Equation 10 · A Neutron Star Is a Redshift Standard
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Symbol M
M is part of the quantity the equation computes from the expression on the right.
Symbol M_odot
dot is an input to the expression that computes the quantity on the left.
=
The expressions on both sides represent the same quantity under the stated assumptions.
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What the article says around this equation
— 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\, with a radio-timing mass fixed independently by Shapiro delay to 2.080.07\, [ 4 ] , giving a compactness near 0.25 and a surface redshift 0.40 — 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\, with a radio-timing mass fixed independently by Shapiro delay to 2.080.07\, [ 4 ] , giving a compactness near 0.25 and a surface redshift 0.40 — 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=1.4180.037\, and R=11.36^{+0.95}_{-0.63} km [ 3 ] , which maps to =0.2570.026 — 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.
Sources cited in the surrounding passage
- [4] Refined Mass and Geometric Measurements of the High-mass PSR J0740+6620 ↗
- [3] A NICER View of the Nearest and Brightest Millisecond Pulsar: PSR J0437-4715 ↗
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