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Give Me a Few Hours: Exploring Short Timescales in Rubin Observatory Cadence Simulations

The limiting temporal resolution of a time-domain survey in detecting transient behavior is set by the time between observations of the same sky area. We analyze the distribution of visit separations for a range of Vera C. Rubin Observatory cadence simulations. Current simulations are strongly peaked at the 22 minute visit pair separation and provide effectively no constraint on temporal evolution within the night. This choice will necessarily prevent Rubin from discovering a wide range of astrophysical phenomena in time to trigger rapid followup. We present a science-agnostic metric to supplement detailed simulations of fast-evolving transients and variables and suggest potential approaches for improving the range of timescales explored.


INTRODUCTION
For time-domain surveys, the temporal pattern of observations, or cadence, determines which astrophysical phenomena can be observed. Accordingly, survey designers choose cadences based on their scientific goals in conjunction with the constraints imposed by their instruments (cf. Bellm 2016).
The Vera C. Rubin Observatory (Ivezić et al. 2019) aims to conduct a Legacy Survey of Space and Time (LSST) that addresses four broad science pillars: probing Dark Energy and Dark Matter, taking an inventory of the Solar System, exploring the transient optical sky, and mapping the Milky Way. Given the scale of the survey and the breadth of its scientific aims (Abell et al. 2009), the project is conducting extensive simulations (Connolly et al. 2014) of potential cadences and evaluating them according to community-supplied metrics, which provide scientifically-motivated scores for evaluating the relative performance of different cadence simulations. Bianco et al. (2021) provides an overview of this process, which makes use of the OpSim simulation framework ; Reuter et al. (2016), a feature-based scheduler (Naghib et al. 2019), and the Metrics Analysis Framework (MAF; Jones et al. 2014).
As a supplement to metrics which treat specific classes of transients (e.g., Andreoni et al. 2021), variables, and accreting sources (e.g., Bonito et al. 2021, Raiteri et al. in prep.), we present a source-agnostic analysis of the time gaps present in current cadence simulations. While detailed metrics simulating specific object classes are important in determining the science impacts of specific cadence choices, they require extensive development by domain experts and may not span the discovery space. Additionally it is challenging to weight specific object classes against one another. Simple metrics in conjunction with knowledge of the survey design can provide a useful supplement to scientifically-motivated analyses.
The (logarithmic) time separation of visits to a given sky area encapsulates the most basic information content of a time-domain survey. Our goal is to maximize the information we gain from these visits about timevarying objects. As discussed by Richards et al. (2018), for a sparsely-sampled time-domain survey, an ideal cadence for source class-agnostic discovery and variability characterization would be uniform in log ∆t-it would be sensitive to variations on all timescales, from the length of a single exposure up to the total survey duration.
In practice, of course, a ground-based survey cannot achieve this uniformity due to diurnal and seasonal cycles. However, the cadence families explored in LSST simulations at the time of this writing (Jones et al. 2020) are still far from effective at probing the full range of accessible timescales. In particular, the use of closelyspaced observation pairs leaves an "intra-night desert" preventing real-time discovery and timely followup of any phenomena varying on timescales of a few hours to a day. This includes stellar flares; young supernovae; gamma-ray bursts, orphan afterglows, and other relativistic transients; kilonovae; and rare new kinds of fast extragalactic transients. This also includes a variety short-timescale accretion variability: Young Stellar Objects (YSOs) show short-timescale bursts and dipping events due to a variety of physical mechanisms, including accretion rate changes, disk warping, stellar flares, and starspots (e.g., Bonito et al. 2018). Among Active Galactic Nuclei (AGN), low-mass supermassive black holes and accreting intermediate mass black holes are expected to be most variable on hours to days timescales (e.g., Burke et al. 2021). Likewise, the most dramatic active phases of extreme flaring blazars exhibit shorttimescale variability that can help identify the underlying emission physics (e.g., Raiteri et al. 2021a,b).
In this paper we present a new scalar metric for evaluating the temporal sampling of a time-domain survey on timescales of interest ( §2). In §3 we evaluate this metric on current LSST cadence simulations, with particular focus on sampling at short timescales. We close in §4 with a range of ideas for diversifying the cadences of the Rubin Observatory's LSST.

