The same mass discrepancy appears in rotation, satellites, lensing, and structure formation, but each probe has distinct systematics.
The same mass discrepancy appears in rotation, satellites, lensing, and structure formation, but each probe has distinct systematics.
Galactic astronomy observes projected light, velocities, and abundances from one moving vantage point. The inverse problem is underdetermined until geometry, selection, and a physical model are made explicit.
Definition: The extended gravitating component surrounding a galaxy and dominating its mass at large radii in standard models.
Why it matters here: It connects local rotation evidence to satellite motions, lensing, and cosmological structure formation.
Relationship: Its density profile determines the halo contribution to the circular-speed curve.
Limitation or common confusion: It is distinct from the sparse stellar halo and its shape is not fixed by one probe.
Definition: A cusped spherical density law \(\rho=\rho_s/[x(1+x)^2]\), with \(x=r/r_s\), motivated by collisionless simulations.
Why it matters here: It provides a standard parameterized halo model for comparison with dynamical data.
Relationship: The scale density \(\rho_s\) and scale radius \(r_s\) set concentration and enclosed mass.
Limitation or common confusion: Baryonic evolution and limited radial data can make an NFW fit non-unique.
Definition: The total gravitating mass per unit volume near the Sun.
Why it matters here: Vertical stellar motions constrain the combined local inventory of stars, gas, and dark matter.
Relationship: The vertical Jeans and Poisson equations connect tracer density and velocity dispersion to gravitational density.
Limitation or common confusion: It is not the same quantity as mass enclosed inside the solar circle.
Definition: The separation of an observed gravitational field into bulge, disk, gas, and halo contributions.
Why it matters here: It tests whether known baryons can account for the rotation curve and local force.
Relationship: Component contributions add through the potential, often displayed as contributions to \(v_c^2\).
Limitation or common confusion: Different stellar mass-to-light ratios can trade off against halo parameters.
Definition: An object population whose positions and velocities respond to the gravitational potential.
Why it matters here: Stars, gas, and satellites probe different radii and systematic uncertainties.
Relationship: A tracer distribution enters Jeans, orbit, or rotation models rather than equaling the mass distribution.
Limitation or common confusion: Tracer density need not follow total mass density.
The central relation for this lecture is:
Define every symbol before substitution. State the coordinate system, units, and approximation. A formula is evidence only when its assumptions match the tracer and regime.
The evidence display for this lecture is the labeled model/data relationship introduced above. Read the axes and annotations before accepting the inferred trend.
Data context: the accompanying values are standard published or survey-like values; see the course reference log for provenance level and spot-check targets.
It cannot by itself separate the radial mass contributions of disk, bulge, and halo.
Write the units beside each intermediate quantity. The numerical result is generated from the shared course constants and recomputed independently during review.
Ask whether changing the distance prior, selection function, or mass decomposition could move the conclusion. This is where a plausible diagram can become a misleading argument.
Prompt: Compare the enclosed mass from the local circular speed with a baryonic benchmark and state what is actually inferred.
First estimate the direction of the answer. Then calculate. Finally name one assumption that could reverse the interpretation.
OpenStax Astronomy 2e, Chapter 25, sections 25.1–25.4, and Chapter 26 for comparative context. Exact section and embedded-figure offsets were checked against the local extracted text before release.
Additional sources: Gaia Collaboration (2018, 2021) releases; Bland-Hawthorn & Gerhard (2016), ARA&A 54, 529; McMillan (2017), MNRAS 465, 76; Eilers et al. (2019), ApJ 871, 120; Bland-Hawthorn et al. (2019), Science 365, 859.
References are standard published values not independently re-fetched in this production session unless explicitly marked level 1 in reference-log.md.