has matched-filter denominator $80$ e$^{-}$ and ${\rm S/N}=1.5\times10^{3}$. Most GBTDS overlaps are partial ($\tau_{\rm eff}\simeq60$ s against a $67$ s exposure; [25, 27]), but the bookkeeping is right on average and ${\rm S/N}\gg Q$ at the bulge, so the yield is safe.

We quote ranges and yields at $Q=8$, where the expected Gaussian false-alarm count falls below one event. The number of independent trials is large (Roman’s GBTDS alone supplies $\sim\!1.1\times10^{6}$ reads per star for $\sim\!1.5\times10^{8}$ usable stars, or $1.7\times10^{14}$ read-trials). A matched filter run over a handful of trial durations multiplies that by a factor of a few, not by $10^{2}$. A $5\sigma$ threshold would yield $\sim\!5\times10^{7}$ Gaussian false alarms and even $7\sigma$ leaves a few hundred; at $8\sigma$ the Gaussian expectation is of order $0.1$ events.

Gaussian trials are not what limits this search, however, and a threshold in units of $\sigma$ is not the natural statement of its sensitivity. At $Q=8$ the range is already $r_{\rm max}=109$ kpc on a faint host, past the far edge of the Galaxy, so a harder cut costs no stars. It costs only the width of the illuminated strip and the sweep over which the flash stays above threshold: $N_{\rm det}/f_{\rm b}$ falls from $0.061$ at $Q=8$ to $0.040$ at $Q=20$ and $0.016$ at $Q=100$, and collapses only near $Q\simeq1.5\times10^{3}$, where $r_{\rm max}$ drops to the distance of the bulge (Figure 4c). The Gaussian false-alarm expectation falls by some seventy decades over that same interval. The threshold should therefore be set by the measured rate of PSF-coincident instrumental and stellar transients (§ 5) rather than by the Gaussian tail, and the sensitivity of the search is properly quoted as a pair: the fluence at which the star-offset control rate is tolerable, and the yield that survives there. The shaded band of Figure 4c is the decade in $Q$ at which a $10^{-4}$–$10^{-6}$ survivor fraction of the duration-cut sample of § 5 would leave of order one event. For Roman the $8\sigma$ fluence is $640$ detected photons, an average of $11$ e$^{-}$ s$^{-1}$ over $\tau_{\rm eff}$ ($m_{\rm AB}=25.0$ in the F146 photon-rate zeropoint), against a peak of $2.0\times10^{3}$ e$^{-}$ s$^{-1}$ for a bulge flash. We use $Q=8$ throughout because that control rate cannot be measured before the data exist, and Figure 4c gives the yield penalty for any harder cut. The limits in Table tab:surveys are Poisson limits for a background-free search; § 5 shows those contours are not achievable once PSF-coincident stellar and instrumental transients are included, and the estimates there are what would have to be subtracted to reach them.

A $W149=17$ giant at $8$ kpc contributes $\dot N_{\rm src}\simeq1.7\times10^{4}$ e$^{-}$ s$^{-1}$ to the denominator of Equation (6), so the same flash has ${\rm S/N}=117$ and $r_{\rm max}=31$ kpc. That is still a Galactic range, but it is not “visible from anywhere in the Galaxy.” The dashed curve of Figure 4c is an upper bound on that secondary sample: host shot noise at the full column and filling factor unity. The true giant subsample is the magnitude-selected bright tail, whose size we do not assign without a luminosity function.

Expected yields

The probability $p_{\rm geo}$ that a given transfer illuminates us is the swept solid angle divided by $4\pi$. Events remain above threshold out to impact parameter $b_{\rm max}(r)$, the value of $b$ at which $W(b)/W_{\rm max}=(r/r_{\rm max})^{2}$, so

the leading factor accounting for the disjoint launch and arrival leak strips. At the bulge $b_{\rm max}\simeq4.9$ for Roman (the largest $b$ with $W(b)/W_{\rm max}=(8\,{\rm kpc}/r_{\rm max})^{2}$). At $4$ kpc, the characteristic distance of the high-latitude disk column, $b_{\rm max}\simeq5.5$ for Rubin and $5.4$ for Euclid $H_E$. Because $b_{\rm max}$ is a function of $r$ it belongs inside the yield integral. We integrate $p_{\rm geo}(r)$ over the disk-plus-bulge column. Evaluating at $8$ kpc instead changes $N_{\rm det}$ by $\sim20$% at the fiducial, which we ignore next to the range in piston residual; near $v_{\rm max}\simeq250\,{\rm km\,s^{-1}}$, where $r_{\rm max}$ crosses the bulge, the one-zone value drops discontinuously to zero while the integral still returns a disk-only harvest of order $0.01\,f_{\rm b}$. With $R_{\rm L}$ transfers launched per unit time per system and $T_{\rm obs}$ of open shutter per star, the expected number of detections is

