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Dark Matter Host

Gravitational Lensing Physics

\[\theta_E = \sqrt{\frac{4GM}{c^{2}}\,\frac{D_{LS}}{D_L D_S}}\]
$21.99 USD
$21.99 USD
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Meet Dark Matter Host. 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. About five-sixths of all matter is something never directly detected. Pixel-art full-wrap black ceramic mug in 11 or 15 oz; equation, symbols and sources in the physics panel below.

Shipping calculated at checkout by destinationMade to order, ships in ~10 days

Details

Size & material11oz · 15oz

Black glossy ceramic mug with a C-handle. Lead- and BPA-free.

  • 11oz: 0.33 l
  • 15oz: 0.44 l
CareDishwasher & microwave safe

Dishwasher safe (top rack) or hand wash. Microwave safe.

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Made to order: about 10 days of production and handling before it ships.

Delivery times & where we ship

Returns & replacements21 days

Every item is printed to order, so we can’t accept returns or exchanges for change of mind, or if you ordered the wrong size or colour.

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.

Full refund & replacement policy

The physics

Gravitational lensing maps mass whether or not it shines. In the Bullet Cluster the mass is offset from the hot gas, and about five-sixths of all matter is dark (Planck 2018).

Dark Matter Host throws the party, but you can only see the guests.

Mass bends light, as Einstein's general relativity predicts. A lens of mass M bends a background source into a ring of angular radius θ_E = √[(4GM/c²)·D_LS/(D_L D_S)], the formula on this mug. Measure how background galaxies are distorted and you can map where the mass is, seen or not.

In the Bullet Cluster, two galaxy clusters have passed through each other. Their hot gas, which holds most of the ordinary matter and glows in X-rays, collided and stalled in the middle. Lensing shows most of the mass sailed on with the galaxies. In 2006 Clowe and colleagues measured that offset at 8σ: the mass is where the gas isn't. Vera Rubin's measurements of galaxy rotation in the 1970s had already pointed to unseen mass.

A worked number: a single star of one solar mass halfway to a source 8 kpc away has θ_E ≈ 1 milliarcsecond. Massive galaxy clusters bend light into arcs with Einstein radii of tens of arcseconds. Planck 2018 gives Ω_c h² = 0.120 against Ω_b h² = 0.0224 for ordinary matter, so about five-sixths of all matter is something never directly detected.

“You'll never see me at my own party,” says the Host. “Watch how the light bends around me.”

Equations

\[\theta_E = \sqrt{\frac{4GM}{c^{2}}\,\frac{D_{LS}}{D_L D_S}}\]
\[M(r) = \frac{v^{2} r}{G}\]
SymbolMeaningUnit
\(\theta_E\) Einstein radius (angular) \(\mathrm{rad}\)
\(G\) Newtonian constant of gravitation \(\mathrm{m³·kg⁻¹·s⁻²}\)
\(M\) mass of the lens (within the Einstein radius) \(\mathrm{kg}\)
\(c\) speed of light in vacuum \(\mathrm{m/s}\)
\(D_L\) angular-diameter distance to the lens \(\mathrm{m}\)
\(D_S\) angular-diameter distance to the source \(\mathrm{m}\)
\(D_{LS}\) angular-diameter distance from lens to source \(\mathrm{m}\)
\(M(r)\) mass enclosed within radius r \(\mathrm{kg}\)
\(v\) circular orbital speed at radius r \(\mathrm{m/s}\)
\(r\) radius from the centre \(\mathrm{m}\)

Sources

  1. Clowe et al. (2006) A Direct Empirical Proof of the Existence of Dark Matter, ApJ 648, L109
  2. Planck Collaboration (2020) Planck 2018 results VI. Cosmological parameters, A&A 641, A6
  3. Clowe et al. (2006), arXiv preprint

Source Clowe, D. et al. (2006). A Direct Empirical Proof of the Existence of Dark Matter. The Astrophysical Journal 648, L109–L113.doi.org/10.1086/508162

Field notes

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