Dark Classification Matters: Searching for Primordial Black Holes with LSST

TL;DR

The paper tackles constraints on primordial black holes as dark matter using LSST microlensing, leveraging simulated LSST light curves to train discriminants that separate microlensing signals from constant variability. It introduces tail-modeling of discriminant distributions (Pareto for the BIC ratio and Johnson $S_B$ for the BDT) to extrapolate extremely low false positive rates, enabling robust efficiency estimates $ar{oldsymbol{3E}}(t_E)$ and event-rate calculations under an isothermal DM halo. The study finds that 1-year LSST projections can yield competitive PBH bounds in the $10^{-6}$–$10 ext{ M}_igodot$ range when FPR is controlled at about $10^{-7}$ per star per year, with 10-year data pushing sensitivity by another order of magnitude; naive or high-FPR analyses substantially overstate reach. The work provides a principled framework for FPR-controlled microlensing searches in large surveys and highlights foreground modeling and potential follow-up strategies as key factors shaping the final constraints on compact dark matter objects.

Abstract

We present projected constraints on the abundance of primordial black holes (PBHs) as a constituent of dark matter, based on microlensing observations from the upcoming Legacy Survey of Space and Time (LSST) at the Vera C. Rubin Observatory. We use a catalogue of microlensing light curves simulated with Rubin Observatory's OpSims to demonstrate that competitive constraints crucially rely on minimising the false positive rate (FPR) of the classification algorithm. We propose the Bayesian information criterion and a Boosted Decision Tree as effective discriminators and compare their derived efficiency and FPR to a more standard $χ^2$-test.

Figures (7)

• Figure 1: Skymap of the number of $i$-band visits (NVisits$_i$) during the first year of the LSST survey, simulated using the baseline_v4.3.1_10yrs strategy. The coverage reflects the depth variations across the sky due to the adopted survey cadence. We restrict the map to $-75^\circ\leq \delta \leq+15^\circ$ where the expected airmass is $\leq 1.4$. The plot is centered at right ascension $\alpha=0^\circ$ and declination $\delta=0^\circ$, with RA and declination lines marked every 15$^\circ$.
• Figure 2: Classifier outcomes: $\chi^2 /\text{d.o.f. ratio}$, BDT output, and BIC ratio as defined above for the signal-less constant class on the left and microlensing events on the right. The magnitude difference in the event is indicated by the colour gradient.
• Figure 3: $99\%$ tail distributions of BIC ratio and BDT outputs for the constant class, and best fit closed-form distributions used to extrapolate to expected FPR $=10^{-7}$.
• Figure 4: Efficiency after 1 year of data defined as the fraction of events for which the classifier output exceeds the cuts (BDT score and BIC as in table \ref{['tab:cuts']}), for the two classifiers described in text. Here we binned the data linearly with $\Delta t_{\rm E} = 5$ days. The dashed curves provide the fit of to the function \ref{['eq:efficiencyfunc']} of the first $100$ days: it is seen that while this provides a reasonable fit for this period, it overestimates the efficiency for larger Einstein crossing times. The continuous curves provide the fit to \ref{['eq:efficiencyfunc2']}.
• Figure 5: Projected constraints on the PBH parameter space from gravitational microlensing by the LSST. We show the 1 year and the 10 year projections with filled and continuous lines respectively. In blue, we indicate the constraints obtained using the $\chi^2$/d.o.f. ratio test described in text along with a cut on the fitted $u_0$ parameter ($\tilde{u}_0$). In red, we show the constraints derived using the BIC with threshold cut as described; the BDT gives equivalent constraints. With the dashed line we indicate the constraints we would have derived had we ignored the FPR of our classifier. With the dotted lines we indicate the constraints if we assume the foreground can be distinguished using spectroscopic information. In gray existing microlensing constraints, in light blue existing gravitational wave constraints. See text for further details.