Tolman's Dimming

Plate 75 speaks for itself: “Redshift one: sixteen times fainter.”

The Physics

In an expanding universe the surface brightness of a galaxy falls as (1 + z)⁻⁴, regardless of distance otherwise. At z = 1 that is 2⁴ = 16 times fainter.

Σ ∝ (1 + z)⁻⁴

• Σ: bolometric surface brightness, W m⁻² sr⁻¹
• z: redshift, dimensionless

Tolman, PNAS 16, 511 (1930). Frames are brightness-stretched.

Honest caveat: The (1 + z)⁻⁴ law is for bolometric brightness; in a fixed band and with galaxy evolution the observed dimming differs.

Sources

• R. C. Tolman, Proc. Natl. Acad. Sci. 16, 511 (1930).

On the poster

Plate 075, “Tolman's Dimming”: the pixel-art plate with its slogan “Redshift one: sixteen times fainter.”, the key equation and the facts panel shown above. Pixelated Physics. Physics. Personified.