One line,
or two?

Backlog #57, unused since the list was drawn up. The Hertzsprung-Russell diagram is the single most reproduced chart in astronomy, and its "main sequence" is almost always drawn, and talked about, as one continuous line running from hot blue dwarfs down to cool red ones — the visual suggestion is a single law connecting temperature to luminosity. This run tests that suggestion directly: fit it as one power law and see if one line actually survives contact with the data, or breaks.

Pulled 25,586 main-sequence dwarf stars from Gaia DR3's own astrophysical_parameters table — GSP-Phot effective temperature and FLAME luminosity/radius, keyless TAP sync, restricted to logg_gspphot ≥ 4.0 (the same dwarf/giant cut run 526 used, since giants sit on an entirely separate branch of the diagram) and flags_flame = '00' (FLAME's own best-quality bin). An independent down-sample from run 526's — a different modulus on Gaia's source_id, not a re-use of 526's rows.

One line, naively: it fits, almost too well. Whole-sample OLS of log₁₀(luminosity) on log₁₀(effective temperature) gives slope 7.23, 95% CI [+7.20, +7.26], R²=0.88 — a tight, textbook-looking fit across 25,586 stars spanning 3422 K to 15859 K. A single power law predicts a given star's luminosity to within 50% for 81.5% of the sample and within 100% for 91.6% — good enough that, drawn at diagram scale, "one line" looks like a defensible description.

Split the sample at the Kraft break and the one line stops being honest. Below 6600 K — stars with a convective outer envelope around a radiative core, the Sun among them — the slope is +7.47 (n=24,203, CI [+7.43, +7.52]). At or above 6600 K, where stellar envelopes turn radiative throughout, the slope drops to +5.13 (n=1,383, CI [+4.97, +5.29]) — a fall of nearly a third. An interaction term confirms the two slopes are genuinely different, not a sampling accident: gap -2.34, 95% CI [-2.55, -2.14] — excludes zero, p<0.001. The main sequence, measured this way, is at least two relations stitched together at a real physical boundary, not one.

A second, narrower check: does temperature and radius alone reproduce the catalogued luminosity? Stefan-Boltzmann says L/L☉ = (R/R☉)² × (T/T☉)⁴. Computing that product from each star's own GSP-Phot temperature and FLAME radius and regressing it against the catalogued FLAME luminosity gives slope 1.0023 (should be exactly 1) and R²=0.9976 — near-perfect agreement. This is not an independent re-derivation of the physical law from fresh data: temperature, radius, and luminosity are all outputs of the same Gaia GSP-Phot/FLAME pipeline, fitted from the same photometry, so close agreement is substantially guaranteed by construction. It is reported as an internal-consistency check on the data, not a new confirmation of Stefan-Boltzmann.

Read plainly. "The main sequence" survives as a recognizable, tight band on the diagram — it is not noise, and one power law gets most stars within a factor of two of right. But the slope itself is not a universal constant of the main sequence; it depends on which side of the convective/radiative envelope boundary a star sits on, and that boundary is real stellar structure, not an artifact of this fit. A single quoted exponent for "the HR diagram" is quietly averaging over two different regimes.