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Equation 4 · Part 10 · A Neutron Star Is a Redshift Standard

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zs=(1−2GMRc2)−1/2−1z_s = \left(1 - \frac{2GM}{Rc^2}\right)^{-1/2} - 1
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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 relation itself is old and simple. For a spherical, non-rotating exterior, the surface redshift zsz_s follows from the mass M and radius R as zs=(1−2GMRc2)−1/2−1z_s = \left(1 - \frac{2GM}{Rc^2}\right)^{-1/2} - 1. — a function of the star’s compactness alone, so that whatever fraction of a percent of uncertainty NICER puts on M and R propagates directly into the redshift. The paper works through six NICER-mapped pulsars this way, and two of them mark the range worth remembering. PSR J0740+6620, the most massive precisely-timed neutron star known, comes in at roughly 2.07\,M⊙M_\odot with a radio-timing mass fixed independently by Shapiro delay to 2.08±\pm0.07\,M⊙M_\odot [ 4 ] , giving a compactness near 0.25 and a surface redshift zsz_s≃\simeq0.40…

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Learn the underlying idea

An exponent tells how a base is used in multiplication. In x³, x is the base and 3 is the exponent: x³ = x × x × x.

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Sources cited in the surrounding passage

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