Historical content. This page belongs to the former “solved problems” section. The Tratado de Fundamentos (v35, Jun 2026) does not present these problems as solved: it develops them in full, classifies several results as conditional and keeps seven open fronts. The values of S and the thresholds quoted here may correspond to the earlier formulation. The current classification of each result is in the status of the results.

Too-Big-To-Fail Problem

Why do the most massive predicted subhalos not host bright galaxies as they should?

This page is a translation of the Spanish original. Where they differ, the Spanish text prevails.

The Problem

ΛCDM simulations predict subhalos so massive that they should have formed visible luminous galaxies. However, the observed satellite galaxies are significantly less massive than expected.

The Conflict

ΛCDM Simulations

  • ~10 subhalos with V_max > 30 km/s
  • High central concentrations
  • “Too massive to fail”
  • They should be visible as bright dSphs

MW Observations

  • Only ~3-4 satellites with V_max > 30 km/s
  • Most have V_max ~ 10-20 km/s
  • Concentrations lower than predicted
  • Fornax, Sculptor, etc. are “small”

Why “Too Big To Fail”?

The name comes from the idea that these massive halos are “too big to fail” at forming stars. In the ΛCDM paradigm:

  • Halos with M > 10⁹ M☉ should easily retain gas
  • Reionization does not significantly affect them
  • Supernova feedback should not expel all the gas
  • Conclusion: they should exist but are not observed

The MCMC Solution

The MCMC reduces the central masses of subhalos through the local Mp/Ep tension:

Mp/Ep Tension in Halos

In high-density regions, the tension between mass and space generates an effective pressure that counteracts collapse:

$$P_{tension} = \frac{c^4}{8\pi G} \cdot \left(\frac{Mp - Ep}{Mp + Ep}\right)^2 \cdot \nabla^2 \Phi$$

This pressure is greater in regions of high gravitational gradient (halo centers), reducing the central concentration.

Reduction of the Concentration Parameter

The concentration parameter c = r_vir/r_s is reduced:

$$c_{MCMC} = c_{CDM} \cdot \left(1 - \beta \cdot \ln\left(\frac{M}{M_c}\right)\right)$$

With β ≈ 0.15 and Mc ≈ 10¹⁰ M☉.

Quantitative Comparison

Satellite V_max (ΛCDM) V_max (MCMC) V_max (Obs)
Massive subhalo 1 ~45 km/s ~28 km/s ~25 km/s (Fornax)
Massive subhalo 2 ~40 km/s ~25 km/s ~22 km/s (Sculptor)
Massive subhalo 3 ~38 km/s ~22 km/s ~18 km/s (Leo I)
Massive subhalo 4 ~35 km/s ~20 km/s ~17 km/s (Carina)
Reduced V_max ~30%
Lower central concentration

The MCMC subhalos are consistent with the observed satellites

Connection with Cusp-Core

Same Mechanism

The Too-Big-To-Fail problem and the Cusp-Core problem are intimately related in the MCMC:

  • Cusp-Core: ρ_lat smooths the central profile
  • TBTF: The same pressure reduces V_max
  • Result: The earlier corpus presented both problems as solved simultaneously

In ΛCDM, separate mechanisms are required for each problem.

Why Does It Work?

ΛCDM Solutions

  • Extreme SNe feedback
  • Requires DM-baryon coupling
  • Fine-tuning of efficiencies
  • Timing problems

MCMC

  • Intrinsic effect of DM
  • Requires no baryons
  • Universal scaling with mass
  • Consistent at all z
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