Faintsol

Faintsol, a young sun-child of the Paradox Parlour, glows at only about 70% of today's light, yet beneath her the early Earth kept liquid seas.

The Physics

As the Sun fuses hydrogen into helium, its core gets denser and hotter, so it slowly brightens. Standard solar models give about 70% of today's luminosity some 4.5 billion years ago. With today's atmosphere and albedo, that would leave the early Earth's average temperature below freezing for roughly its first two billion years. But the geological record shows liquid water on Earth more than 3.8 billion years ago. Carl Sagan and George Mullen stated this paradox in 1972.

L(t) ≈ [1 + (2/5)(1 − t/t_⊙)]⁻¹ L_⊙

• L(t): solar luminosity at age t
• t: age of the Sun at that time
• t_⊙: present age of the Sun, about 4.57 billion years
• L_⊙: present solar luminosity, 3.828 × 10²⁶ W (IAU nominal value)

This is Gough's interpolation fit to standard solar models (see Gough, Solar Physics 74, 21, 1981), with t counted from the start of the main sequence; at t = 0 it gives L ≈ 0.71 L_⊙.

Honest caveat: The paradox is not fully settled. The leading explanations are a stronger greenhouse effect (more CO₂, possibly methane), and maybe lower albedo from fewer clouds or less land. How much each contributed, and whether the carbon-cycle evidence allows enough CO₂, is still debated. A more massive young Sun losing mass in a strong wind has also been proposed, but observations of young Sun-like stars do not favour it. The Sun's brightening itself is well established.

On the sticker

Faintsol holds a small amber sun-orb that is dimmer than the Sun of today. Printed text: FAINTSOL with the line L ≈ 0.7 L⊙. Pixel-art kiss-cut vinyl sticker, white, in 2″, 3″, 4″ and 6″ sizes.