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Measuring our peculiar velocity from spectroscopic redshift surveys

T0 review · 2 major / 6 minor · reviewed 2026-08-11 · deepseek-v4-flash

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Pith's one-line read The finger-of-the-observer effect — an oscillatory imprint of the observer's own velocity in the galaxy power-spectrum monopole — can be measured in full-sky surveys and, when boosted by artificial Doppler shifts, yields both the…

desk verdict B-FOTO is a genuinely new and well-derived method for measuring the Solar System's peculiar velocity from galaxy clustering, but the headline forecast numbers assume an exact no-FOTO baseline that real surveys will have to marginalize over. read the letter →

arxiv 2412.03953 v2 pith:43N2MSR2 submitted 2024-12-05 astro-ph.CO

Mohamed Yousry Elkhashab , Cristiano Porciani , Daniele Bertacca This is my paper · ORCID
classification astro-ph.CO
keywords finger-of-the-observereffectpeculiarvelocitypowerspectrummonopoleredshift-spacedistortionscosmicmicrowavebackgrounddipoleDopplerboostinggalaxyredshiftsurveysdarkenergyequationofstate
topics Dark Energy
open problems Dark Energy
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

This paper argues that the Solar System's motion with respect to the cosmic matter frame is not just a nuisance for galaxy clustering but a measurable signal. The motion imprints a dipole on the observed galaxy density, which in turn produces damped oscillations in the monopole of the power spectrum on ultra-large scales, a feature the authors call the finger-of-the-observer (FOTO) effect. Using 140 mock catalogues that mimic Euclid-like H$\alpha$ and SKAO-like HI surveys, they show the oscillations are detectable with signal-to-noise up to about 7 for an all-sky H$\alpha$ survey, and that correcting galaxy redshifts to the CMB frame does not erase them. The paper's new step is to apply deliberate artificial Doppler shifts to the same catalogue: the resulting 'boosted' B-FOTO signal contains a term proportional to the dot product of the true Solar velocity and the artificial shift, so combining several shifts allows simultaneous inference of the velocity's magnitude, its direction, and cosmological parameters. If the method works on real data, it offers an independent test of the kinematic interpretation of the CMB dipole and a new probe of the expansion history from spectroscopic surveys.

What carries the argument

The load-bearing object is the dipole term that the observer's velocity adds to the observed galaxy overdensity, $\delta_{\mathrm{dip}} = \alpha_o (v_\odot\cdot \hat{r})/(aHr)$, where $\alpha_o$ packages the survey selection through evolution and magnification bias. In a full-sky survey this dipole generates the FOTO correction to the power-spectrum monopole, $P_{0,\mathrm{dip}}(k) = \frac{16\pi^2}{3}\frac{v_\odot^2}{H_0^2}\frac{I_1^2(k)}{\int \bar{n}^2 d^3r}$, with the integral $I_\ell(k)=\int \frac{r\bar{n}\,\alpha_o}{aH/H_0}\, j_\ell(kr)\,dr$, whose spherical Bessel factor $j_1^2$ produces the characteristic oscillations. The paper's central machinery for measuring the velocity vector is the artificial Doppler boost of Eq. (5.4), which replaces the FOTO signal with the three-term B-FOTO expression of Eq. (5.7); the middle term, proportional to $v_\odot\cdot v_{\mathrm{art}}$, is what couples the direction of the Solar velocity to the data, while the $v_{\mathrm{art}}^2$ term amplifies the cosmological information.

What would settle it

Run the B-FOTO pipeline on a real spectroscopic survey or on independent mocks and compare the recovered Solar velocity vector with the Planck CMB-dipole value: agreement within the claimed ~10% magnitude and ~9 degree direction supports the method, while a significant offset — or a nonzero velocity recovered from mocks built with a comoving observer — would falsify it.

Watch

Extended reading notes

Core claim

On the paper's own terms, the claim is that the observer's peculiar velocity leaves a deterministic, oscillatory fingerprint in the monopole of the galaxy power spectrum, the finger-of-the-observer (FOTO) effect, and that this fingerprint is not a nuisance to be removed but a resource. By re-assigning every galaxy redshift with an artificial Doppler shift $v_{\mathrm{art}}$ while leaving angular positions and fluxes unchanged, the power-spectrum monopole acquires the B-FOTO signal of Eq. (5.7): a term $\propto v_\odot^2 I_1^2$ from the true velocity, a term $\propto v_{\mathrm{art}}^2 (I_1+J_1)^2$ that depends only on the artificial velocity and the cosmology, and the key cross-term $2 v_\odot \cdot v_{\mathrm{art}} I_1(I_1+J_1)$, whose dependence on the angle between the two velocity directions breaks the degeneracy between magnitude and direction of the Solar velocity. With five carefully chosen artificial velocity vectors applied to 140 relativistic mock catalogues of a Euclid-like H$\alpha$ survey and an SKAO-like HI survey, the paper recovers the input Solar velocity to about 10% in magnitude (39 km/s for H$\alpha$) and about 9 degrees in direction, and constrains $\Omega_{\mathrm{m},0}$ to about 2.7% (H$\alpha$) in a flat $\Lambda$CDM model, or a derived combination $\Sigma$ of $\Omega_{\mathrm{m},0}$ and the dark-energy equation-of-state $w$ to about 4–9%. The FOTO signal also survives a CMB-frame redshift correction as the C-FOTO residual, because relativistic aberration and Doppler magnification are not removed by the radial shift.

