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Equation 20 · Part 10 · 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

Capital delta attached to a quantity marks a difference between two values of that quantity; the article’s sign convention determines the order.

Its job in the formula

Capital delta attached to a quantity marks a difference between two values of that quantity; the article’s sign convention determines the order.

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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Learn the underlying idea

Addition combines quantities; subtraction measures the signed difference between them. Parentheses show what is combined before the rest of the expression is evaluated.

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Sources cited in the article section

These citations provide research context; check each source for the exact claim it supports.