Galaxies are cosmic marvels, their properties revealing hidden secrets. Mass estimation techniques and rotation curves unveil the presence of dark matter, a mysterious substance shaping galactic structure and evolution.

Mass-to-light ratios vary across galaxy types, hinting at dark matter's crucial role. From spirals to ellipticals and dwarf spheroidals, these ratios offer clues about galactic composition and the universe's unseen matter.

Galactic Properties and Dark Matter

Mass estimation of galaxies

• Astronomers estimate galaxy mass using rotation curves that plot orbital velocities of stars and gas vs. distance from galactic center
  • Construct curves using Doppler shifts of spectral lines from different galaxy regions
• Kepler's laws predict orbital velocities should decrease as distance from galactic center increases
  • Orbital velocity $v = \sqrt{\frac{GM}{r}}$ where $G$ is gravitational constant, $M$ is mass enclosed within orbit, $r$ is orbital radius
• Observed rotation curves often show flat or rising velocities at large distances (outer regions of galaxies)
  • Implies additional mass beyond visible matter in galaxy
• Discrepancy between observed and predicted rotation curves allows estimation of galaxy's total mass
  • Accounts for both visible matter (stars, gas, dust) and dark matter
• Galactic halos, extending far beyond the visible disk, contribute significantly to the total mass

Mass-to-light ratios across galaxy types

• Mass-to-light ratio ($M/L$) is a galaxy's total mass divided by its luminosity
  • Expressed in solar units ($M_{\odot}/L_{\odot}$)
• Spiral galaxies have $M/L$ ratios of 10-20 $M_{\odot}/L_{\odot}$ (Milky Way, Andromeda)
  • Indicates significant amounts of dark matter present
• Elliptical galaxies have higher $M/L$ ratios, typically 50-100 $M_{\odot}/L_{\odot}$ (M87, Centaurus A)
  • Suggests even greater proportion of dark matter compared to spirals
• Dwarf spheroidal galaxies have the highest $M/L$ ratios, up to 1000 $M_{\odot}/L_{\odot}$ (Draco, Ursa Minor)
  • Implies these small, faint galaxies are dominated by dark matter
• Variation in $M/L$ ratios among galaxy types suggests dark matter plays crucial role in galactic structure and evolution
  • Particularly important in low-luminosity and low-surface-brightness galaxies (dwarf irregulars, ultra-diffuse galaxies)
• Stellar populations within galaxies influence their mass-to-light ratios

Dark matter in galactic evolution

• Flat rotation curves provide strong evidence for presence of dark matter halos surrounding galaxies
  • Extended halos explain observed orbital velocities at large galactic radii (beyond visible disk)
• Gravitational lensing observations reveal unseen mass in galaxies and galaxy clusters
  • Gravitational deflection of light from background sources greater than expected from visible matter alone (bullet cluster, Abell 1689)
• Velocity dispersions of galaxies in clusters suggest additional mass present
  • Needed to explain high velocities and prevent clusters from dispersing
• Cosmological simulations of structure formation require dark matter to reproduce observed large-scale structure of universe
  • Cold dark matter (CDM) models successfully explain formation and evolution of galaxies and clusters (Millennium Simulation, IllustrisTNG)
• Dark matter halos influence formation and evolution of galaxies by:
  1. Providing gravitational potential wells for baryonic matter to collapse and form stars
  2. Shaping morphology and dynamics of galaxies through gravitational interactions (tidal stripping, mergers)
• Nature of dark matter remains major unsolved problem in astrophysics
  • Candidates include weakly interacting massive particles (WIMPs), axions, modified gravity theories (MOND)

Galaxy Composition and Structure

• Galaxy morphology describes the overall shape and structure of galaxies (e.g., spiral, elliptical, irregular)
• The interstellar medium, consisting of gas and dust, plays a crucial role in star formation and galactic evolution
• Active galactic nuclei are highly energetic central regions found in some galaxies, powered by supermassive black holes
• Galaxy clusters are large-scale structures containing hundreds to thousands of galaxies bound by gravity