Missing Satellites Problem
Why does the Milky Way have ~50 satellite galaxies when ΛCDM simulations predict ~500?
The Discrepancy
A factor of ~10× difference that has persisted since the 1990s
Context
CDM Simulations
- Aquarius, Via Lactea II
- ~500 subhalos with M > 10⁷ M☉
- Universal hierarchical structure
- Excess at all masses
MW Observations
- ~60 known satellites (2024)
- Ultra-faints discovered with DES
- Completeness limited to R < 300 kpc
- Even so, ~10× factor missing
The MCMC Solution
The MCMC suppresses the formation of low-mass subhalos through the Law of Cronos:
Law of Cronos in Small Halos
The temporal flow depends on the local density:
In low-mass halos (high relative density), Θ > 1 implies that time passes more slowly. This has two effects:
- Delayed formation: Small halos form later
- Reduced accretion: Less cosmic time to grow
Suppression Function
The abundance of subhalos is modified by a factor:
With Mc ≈ 10⁸ M☉ and α ≈ 0.6, derived from the Law of Cronos.
Quantitative Result
| Mass Range | N (ΛCDM) | N (MCMC) | N (Observed) |
|---|---|---|---|
| > 10⁹ M☉ | ~15 | ~12 | ~11 (LMC, SMC, Sgr...) |
| 10⁸ - 10⁹ M☉ | ~100 | ~35 | ~30 |
| 10⁷ - 10⁸ M☉ | ~400 | ~20 | ~20 |
| Total | ~500 | ~65 | ~60 |
The MCMC reproduces the observed count without the need for extreme baryonic feedback
Comparison with Other Solutions
ΛCDM Solutions
- Reionization: Suppresses small halos but not enough
- SN feedback: Requires extreme efficiency
- WDM: Introduces a new undetected particle
- SIDM: Helps but does not fully resolve it
MCMC
- Suppression emerges from the ontology
- Requires no new particles
- Consistent with other observables
- Verifiable quantitative prediction
Verifiable Predictions
- Radial distribution: More satellites near the galactic center
- Luminosity vs mass: Modified relation at M < 10⁸ M☉
- M31: Similar prediction (~80 satellites expected)
- Local groups: Universal suppression in similar environments