where $f_{\rm b}$ is the fraction of stars hosting a continuously operating optical beamer of the kind in § 2.2, a $10$ km or $40$ km array of intercept-matched tiles at a $\lambda/10$ lock, at $m_{\rm s}\simeq10^{3}$ kg, $v_{\rm max}\gtrsim250\,{\rm km\,s^{-1}}$ and $a_{\rm max}\simeq1$ gee, with $\lambda$ in $0.3$–$2.3\,\mu{\rm m}$. An ideal lock produces no halo (§ 2.2); unlocking the loop saturates at $f_{\rm leak}=0.17$ because the tile Airy still hits the sail. $a_{\rm max}$ and $m_{\rm s}$ are fixed to the tonne-at-a-gee Earth–Mars analog, and $r_{\rm max}$ is a steep function of $v_{\rm max}$ (Figure 1b). The search is a null test of that array, which is the practical optical design, not a constraint on beam-driven light sails as a class. Following GL15 [1], where we argued that the infrastructure has high capital and low operating cost and would be used constantly, it seems reasonable to adopt one transfer every $6$ h as a reference and to quote limits on the mean launch rate per star in those units, $\Gamma_{6{\rm h}}\equiv 6\,{\rm h}\,f_{\rm b}R_{\rm L}$. Yields scale linearly with $R_{\rm L}$. At one launch per $6$ h, $N_{\rm det}=0.061\,f_{\rm b}$, so even $f_{\rm b}=1$ is far below one detection. $N_{\rm det}=1$ requires $\Gamma_{6{\rm h}}\simeq16$, a launch every $\sim20$ min, and a background-free null search limits $\Gamma_{6{\rm h}}\lesssim49$, three times that rate. The $\Gamma_{6{\rm h}}\lesssim49$ contour does not restrict $f_{\rm b}$ alone, since $f_{\rm b}\le1$ by construction. The first-ring level is an upper envelope set by uniformly illuminated hard-edged tiles, and by the omitted figure and correlated-piston terms of § 2.2; a civilization paying for $1.5$ TW has reason to apodize, while tile-to-tile amplitude errors and tilt go the other way.

Table tab:surveys collects the result for a fiducial beamer moving a $10^{3}$ kg payload at $v_{\rm max}=400\,{\rm km\,s^{-1}}$ at $1$ gee, a $2.2$ d opposition-class Earth–Mars crossing rather than a Hohmann analog. Because the intercept-matched pitch scales with the laser wavelength, $\theta_{\rm el}=1.22\lambda/p$ and therefore $\tau_{\rm eff}$ are the same in every row; the rows differ in collecting area, sampling and stellar column rather than in the shape of the event. A $1$ m pitch on either envelope is a tens-of-minutes $m\sim23$ bump and is not this search. Magnitudes are in the survey photon-rate zeropoint referred to the tabulated $\lambda$ (F146: $1$ e$^{-}$ s$^{-1}\equiv27.6$ AB); a monochromatic $f_{\nu}$ spread over the full F146 width is $\simeq0.6$ mag brighter, and we use the photon-rate convention throughout, so the Roman–Rubin magnitude offset is not photon energy alone. Star counts toward the bulge are taken from the Cycle 7 W149$<25$ prediction of [25] ($2.40\times10^{8}$ stars in $1.96$ deg$^{2}$, i.e. $1.22\times10^{8}$ deg$^{-2}$), rescaled to the $1.7$ deg$^{2}$ GBTDS footprint recommended by [27], and assigned a disk-plus-bulge distance distribution centered at $8.2$ kpc, and multiplied by a filling factor of $0.7$ after bright-star masking. High-latitude columns of $3\times10^{4}$ and $1.5\times10^{4}$ stars deg$^{-2}$ are used for the Rubin and Euclid footprints [22, 29]. Figure 4 shows the range as a function of transit speed and the null-search limit as a function of RMS tile piston.

