Question 1

What is an Einstein ring and when does it form?

Accepted Answer

An Einstein ring is a complete circular image of a background source formed when the source, gravitational lens, and observer are in perfect alignment. Light from the source passes around all sides of the lens equally, arriving at the observer from all directions around the lens—forming a ring of angular radius θ_E = √(4GM·D_LS/(c²·D_L·D_S)), the Einstein radius, where D_L, D_S, and D_LS are the angular diameter distances to the lens, source, and between lens and source. Perfect alignment is rare; more commonly, near-alignment produces partial arcs. Einstein rings and arcs have been observed in hundreds of galaxy-galaxy and cluster-galaxy lens systems by the Hubble Space Telescope.

Question 2

How is gravitational lensing used to weigh galaxy clusters?

Accepted Answer

Massive galaxy clusters act as gravitational lenses on background galaxies. The Einstein radius and degree of arc distortion are related to the projected mass distribution of the cluster by the lens equation. Strong lensing (multiple images, arcs near cluster cores) constrains the mass within the Einstein radius precisely. Weak lensing (statistical alignment of background galaxy shapes) maps the mass distribution out to large radii. Combining strong and weak lensing data produces detailed mass maps of clusters, revealing that total cluster mass (including dark matter) typically exceeds the visible stellar mass by 50-100× and the hot intracluster gas by 5–10×.

Question 3

What is microlensing and how is it used to detect exoplanets?

Accepted Answer

Gravitational microlensing occurs when a foreground star (or compact object) passes in front of a more distant background star. The lens star's gravity focuses background star light, causing a temporary symmetric brightness amplification—a characteristic light curve with a duration of days to weeks. If the lens star hosts a planet, the planet's additional gravity creates a brief anomaly (spike or dip) superimposed on the main lensing light curve. By fitting the anomaly's shape and duration with planet-star mass ratio and separation models, planet masses and orbital separations can be inferred. Microlensing is particularly sensitive to planets near the Einstein ring radius (a few AU), complementing transit and radial velocity methods.

Question 4

How did gravitational lensing provide evidence for dark matter in the Bullet Cluster?

Accepted Answer

In the Bullet Cluster, X-ray observations show hot gas concentrated between two colliding clusters, slowed by electromagnetic interactions, while lensing mass maps show mass peaks coinciding with the collisionless galaxies, not the gas. Since the mass follows the collisionless component it cannot be ordinary matter, making the Bullet Cluster one of the strongest direct evidences for dark matter.

Question 5

How is gravitational lensing used in cosmology?

Accepted Answer

Gravitational lensing responds to all matter, dark and baryonic. Cosmic shear measures the growth of structure and geometry of spacetime, constraining dark energy. Lensing magnification boosts background galaxy brightness, and cross-correlating lensing maps with surveys constrains the Hubble constant and neutrino mass.

Question 6

What does the Black-hole mass slider actually change in the rendering?

Accepted Answer

The mass slider (0.2 to 3 solar masses) directly scales the Schwarzschild-like radius uRs = 0.10 x mass, which sets the size of the event-horizon shadow, the photon-sphere ring, and the Einstein-ring radius (uRs x 1.9). All three visual features grow or shrink together since they derive from the same mass-dependent scale.

Question 7

How is the deflection angle actually computed in the shader?

Accepted Answer

For each pixel the shader computes the impact parameter b and bends the sampled background direction toward the lens by deflect = uRs / b, a Schwarzschild-like 1/b falloff matching the real deflection formula alpha = 4GM/(c^2 b). The result is clamped to 2.5 to prevent a singular blow-up at the lens centre.

Question 8

What does the Star density slider control, and why does it matter for lensing?

Accepted Answer

Star density (10-100%) sets how many background stars are scattered behind the lens. A higher density means more stars pass close enough to the Einstein radius to be caught being stretched into an arc, mirroring how real microlensing surveys need many background sources to catch lensing events.

Question 9

Why does dragging the black hole on the canvas change which stars get lensed?

Accepted Answer

Dragging repositions the lens centre used to compute the impact parameter b for every point in the field. Moving the lens brings a different set of background stars within the critical Einstein-radius band, which is why the ring and arcs appear to follow the black hole as it moves.

Question 10

Why did Eddington's 1919 eclipse expedition matter so much for confirming this effect?

Accepted Answer

General relativity predicted light bending by the Sun at exactly twice the Newtonian value. Eddington's team photographed the 1919 total solar eclipse to measure the tiny shift in star positions near the solar limb; the result matched Einstein's prediction, providing the first direct experimental confirmation of general relativity.

🔭 Gravitational Lensing: Einstein Rings

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