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Astrophysics operators

28 operators in the astrophysics category of the live registry. Each is a named formula you can compose inside a state contract or call directly through POST /api/zeq/compute. KO42 is always on; add up to three more per call (total ≤ 4), per the 7-step protocol.

OperatorDescriptionEquation
APX1Stellar luminosity with Zeq modulation: Stefan-Boltzmann law L=4piR^2sigmaT^4 modulated by 1.287 Hz sinusoidal term.L = 4\pi R^2 \sigma T^4 \cdot [1 + \alpha \sin(2\pi \cdot 1.287t)]
APX10Hawking temperature: black hole thermal radiation temperature inversely proportional to mass (T_H = hbarc^3 / 8piGM*k_B).T_H = \frac{\hbar c^3}{8\pi G M k_B}
APX11Bekenstein-Hawking entropy: black hole entropy proportional to event horizon area (S = k_Bc^3A / 4Ghbar).S_{BH} = \frac{k_B c^3 A}{4G\hbar}
APX12Black hole evaporation time: Hawking radiation timescale scaling as M^3 for complete evaporation.t_{evap} = \frac{5120\pi G^2 M^3}{\hbar c^4}
APX13Gravitational wave strain: quadrupole radiation formula relating strain to mass quadrupole moment second derivative.h = \frac{4G}{c^4 r}(I\ddot{Q})
APX14Gravitational wave frequency: GW frequency equals twice the orbital frequency for circular binary inspiral.f_{GW} = 2f_{orb}
APX15Gravitational wave luminosity: Peters formula for energy loss rate from binary inspiral using chirp mass.\dot{E}_{GW} = \frac{32G}{5c^5}(M_c\omega)^{10/3}
APX16Chirp mass: characteristic mass combination (m1*m2)^(3/5)/(m1+m2)^(1/5) governing gravitational waveform evolution.M_c = \frac{(m_1 m_2)^{3/5}}{(m_1 + m_2)^{1/5}}
APX17Cosmological redshift with Zeq modulation: standard redshift z = (lambda_obs - lambda_emit)/lambda_emit with 1.287 Hz modulation.z = \frac{\lambda_{\mathrm{obs}} - \lambda_{\mathrm{emit}}}{\lambda_{\mathrm{emit}}} \cdot [1 + \alpha \sin(2\pi \cdot 1.287t)]
APX18Hubble law (astrophysics formulation): recession velocity proportional to distance via Hubble constant H_0.v = H_0 d
APX19Luminosity-angular diameter distance relation: d_L = (1+z)*d_A connecting observable distances in expanding spacetime.d_L = (1+z)d_A
APX2Hydrostatic equilibrium: pressure gradient balanced by gravitational force per unit volume in stellar interiors.\frac{dP}{dr} = -\frac{Gm\rho}{r^2}
APX20Cosmic density parameters: matter, dark energy, and curvature densities summing to unity (flat universe constraint).\Omega_m + \Omega_\Lambda + \Omega_k = 1
APX21Critical density: rho_c = 3H_0^2 / (8pi*G), the density for a spatially flat universe.\rho_c = \frac{3H_0^2}{8\pi G}
APX22Scale factor evolution: a(t) ~ t^(2/3) in matter domination, exponential in dark-energy domination.a(t) \propto t^{2/3} \text{ (matter)}, \quad e^{Ht} \text{ (dark energy)}
APX23CMB temperature constant: T_CMB = 2.725 K, the present-day cosmic microwave background temperature.T_{CMB} = 2.725 \text{ K}
APX24Density contrast: fractional overdensity (rho - rho_bar)/rho_bar for cosmic structure formation.\delta = \frac{\rho - \bar{\rho}}{\bar{\rho}}
APX25Matter power spectrum: P(k) = |delta_k|^2, Fourier-space variance of density fluctuations.P(k) = |\delta_k|^2
APX3Nuclear energy generation: luminosity gradient proportional to local density and energy generation rate in stellar cores.\frac{dL}{dr} = 4\pi r^2 \rho \epsilon
APX4Radiative temperature gradient: temperature change with radius governed by opacity, density, and luminosity in stellar envelopes.\frac{dT}{dr} = -\frac{3\kappa\rho L}{16\pi ac T^3 r^2}
APX5Main-sequence lifetime: stellar lifetime scaling as M^(-2.5) relative to solar values (~10 Gyr for 1 solar mass).t_{MS} = 10^{10}\left(\frac{M}{M_\odot}\right)^{-2.5} \text{ yr}
APX6Chandrasekhar mass limit: maximum mass (~1.4 solar masses) for a white dwarf supported by electron degeneracy pressure.M_{Ch} = 1.4 M_\odot
APX7Neutron star radius: characteristic ~10 km radius for neutron-degenerate stellar remnants.R_{NS} \approx 10 \text{ km} = \frac{2GM}{c^2} \cdot k_{NS}
APX8Pulsar spin-down: period-derivative relation to magnetic field strength, radius, angular velocity, and moment of inertia.P\dot{P} = \frac{B^2 R^6 \Omega^4}{6c^3 I}
APX9Schwarzschild radius with Zeq modulation: r_s = 2GM/c^2 modulated by exponential 1.287 Hz sinusoidal term.r_S^{\mathrm{APX}} = \frac{2GM}{c^2} \cdot e^{\alpha \sin(2\pi \cdot 1.287t)}
NYX1Nyx intensity operator 1: azimuthal integral of spectral intensity for 1D astrophysical radiation field analysis.N_1 = \int_0^{2\pi} I(\theta)d\theta
NYX2Nyx intensity operator 2: full solid-angle integral of spectral intensity for 2D sky brightness mapping.N_2 = \int_0^\pi \int_0^{2\pi} I(\theta,\phi)\sin\theta\,d\theta\,d\phi
NYX3Nyx intensity operator 3: frequency-integrated Planck-weighted intensity for bolometric astrophysical luminosity.N_3 = 4\pi\int_0^\infty I_\nu B_\nu(T)d\nu

Compute with one of these​

curl -sS -X POST https://zeqsdk.com/api/zeq/compute \
  -H "Authorization: Bearer $ZEQ_KEY" \
  -H "Content-Type: application/json" \
  -d '{"operators":["APX1"],"inputs":{}}'

The response carries the bare physics value, its unit and uncertainty, the generated master equation, and a signed envelope you can verify on any node.

See also​