Roman

The Galactic Bulge Time Domain Survey monitors $1.7$ deg$^{2}$ of the bulge in the wide F146 filter at $\sim\!12$ min cadence with $\sim\!67$ s exposures through six $\sim\!70$ d seasons [25, 27], accumulating $3.4\times10^{6}$ s of open shutter per star ($39$ days), $7.0\times10^{14}$ star-seconds before the filling factor and $5.0\times10^{14}$ after, sampled at $3.04$ s. That is two orders of magnitude more than Rubin and four more than Euclid. With $\tau_{\rm eff}\simeq60$ s the $8\sigma$ matched-filter range is $109$ kpc on a faint host, so the flash is visible from anywhere in the Galaxy if the beam points at us. On a $W149\simeq17$ giant, host shot noise in Equation (6) brings $r_{\rm max}$ to $31$ kpc. In F146 the photon-rate zeropoint is $1$ e$^{-}$ s$^{-1}\equiv27.6$ AB, so $m_{\rm pk}=19.4$ at $8$ kpc. The geometric probability that the beam points at us is $\Delta\phi_{\rm eff}\times2b_{\rm max}\theta_{\rm el}/2\pi$, i.e. $N_{\rm det}\simeq0.061f_{\rm b}$ at the $\lambda/10$ lock and $N_{\rm det}\simeq0.092f_{\rm b}$ if the loop is off, so a null search limits $\Gamma_{6{\rm h}}\lesssim49$ ($\lambda/10$) or $\lesssim33$ (loop off), before background subtraction. At the fiducial rate neither contour cuts $f_{\rm b}$ below unity.

The GBTDS observes almost entirely in F146, so the color veto of point (ii) is unavailable at the facility that supplies essentially all of the star-seconds. A second band at the same instant is what would color the flash, and the GBTDS does not take one (§ 4.5).

Roman is in cruise, and the GBTDS processing configuration is still open. Roman cannot downlink every read and instead averages groups of reads into resultants on board. The slope recovered from those uneven combinations [26] degrades only as the square root of the resultant spacing, so a $\sim\!10$ s effective sampling is entirely workable. What is essential is that the jump information survive: the onboard cosmic-ray identification step, which necessarily examines read-to-read differences, should preserve a compact record of rejected jumps (position, amplitude, read index) rather than discarding them. The information is otherwise irrecoverable. At $\sim5\,{\rm cm^{-2}\,s^{-1}}$ over $\sim300\,{\rm cm^{2}}$ of focal plane and the $\sim\!2\times10^{7}$ s the WFI integrates over the survey (six pointings at $3.4\times10^{6}$ s each), that record is a few hundred GB, a negligible downlink. The computational cost of a PSF-matched fit over $1.7\times10^{14}$ samples is not negligible; “no added cost” here means no added observing cost.

The Roman background in Equation (6) is not a free guess. We take $7.4$ noise pixels (F146, WFI center) times the [25] season-midpoint sky plus thermal rate ($3.43+1.07$ e$^{-}$ pix$^{-1}$ s$^{-1}$) and add $\sim\!2$ e$^{-}$ pix$^{-1}$ s$^{-1}$ of residual crowding, giving $B\simeq50$ e$^{-}$ s$^{-1}$ in the aperture. Zodiacal light toward the bulge is $2.5$–$7$ times the minimum [25]. At $t_{\rm samp}=3.04$ s the single-read read-noise term ($41.6$ e$^{-}$) dominates $B t_{\rm samp}$ in variance (a factor $3.4$ in $\sigma$); over $\tau_{\rm eff}=60$ s the background and the differenced read noise are comparable, which is why Equation (6) is the right denominator.

