How do we measure the mass of galaxies?

Determining the mass of an entire galaxy is one of the grand challenges in astrophysics, partly because the vast majority of that mass is entirely invisible to our telescopes. We cannot simply place a galaxy on a cosmic scale; instead, we must rely on the gravitational fingerprints it leaves on the objects moving within it and the light passing near it. ^[2][4] The foundational principle, whether dealing with a planet orbiting a star or a star orbiting a galactic center, lies in applying the laws of gravity to observed motions. ^[1][7]

# Gravitational Clues

When astronomers measure the mass of something small, like a star, they often use binary systems where the orbital period and separation yield a precise mass using Kepler’s Third Law. ^[1] Applying this directly to a galaxy containing billions of stars is impossible due to the complexity. Therefore, we shift our focus to the bulk dynamics—how fast material orbits the galaxy's center of mass. ^[4] The general relationship derived from Newtonian mechanics dictates that the orbital velocity ($v$) of an object at a specific distance ($r$) is related to the total mass ($M$) enclosed within that radius: $v^2$ is proportional to $GM/r$. ^[1][7] By measuring the velocity of test particles, such as distant stars or clouds of hydrogen gas, at various distances from the center, we can map out the enclosed mass distribution. ^[4]

For spiral galaxies, like our own Milky Way, this means observing the rotation curve, which plots orbital velocity against the distance from the core. ^[2][7] This is the primary way we establish the total mass budget, including the elusive dark matter component. ^[2]

# Rotation Curves

The measurement process for a spiral galaxy typically involves observing the Doppler shift of light emitted by moving gas, particularly the $\text{21-cm}$ line from neutral hydrogen, which permeates the galactic disk. ^[7] This allows astronomers to map the speed of material far out into the halo. If a galaxy's mass consisted only of the stars and gas we can see (baryonic matter), we would expect the orbital speed to decrease noticeably as the distance from the bright central bulge increases—similar to how outer planets orbit the Sun more slowly than inner ones. ^[2][5]

However, observations consistently reveal a surprising flatness in the rotation curve. ^[2][7] Beyond the visible edge of the stellar disk, the orbital speeds of stars and gas clouds remain unexpectedly high, sometimes even increasing slightly before leveling off. ^[5][7] This observation is the most compelling evidence for dark matter. ^[2] It implies that a massive, spherical halo of non-luminous material must extend far beyond the visible boundaries of the galaxy, providing the extra gravitational pull needed to keep the outermost material moving so quickly. ^[4][5] When we calculate the mass required to sustain these high velocities, it vastly outweighs the mass accounted for by all the stars, dust, and gas combined, often showing that dark matter constitutes about 90 percent of the galaxy's total mass. ^[4][5][7]

In contrast, elliptical galaxies present a different kinematic challenge because their stars do not orbit in neat, predictable circles like gas in a spiral disk; instead, they move on complex, three-dimensional, randomly oriented orbits. ^[2] To weigh these galaxies, astronomers measure the velocity dispersion—the statistical spread or random motions of the stars within the system—and use more complex dynamical models based on the virial theorem to estimate the total mass required to keep the galaxy gravitationally bound. ^[2]

How did astronomers discover that mass was missing from the Milky Way galaxy?

# Lensing Effects

While kinematic methods rely on motion, gravitational lensing provides an entirely independent, geometric way to map mass, which is crucial for verifying the results derived from rotation curves. ^[2] This phenomenon occurs because any mass, visible or dark, warps the spacetime around it, bending the path of light traveling from a distant background object. ^[6]

There are two main types of lensing used:

1. Strong Lensing: If a massive galaxy happens to lie directly between us and an even more distant light source, its gravity can distort the background light so severely that we observe multiple images of the same source, or the light is smeared into dramatic arcs. ^[2] The geometry of these arcs and image positions precisely constrains the mass distribution of the foreground lensing galaxy. ^[2]
2. Weak Lensing: This is much more subtle and occurs more frequently. It involves a statistical analysis of how the shapes of millions of distant galaxies are slightly distorted by the foreground galaxy’s pervasive gravitational field. ^[2] While the effect on any single galaxy is minute, averaging the distortions across the field allows astronomers to reconstruct the total mass distribution, which again includes the dark matter halo. ^[2][6]

It is interesting to note the inherent difference in measurement. Rotation curves measure the mass inside a specific radius, while lensing measures the mass distribution across the entire projected area causing the bending. If the two methods yield similar total mass figures for the same galaxy, trust in the dark matter hypothesis solidifies significantly. ^[2]

# Stellar Light

If we focus only on the visible material, we are estimating the stellar mass of the galaxy. ^[3] This is derived by calculating the total light output, or luminosity, of the galaxy and then applying a conversion factor known as the Mass-to-Light ratio ($M/L$). ^[5][6] This conversion is not universal; the $M/L$ ratio depends heavily on the composition of the stellar population—namely, the average age and metallicity of the stars. ^[5] A galaxy dominated by old, red stars will have a lower luminosity for a given mass than a galaxy rich in young, bright blue stars. ^[3] Consequently, deriving the stellar mass from the light requires sophisticated spectral analysis to model the history of star formation within that system. ^[6]

When calculating the stellar mass for a galaxy like the Milky Way, the result is typically around $5 \times 10^{10}$ solar masses ($M_{\odot}$), which accounts for only a small fraction of the total mass, which is estimated to be closer to $10^{12} M_{\odot}$. ^[5] This highlights that the $M/L$ technique effectively weighs only the luminous component, severely underestimating the total gravitational potential. ^[5][7]

What are the three things used to measure mass?

# Mass Budget

To arrive at the total mass of a galaxy, scientists must account for three main components: the stars, the interstellar gas and dust, and the dark matter halo. ^[1][4][5]

The relative proportions shift depending on the galaxy's environment and history. Dwarf galaxies often have a higher ratio of dark matter mass to visible mass than large spirals. ^[5]

Consider a hypothetical scenario for a typical spiral galaxy whose measured rotation velocity at 50 kiloparsecs is $220 \text{ km/s}$. ^[7] If we only used the observed stellar mass ($M_{\text{stars}}$) to calculate the expected gravitational pull at that radius, we might calculate an enclosed mass of only $1 \times 10^{11} M_{\odot}$. However, using the observed velocity in the mass equation ($M = v^2 r / G$) yields a total enclosed mass, $M_{\text{total}}$, closer to $1.5 \times 10^{12} M_{\odot}$. The difference, $1.4 \times 10^{12} M_{\odot}$, must be attributed to the non-baryonic dark matter component distributed throughout that radius. ^[1][4]

The existence of such a dominant, invisible mass component has profound implications. If we were to mistakenly assume the total mass of our local galactic neighborhood was only the sum of the visible stars, our models for how fast galaxies should cluster together or the timescales over which they might merge would be drastically incorrect. Measuring the mass accurately, therefore, isn't just about cataloging objects; it is a necessary input for understanding the physical processes driving cosmic structure formation across billions of years. ^[7] We are effectively weighing the gravitational scaffolding upon which the visible universe is built. ^[4]