Equation 12 · A Neutron Star Is a Redshift Standard
What does this equation mean?
Read the formula alongside the article passage below. Each part has a deeper page with its role in the equation, the supporting passage and nearby citations.
This equation states an equality: the expressions on both sides have the same value under the article’s assumptions. Read the equation part by part below; each part has a contextual explanation and a link to its mathematical background.
Read it piece by piece
Symbol z_s
is part of the quantity the equation computes from the expression on the right.
=
The expressions on both sides represent the same quantity under the stated assumptions.
See an illustrated explanation →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.
How to interpret it
Read it with the definitions, units, and assumptions supplied by the article.
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…
Read the full surrounding passage
— 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 ↗
These citations give research context. Read each source to check which claims it supports.
Return to A Neutron Star Is a Redshift Standard