First constraints on the intrinsic CMB dipole and our velocity with Doppler and aberration
Pedro da Silveira Ferreira, Miguel Quartin
备注：
Improved analysis of the intrinsic dipole terms; more robust interpretation of the results; accepted for publication in PRL. The original methodology described in v1 is now part of a separate companion paper (arXiv:2107.10846)
We test the usual hypothesis that the Cosmic Microwave Background (CMB) dipole, its largest anisotropy, is due to our peculiar velocity with respect to the Hubble flow by measuring independently the Doppler and aberration effects on the CMB using Planck 2018 data. We remove the spurious contributions from the conversion of intensity into temperature and arrive at measurements which are independent from the CMB dipole itself for both temperature and polarization maps and both SMICA and NILC component-separation methods. Combining these new measurements with the dipole one we get the first constraints on the intrinsic CMB dipole. Assuming a standard dipolar lensing contribution we can put an upper limit on the intrinsic amplitude: 3.7 mK (95% CI). We estimate the peculiar velocity of the solar system without assuming a negligible intrinsic dipole contribution: $v = (300^{+111}_{-93})$ km/s with $(l,b) = (276 \pm 33, 51 \pm 19)^\circ$ [SMICA], and $v = (296^{+111}_{-88})$ km/s with $(l,b) = (280 \pm 33, 50 \pm 20)^\circ$ [NILC] with negligible systematic contributions. These values are consistent with the peculiar velocity hypothesis of the dipole.
An observer in relative motion to the Cosmic Microwave Background (CMB) rest frame is sensitive to both aberration and Doppler effects. Both effects introduce similar but non-identical off-diagonal couplings in the spherical harmonic coefficients. The CMB temperature dipole may have additional contributions from an intrinsic component, which in turn produces different aberration and Doppler couplings. Moreover, the standard conversion from intensity measurements into temperature also introduces spurious Doppler-like couplings. In order to learn about the intrinsic dipole it is therefore import…
The aberration and Doppler coupling effects of the Cosmic Microwave Background (CMB) were recently measured by the Planck satellite. The most straightforward interpretation leads to a direct detection of our peculiar velocity $β$, consistent with the measurement of the well-known dipole. In this paper we discuss the assumptions behind such interpretation. We show that Doppler-like couplings appear from two effects: our peculiar velocity and a second order large-scale effect due to the dipolar part of the gravitational potential. We find that the two effects are exactly degenerate but only if w…
We introduce a $\textit{frequency-dependent}$ Doppler and aberration transformation kernel for the harmonic multipoles of a general cosmological observable with spin weight $s$, Doppler weight $d$ and arbitrary frequency spectrum. In the context of Cosmic Microwave Background (CMB) studies, the frequency-dependent formalism allows to correct for the motion-induced aberration and Doppler effects on individual frequency maps with different masks. It also permits to deboost background radiations with non-blackbody frequency spectra, like extragalactic foregrounds and CMB spectra with primordial s…
The motion of our solar system relative to the CMB rest frame leads to subtle distortions in the observed CMB sky map due to the aberration effect. Usually the corresponding peculiar velocity is determined from the CMB dipole but neglecting intrinsic dipole contributions. Here it is investigated whether certain invariant scalar measures, which are derived from first and second order covariant derivatives on the sphere, can detect the distortions caused by the aberration effect at high multipoles. This would in principle allow to disentangle the Doppler from intrinsic dipole contributions provi…
In the frame of the Solar System, the Doppler and aberration effects cause distortions in the form of mode couplings in the cosmic microwave background (CMB) temperature and polarization power spectra and hence impose biases on the statistics derived by the moving observer. We explore several aspects of such biases and pay close attention to their effects on CMB polarization which previously have not been examined in detail. A potentially important bias that we introduce here is $\textit{boost variance}$---an additional term in cosmic variance, induced by the observer's motion. Although this a…
Our velocity relative to the cosmic microwave background (CMB) generates a dipole from the CMB monopole, which was accurately measured by COBE. The relative velocity also modulates and aberrates the CMB fluctuations, generating a small signature of statistical isotropy violation in the covariance matrix. This signature was first measured by Planck 2013. Galaxy surveys are similarly affected by a Doppler boost. The dipole generated from the number count monopole has been extensively discussed, and measured (at very low accuracy) in the NVSS and TGSS radio continuum surveys. For the first time, …
