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Equation 20 · Part 12 · A Neutron Star Is a Redshift Standard

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ΔE/E≈veq/c=2πνR/c≈1.3×10−1(ν/500 Hz)(R/12 km)\Delta E/E \approx v_{eq}/c = 2\pi\nu R/c \approx 1.3\times10^{-1}(\nu/500\,\text{Hz})(R/12\,\text{km})
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What this part means

A raised number can be a power. When it is a label or bound, it selects a case or the upper limit of a sum; the formula’s structure distinguishes these uses.

Its job in the formula

A raised mark can be a power or an index. Its position and the surrounding notation determine which.

The passage around this formula

The mechanism behind that contradiction is simple enough to state in one line, and the paper’s authors compute it carefully because the commonly quoted version understates it by an order of magnitude. Surface rotation Doppler-broadens any spectral line by a fraction of its energy equal to the star’s equatorial velocity over the speed of light, Δ\Delta E/E ≈\approx veqv_{eq}/c = 2π\piν\nu R/c ≈\approx 1.3×\times10^{-1}(ν\nu/500\,Hz\text{Hz})(R/12\,km\text{km}) , where ν\nu is the star’s spin frequency and R its radius.

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Sources cited in the article section

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