Rubin

Rubin has the best per-flash sensitivity of the three, by virtue of its collecting area: at $v_{\rm max}=400\,{\rm km\,s^{-1}}$ a single halo flash is detected at matched-filter ${\rm S/N}\simeq2.6\times10^{3}$ from $8$ kpc and the full-fluence range extends to $145$ kpc. A single $30$ s visit captures at most half of the $60$ s flash, so the S/N that the cadence actually supplies is $\simeq1.8\times10^{3}$ and the corresponding range is $\sim120$ kpc rather than the $145$ kpc of the full $60$ s matched filter. Its limitation is time per star, and the relevant time is single-band. The flash is monochromatic, so it is caught only while Rubin is in the matching filter: of the $825$ visits of $30$ s the baseline ten-year cadence delivers per field, the $\sim\!184$ taken in $r$ are the ones that count [22], or $5.5\times10^{3}$ s, $620$ times less than Roman. Even with $5\times10^{8}$ stars in the WFD footprint the yield is $N_{\rm det}\simeq7.4\times10^{-4}f_{\rm b}$ ($\lambda/10$) or $9.0\times10^{-4}f_{\rm b}$ (loop off). Counting all $825$ visits would overstate this by a factor of $4.5$. Rubin’s other visits color the host. The filters are sequential, so a $60$ s flash is gone before the next filter and the color of the flash itself is not measured. A $30$ s visit is shorter than the $87$ s doublet and catches one first-ring peak at a time.

Two things would improve this and cost little. First, the current LSST baseline takes single $30$ s exposures; $2\times15$ s snap mode is not in use. Retaining it in at least part of the survey would halve $t_{\rm samp}$ and supply a built-in coincidence veto: a $\sim60$ s flash appears in both snaps, while a cosmic ray or a sub-second glint appears in only one. Second, single-snap PSF-consistent positive residuals should be preserved in the alert stream or in a dedicated auxiliary table rather than being suppressed as artifacts; at present such detections are precisely what difference-imaging pipelines are tuned to discard.

Euclid

Euclid’s reference observing sequence spends only four $566$ s VIS exposures and four $87$ s NISP exposures per field, so $T_{\rm obs}$ is three to four orders of magnitude below Roman’s. NISP is sampled up the ramp in MACC$(4,16,4)$; the $22$ s of Table tab:surveys is one of the four groups that make up the $87$ s integration. With $\tau_{\rm eff}\simeq60$ s the NISP integrations no longer dilute the flash into invisibility ($r_{\rm max}=101$ kpc in $H_E$), but the yield remains $\ll1$ per host fraction and a null search does not constrain $f_{\rm b}$. Because VIS and NISP observe simultaneously through a dichroic [30, 31], Euclid is the only one of the three that can establish that a flash present in one band was truly absent in another at the same instant, which no sequential multiband survey can do, and which Roman cannot do at all. The test applies to a flash that occurs during a Euclid exposure. A later transfer repeats only $\sim10^{-3}$ times per watched star (§ 3), so pointing Euclid at a Roman candidate afterward does not re-catch the flash, and the Wide Survey avoids the Galactic bulge, where the Roman star-seconds are. In addition, if the beamer’s linewidth is intrinsically narrow, a monochromatic flash at $1.25$–$1.85\,\mu{\rm m}$ would appear in the concurrent NISP red grism as an unresolved feature on a stellar trace with no continuum counterpart. That search can be run on existing Q1 and Q2 frames at no observational cost; we do not assume the linewidth the grism would require.

Backgrounds

The dominant background is cosmic rays. For Roman at L2 the probability that a cosmic ray lands within a stellar PSF in a given read is $\sim\!10^{-4}$, so over the GBTDS each star accumulates $\sim\!10^{2}$ coincidences and the survey as a whole $\sim\!2\times10^{10}$. The discriminant is morphology and duration: a cosmic ray deposits charge in a contiguous track of one to a few pixels in a single read, whereas a flash illuminates the full PSF in the correct proportions for $\sim\!\tau_{\rm eff}$. A PSF-matched fit with a $\chi^{2}$ cut across $\gtrsim10$ pixels, requiring the excess to persist over more than one read, suppresses ordinary tracks by many orders of magnitude. The residual population is the extended, quasi-circular events known as snowballs in H4RG and H2RG devices. On-orbit JWST/NIRSpec at L2 records $0.0015$ snowballs ${\rm cm^{-2}\,s^{-1}}$ for cores of $\gtrsim9$ pixels ($0.3$ per $14.6$ s frame), roughly $100$ times the ground-test rate [39]. Scaled to the WFI, that is of order $10^{7}$ events over the survey, and at a stellar column of $1.2\times10^{8}$ deg$^{-2}$ essentially every one of them lands in a cataloged PSF. The deposit itself is a single-read charge dump. A persistence cut that requires the excess to last more than one read therefore removes the $10^{7}$ cores; what remains is the fainter post-saturation persistence, not a $60$ s PSF-shaped flash. The blank-sky control is what measures any residual. For Rubin the analogous residuals are sub-second satellite and debris glints [34, 33], optical ghosts and unmasked bright-star artifacts.

