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Astronomy & space · Advanced university

Galaxies, dynamics and dark-matter evidence

Galaxies contain stars, gas, dust and other gravitating components. Their morphology does not alone determine all their dynamical properties.

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Prerequisites

Gravity, circular motion and observational uncertainty.

Study notes

Structure

Galaxies contain stars, gas, dust and other gravitating components. Their morphology does not alone determine all their dynamical properties.

Dynamics

In a simplified spherical model, circular speed obeys v²=GM(<r)/r. Inferring enclosed mass therefore uses a geometric and dynamical model.

Evidence

Rotation curves, gravitational lensing and other observations constrain mass distributions. The evidence for unseen gravitating components is not a direct photograph of dark matter.

Uncertainty

Inclination, distance, noncircular motion and mass-to-light estimates affect interpretation. Multiple independent probes help test explanations.

Worked examples

In units G=1, circular speed is 4 at radius 3 in a spherical model. Find enclosed mass.

M=v²r/G=16×3.

48

A flat rotation curve in the stated spherical model implies enclosed mass changes how with radius?

With constant v, M(<r)=v²r/G grows linearly.

Approximately proportionally to radius

Check your understanding

  1. Which is an additional gravitational probe of mass distribution?

    1. Gravitational lensing
    2. Only a galaxy's name
    3. Only visible colour without a model
    4. A telescope's price

  2. Why is converting luminosity directly into total mass model-dependent?

  3. At fixed circular speed in the spherical model, radius doubles. Find the inferred enclosed-mass factor.

  4. Explain why combining lensing and dynamics can be more informative than either alone.

Answers and marking guidance

Answers and marking notes
  1. Gravitational lensing

    Lensing responds to gravitational effects on light propagation.

  2. Stellar populations have different mass-to-light ratios, and gas or nonluminous components can contribute. Luminosity alone does not uniquely fix mass.

    Credit population models and unseen components.

  3. 2

    M scales with r when v is fixed.

  4. The methods constrain gravitational effects through different data and assumptions. Agreement can strengthen or challenge a mass model while revealing systematics.

    Credit complementary constraints, not a guarantee of unique truth.

Further reading and review references

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