Gravitational waves from a source moving relative to us can suffer from special-relativistic effects such as aberration. The required velocities for these to be significant are on the order of $1000\,\textrm{km s}^{-1}$. This value corresponds to the velocity dispersion that one finds in clusters of galaxies. Hence, we expect a large number of gravitational-wave sources to have such effects imprinted in their signals. In particular, the signal from a moving source will have its higher modes excited, i.e., $(3,3)$ and beyond. We derive expressions describing this effect, and study its measurabi…
We study the parity-odd part (that we shall call Doppler term) of the linear galaxy two-point correlation function that arises from wide-angle, velocity, Doppler lensing and cosmic acceleration effects. As it is important at low redshift and at large angular separations, the Doppler term is usually neglected in the current generation of galaxy surveys. For future wide-angle galaxy surveys such as Euclid, SPHEREx and SKA, however, we show that the Doppler term must be included. The effect of these terms is dominated by the magnification due to relativistic aberration effects and the slope of th…
The observed dipole anisotropy of the cosmic microwave background (CMB) temperature is much larger than the fluctuations observed on smaller scales and is dominated by the kinematic contribution from the Doppler shifting of the monopole due to our motion with respect to the CMB rest frame. In addition to this kinematic component, there is expected to be an intrinsic contribution with an amplitude about two orders of magnitude smaller. Here we explore a method whereby the intrinsic CMB dipole can be reconstructed through observation of temperature fluctuations on small scales which result from …
In the concordance model of the Universe, the matter distribution - as observed in galaxy number counts or the intensity of line emission (such as the 21cm line of neutral hydrogen) - should have a kinematic dipole due to the Sun's motion relative to the CMB rest-frame. This dipole should be aligned with the kinematic dipole in the CMB temperature. Accurate measurement of the direction of the matter dipole will become possible with future galaxy surveys, and this will be a critical test of the foundations of the concordance model. The amplitude of the matter dipole is also a potential cosmolog…
Although theoretically expected to be Statistically Isotropic (SI), the observed Cosmic Microwave Background (CMB) temperature \& polarization field would exhibit SI violation due to various inevitable effects like weak lensing, Doppler boost and practical limitations of observations like non-circular beam, masking etc. However, presence of any SI violation beyond these effects may lead to a discovery of inherent cosmic SI violation in the CMB temperature \& polarization field. Recently, Planck presented strong evidence of SI violation as a dipolar power asymmetry of the CMB temperature field …
Our velocity relative to the rest frame of the cosmic microwave background (CMB) generates a dipole temperature anisotropy on the sky which has been well measured for more than 30 years, and has an accepted amplitude of v/c = 0.00123, or v = 369km/s. In addition to this signal generated by Doppler boosting of the CMB monopole, our motion also modulates and aberrates the CMB temperature fluctuations (as well as every other source of radiation at cosmological distances). This is an order 0.1% effect applied to fluctuations which are already one part in roughly one hundred thousand, so it is quit…
Previous studies have found our velocity in the rest frame of radio galaxies at high redshift to be substantially larger than that inferred from the CMB temperature dipole anisotropy. We construct a full sky catalogue NVSUMSS, by merging the NVSS and SUMSS catalogues and removing local sources by various means including cross-correlating with the 2MRS catalogue. We take into account both aberration and Doppler boost to deduce our velocity from the hemispherical number count asymmetry, as well as via a 3-dimensional linear estimator. Both the magnitude and direction depend on cuts made to the c…
The largest fluctuation in the CMB sky is the CMB dipole, which is believed to be caused by the motion of our observation frame with respect to the CMB rest frame. This motion accounts for the known motion of the Solar System barycentre with a best-fit amplitude of $369$ km/s, in the direction ($\ell= 264^\circ$, $b=48^\circ$) in galactic coordinates. Along with the CMB dipole signal, this motion also causes an inevitable signature of statistical anisotropy in the higher multipoles due to the modulation and aberration of the CMB temperature and polarization fields. This leads to a correlation …
