Step 10 — Case study & triggers: Sgr A* flares vs a Galactic supernova

What the paper argues (plain English): Two “natural experiments” showcase how the flux→drift template plays out in the wild:

Sgr A* (our Galactic-center black hole) occasionally flares with luminosity \(L\!\sim\!10^{29}\,\text{W}\) lasting \(\Delta t\!\sim\!10^4\) s. Even for a pulsar right there at \(r\!=\!1.2\times10^{13}\) m, the implied time-potential step is only \(\Delta\Phi\!\sim\!-6.9\times10^{-25}\) — far below present pulsar-timing sensitivity. Conclusion: conceptually clean, but sub-threshold today.
Galactic core-collapse supernova (SN): the neutrino burst is a gigantic outbound flux, \(L_\nu\!\sim\!3\times10^{45}\,\text{W}\) for \(\sim10\) s. At a typical Galactic distance \(r\!\sim\!10\) kpc, this gives \(\Delta\Phi\!\sim\!+8\times10^{-19}\). That’s within roughly an order of current optical-clock stability, making it a promising “target of opportunity.” The strategy: phase-lock your template to the neutrino burst and cross-correlate a network of precision clocks.

Operational trigger & requirements (how to run it):

Trigger: use SNEWS 2.0; capture data in a ±6 h window around the alert at ≥ 1 Hz; map neutrino counts into a luminosity proxy \(L_\nu(t)\) (priors/ranges are acceptable).
Time transfer & publishing: each site provides UTC/TAI-traceable time transfer (GPSCV, TWSTFT, or stabilized fiber), plus the measured clock noise \(S_y(f)\) and whitening filter used.
Pre-registered pass/fail: after alignment, demand (i) correct sign, (ii) zero-lag correlation, and (iii) amplitude \(\lambda=G/(c^4 r)\) within errors. Otherwise, report a combined constraint.

Quick scaling intuition: integrate the drift law \(\partial_t\Phi\approx -(G/c^4)\,L(t)/r\) over the burst → \(\Delta\Phi\!\approx\!-(G/c^4)\,E/r\), where \(E\) is the radiated energy crossing your sphere. The SN simply has the enormous \(E\) that Sgr A* flares lack at accessible \(r\). (Numbers are those quoted above from the paper.)

Glossary (for this step)

Symbol	Name	Meaning (units)	Typical value/example	Metaphor
\(L(t)\)	Luminosity	Power crossing a sphere at \(r\) (W)	Sgr A*: \(10^{29}\) W; SN: \(3\times10^{45}\) W	“Brightness push” on time
\(\Delta\Phi\)	Time-potential step	Integrated drift from a transient (–)	Sgr A*: \(-6.9\times10^{-25}\); SN: \(+8\times10^{-19}\)	“Net nudge of the time-dial”
\(r\)	Distance (areal)	Source→clock separation (m)	Sgr A*: \(1.2\times10^{13}\) m; SN: \(10\) kpc	“Lever arm” (farther = weaker)
SNEWS 2.0	Neutrino trigger	Multi-detector alert for Galactic SNe	Use ±6 h, ≥ 1 Hz logging	“Fire alarm” for the burst
\(\lambda\)	Flux→drift gain	Predicted slope \(G/(c^4 r)\) (s²·kg\(^{-1}\)·m\(^{-1}\))	Check sign, zero-lag, 1/r	“Gear ratio” from flux to drift

Next up: Step 11 — Sensitivity & feasibility (bounds-first): ideal analysis limits, real-world noise, and what you actually report.

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