METRICS
To analyze the current simulations, we used the existing MAF metric lsst.sims.maf.metrics.TgapsMetric with logarithmic bins from 30 seconds to 10 years. 1 . We computed pairwise separations (allGaps=False) between observations in any filter and summed the re-  (Table 1).
sulting histograms for an NSIDE=64 healpix grid 2 . We also computed a normalized cumulative distribution function (CDF) of the resulting histogram.
Using this cumulative histogram as a conceptual starting point, we defined a new metric (TgapsPercentMetric) which represents the percentage of observation pairs with separations between 2 hours and 14 hours (same night revisits) and between 14 and 38 hours (next-night revisits). We selected these intervals due to their importance for identifying fast-evolving transients, but the metric can be configured to use any desired time window. The resulting code is publicly available in the central rubin sim MAF metric repository 3 .

RESULTS
We evaluated our metrics on OpSim simulations from the v1.5, v1.7, and v1.7.1 families (Jones et al. 2020). Figure 1 presents these time gap histograms for several illustrative example runs, and Table 1 summarizes the TgapsPercentMetric for each.
Despite the possibility of observing fields with time gaps longer than two hours but before the end of the current night, we find that less than 1% of visits are spaced in this critical timescale across all survey families. We stress that there is no inherent limitation preventing observations in this time range.
Perhaps surprisingly, given the fiducial 3-day cadence of the main Wide-Fast-Deep survey, one-night cadence timescales are somewhat better covered. Many simulation families show 7-12% of visit gaps at one-day timescales, although a subset have sub-percent fractions at 1-day timescales as well. The latter observing strategies would be catastrophic for discovery of fast-evolving transients.
We also compared these simulations to comparable histograms from the Zwicky Transient Facility (ZTF; Bellm et al. 2019a;Graham et al. 2019). While ZTF has a field of view five times larger than LSSTCam, and therefore on average revisits a given area of sky five times more often (Bellm 2016), the ZTF surveys have also explicitly sought to span a wide range of timescales. These have included "movie mode" continuous-cadence observations, 6 visit per night transient searches, twilight searches for moving objects, as well as slower 2, 3, and 4-day cadence surveys (Bellm et al. 2019b).

Survey Footprint
Generally, we expected the increased number of visits in simulations which use a smaller main survey (Wide-Fast-Deep) footprint would provide more effective time sampling. However, current simulation families do not distribute the additional visits at short timescales and so do not provide a major improvement in the relevant metrics. The wfd depth, filt dist, and footprint simulations are comparable to or slightly worse than the current baseline simulations, with the exception of the fbs 1.7footprint tunefootprint # simulations, which have extremely low (sub-percent) coverage at 1day timescales.

Visit Pairs
Paired observations need to be closely spaced (up to ∼ one hour) for linking of main-belt asteroids to succeed (Jones et al. 2018) due to the N 2 combinatoric explosion of source pairs to consider when constructing tracklets. Current simulation families explore the effect of varying both the visit pair separation as well as the filters used in the visit pair.
The pair times family considered spaces as large as 55 minutes. The largest pair-spacing simulation, pair times 55, provides the best metric values for both the 2-14 and 14-38 hour timescales of all the simulations to date.
With the exception of stellar flares, most of the classes of fast transients motivating this work above will not vary appreciably on timescales less than an hour. Accordingly this suggests that switching filters between observations in a pair (as in the current baseline) is preferable, so that the second observation provides nonredundant information (color).