Load-bearing premise

The pipeline assumes the power-spectrum monopole that a comoving observer would measure, $P_{0,\mathrm{com}}(k)$, is known exactly — in the mocks it is supplied by the average of the 140 CRF catalogues — and that the FOTO dipole does not correlate with the density field, so errors in modeling the survey baseline (galaxy bias, redshift-space distortions, window function, large-scale systematics) directly contaminate the recovered velocity and cosmological parameters.

Editorial extensions

If this is right

  • The FOTO effect is detectable in an all-sky H-alpha survey at signal-to-noise about 6.8 and remains at about 4 after masking the Galactic and Ecliptic planes, so ongoing and future spectroscopic surveys can search for it.
  • Converting galaxy redshifts to the CMB frame does not erase the signal; the residual C-FOTO term, sourced by relativistic aberration and Doppler magnification, can be larger than the original, so analyses that 'correct' redshifts must still account for the observer's motion.
  • Combining B-FOTO measurements from several artificial Doppler shifts yields the Solar velocity vector, to about 10% magnitude and 9 degrees direction for the H-alpha survey, providing a direct test of the kinematic interpretation of the CMB dipole.
  • In a flat $\Lambda$CDM model the same B-FOTO data constrain $\Omega_{\mathrm{m},0}$ to about 2.7% (H-alpha) and 1.8% (HI) in the idealized full-sky case, and a wCDM extension constrains a derived combination of $\Omega_{\mathrm{m},0}$ and $w$ to about 4–9%.
  • Because the B-FOTO cross term depends on the angle between the true and artificial velocities, the method measures the direction of the Solar motion, not just its speed, which distinguishes it from projected number-count dipole analyses.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • In a real survey there is no ensemble of comoving-frame mocks to supply the no-FOTO baseline, so $P_{0,\mathrm{com}}(k)$ must be modeled; an editorial inference is that the technique's practical reach will be set by how well large-scale systematics and the survey window can be calibrated, exactly the scales where the FOTO oscillations live.
  • The multipole formula in Eq. (2.29) shows that odd power-spectrum multipoles carry imaginary FOTO components that the paper does not use; adding them to the likelihood is a natural extension that could sharpen the direction measurement or break the $\Omega_{\mathrm{m},0}$–$w$ degeneracy without an external prior.
  • The same artificial-shift procedure could be applied to radio-continuum or 21-cm intensity-mapping surveys, whose selection functions differ but whose sky coverage is large; if those functions are characterized, B-FOTO would offer an independent kinematic test in the regime where projected number-count dipoles are currently disputed.
  • If a real survey returns a Solar velocity that disagrees with the Planck CMB-dipole value beyond the claimed precision, that would be evidence for an intrinsic CMB dipole component or a large-scale bulk flow — a new-physics signature that the paper explicitly identifies as the motivation for the measurement.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

2 major / 6 minor

Summary. The paper develops the finger-of-the-observer (FOTO) effect: the observer's peculiar velocity imprints a dipole in the observed galaxy overdensity, which in turn produces oscillatory contributions to the power-spectrum multipoles measured in spectroscopic redshift surveys. The authors derive the full-sky multipole expression (Eq. 2.29), validate it against 140 LIGER mock catalogues mimicking H-alpha and HI-selected surveys, and find that the FOTO monopole could be detected with S/N up to 6.8 for a full-sky Euclid-like H-alpha sample. They then show that applying artificial Doppler redshift corrections produces a 'boosted' B-FOTO signal (Eq. 5.7) that contains a term proportional to v_sun dot v_art, enabling simultaneous constraints on the magnitude and direction of the solar peculiar velocity and on cosmological parameters. Using five artificial velocity vectors, they report Delta v_sun ~ 39 km/s (10.5%), direction to ~9 degrees, Delta Omega_m,0 = 0.0084 (2.7%) for the H-alpha survey, and constraints on a derived dark-energy parameter Sigma.

