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Sandbox Physics
A dark planet bends starlight

AC23 · L4

Read a dark planet’s mass from Earth and space

Open Dong et al., arXiv:2601.00057v1, beside Figure 2 and supplement S5–S11. The event combines a finite-source scale with a difference between Earth and Gaia viewpoints. Then read the separate host-star search and the fixed Roman survey forecast to see how a mass measurement, an isolation claim and a predicted yield answer different questions.

Start with the finite stellar disk in Figure 1

The event is KMT-2024-BLG-0792/OGLE-2024-BLG-0516. In the fixed author version, Figure 1 shows a broad, finite-source feature. Read its time axis and the enlarged event region before reading a physical mass from the abstract. The fitted source radius is comparable to the Einstein radius, so a point-source peak would describe the wrong light curve.

The main text reports ρ=0.991±0.002\rho=0.991\pm0.002 and tE=0.842±0.002 dt_E=0.842\pm0.002\,\mathrm d. Those two fit quantities set the source-crossing clock. Independent information about the source star supplies an angular radius, which converts the fitted ratio into an Einstein angle. Follow that conversion in the supplement and carry the stellar uncertainty with it.

Read the alternative blending discussion in S5–S11 as part of that measurement. The star’s inferred unlensed brightness helps set its angular size. Changing how much light belongs to the source can therefore affect the angular scale used later for the lens mass.

Reading: Dong et al., A Saturn-mass microlensing object, arXiv:2601.00057v1; Science

Follow the two viewpoints through Figure 2

Figure 2A draws Earth and the spacecraft at different locations. The lens and background star then line up slightly differently. Panels showing the trajectories and light curves connect this geometric displacement to observable differences. The useful quantity is the two-dimensional trajectory change, which can include both peak-time and closest-approach changes.

In the preceding chapter, finite-source information gave θE\theta_E. The ground-space comparison supplies πE\pi_E. Their combination M=θE/(κπE)M=\theta_E/(\kappa\pi_E) explains how this event gains a physical mass scale. The fixed author version, identified as published in Science, reports a mass in Jupiter units of 0.219−0.046+0.075 MJ0.219^{+0.075}_{-0.046}\,M_{\mathrm J}.

Now turn to the supplementary solution weights. Different signs of the impact parameters can produce several parallax solutions. Check which data favor one and which additional weights come from assumed populations. A single peak-time subtraction would discard part of this structure.

Reading: Dong et al., A Saturn-mass microlensing object, arXiv:2601.00057v1; Science

Ask a separate question about the missing host

A lens can have a planet-like mass and still orbit a star far away. Open Mróz et al., arXiv:2609.12743v1, a separate preprint marked submitted to A&A in the metadata checked on 3 November 2026. Its Figures 2–3 use later VLTI/GRAVITY measurements to search for light from a possible host.

Read the angular separation and contrast axes first. Contrast describes the flux of a detectable companion relative to the target. Converting it into a host-mass limit uses distance, extinction and a stellar brightness model. The analysis of correlated noise changes the sensitivity; Appendix B explains why independent-noise assumptions can be too optimistic.

The paper reports no luminous host within its tested projected range, reaching about 90 astronomical units, with a conditional five-sigma host-mass limit around one half to six tenths of a solar mass. Fainter, more distant or differently configured hosts remain a separate part of the question. The mass measurement and the search for a host should each keep their own assumptions.

Reading: Mróz et al., host-star limits, arXiv:2609.12743v1, submitted to A&A

Read a Roman forecast as a selection experiment

Johnson et al., arXiv:2006.10760v2, is a fixed 2020 forecast. Open sections 2 and 5, Figures 3–5 and Appendix A. Read the assumed survey schedule and photometric detection cuts before comparing predicted planet numbers. The curves include finite-source effects, and the yield also depends on an assumed mass distribution.

A short lensing feature may fall between measurements or fail the consecutive-point requirement. A larger source can broaden the feature and reduce its peak at the same time. Both changes matter for whether a survey detects it. The forecast’s accepted events are the result of these choices, not a direct picture of every lens in the Galaxy.