We do not claim these can be eliminated a priori. Instrumental transients are, to a good approximation, uncorrelated with the positions of cataloged stars, whereas the signal is by construction coincident with them. In GBTDS fields that coincidence is with a resolved source (§ 4.1); the yield uses the masked faint column of that section. Running the identical PSF-matched search at a large ensemble of blank-sky positions therefore yields an empirical false-alarm rate, with all the non-Gaussianity of the real detector included and no modeling required. That control fails for the classes most likely to mimic the signal: persistence from previously saturated sources, inter-pixel capacitance and cross-talk ghosts at fixed offsets from bright stars, brighter-fatter residuals, and undersampled-PSF differencing residuals in crowded fields. In GBTDS fields at $1.2\times10^{8}$ stars deg$^{-2}$, undersampled differencing where sources overlap will itself produce PSF-consistent positive residuals at stellar positions at some rate; the star-offset control partially handles that blending, and diffraction spikes are a further, smaller, stellar-position background. A second control runs the same search at positions offset by a few arcseconds from real stars. It preserves the local crowding and bright-star environment while breaking the coincidence, and it measures the false-alarm rate. Injection-recovery of synthetic flashes measures the efficiency of that cut. The search is then a measurement of an excess of PSF-consistent short transients at stellar positions over both the blank-sky and the star-offset rates. Glints and satellite trails are not perfectly isotropic, being concentrated near the geostationary belt and in twilight, so for Rubin the blank-sky sample should be matched in airmass, hour angle and time of night.

Impulsive spikes in M-dwarf flare continua have been resolved at one-second cadence [37], and a one-second-cadence imaging survey records rise times of $5$–$100$ s at $\sim\!0.7$ day$^{-1}$ per active M dwarf [35]. The GBTDS $W149<25$ column splits as $\sim3.4\times10^{7}$ disk stars and $\sim1.7\times10^{8}$ bulge stars in $1.7$ deg$^{2}$. Taking $70$% of the disk as M dwarfs and $15$% of those as magnetically active gives $\sim4\times10^{6}$ active dwarfs and $\sim4\times10^{6}\times0.7\times39\sim10^{8}$ impulsive events over the open shutter. They are PSF-shaped by construction, so a $\chi^{2}$ cut does not reject them. A duration cut that requires the excess to be confined to $\sim\tau_{\rm eff}$ and not to persist into the next visit removes classical hour-scale flares; the Aizawa rise times already sit in the $5$–$100$ s window, and even a $10$% survivor fraction leaves $\sim10^{7}$ events. Quasi-periodic pulsations on M dwarfs occupy the same tens-of-seconds window: confirmed TESS $20$ s QPPs have periods of a few to ten minutes [36], and a $17$% subset of complex flares is a peak-bump pair on a minutes-to-hours envelope. Period alone does not discriminate. Duty cycle does: a QPP is a multi-cycle modulation of a long flare, whereas the leak is two peaks $87$ s apart and then quiescence, or, for about three detections in four, a single $\sim30$ s peak. Host type separates those disk M-dwarf flares from bulge giants in the giant-host sample below.

The primary search is the faint-column excess, single peaks on the masked $W149<25$ stars, with $N_{\rm det}\sim0.06\,f_{\rm b}$. The $\sim10^{8}$ impulsive events over the open shutter outnumber $N_{\rm det}$ by a factor $\sim10^{9}$, and we have not shown a rejection at that level. Most of those hosts are photometrically classifiable as disk dwarfs rather than bulge giants. A giant-only subsample, $W149\simeq14$–$17$ at $8$ kpc, is a secondary search on unmasked bright stars with host-noise $r_{\rm max}=31$ kpc. The bulge $W149<25$ column is dwarf-dominated ($W149=25$ is $M\simeq10.5$), so the giant cut is a magnitude selection, not the disk fraction. Sunlit debris and asteroid glints, including the sub-second population [34, 33], land on cataloged stars by chance at a computable rate. A tens-of-seconds PSF-shaped brightening of a star is not, by itself, unique. The doublet, about one chord in four, is the confirmation test for lines of sight that clip the ring, not the detection the yield counts. Because PSF-coincidence is weak in the bulge and Roman has no color, the discriminants in the fields that carry essentially all of the star-seconds reduce to duration and morphology, with host type available only in the giant-host sample.