Significance. If the claims hold, the paper introduces a genuinely new observable for testing the kinematic interpretation of the CMB dipole and for extracting cosmological information from galaxy surveys; it uses the 3D clustering monopole rather than projected number counts, and the B-FOTO technique provides directional information on the solar velocity that previous monopole analyses lacked. The derivation of the FOTO multipoles in Appendix A is explicit, the B-FOTO expression is derived from the linear RSD model rather than fitted, and the mock suite is substantial. The paper is also honest about its limitations: full-sky geometry, exact bias knowledge, and control of large-scale systematics are all stated as assumptions. The main caveat is that the numerical validation against LIGER mocks is partly a self-consistency check, since the mocks are generated with the same relativistic RSD framework used in the analytic model; the agreement is nevertheless a useful test of the numerical implementation.

major comments (2)
  1. [Sec. 4.2.1, Eq. (5.7), Fig. 3] The inference pipeline uses the data vector d = P0,HRF minus the mean of the CRF mocks, where the CRF mean is described as "a proxy for an exact theoretical model that does not include the FOTO effect." In a real survey no CRF ensemble exists, so the no-FOTO baseline P0,com(k) must be modelled and marginalised over, including galaxy bias, redshift-space distortions, window function, and shot noise. The B-FOTO signal is a difference of large quantities, and at k <~ 5 x 10^-3 h/Mpc the FOTO oscillations are comparable in amplitude to P0,com itself, so errors in the baseline directly contaminate the v_sun dot v_art term in Eq. (5.7). The paper does not quantify how the quoted uncertainties (Delta v_sun = 39 km/s, Delta Omega_m,0 = 0.0084, direction ~9 degrees) inflate when P0,com is marginalised over with a flexible model, nor does it test for bias from an incorrect baseline shape. This is the key missing element for the headline claims.
  2. [Secs. 4.2 and 5.3.2-5.3.3] The cosmological constraints assume exact knowledge of the evolution bias E(z), magnification bias Q(z), and linear bias b(z). A robustness test is presented only for the velocity magnitude against 1% and 10% errors on alpha_o (Sec. 4.2); the density and dark-energy inference are not tested against bias uncertainties. Since I1(k) and J1(k) in Eq. (5.7) depend on alpha_o, alpha_c, and the mean number density, errors in these functions will bias and broaden the Omega_m,0 and Sigma posteriors. Before quoting Omega_m,0 to 2.7% and Sigma to 5%, the authors should propagate realistic uncertainties in E, Q, and b through the B-FOTO likelihood.
minor comments (6)
  1. [Sec. 2.3.1] The statement that cross-correlation terms are neglected should be made precise: the delta_dip-delta_com cross term has zero ensemble average and contributes only to the covariance, which is already captured by the mock-based matrix C. As written, the sentence leaves the impression that the multipole formula is approximate at the level of individual realisations.
  2. [Abstract and Sec. 4] The abstract quotes an S/N "up to 7" while the maximum value quoted in the text is 6.8; round consistently to one decimal or quote 6.8.
  3. [Sec. 5.3.1, Fig. 10] The sentence "this plot compresses the information in the maps by averaging over spherical circles" is vague; specify exactly how the bottom panel is constructed from the directional posterior samples.
  4. [Sec. 5.3.3] The derived parameter Sigma and the fitted values of gamma are introduced after the posterior plots; define Sigma before Fig. 13 and state how gamma is chosen.
  5. [Sec. 4.2.1] The covariance matrix is estimated from the 140 HRF mocks, but the data vector uses the mean of the CRF mocks; state explicitly whether the CRF mean is treated as noiseless, since this affects the effective covariance of the data vector.
  6. [Eq. (5.7)] The first and last lines of Eq. (5.7) are equivalent; keeping only the final compact form would avoid the appearance of two different expansions of the same quantity.

Circularity Check

0 steps flagged · score 2.0 of 10

No significant circularity: the B-FOTO formula is derived in this paper and the inference runs are injection-recovery tests; the only self-referential element is validation against the authors' own LIGER mocks, which does not enter the derivation.

