Cosmology and astrophysics

Dark matter

Galaxy rotation curves suggest a gravitating component that does not shine; accelerating cosmic expansion points to a component with negative pressure. The microscopic nature of both remains unknown.

V_c²(r)=GM(<r)/r. A spherical halo with ρ∝r⁻² gives V_c≈constant.

Definition: Rotation curve V_c(r)

Dark matter is inferred through gravity rather than detected directly by its light: evidence includes galaxy rotation curves, gravitational lensing, and structure formation. It is not necessarily black holes or any specific particle confirmed to date.

Adjust parameters to explore the physical relation. The illustration is schematic, not to astronomical scale.

Model and observations

Dark matter is inferred gravitationally through lensing, galaxy dynamics, and large-scale structure; it is not synonymous with ordinary black holes. Dark energy names the component driving accelerated expansion in the standard model, often parameterized by the cosmological constant Λ.

Example: A quick estimate

Use the relation above to predict the trend when one parameter changes, then check it in the simulation.

Solution

Hold other quantities fixed and apply the equation. The simulation illustrates a trend; it does not replace real data or uncertainty analysis.

For a nearly circular orbit, centripetal balance gives $V_c^2(r)=GM(<r)/r$ . If most mass were confined to the bright disk, the outer speed would fall roughly as $r^{-1/2}$ ; a nearly flat rotation curve suggests mass continues beyond the luminous region. This is not a standalone proof: inclination, distance, gas, and stellar distributions must be modeled. Gravitational lensing provides an independent probe through light deflection, while clusters and the CMB constrain dark matter on larger scales.

In the standard model, cold dark matter interacts very weakly electromagnetically and is nonrelativistic as structure forms; its halos provide the gravitational scaffold for galaxies. Candidates such as axions or weakly interacting massive particles remain hypotheses, with no confirmed particle detection. Zwicky used the dynamics of the Coma cluster to highlight missing mass; Einstein’s gravitational framework underlies mass inferences. Testing candidates requires comparing direct searches, astronomical signals, and simulations, while keeping dark matter distinct from dark energy.

Quick check

What is the best use of the simulation or equation?

What should be considered when drawing conclusions about an astronomical phenomenon?

References

Bradley W. Carroll and Dale A. Ostlie (2017). An Introduction to Modern Astrophysics