Triplet Observations
"Triplet" observations (the "Presto-Color" strategy, Bianco et al. 2019) add a third nightly observation in one of the two filters of the visit pair, and so present the best means of capturing the intranight variability of fast transients. Suprisingly, the current third obs pt# simulations show almost no improvement in 2-14 hour timescale coverage. The current triplet implementation thus provides little improvement over the baseline strategy, as it does not provide sufficiently wide time sampling nor enough additional visits to substantially change the fraction of observations in the intra-night desert. Further improvements to the current LSST implementation of this survey strategy are necessary for triplet observations to reach their potential. Scheduling multiple images with wide spacing during the night may benefit from scheduling algorithms that optimize field selection on nightly timescales (e.g., Bellm et al. 2019b).

Rolling Cadences
Rolling cadences provide the best means of allocating additional observations into the 2 hours-1 night window critical for rapid discovery of fast-evolving transients. Current simulations show a wide range of performance; the rolling scale and alt roll simulations have very poor (sub-percent) coverage of one-day timescales. rolling nm scale1.0 nslice2 is close to the baseline, and rolling nm scale0.90 nslice3 fpw0.9 nrw1.0 approaches the pair times 55 simulation in its effective timescale coverage. We suggest continued investigation into how best to distribute the rolling visits in time.

Per-filter Time Gaps
So far we have considered pairwise time gaps between observations in any pair of filters. Analysis of shorttimescale variability will be more straightforward when those two visits are in the same filter, however. Figure 2 shows the per-band time gap histograms between observations in the same filter for the baseline nexp1 simulation. We excluded the Deep Drilling Fields, which observe only a small sky area and cycle through the available filter set on a daily basis.
Overall, the morphology of the per-band time-gap histograms is quite similar to the total histograms ( Figure  1). There are very few observation pairs in the 2-14 hours range (TgapsPercentMetric ranges from 0.0% (g & y bands) to 1.6% (u)). The 14-38 hour interval shows a larger revisit fraction, with TgapsPercentMetric ranging from 6.1% (g) to 10.2% (z). The per-band sampling on one-day timescales is thus larger than expected given the notional baseline cadence, although we note that the histograms show a long tail of revisit times extending from weeks to months.

Comparison to ZTF
For an informative comparison to an existing sky survey, we also computed histograms and the TgapsPercentMetric on ZTF's on-sky pointing history. We included pointings from all public and private surveys from March 2018-September 2021. We determined pairwise time gaps for each discrete ZTF field, neglecting the overlaps at the field edges, which typically provide additional sampling on sub-hour timescales. Figure  1 shows the resulting time gap histogram, and Table 1 lists the corresponding metrics.
As discussed in Bellm (2016), the areal survey rate (the instantaneous field of view of a survey camera divided by its exposure time and any overheads) determines the number of exposures of a field a survey can obtain on average. Due to its wider field of view, ZTF obtains a factor of five more yearly exposures per field than LSST. Despite this advantage and a significant focus of a subset of the private ZTF surveys on high-cadence ob- servations (Bellm et al. 2019b), we see that ZTF has only 3.6% of its observations in the 2-14 hour window and 17.7% in the 14-38 hour window. This is due to the presence of other large observing programs (e.g., the public 2-and 3-day cadence Northern Sky Survey). We may thus take the ZTF numbers as a practical upper bound which LSST can achieve with its multi-faceted survey goals, and suggest that LSST target 1-2% for 2-14 hours and 10-15% for the 14-38 hour window.

