Cosmology
The Ostriker-Vishniac Effect: Second-Order CMB Anisotropy from Reionization Flows
At angular scales below one arcminute — multipoles of ℓ ≈ 2000-3000, where the smooth primary cosmic microwave background has already damped away — a faint microkelvin-level signal survives that no first-order physics can produce. This is the Ostriker-Vishniac effect: a second-order temperature anisotropy imprinted when free electrons in the ionized intergalactic medium, streaming along with the cosmic web at hundreds of km s⁻¹, Doppler-scatter CMB photons — but only where the electron density and the bulk velocity are correlated.
Named for Jeremiah Ostriker and Ethan Vishniac (1986-1987), the effect is the small-scale, linear-regime limit of the kinetic Sunyaev-Zel'dovich effect. Because the ordinary first-order Doppler signal cancels along the line of sight, the density-weighted residual — proportional to the product δv rather than v alone — becomes the dominant CMB anisotropy at arcminute scales and a direct fingerprint of when and how the Universe reionized.
- RegimeSecond-order (nonlinear) CMB secondary anisotropy
- Peak scaleℓ ≈ 2000-3000 (arcminute scales, θ ~ 1′-2′)
- Amplitude~1 μK level; D_ℓ at ℓ=3000 of order a few μK²
- Driven byCorrelated density × velocity (δv) of reionized electrons
- First describedOstriker & Vishniac 1986; Vishniac 1987
- Observed withSPT, ACT (arcminute-resolution CMB surveys)
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What It Is and Why It Matters
The Ostriker-Vishniac (OV) effect is a secondary anisotropy of the cosmic microwave background — a temperature fluctuation imprinted not at the surface of last scattering (z ≈ 1100) but much later, when CMB photons re-scatter off free electrons liberated during cosmic reionization (z ≈ 6-15). Crucially, it is a second-order effect: it survives only because it depends on the correlated product of the electron density contrast δ and the peculiar velocity v, not on either quantity alone.
Why does this matter? On arcminute scales (ℓ ≳ 2000), the primary CMB fluctuations are exponentially suppressed by Silk damping, and even the first-order Doppler signal from reionization cancels out. The OV effect is one of the very few sources of genuine sky signal that remain. It therefore acts as a clean, small-scale probe of when the Universe reionized and how ionized gas traced the growing cosmic web — information encoded in a regime where nothing else competes.
The Mechanism, Step by Step
Reionization refills the Universe with free electrons, giving CMB photons a fresh chance to Thomson-scatter. Each scatter off a moving electron Doppler-shifts the photon by δT/T ≈ (v/c)·n̂, where v is the electron's peculiar velocity. Naively this is a first-order effect ∝ v.
But it cancels. Peculiar flows are irrotational (curl-free) on linear scales, and as a photon traverses many independent flow regions along the line of sight, the positive and negative Doppler shifts average to near zero on small angular scales. What breaks the cancellation is modulation of the scattering probability: the optical depth is higher where the electron density is higher. So regions with more electrons (larger δ) that also happen to be moving contribute a net, uncancelled signal.
The surviving anisotropy is thus sourced by the momentum field q = (1+δ)v ≈ δv — the product of density and velocity. This is intrinsically second order in perturbation theory. In Fourier space the effect couples large-scale velocity modes to small-scale density modes, funneling power to high ℓ.
Characteristic Numbers, Scales, and the Key Relation
The OV signal is set by the momentum power spectrum. The line-of-sight temperature integral is δT/T = (σ_T n̄_e / c) ∫ e^(−τ) (n̂·v)(1+δ) a dη, whose second-order piece — the ⟨δv⟩ cross term — is the Vishniac source. Its angular power spectrum peaks at ℓ ≈ 2000-3000, corresponding to angular scales θ ~ 1′-2′, with an amplitude at the microkelvin level (band power D_ℓ = ℓ(ℓ+1)C_ℓ/2π of order a few μK² at ℓ = 3000).
The amplitude scales with the Thomson optical depth to reionization, τ ≈ 0.054 (Planck), and grows roughly logarithmically with reionization redshift — earlier, more extended reionization boosts the signal. Peculiar velocities of the sourcing gas are ~100-300 km s⁻¹, and the relevant density structures are the mildly nonlinear filaments and sheets of the cosmic web. Because Thomson scattering is achromatic, the OV effect has a pure blackbody (thermal) spectrum — unlike the thermal SZ effect, it cannot be removed by its frequency signature.
How It Is Observed and Detected
Isolating OV/kSZ power requires arcminute-resolution, high-sensitivity CMB maps at ℓ ≳ 3000, the domain of the South Pole Telescope (SPT) and the Atacama Cosmology Telescope (ACT), both operating near 90-220 GHz. At these scales, several signals overlap: the thermal SZ effect, the cosmic infrared background (CIB), radio point sources, and the kSZ/OV signal. The kSZ (which includes the post-reionization OV component plus patchy reionization) is separated using its distinctive blackbody spectrum — it vanishes in a y-map and has no CIB-like frequency tilt.
Current constraints are upper limits and marginal detections: SPT reports a total kSZ band power D₃₀₀₀ ≈ 2.9 ± 1.3 μK², with the patchy-reionization piece bounded to roughly 2-5 μK², and ACT places D₃₀₀₀^kSZ ≲ 8.6 μK². The homogeneous, post-reionization OV term is the smoother 'floor' beneath the patchy signal. Cross-correlating CMB maps with galaxy velocity fields (the 'pairwise kSZ' method) provides a complementary, higher-significance handle on the same ionized-gas momentum.
