WARPLAB

What am I looking at?

What you are looking at

A star passing almost in front of a more distant one bends its light and brightens it for weeks: gravitational microlensing. The first tab shows the sky round the lens and the light curve it makes, and how a planet round the lens star adds a short blip. The second tab holds two real OGLE events: fit a single lens, then a star with a planet, and compare the planet's mass ratio and separation with the published values. A microlensing event in the live feed opens here too: its OGLE light curve is loaded beside them and fitted with a single lens as the page opens.

Controls

On this device:

Mouse

  • Click a Try button for OGLE-2012-BLG-0406's planet, a Jupiter or an Earth.
  • Drag the time slider, or click a numbered step, to move the background star along its path; Play and Pause run it on its own (not in the stepped version).
  • Drag Closest approach, Einstein time, Mass ratio, Separation and Path angle; the sky and the curve follow.
  • Click OGLE data, pick an event, then Fit a single lens, Fit with a planet or Published model.
  • Click the badge under the event's facts for the data's source and credit.

Keyboard

  • Tab to a button (Try, Play, a step, an event, a Fit button, Published model); Enter or Space presses it.
  • Tab to a slider; the arrow keys move it, Home and End jump to its ends.
  • On the tabs, the left and right arrows switch between Lens and planet and OGLE data.
  • H or ? opens this panel. Esc closes it.
Other devices

Touch

  • Tap a Try button for a real or a typical planet.
  • Slide the time control with your finger, or tap a step.
  • Slide the five lens controls; the sky and the curve follow.
  • Tap OGLE data, an event, then a Fit button.
  • Tap the source badge for where the data come from.

Glossary

Microlensing
A star's gravity bending the light of a star behind it into images too close together to see apart. Their total is brighter than the source alone, so the background star brightens and fades as the lens passes.
Why it matters It needs no light from the lens or its planet, so it finds planets round faint stars thousands of light-years away.
Einstein radius
The ring a source exactly behind the lens would form. Every length here is in Einstein radii; for a star half the Sun's mass halfway to the Galactic centre it is about 2 AU on the lens's plane.
Einstein time t_E
The days the source takes to cross one Einstein radius. It mixes the lens's mass, the distances and the relative speed, so alone it does not give the mass.
Why it matters It sets how long the event lasts; most bulge events take 10 to 100 days.
Closest approach u₀
The source's smallest distance from the lens, in Einstein radii, at the time t₀. A point lens magnifies by A(u) = (u² + 2)/(u √(u² + 4)): 1.34 at u = 1, about 1/u when u is small.
Magnification A
How many times brighter the source looks: the sum of its images' brightnesses. Its curve against time is the light curve.
Images and parity
A single lens makes two images, a binary lens three or five. Each is the source seen magnified and distorted; half of them are mirror-flipped (negative parity, hollow on the sky view).
Mass ratio q
The planet's mass over its star's. Jupiter round the Sun is 10⁻³, the Earth 3 × 10⁻⁶. OGLE-2012-BLG-0406Lb's is 5.8 × 10⁻³: about 3.6 Jupiter masses round a 0.59 M☉ star.
Why it matters The blip's length and size give q directly; the planet's mass in kilograms needs the star's.
Separation s
The planet's distance from its star projected on the sky, in Einstein radii. Planets near s = 1 make the largest caustics and are found most often.
Why it matters s and 1/s give much the same central caustic, so some events have two answers; the planetary caustic of OGLE-2012-BLG-0406 settles it at 1.35.
Caustic
The closed curves on the sky where a point source's magnification is infinite and two extra images appear or vanish. A planet beyond s = 1 has a small caustic about s − 1/s from its star.
Why it matters Crossing or passing one makes the planet's blip.
Source radius ρ
The background star's radius in Einstein radii. Near a caustic the star's disc is not a point: its edge crosses first, and the spike is rounded off.
Source and blend flux
The light is F = F_s A + F_b: the source's flux, magnified, plus light from stars in the same seeing disc that is not. The fit solves both exactly.
χ²/ν
The sum of (data − model)² / error² over the points, divided by the degrees of freedom (points less the parameters fitted). Near 1, the model fits within the errors.
Why it matters A single lens on the planet's event leaves χ²/ν far above 1; adding the planet brings it near 1.
OGLE Early Warning System
OGLE's real-time pipeline (Udalski 2003): it finds microlensing events in the bulge each night with the 1.3 m Warsaw Telescope at Las Campanas and publishes their photometry and a single-lens fit.
Roman's bulge survey
NASA's Nancy Grace Roman Space Telescope will watch 1.7 deg² towards the Galactic centre once every 12.1 minutes for six seasons of 70.5 days (STScI), expecting more than a thousand planets (NASA).

All help and questions

Planets by microlensing

A lens star brightens a star behind it; a planet adds a blip. Fit real OGLE data and weigh the planet.

  • Lens star
  • Planet
  • Background star
  • Its images (size: brightness)
  • Caustic
  • Einstein ring
11.5235-80-60-40-20020406080Days from closest approachMagnification
  • With the planet
  • Without it

Pick a step, or drag the time slider.

How close the source passes the lens, in Einstein radii. Smaller means brighter at the peak.

Days the source takes to cross one Einstein radius. It sets how long the event lasts.

The planet's mass over the star's: 10⁻³ is a Jupiter round the Sun, 3 × 10⁻⁶ an Earth.

Planet to star, projected on the sky, in Einstein radii. Near 1 the planet's caustic is largest.

The angle between the source's path and the star–planet line.

Magnification now
1.18×
Without the planet
1.18×
The planet adds
−0.3%
Largest blip
214.1%
Planet, if the star has 0.5 M☉
3.0 Jupiter masses

How a star becomes a lens

When a star passes almost in front of a more distant one, its gravity bends the distant star's light into two images either side of the Einstein ring. They are too close together to see apart, but together they are brighter: the background star brightens and fades over weeks, in a curve set by u₀ and t_E alone.

What the planet adds

A planet adds its own small lens. Its caustic, the line where the images become infinitely bright for a point source, sits about s − 1/s from the star along the star–planet line. When the source crosses or skirts it, the curve jumps for a few hours to days. The blip's length gives q; its timing gives s.

Data and credits

Photometry: the OGLE-IV Early Warning System, ogle.astrouw.edu.pl/ogle4/ews/ews.html (A. Udalski 2003, Acta Astron. 53, 291; A. Udalski, M. K. Szymański and G. Szymański 2015, Acta Astron. 65, 1), shown as the EWS page asks. The planet: R. Poleski et al. 2014, ApJ 782, 47.

Method: the lens equation as Witt and Mao's (1995) fifth-order polynomial, Gould's (2008) hexadecapole away from caustics and contour integration with Bozza's (2010) correction near them, checked against VBBinaryLensing and MulensModel.

OGLE Early Warning SystemUdalski 2003Udalski et al. 2015Poleski et al. 2014