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Equation 12 · A Neutron Star Is a Redshift Standard

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zs=0.257±0.026z_s=0.257\pm0.026

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Inputs and operations0.257pm0.026
Result or conditionz_s
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zsz_s

Symbol z_s

zsz_s is part of the quantity the equation computes from the expression on the right.

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=

=

The expressions on both sides represent the same quantity under the stated assumptions.

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subscript

subscript

The lower label selects a particular version, component, or indexed member of the quantity. For example, x₀ and xₜ can be values at different positions.

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— 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 — the deepest gravitational potential in the sample, though also, because its radius is the harder-measured half of the pair, the least precisely known redshift, at…
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— 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 — the deepest gravitational potential in the sample, though also, because its radius is the harder-measured half of the pair, the least precisely known redshift, at roughly fifteen to sixteen percent. PSR J0437-4715 sits at the opposite end: the nearest and brightest rotation-powered millisecond pulsar NICER has targeted, with a radio-timing mass prior tight enough to pin the pair at M=1.418±\pm0.037\,M⊙M_\odot and R=11.36^{+0.95}_{-0.63} km [ 3 ] , which maps to zsz_s=0.257±\pm0.026 — a ten-percent redshift standard, the tightest of the six, built entirely from timing and pulse-shape data with no spectroscopy anywhere in the derivation.

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