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Dark Matter Host

Gravitational Lensing / Invisible Mass Physics

\[v(r)^{2} = \frac{G M(r)}{r} \;\Rightarrow\; M(r) = \frac{v^{2} r}{G}\]
$29.99 USD
$29.99 USD
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Size guide S–5XL · inches

Meet Dark Matter Host. Most of the mass holding galaxies together has never been seen. Dark matter gives off no light we can detect, yet its gravity shapes galaxies and bends light. In the Bullet Cluster, two colliding galaxy clusters, the hot gas slammed together and stalled, but lensing shows most of the mass sailed on with the galaxies: mass where the gas isn't. About five-sixths of all matter is something never directly detected. Dark Matter Host wears it in pixel art on a unisex tee. The physics panel below has the equation, every symbol and the sources.

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Details

Size & fitS–5XL

Unisex heavy cotton (Gildan 5000), classic fit.

SizeWidthLengthSleeve
S182815.1
M202916.5
L223018
XL243119.5
2XL263221
3XL283322.4
4XL303423.7
5XL323525

Pour l'échelle : la taille M mesure 20 in (50.80 cm) de large, soit environ 3.143 × 1034 longueurs de Planck (lP = 1.616255 × 10−35 m). Un mètre ruban est plus rapide.

Measurements in inches, ±1.5 in tolerance.

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Returns & replacements21 days

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Print defect, misprint, damage or the wrong item? We’ll send a free replacement, or a refund if you prefer. Report it within 21 days of delivery with a photo; no need to send it back.

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The physics

When two galaxy clusters collided in the Bullet Cluster, their hot gas slammed together and stalled, but bent background light shows most of the mass sailed on with the galaxies. Orbital speeds and lensing both find far more mass than stars and gas can account for: about five-sixths of all matter is something never directly detected.

The Host is never in the picture. The picture is bent around them.

Weigh a galaxy cluster three ways. Count the light from its stars. Measure the X-rays from the hot gas between the galaxies, which outweighs the stars. Then measure how strongly the cluster bends the light of galaxies far behind it, using the second formula on this page, which turns a lensing angle into a mass. The third number is several times the first two put together. Fritz Zwicky saw a version of this in the 1930s from how fast the galaxies of the Coma cluster move. Vera Rubin and Kent Ford saw it in 1970 from how fast the outer parts of the Andromeda galaxy rotate, the first formula.

The sharpest picture came in 2006. The Bullet Cluster is two clusters that have passed through each other. Their hot gas collided, slowed and piled up in the middle, glowing in X-rays. Their galaxies, mostly empty space, sailed on through. Douglas Clowe and colleagues mapped the lensing and found the mass travelling with the galaxies, not with the gas, even though the gas holds most of the ordinary matter. Whatever carries most of the mass went through the collision almost without touching anything.

The cosmic microwave background says the same thing from the far end of time. The Planck satellite's 2018 results put about five times as much dark matter as ordinary matter in the universe: roughly 85 percent of all matter.

What it is remains open. No dark-matter particle has been detected directly, despite decades of searching. A minority of physicists argue for modifying gravity instead, though the Bullet Cluster is hard for most such theories to explain.

The Host never casts a shadow. They cast a weight.

Equations

\[v(r)^{2} = \frac{G M(r)}{r} \;\Rightarrow\; M(r) = \frac{v^{2} r}{G}\]
\[\theta_E = \sqrt{\frac{4GM}{c^{2}}\,\frac{D_{LS}}{D_L D_S}}\]
SymbolMeaningUnit
\(v(r)\) orbital speed at radius r \(\mathrm{m/s}\)
\(M(r)\) mass enclosed within r \(\mathrm{kg}\)
\(r\) galactocentric radius \(\mathrm{m}\)
\(\theta_E\) Einstein radius \(\mathrm{rad}\)
\(D_L, D_S, D_{LS}\) angular-diameter distances to lens, to source, lens→source \(\mathrm{m}\)

Sources

  1. Rubin & Ford (1970) Rotation of the Andromeda Nebula, ApJ 159, 379
  2. Zwicky (1937) On the Masses of Nebulae and of Clusters of Nebulae, ApJ 86, 217
  3. Encyclopaedia Britannica — Dark matter
  4. PDG 2024 review — Dark matter
  5. NASA Science — Dark Matter
  6. Planck Collaboration (2020) Planck 2018 results VI. Cosmological parameters, A&A 641, A6
  7. Clowe et al. (2006) A Direct Empirical Proof of the Existence of Dark Matter, ApJ 648, L109

Source Zwicky, F. (1937). On the Masses of Nebulae and of Clusters of Nebulae. The Astrophysical Journal 86, 217.doi.org/10.1086/143864

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