Black Hole Accretion Calculator
Black Hole Accretion Calculator is a scientifically accurate, free online tool designed to compute key physical parameters of matter falling onto black holes through an accretion disk. This calculator strictly adheres to peer-reviewed general relativistic and astrophysical formulas used by professional researchers worldwide.
About the Black Hole Accretion Calculator
Black holes grow by accreting surrounding gas and plasma, forming a hot, luminous accretion disk. The Black Hole Accretion Calculator allows you to calculate critical quantities such as the Eddington luminosity, maximum stable accretion rate, radiative efficiency, inner disk temperature, and total luminosity from real physics equations derived from Einstein’s general relativity and radiative transfer theory.
Why Black Hole Accretion Matters
Accretion onto black holes is one of the most efficient energy-generation mechanisms in the universe, converting up to 42% of rest-mass energy into radiation (compared to ~0.7% for nuclear fusion). This process powers quasars, active galactic nuclei (AGN), X-ray binaries, and gamma-ray bursts. Understanding accretion physics is essential for interpreting observations from telescopes like Chandra, XMM-Newton, Event Horizon Telescope, and the upcoming Lynx and Athena missions.
Scientific Formulas Used (Peer-Reviewed)
- Eddington Luminosity: LEdd = 3.28 × 10⁴ (M/M⊙) L⊙ (K. S. Thorne, 1974; valid for Thomson scattering in ionized plasma)
- Eddington Accretion Rate: ṀEdd = LEdd / (η c²)
- Radiative Efficiency (η): Novikov-Thorne model (1973) for Kerr spacetime, η ≈ 0.057–0.42 depending on spin
- Inner Disk Temperature: Tin ≈ [3GMṀ / (8π σ r_in³)]1/4 (Shakura-Sunyaev 1973, corrected for GR)
- Accretion Luminosity: L_acc = η Ṁ c²
When and Why You Should Use This Calculator
Use this tool when:
- Estimating whether an observed quasar is accreting near, below, or above the Eddington limit
- Modeling X-ray binary outbursts
- Teaching astrophysics courses on black hole physics
- Planning observing proposals that require accretion rate estimates
- Interpreting multi-wavelength spectra of AGN
User Guidelines
1. Enter the black hole mass in solar masses (M⊙)
2. Choose the radiative efficiency η (0.057 for Schwarzschild, up to 0.42 for maximal Kerr spin)
3. Input the desired accretion rate as a fraction of the Eddington rate (0.001–10 typical)
4. Click “Calculate” to get instantaneous, accurate results
The calculator assumes a thin, optically thick accretion disk in the Novikov-Thorne relativistic model — the standard model used in virtually all modern black hole research papers.
Purpose of This Tool
To democratize access to high-precision black hole astrophysics calculations that previously required specialized software (e.g., XSPEC, ISIS, or custom Python scripts). Whether you are a graduate student writing a thesis, a professor preparing a lecture, or an amateur astronomer curious about supermassive black holes, this Black Hole Accretion Calculator delivers professional-grade results in seconds.
Physical Insights You Can Gain
• A 10⁸ M⊙ black hole accreting at the Eddington rate releases ~3×10⁴⁶ erg/s — outshining an entire galaxy
• Spin is critical: a maximally spinning black hole radiates nearly 8× more power than a non-spinning one at the same Ṁ
• Super-Eddington accretion (Ṁ > Ṁ_Edd) may occur in tidal disruption events and ULXs
For deeper reading on the physics of accretion disks, visit the Wikipedia page on Black Hole Accretion.
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