Discussion and conclusions

We have presented the optical and near-infrared branch of the light-sail leakage transient of GL15 [1]. Fresnel matching would shrink the aperture to $20$–$100$ m at $1\,\mu{\rm m}$ (Equation (1)), and that aperture cannot radiate $1.5$ TW. Spreading that power at $\sim20\,{\rm kW\,m^{-2}}$ is a $10$ km array, near the emitters’ thermal limit; holding the published $10^{3}\,{\rm W\,m^{-2}}$ loading takes a $\sim40$ km array ($1.2\,{\rm kW\,m^{-2}}$), and that aperture is heavy. At fixed $D_{\rm s}$, a $\lambda/10$ piston on $40$ m tiles leaks $0.054\,P_{\rm A}$ into a first-ring halo at $m_{\rm AB}\simeq19.4$ in F146 at $8$ kpc, with $\tau_{\rm eff}\simeq60$ s (Figure 2). At intercept match that fraction is independent of $P_{\rm A}$ from $10$ GW to $10$ TW, and for a thermally sized sail so is the peak magnitude (Figure 3), so a $10$ GW plant of the kind committed for AI training is already a Galactic flash. The typical detection is a single $\sim30$ s peak; about one in four is a pair $87$ s apart. On a faint host Roman’s GBTDS reaches $r_{\rm max}=109$ kpc at $8\sigma$; on a $W149\simeq17$ giant the range is $31$ kpc. One launch per $6$ h gives $N_{\rm det}=0.061\,f_{\rm b}$. $N_{\rm det}=1$ requires $\Gamma_{6{\rm h}}\simeq16$; a background-free null search limits $\Gamma_{6{\rm h}}\lesssim49$ ($\lambda/10$) or $\lesssim33$ (loop off), three times the rate at which one detection is expected, and neither contour restricts $f_{\rm b}$ below unity. Neither the reflection nor a later transfer supplies a second flash. Because $r_{\rm max}$ already exceeds the Galaxy on a faint host, the threshold is set by PSF-coincident stellar and instrumental transients, and Figure 4c gives the yield surviving any harder cut.

The limit is a limit on that array and on the tolerance to which it is held, not on beam-driven light sails as a class. The ramp search does not constrain meter-class tiling, which leaks a tens-of-minutes $m\sim23$ bump. The recommended search requires (i) that Roman preserve a compact record of rejected ramp jumps while the GBTDS configuration is still open, (ii) that Rubin retain PSF-consistent single-visit positive residuals, and (iii) that all three be searched against blank-sky and star-offset controls, with a giant-host cut against disk-dwarf flares as a separate sample from the faint-column search. Figure 2a is an ensemble average; a single realization is a speckle we do not develop as a discriminant (§ 2.2). Wide-field optical time-domain surveys [40, 44] and searches for hour-scale extragalactic flashes [41] or century-scale vanishings [38] have already covered large sky areas, but none has the bulge stellar column, the star-coincidence requirement, and the tens-of-seconds ramp sampling of the GBTDS together. If intensity-limited optical beamers of this kind are commonly employed in our Galaxy, this activity could be revealed by a PSF-matched ramp search of Roman, Rubin and Euclid at no additional observing cost. Nearby multiply-transiting systems near projected conjunction, the strategy we proposed in GL15 [1] and the window [16] takes for intercepting leaked propulsion once the orbits are known, remain the right targets for dedicated instruments; the surveys’ statistical reach is over $10^{8}$–$10^{9}$ distant stars.

Acknowledgements

This work was supported in part by the Galileo Project. We thank the Roman, Rubin and Euclid project teams for making detailed survey specifications publicly available. We thank J. Xavier Prochaska for providing access to AI models that were used to conduct independent AI reviews. This manuscript was prepared with the assistance of the Anthropic AI model Claude Opus 5 and X.ai model Grok 4.6. All text that was not written by the authors was reviewed and approved by the authors, and all references have been verified.¹ This research made use of Astropy [45], NumPy [46], SciPy [47] and Matplotlib [48].