DISCUSSION
The existing survey simulations analyzed in §3 generally exhibit sub-percent revisit fractions within the night ( Table 1). Modifications of the existing triplet and rolling cadence strategies may already be enough to improve this sampling. However, we also suggest exploration of more unique cadence modes not present in the existing survey families.
Asteroid discovery drives the requirement for visit pairs spaced by an hour or less. However, most Main Belt Asteroids (∼ 80%; M. Juric, priv. comm) are discovered in the first three years of the survey (Ridgway et al. 2014). Accordingly a move to much wider visit pairs (> 2 hours) later in the survey might enhance fast transient discovery without compromising LSST's solar system science: with the majority of new asteroids discovered and the false-positive rate well-understood, identifying tracklets over wider temporal spacing could be tractable. Alternatively, new asteroid discovery algorithms show promise in discovering asteroids independent of the input cadence (Moeyens et al. 2021).
Because the current LSST Deep Drilling Fields are scheduled as single contiguous blocks of observations, they also do not provide leverage for intra-night variability. Scheduling approaches that separated observations of a Deep Drilling Field widely within the night would be extremely valuable for identifying short-timescale variability, albeit over a limited sky area.
Throughout this work we have largely focused on pairwise time separations between observations in any pair of filters. In practice, identifying rapid shorttimescale variability-especially in near real-time-is most straightforward if those observations are both taken in the same filter. Making use of heterogeneous filters will require model-dependent assumptions about the source spectral energy distribution and extinction. Although this challenge will be present in analysis of LSST's multi-band data at all timescales, the limited number of data points available for fast transients will make such interpretation particularly difficult. For this reason, the Presto-Color triplet strategy (Bianco et al. 2019) explicitly requests two widely-spaced visits within the night in the same filter.
Were additional visits available, we would suggest the observing time be used to provide a "variability wedding cake" survey approach that would more broadly explore the discovery space in log ∆t. This might include pointand-stare continuous-cadence ("movie-mode") observations of single fields to provide sensitivity to very short timescale variability; short high-cadence campaigns on a limited sky area (e.g., Bonito et al. 2018); adding third (triplet) observations within the night to Wide-Fast-Deep fields; and maximizing the season length to provide sampling on many month timescales. For efficiency these additional observations might only use a subset of the available filters. Reserving a few percent of observing time for a series of such experiments throughout the survey might yield outsized scientific returns.
The Vera C. Rubin Observatory's Legacy Survey of Space and Time will transform time-domain astronomy over the next decade. Fulfilling its discovery potential across a wide range of science requires challenging cadence optimization. In particular, efficient asteroid discovery requires closely-spaced visit pairs early in the survey. The moderate number of available visits per year (∼80, on average) to a given sky position and the need for effective sampling of supernovae on timescales of months further limit the ease with which LSST can observe short variability timescales. Nevertheless, we argue that LSST should consider creative opportunities to enable exploration of the widest range of time-domain astrophysics.
We thank Lynne Jones, Peter Yoachim, and Mario Juric for useful discussions.
This paper was created in the Rubin LSST Transient and Variable Star (TVS) Science Collaboration 4 . The authors acknowledge the support of the Vera C. Rubin Legacy Survey of Space and Time Transient and Variable Stars Science Collaboration that provided opportunities for collaboration and exchange of ideas and knowledge and of Rubin Observatory in the creation and implementation of this work. Publication support was provided by the Heising-Simons Foundation through the "Preparing for Astrophysics with LSST" grant to TVS and other LSST Science Collaborations. The authors also acknowledge the support of the LSST Corporation, which enabled the organization of workshops and hackathons throughout the cadence optimization process by directing private funding to these activities. This research uses services or data provided by the Astro Data Lab at NSF's National Optical-Infrared Astronomy Research Laboratory. NOIRLab is operated by the Association of Universities for Research in Astronomy (AURA), Inc. under a cooperative agreement with the National Science Foundation.
ECB gratefully acknowledges support from the NSF AAG grant 1812779 and grant #2018-0908 from the Heising-Simons Foundation.
ECB acknowledges further support from the Vera C. Rubin Observatory, which is supported in part by the National Science Foundation through Cooperative Agreement 1258333 managed by the Association of Universities for Research in Astronomy (AURA), and the Department of Energy under Contract No. DE-AC02-76SF00515 with the SLAC National Accelerator Laboratory. Additional LSST funding comes from private donations, grants to universities, and in-kind support from LSSTC Institutional Members.