Where It Operates and How It Differs from Related Effects
The OV effect operates after reionization completes (z ≲ 6), sourced by the smooth, fully ionized intergalactic medium whose density traces linear-to-mildly-nonlinear large-scale structure. In this strict sense it is the linear kinetic SZ effect from the post-reionization epoch. It is distinct from — though continuous with — the patchy kSZ signal generated during reionization, when the ionization fraction itself is inhomogeneous (ionized bubbles of ~5-20 Mpc surrounding the first galaxies) and modulates the Doppler signal independently of density.
Both belong to the kinetic SZ family and share a blackbody spectrum, distinguishing them from the thermal SZ effect (a spectral y-distortion from hot cluster electrons, nulling at 217 GHz). The OV effect also differs from primary CMB Doppler anisotropy, which is first order and cancels on the very scales where OV survives. In practice, observers lump OV and patchy kSZ into a single 'total kSZ' band power and model the two contributions separately.
Open Questions and Significance
The central open question the OV/kSZ signal addresses is the timing and duration of reionization. Because the homogeneous OV amplitude grows with the redshift and extent of reionization while the patchy component tracks its 'burstiness,' splitting the measured D₃₀₀₀^kSZ into these two pieces would pin down when the first ionizing sources switched on and how quickly bubbles overlapped — breaking degeneracies left by the integrated Planck optical depth τ ≈ 0.054.
Key challenges remain. The signal is buried under tSZ, CIB, and point-source foregrounds whose cross-correlations are imperfectly known, and non-Gaussian, connected four-point contributions (10-30%) complicate analytic modeling. Upcoming instruments — SPT-3G, Advanced ACTPol, Simons Observatory, and CMB-S4 — aim to detect the patchy kSZ at high significance and cleanly separate the OV floor. Success would turn a subtle second-order scattering effect into one of the sharpest available tools for studying the epoch of cosmic dawn and reionization.
| Effect | Physical driver | Order / dependence | Characteristic scale / signature |
|---|---|---|---|
| Ostriker-Vishniac | Density-modulated Doppler from linear-regime ionized gas (δv) | Second order; ∝ (peculiar velocity)²-weighted density | ℓ ~ 2000-3000; ~μK; blackbody spectrum |
| Linear kinetic SZ | Bulk peculiar motion of ionized gas, post-reionization | First order in v, but cancels unless modulated → same as OV | Overlaps OV at ℓ ≳ 2000; blackbody |
| Patchy kSZ | Inhomogeneous ('patchy') ionization fraction during reionization | Modulation by ionization bubbles, not just density | ℓ ~ 2000-8000; bubble scale ~5-20 Mpc |
| Thermal SZ | Inverse-Compton off hot cluster electrons (thermal pressure) | First order in electron pressure ∫nₑTₑ dl | y-distortion; null at 217 GHz; ℓ ~ 3000 |
| Primary Doppler | First-order line-of-sight velocity at last scattering | First order in v | Cancels on small scales (θ ≲ 7′) |
Frequently asked questions
Why is the Ostriker-Vishniac effect a 'second-order' effect?
Because it depends on the product of two first-order quantities — the electron density contrast δ and the peculiar velocity v — rather than on either alone. The pure first-order Doppler signal (∝ v) cancels along the line of sight on small angular scales, so the leading surviving term is the δv cross-correlation, which is second order in cosmological perturbation theory.
How is the OV effect related to the kinetic Sunyaev-Zel'dovich effect?
The OV effect is essentially the linear-regime, post-reionization kinetic SZ effect from the smooth ionized intergalactic medium. The broader kSZ signal also includes the 'patchy' component generated during reionization by inhomogeneous ionized bubbles. Observers usually treat total kSZ = OV (homogeneous) + patchy, all sharing a blackbody spectrum.
At what angular scale does the OV effect peak, and how strong is it?
It peaks at multipoles ℓ ≈ 2000-3000, corresponding to arcminute angular scales (θ ~ 1′-2′), well below the Silk-damping tail of the primary CMB. The amplitude is at the microkelvin level — the band power D_ℓ = ℓ(ℓ+1)C_ℓ/2π at ℓ = 3000 is of order a few μK².
Why doesn't the ordinary Doppler effect from reionization show up instead?
Peculiar velocity flows are irrotational on linear scales, so as a CMB photon crosses many independent moving regions, the alternating red/blue Doppler shifts cancel to near zero on small angular scales. Only by weighting the velocity by the local electron density (which sets the scattering probability) does an uncancelled net signal — the OV effect — remain.
How can the OV effect be distinguished from the thermal SZ effect?
The OV/kinetic effect is pure Doppler Thomson scattering, so it preserves a blackbody spectrum and has no special frequency. The thermal SZ effect is an inverse-Compton spectral distortion (a y-distortion) that nulls at 217 GHz and appears as a decrement below and increment above it. Multi-frequency CMB maps exploit this spectral difference to separate them.
What does measuring the OV effect tell us about cosmic reionization?
Its amplitude grows roughly logarithmically with reionization redshift and with the Thomson optical depth (τ ≈ 0.054 from Planck), while the patchy component tracks how bursty and inhomogeneous reionization was. Splitting the measured kSZ band power into homogeneous OV and patchy pieces constrains when reionization began, how long it lasted, and the sizes of ionized bubbles (~5-20 Mpc).