Zodiacal dust replenishment

Why must the dust glowing between the planets be far younger than the solar system holding it?

On a very dark evening, a faint cone of light leans up from where the Sun set: sunlight scattered off dust spread through the inner solar system. The obvious reading is that it is leftover — primordial rubble that never got swept into a planet. That reading is almost exactly wrong. The dust is young, and something has to be making more of it right now. What removes it, and how fast?

Start by asking what a grain in orbit feels besides gravity. Sunlight carries momentum, so the grain is pushed outward. The ratio of that push to the Sun's pull has a standard name, β, and it can be built from first principles: radiation acts on cross-section πs², gravity on mass (4/3)πs³ρ, so for a grain of radius s and density ρ,

β = 3L / (16π c GM s ρ)

With L = 3.83 x 10^26 W, ρ = 2500 kg/m³ and s = 10 micrometres, that comes to about 0.023. Notice both forces fall as one over distance squared, so β is a property of the grain and not of where it sits. Set β = 0.5 and the grain is effectively unbound the moment it is released: that happens near s ≈ 0.5 micrometres. Sub-micron debris leaves on hyperbolic paths and never joins the cloud at all.

But that is a radial force, and a radial force only resizes an orbit. It cannot make a grain spiral in. So where does a tangential force come from?

Here is the step worth slowing down for. Go into the grain's own frame, moving at speed v. Sunlight no longer arrives from straight ahead of the Sun; aberration tilts it forward by an angle of about v/c. The absorbed momentum therefore has a small component pointing backwards along the direction of travel. The grain re-radiates that energy as heat, but it does so symmetrically in its own frame, carrying away no net direction. What is left is a pure drag, of size β times gravity times v/c.

How small is that? At 1 AU, v/c = 29.8 / 300000 ≈ 1 x 10^-4, so the drag is about 2 x 10^-6 of the Sun's gravity. Instantaneously negligible. But orbits integrate. Using the standard relation between a transverse acceleration and the drift of the semi-major axis, da/dt = 2a·a_T/v, and substituting a_T = βGMv/(a²c):

da/dt = -2βGM / (ac), so t = a²c / (4βGM)

Put in one astronomical unit and the solar GM = 1.327 x 10^20, and the whole thing collapses to a memorable form: about 400/β years from 1 AU, scaling as the square of the starting distance. Our 10-micrometre grain therefore falls in from 1 AU in roughly 17,000 years, from the asteroid belt at 3 AU in about 160,000 years, and even from 30 AU in some 16 million years.

Now hold that against 4.6 billion years. A grain born with the solar system and starting in the asteroid belt has had time to make the trip nearly thirty thousand times over. The cloud we see cannot be a survivor. It is a steady state: something is feeding it at roughly the rate the Sun is eating it. Estimates of the cloud's total mass sit near 10^16 kg and are uncertain by something like an order of magnitude, so the required supply is of order 10^11 kg a year — a figure I offer only as an order of magnitude.

What supplies it? Comets shedding dust each perihelion, collisions grinding asteroids, and material from the Kuiper belt drifting sunward. The split between these is genuinely contested; dynamical modelling in the last fifteen years has argued that Jupiter-family comets dominate, at something like 85 to 90 per cent, but that is a model-dependent conclusion and not a measurement.

Three refinements, because this force is easy to confuse with its neighbours.

Poynting-Robertson drag is not radiation pressure. Radiation pressure is the radial β term, which settles once and for all whether a grain is bound; the drag is the tiny transverse remainder of order v/c, and it is that remainder, not the big radial push, that governs how long the cloud lives.

Nor is it the Yarkovsky effect, which shifts asteroid orbits by thermal recoil. Yarkovsky requires thermal lag: a body that stays hot into its own afternoon, so that its emission is lopsided. A 10-micrometre grain conducts heat across itself almost instantly and is essentially isothermal, so it has no afternoon and no Yarkovsky force. Conversely, β scales as 1/s, so the drag fades to nothing on bodies of any size. The two mechanisms hand off somewhere between the grain and the boulder.

And the drag is not always what removes a grain. Larger particles can be shattered by mutual collisions faster than they can spiral in, so the true lifetime is the shorter of two clocks. That does not rescue the primordial reading — collisions only destroy dust faster.

The refuting observation: inward drift makes a specific, otherwise unmotivated prediction. Grains spiralling sunward must pass through Earth's orbital resonances, where drag and resonance can balance and hold them temporarily, building a circumsolar ring of enhanced density with a blob trailing Earth around its orbit. Infrared sky surveys since IRAS have found exactly such a ring and trailing enhancement. If the dust were static and primordial, there would be nothing drifting for a resonance to catch, and no reason for the enhancement to sit behind Earth rather than symmetrically around it.

• Why a debris disc seen around another star is evidence for an unseen collisional population rather than for leftover material.

Every term the collection defines is gathered in the glossary.