Named Observed Systems

A named black-hole system is useful when it connects several methods to one physical source. It is also dangerous: a familiar name can make a model-dependent mass, spin, or horizon interpretation sound like a directly recorded fact. This directory keeps the layers separate. Each page begins with the calibrated observables, states the forward model and nuisance parameters used to infer source properties, and limits its conclusion to the evidence available through 20 August 2026.

Six benchmark systems

System page	Environment	Most direct identification channel	Distinctive scientific use
Sagittarius A*	Galactic Center	Angular astrometry and line-of-sight velocities of short-period stars	Combines a geometric orbit scale with variable horizon-scale interferometry
M87*	Giant elliptical galaxy M87	Stellar and gas dynamics, supplemented by horizon-scale interferometry	Connects a massive compact object, a low-luminosity flow, and a relativistic jet
Cygnus X-1	Wind-fed high-mass X-ray binary	Optical orbital dynamics plus radio parallax	Tests joint binary, accretion-state, corona, and spin models
V404 Cygni	Transient low-mass X-ray binary	Donor-star mass function plus parallax	Exposes obscuration, winds, rapid variability, and nonstationary outbursts
GRS 1915+105	Long-lived microquasar	Donor dynamics and radio astrometry	Links accretion cycles to relativistic ejections without assuming one instability model
NGC 4258 Central Black Hole	Subparsec water-maser disk in an active galactic nucleus	Maser sky positions, Doppler velocities, accelerations, and proper motions	Provides an unusually transparent joint geometric distance and Keplerian mass benchmark

These are benchmarks, not a representative sample. They were selected because their inference chains are unusually instructive and because several independent observables can be compared. They must not be used to infer population frequencies without an explicit selection model.

Observable, calibration, and posterior

The first layer is the recorded datum: a pixel position, spectrum, arrival time, polarization correlation, radio interferometric visibility, or light-curve count rate. Calibration supplies an astrometric reference frame, wavelength or frequency scale, detector response, flux scale, atmospheric correction, and uncertainty covariance. Quality cuts then define which epochs, baselines, spectral states, or orbital phases enter the analysis.

The next layer is a forward model. Stellar or binary dynamics predicts positions and velocities from masses, distance, inclination, and orbital elements. Very-long-baseline interferometry predicts complex visibilities from a time-dependent brightness distribution. X-ray models predict detector counts from an accretion spectrum after absorption and instrumental response. Maser models predict positions, line-of-sight velocities, accelerations, and proper motions from a warped disk and a geometric distance.

Only after this layer should one quote a posterior for mass, distance, inclination, spin, or disk geometry. A credible or confidence interval represents statistical uncertainty under a specified model; calibration, atmosphere, variability, waveform, or source-geometry alternatives add systematic or model uncertainty. Combining two published posteriors is valid only when their shared distance, inclination, ephemeris, calibration, and priors are accounted for once.

Compactness is not a horizon measurement

Orbital dynamics can establish that a large mass lies in a small volume. Accretion efficiency, the absence of surface-powered emission, and horizon-scale images can make a black-hole interpretation overwhelmingly compelling. None is a literal photograph or local detection of an event horizon. A ring-like reconstruction is an emission feature shaped by lensing and plasma; converting its diameter into a spacetime critical curve uses a model library, as the mass-and-shadow calibration in Event Horizon Telescope Collaboration 2019, Paper VI makes explicit. Likewise, agreement with a Kerr prediction within current resolution is not a complete no-hair test; Cardoso and Pani 2019, §§4–6 reviews the additional model and stability tests required for dark compact alternatives.

This evidential ceiling matters most for Sagittarius A* and M87*. The pages route detailed relativistic-orbit and imaging tests to the pages that define their null hypotheses, nuisance models, and statistical comparisons. For X-ray binaries, a dynamical mass can be secure while the continuum-fitting or reflection spin remains conditional on disk structure and alignment; Reynolds 2021, §§2–4 details those assumptions and their principal systematics.

Controlled comparisons

The systems support four particularly useful matched tests:

• infer the angular gravitational scale $GM/(c^2D)$ from dynamics before comparing it with an interferometric ring scale;
• recover a binary mass function from $P$, $K_2$, and $e$ before adding inclination and donor priors;
• compare an X-ray outburst in detector count space under alternative absorption and spectral-response models, rather than comparing only unabsorbed luminosities;
• fit a maser disk with and without warp, eccentricity, and disk self-gravity while retaining the same astrometric and velocity data.

The cutoff date is part of the scientific statement. Later astrometry, calibration releases, image reconstructions, outbursts, or reanalyses can move a posterior without changing the system’s identity.

References

• Cardoso, Vitor, and Paolo Pani. “Testing the Nature of Dark Compact Objects: A Status Report.” Living Reviews in Relativity 22 (2019): 4. DOI.
• Event Horizon Telescope Collaboration. “First M87 Event Horizon Telescope Results. VI. The Shadow and Mass of the Central Black Hole.” Astrophysical Journal Letters 875 (2019): L6. arXiv.
• Reynolds, Christopher S. “Observational Constraints on Black Hole Spin.” Annual Review of Astronomy and Astrophysics 59 (2021): 117–154. DOI.