For current programme context, use NASA’s Galactic Bulge Time-Domain Survey page. The official plan checked on 3 November 2026 describes repeated observations of six fields at a twelve-minute cadence during its intensive seasons. Keep that current plan separate from the schedule assumed in the 2020 calculation. The bulge microlensing programme uses the wide-field camera.

Reading: Johnson et al. (2020), Roman free-floating-planet forecast, arXiv:2006.10760v2 · NASA Roman Galactic Bulge Time-Domain Survey

Work through a small cadence example

Suppose a synthetic feature stays above a chosen brightness threshold for exactly thirty minutes. A regular observation sequence has a random phase relative to that interval. With twelve minutes between observations, some phases give three measurements inside the feature and others give two.

The fraction with at least three is 30/12−2=0.530/12-2=0.5. With fifteen-minute spacing it is zero apart from an exactly aligned phase of zero probability. This is a simple rectangular-feature counting exercise; a real detection threshold uses the noisy light curve and the survey’s actual gaps.

The example shows why a prediction of discovered planets must state its observation and selection rules. Changing the cadence alters the map from a population to a discovery list. Inferring the population requires reversing that map with a measured detection response.

Reading: Johnson et al. (2020), Roman free-floating-planet forecast, arXiv:2006.10760v2

Keep a short reading checklist

For the next short event, write down which observations determine the duration, which determine the finite-source radius, and which determine the parallax vector. Check whether the mass uses those measurements or a population model. Read a host nondetection with its tested separation, flux threshold and stellar assumptions. For a forecast, keep the source population, schedule and detection cuts next to the headline yield.

That sequence lets the evidence accumulate naturally: images give a changing light curve; finite source size and separated viewpoints can add physical scales; later high-resolution observations can test a possible host. A survey then repeats the experiment across a population.

Reading: Dong et al., A Saturn-mass microlensing object, arXiv:2601.00057v1; Science · Mróz et al., host-star limits, arXiv:2609.12743v1, submitted to A&A · Johnson et al. (2020), Roman free-floating-planet forecast, arXiv:2006.10760v2

Exercises and explanations

  1. A short event has a measured source radius but no microlens parallax. Which physical scale has been gained, and which mass ambiguity remains?

    Read the explanation

    With an independent stellar angular radius, ρ\rho supplies θE\theta_E. Mass still shares that Einstein angle with relative lens-source parallax. A duration adds proper motion information but does not measure the missing distance scale.

  2. A forecast predicts a large number of detectable low-mass lenses. What must be known before comparing that number with a real catalog?

    Read the explanation

    Use the same observing schedule, noise and finite-source assumptions, detection criteria and searched population. A catalog count describes the lenses that passed the selection. Inferring the total population also requires the probability of passing it.

Try the prediction

See how source size changes the feature a survey must catch

  1. Compare the planetary and large-source presets. Identify a short brightness threshold interval and predict how sparse observations could miss it.
  2. Return to the paper figures and separate the measured scales from the population and host-star assumptions.

Sources and calculation scope

  1. Dong et al., A Saturn-mass microlensing object, arXiv:2601.00057v1; Science

    Fixed author version, Figure 2 and supplement S5–S11: finite-source scale, ground/Gaia parallax, alternative blending and solution weights. arXiv identifies the paper as published in Science. This guide reads the evidence; it does not rerun that event.

  2. Johnson et al. (2020), Roman free-floating-planet forecast, arXiv:2006.10760v2

    Sections 2 and 5, Figures 3–5 and Appendix A: Cycle 7 survey assumptions, finite-source light curves, detection cuts and mass-function-conditioned yields. These are the fixed 2020 predictions.

  3. Mróz et al., host-star limits, arXiv:2609.12743v1, submitted to A&A

    Read Figures 2–3, sections 4–5 and Appendix B for interferometric contrast, correlated noise and conversion to a conditional host limit. The fixed version remains a submitted preprint in the metadata checked on 2026-11-03.

  4. NASA Roman Galactic Bulge Time-Domain Survey

    Official microlensing survey context checked on 2026-11-03. The cited programme observes the bulge repeatedly with the Wide Field Instrument.

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