CMB Power Spectrum (Acoustic Peaks)
This interactive simulator explores CMB Power Spectrum (Acoustic Peaks) in Астрономия и небо. Cosmic Microwave Background temperature D_ℓ vs ℓ with Sakharov peaks: tune Ω_b h², Ω_c h², n_s, A_s, τ, h and watch the parity flip between odd / even peaks, the Silk damping tail, and the Sachs–Wolfe plateau move. Pedagogical parametric ΛCDM model. Use the controls to change the scenario; watch the visualization and any graphs or readouts to connect the model with lectures, labs, and homework.
Для кого: For learners comfortable with heavier math or second-level detail. Typical context: Астрономия и небо.
Ключевые понятия
- cmb
- power
- spectrum
- acoustic
- peaks
- cmb power spectrum
- astronomy
Как это работает
**CMB temperature power spectrum** — D_ℓ = ℓ(ℓ+1)C_ℓ/2π in μK² as a function of multipole ℓ — the cornerstone observable of precision cosmology. The simulator is a *parametric* model (no Boltzmann code), but it captures the qualitatively correct response of the spectrum to the six standard ΛCDM parameters: **Sachs–Wolfe plateau** at ℓ ≲ 30, **acoustic / Sakharov peaks** at ℓ ≈ 220, 540, 810, … set by the angular sound horizon ℓ_A; baryon-loading **parity** (raising Ω_b h² boosts odd peaks and suppresses even ones), the **Silk damping** tail at high ℓ, the **scalar tilt** n_s, and reionisation suppression e^{−2τ}. Slide Ω_b h² and watch the second peak shrink relative to the first — that's how Planck pinned the baryon density.
Основные формулы
Ещё из «Астрономия и небо»
Другие симуляторы в этой категории — или все 45.
Big Bang Nucleosynthesis (BBN)
Light-element abundance curves H, ⁴He, D, ³He, ⁷Li vs cosmic time / temperature. Weak freeze-out, neutron decay gap, deuterium bottleneck → Y_p ≈ 0.245. Slide η₁₀ and N_eff over the classic BBN curves; observed values overlaid.
EM Calorimeter Shower (Heitler / Rossi)
Toy electromagnetic cascade in a calorimeter: γ → e⁺e⁻, e⁻ → e⁻γ each X₀, with critical-energy cutoff E_c. Animate the branching tree, see N_max ≈ E₀/E_c, t_max ≈ log₂(E₀/E_c) live; presets for Pb, Cu, Si, air.
Bremsstrahlung & Synchrotron Radiation Pattern
Polar plot of dP/dΩ for an accelerating charge: a ∥ v (linear / brems) and a ⊥ v (circular / synchrotron). Pull β = v/c toward 1 — Larmor donut collapses into a forward beam of half-angle ≈ 1/γ; ω_g, ω_c shown for given B.
Фазы Венеры (Галилей)
Гелиоцентрическая геометрия: полный диск и серп у нижнего соединения; вставка — вид с Земли.
Аберрация света (звёзды)
Брэдли: наклон трубы v/c ~ 10⁻⁴; годовая амплитуда ~20,5″ — не параллакс.
Циклы Миланковича
e, наклон, прецессия → учебная кривая инсоляции высоких широт; контекст ледниковых циклов.