A quasar (quasi-stellar object) is an extremely luminous active galactic nucleus (AGN) powered by a supermassive black hole (10⁶–10¹⁰ M☉) accreting material at the centre of a distant galaxy, producing energy output that can exceed the combined light of an entire galaxy by factors of 100–1,000. Quasars were among the first objects identified at cosmological redshifts (z > 0.1), appearing star-like in early optical surveys despite being billions of light-years away, and their spectra showed enormous redshifted emission lines confirming their cosmological distances. Because quasar light has travelled billions of years to reach us, they serve as luminous probes of the early universe, intergalactic medium, and the history of black hole growth throughout cosmic time.
L_Edd = 4π G M m_p c / σ_T ≈ 1.26 × 10³¹ × (M/M_sun) watts
LaTeX: L_{\rm Edd} = \frac{4\pi G M m_p c}{\sigma_T} \approx 1.26 \times 10^{31}\left(\frac{M}{M_\odot}\right)\text{ W}
| Symbol | Meaning | Unit |
|---|---|---|
| L_Edd | Eddington luminosity (maximum accretion luminosity) | watts (W) |
| G | Gravitational constant | N·m²/kg² |
| M | Black hole mass | kilograms (kg) or M☉ |
| m_p | Proton mass (1.67 × 10⁻²⁷ kg) | kg |
| c | Speed of light | m/s |
| σ_T | Thomson scattering cross-section (6.65 × 10⁻²⁹ m²) | m² |
Problem
The quasar 3C 273 has a luminosity of approximately 4 × 10³⁹ W. Assuming it radiates at the Eddington limit, estimate the minimum black hole mass required.
Solution
Step 1 — Use the Eddington luminosity relation: M = L_Edd × σ_T / (4π G m_p c). Step 2 — Rearranging the approximation: M/M☉ = L / (1.26 × 10³¹ W). Step 3 — M/M☉ = 4 × 10³⁹ / 1.26 × 10³¹ ≈ 3.17 × 10⁸. Step 4 — So M ≈ 3.2 × 10⁸ M☉ (320 million solar masses).
Answer
Minimum black hole mass ≈ 3.2 × 10⁸ M☉
| Object Type | Luminosity (W) | Central Engine | Redshift Range | Example |
|---|---|---|---|---|
| Normal Galaxy (Milky Way) | ~4 × 10³⁶ | Quiescent SMBH | z ≈ 0 | Milky Way |
| Seyfert Galaxy | 10³⁷ – 10³⁹ | Low-luminosity AGN | z < 0.1 | NGC 4151 |
| Radio Galaxy | 10³⁸ – 10⁴¹ | AGN with jets | z < 2 | Centaurus A |
| Quasar (radio-quiet) | 10³⁹ – 10⁴² | Accreting SMBH | 0.1 < z < 7 | 3C 273 |
| Blazar / OVV Quasar | 10⁴⁰ – 10⁴² | Relativistic jet pointed at Earth | z ∼ 0.3–5 | BL Lacertae |
| Brightest Known Quasar (J0529) | ~5 × 10⁴¹ | SMBH ~17 billion M☉ | z ≈ 3.96 | J0529-4351 (2024) |
SDSS SkyServer Quasar Spectra
Explore real quasar spectra and redshifts from the Sloan Digital Sky Survey.
Open ToolWolframAlpha Eddington Luminosity
Compute Eddington luminosities and black hole mass estimates.
Open ToolNASA HEASARC Quasar Catalogue
Access the Véron-Cetty catalogue of quasars and active nuclei.
Open ToolWikimedia Commons, CC BY-SA
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