Rogue Planet Infrared Glow Detector

Rogue Planet

Mass 6.0 M_Jup

Age since formation 10 Myr

Distance from Earth 50 pc

Survey telescope

Detection Readout

Below detection threshold

Effective temp.

— K

Luminosity

—

Apparent mag.

—

Limiting mag.

—

How it works

A free-floating ("rogue") planet has no host star, so it can't be found by transits or radial velocity. A young one, however, is still glowing in infrared from the heat of its own formation — this is Kelvin–Helmholtz contraction: gravitational potential energy released as the planet slowly shrinks is radiated away as heat, and that glow fades as the planet ages and cools.

log10(L / L_sun) ≈ -3.6 + 1.6·log10(M / M_Jup) - 0.9·log10(t / 10 Myr)

Stefan–Boltzmann:  T_eff = ( L / (4π R² σ) )^(1/4),  R ≈ 1 R_Jup
Absolute bolometric mag:  M_bol = 4.83 - 2.5·log10(L / L_sun)
Apparent magnitude:  m = M_bol + 5·log10(d / 10 pc)

This cooling-track scaling is a simplified fit in the spirit of gravitational-contraction models (Burrows et al. 1997) for isolated giant planets and brown dwarfs — real evolutionary tracks depend on atmosphere and initial entropy too, but the trend is the same: heavier and younger objects are brighter, and luminosity collapses fast with age.

Mass — sets how much gravitational energy is available to radiate; more massive objects stay hot longer.
Age — luminosity falls roughly as a power law in time as the planet contracts and cools.
Distance — apparent brightness dims with the inverse-square law, so the same planet becomes undetectable if placed far enough away.
Survey telescope — each real infrared survey has a limiting magnitude; if the planet's apparent magnitude is fainter (numerically larger) than that limit, it cannot be detected.

This is one of two real ways astronomers find rogue planets — the other is gravitational microlensing, covered in this site's separate microlensing light-curve simulator. Direct infrared imaging only works for young, still-warm free-floating planets; older ones (like a hypothetical rogue Jupiter at billions of years) are far too cold and faint for any current telescope to image directly, and must instead be found by microlensing.

Rogue planet (thermal glow) Unbound straight-line drift

Telescope view

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