full rationale

The central B-FOTO expression (5.7) is not fitted or derived from the quantity it predicts: it follows from the linear-order RSD overdensity (2.22) and the redshift transformation (5.4), with the calculation carried out in Appendix D. The velocity and density inference in Secs. 4.2 and 5.3 are controlled mock-forecast exercises: the data vector is defined as a single HRF power-spectrum monopole minus the mean of the CRF mocks, which the paper explicitly states is 'a proxy for an exact theoretical model that does not include the FOTO effect'; the model is the analytic FOTO/B-FOTO template. Recovering the injected v_sun and Omega_m,0 is an injection-recovery consistency check, not a parameter renamed as a prediction. The only self-referential aspect is that the LIGER mock catalogues are produced with a code developed in the authors' own Paper I, so the excellent agreement between the analytic model and the mocks (Fig. 3) is an internal consistency test rather than an independent empirical validation. However, LIGER is a publicly available simulation tool based on standard relativistic RSD equations, and this self-citation does not enter the analytic derivation of Eq. (5.7); no uniqueness theorem is imported from the authors, and the paper credits the previously known Kaiser-Rocket effect [3] before proposing its new B-FOTO measurement strategy. The forecast does assume a perfectly known no-FOTO baseline, but that is an idealized modeling assumption, not a circularity.

Assumptions & free parameters 3 free parameters · 6 assumptions · 0 invented entities

No new physical entities are introduced; FOTO, C-FOTO, and B-FOTO are names for observable effects, not new particles, forces, or dimensions. The free parameters are method choices and priors, not fitted physical constants. The domain assumptions are standard for linear relativistic clustering analyses, but they are load-bearing for the claimed extraction.

free parameters (3)
  • Artificial velocity vectors vart (five shifts) = |vart| = 1, 2, 2, 3, 3 times v_sun,true; directions in Table 1
    Chosen by hand to demonstrate B-FOTO; the method's constraining power depends on this choice, and the authors do not optimize it.
  • Maxwellian prior scale sigma for v_sun = 300 km/s
    Adopted as a slightly informative prior (Sec. 4.2.1); Appendix B shows results are largely likelihood-dominated, so this is not a fitted parameter but an input choice.
  • FKP weighting amplitude P0 = 20,000 h^-3 Mpc^3
    Standard FKP weight parameter chosen as typical power at scales of interest; affects variance of the estimator but not the central signal model.
assumptions (6)
  • domain assumption Linear perturbation theory for redshift-space distortions, Eq. (2.19), including Doppler, aberration, and magnification terms.
    The whole FOTO and B-FOTO derivation is performed at linear order in cosmological perturbations and peculiar velocities; nonlinear corrections and velocity dispersion are neglected.
  • domain assumption Flux-limited survey selection with known luminosity function parameters; nbar, E, Q, b are taken as inputs.
    The predicted FOTO amplitude depends on alpha_o built from E and Q; inference assumes these are known exactly (Sec. 4.2).
  • domain assumption Full-sky geometry for the analytic model and the main inference.
    Eqs. (2.25) and (5.7) are exact only for full-sky; partial-sky effects are discussed but not modeled in the inference.
  • domain assumption LIGER mock catalogues reproduce relativistic RSD at linear order.
    Validation uses mocks generated with LIGER from the authors' prior work; the agreement between model and mocks is a code check, not an independent physical test.
  • domain assumption Cross-correlation between the dipole term and the comoving density field is negligible.
    Stated in Sec. 2.3.1 as 'we assume the cross-correlation terms are negligible'; no check is shown in this paper.
  • domain assumption Cosmological background is flat LambdaCDM (or wCDM) with Planck parameters in the mocks.
    The inference on Omega_m,0 and w assumes these background models; fits are performed against mock catalogues generated with the input cosmology.

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Cite this review

Pith. "Pith review of Measuring our peculiar velocity from spectroscopic redshift surveys." pith.science (2026). https://pith.science/paper/43N2MSR2

@misc{pith2026241203953,
  author       = {Pith},
  title        = {Pith review of: Measuring our peculiar velocity from spectroscopic redshift surveys},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/43N2MSR2}},
  note         = {Machine review of arXiv:2412.03953}
}
abstract

Our peculiar velocity imprints a dipole on galaxy density maps derived from redshift surveys. The dipole gives rise to an oscillatory signal in the multipole moments of the observed power spectrum which we indicate as the finger-of-the-observer (FOTO) effect. Using a suite of large mock catalogues mimicking ongoing and future $\textrm{H}\alpha$- and $\textrm{H}\scriptstyle\mathrm{I}$-selected surveys, we demonstrate that the oscillatory features can be measured with a signal-to-noise ratio of up to 7 (depending on the sky area coverage and provided that observational systematics are kept under control on large scales). We also show that the FOTO effect cannot be erased by correcting the individual galaxy redshifts. On the contrary, by leveraging the power of the redshift corrections, we propose a novel method to determine both the magnitude and the direction of our peculiar velocity. After applying this technique to our mock catalogues, we conclude that it can be used to either test the kinematic interpretation of the temperature dipole in the cosmic microwave background or to extract cosmological information such as the matter density parameter and the equation of state of dark energy.

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