Cosmic microwave background (CMB) temperature anisotropies encode the history of the universe, which manifest itself in the angular power spectrum. We test the angular power spectra of small patches from the ESA $\textit{Planck}$ data. Known variations in the power spectra from small patches reveal informative details such as the gravitational lensing and the Doppler boosting effect. We compute the relative shifts of power spectra via comparing patches selected randomly from the CMB. We visualize the relative shifts on a full-sky HEALPix grid (a feature map) and analyze the statistical propert…
Patchy reionization leaves a number of imprints on the small-scale cosmic microwave background (CMB) temperature fluctuations, the largest of which is the kinematic Sunyaev-Zel'dovich (kSZ), the Doppler shift of CMB photons scattering off moving electrons in ionized bubbles. It has long been known that in the CMB power spectrum, this imprint of reionization is largely degenerate with the kSZ signal produced by late-time galaxies and clusters, thus limiting our ability to constrain reionization. Following Smith & Ferraro (2017), it is possible to isolate the reionization contribution in a model…
Cosmic Microwave Background (CMB) experiments, such as WMAP and Planck, measure intensity anisotropies and build maps using a linearized formula for relating them to the temperature blackbody fluctuations. However, this procedure also generates a signal in the maps in the form of y-type distortions which is degenerate with the thermal Sunyaev Zel'dovich (tSZ) effect. These are small effects that arise at second-order in the temperature fluctuations not from primordial physics but from such a limitation of the map-making procedure. They constitute a contaminant for measurements of: our peculiar…
The hierarchy of motions that we are participating is well known, from the Earth's motion around the Sun and Sun's motion in the Milky Way, up to the Local Group's motion within the Virgo Supercluster of galaxies. The dipole anisotropy of the Cosmic Microwave Background (CMB) enables to define Sun's motion with respect to the CMB "absolute" frame. We now present evidence for CMB Galactic dipole signal due to the Sun's motion in the Galaxy, by means of Planck 2018 data and Gaia Early Data Release 3. The signal is weak and frequency depended, the strongest is at 30 GHz, up to 7.6σconfidence. The…
Gravitational lensing of the cosmic microwave background (CMB) is expected to be amongst the most powerful cosmological tools for ongoing and upcoming CMB experiments. In this work, we investigate a bias to CMB lensing reconstruction from temperature anisotropies due to the kinematic Sunyaev-Zel'dovich (kSZ) effect, that is, the Doppler shift of CMB photons induced by Compton-scattering off moving electrons. The kSZ signal yields biases due to both its own intrinsic non-Gaussianity and its non-zero cross-correlation with the CMB lensing field (and other fields that trace the large-scale struct…
Cosmic Microwave Background (CMB) experiments, such as WMAP and Planck, measure intensity anisotropies and build maps using a \emph{linearized} formula for relating them to the temperature blackbody fluctuations. However such a procedure also generates a signal in the maps in the form of y-type distortions, and thus degenerate with the thermal SZ (tSZ) effect. These are small effects that arise at second-order in the temperature fluctuations not from primordial physics but from such a limitation of the map-making procedure. They constitute a contaminant for measurements of: our peculiar veloci…
Measurement of the acoustic peaks of the cosmic microwave background (CMB) temperature anisotropies has been instrumental in deciding the geometry and content of the universe. Acoustic peak positions vary in different parts of the sky due to statistical fluctuation. We present the statistics of the peak positions of small patches from ESA Planck data. We found that the peak positions have significantly high variance compared to the 100 CMB simulations with best-fit LambdaCDM model with lensing and Doppler boosting effects included. Examining individual patches, we found the one containing the …
Recently, it was shown that local variance maps of temperature anisotropy are simple and useful tools for the study of large scale hemispherical power asymmetry. This was done by studying the distribution of dipoles of the local variance maps. In this work, we extend the study of the dipolar asymmetry in local variance maps using foreground cleaned Planck 143 GHz and 217 GHz data to smaller scales. In doing so, we include the effect of the CMB Doppler dipole. Further, we show that it is possible to use local variance maps to measure the Doppler dipole in these Planck channel maps, after removi…
