Field-level large-scale structure meets the CMB

Context

Traditionally, the cosmic microwave background (CMB) is analysed entirely independently of large-scale structure (LSS), and only in post-processing are various LSS-related signals (“secondary anisotropies”) compared between the CMB and the galaxy or cluster field. However, the advent of highly accurate and precise reconstructions of the local Universe from the BORG algorithm opens the possibility of self-consistent, combined inference from LSS and the CMB. The grand goal would be to simultaneously infer the initial conditions of the local Universe and cosmological parameters by forward-modelling secondary anisotropies and foregrounds to the map level, then fitting to the CMB data in conjunction with CMB primary as well as instrumental effects and other nuisance parameters.

Here we perform a more modest first step, namely predicting from existing BORG density fields a particular CMB secondary called the thermal Sunyaev-Zel’dovich (tSZ) effect and comparing it to the CMB measurements. This provides a new benchmark for assessing reconstructions of the local Universe and offers a practical route to extracting additional information from tSZ data through a novel calibration of the mass-observable relation.

The thermal Sunyaev-Zel’dovich effect and constrained simulations

The CMB, generated when the Universe was in its infancy and hence appearing at very high redshift, forms a backlight to our astrophysical observations. However it is not a static backlight, but responds to structures along the line of sight, generating what are called secondary anisotropies in the distribution of its frequency-dependent brightness fluctuations. One of the most important is the tSZ effect, which is the upscattering of CMB photons passing through hot free electrons in galaxy clusters. This modification has a characteristic frequency dependence, allowing the tSZ signal to be isolated from other contributions to the CMB by forming a particular frequency combination called a Compton-y map. This map has hotspots along lines of sight passing through massive clusters.

LSS reconstruction methods such as BORG produce afford constrained simulations or “digital twins” of the local Universe, revealing the full 3D distribution of dark matter which is otherwise completely invisible. As part of this they aim to produce clusters in their correct positions and with their correct dark matter halo masses. This enables us to cross-correlate the reconstructed clusters with the tSZ signal object-by-object, to determine to what extent the reconstruction puts clusters at the positions implied by the tSZ hotspots and with masses consistent with the tSZ signal strength.

CSiBORG-Manticore: the most accurate and precise digital twins of the local Universe

The Aquila Consortium has recently completed the first stage of the Manticore project, a comprehensive set of upgrades to the BORG algorithm yielding (so far) the Manticore-Local reconstruction of the local $\sim$200 Mpc. Following established methodology from previous iterations of BORG, we used the Manticore-Local inferred initial conditions to create the CSiBORG-Manticore (CBM) suite of constrained simulations, which have a high-resolution zoom-in region where the data constraints are strong, surrounded by a lower-resolution region in a full box size of 1 Gpc to capture the impact of longer-wavelength density modes.

To assess the ability of CBM to produce realistic clusters, we develop a metric for quantifying consistency with the Compton-y map from the latest data release of the Planck CMB measurements. Denoted $p_{tSZ}$, this measures the fraction of random sky cutouts with an observed tSZ signal higher than a cutout surrounding a given cluster. It therefore quantifies the probability of a cross-correlation between a reconstructed cluster and measured tSZ signal higher than observed to occur by chance – very low values therefore indicate that the reconstructed cluster is well-centred on the tSZ hotspot, while values exceeding $\sim0.05$ indicate that the cluster is so mis-centred that the measured match with the tSZ signal could well have occurred purely by chance.

We calculate $p_{tSZ}$ for a range of local clusters for three constrained simulations – CBM, CSiBORG-2 (CB2, based on an older, pre-Manticore BORG chain) and SLOW, an external simulation not based on BORG. The results are shown in Fig 1, where we see that in almost all cases the BORG-based simulations produce $p_{tSZ}<0.05$ (i.e. significant detection of the cluster at the correct angular position), while SLOW almost always produces $p_{tSZ}>0.05$, indicating results of too low quality to be meaningfully compared with the CMB. Another advantage of BORG relative to SLOW is that it produces an entire posterior of initial conditions, allowing us to run multiple data-constrained simulations and hence produce error bars on quantities like $p_{tSZ}$; SLOW by contrast produces just one, so its uncertainty is unquantified.

Alternative to a wide image Quality of cluster reconstruction measured against the tSZ signal from the CMB for a set of local clusters for three local-Universe reconstructions. Values below the dotted red line indicate a good match between the reconstructed clusters and tSZ hotspots. The high-performing simulations are CSiBORG2 (CB2) and especially the new CSiBORG-Manticore (CBM), while the non-BORG-based SLOW simulation performs poorly.

A more detailed picture is provided by Fig 2, which shows the Compton-y signal as a function of angular separation (normalised by the cluster angular diameter) for all high-mass haloes in the CSiBORG simulations. This shows that the clusters are well aligned with the tSZ signal, that CBM is an advance on CB2, and that this degree of cross-correlation could not possibly have arisen by chance (grey band).

Alternative to normal image Stacked radial tSZ profiles around the 10 highest-mass halos in the CB2 and CBM simulations. The correlation between BORG and the CMB is highly significant relative to a randomised reconstruction (grey band).

A new mass-observable relation

The above tests compare only the angular positions of reconstructed halos with hotspots of the tSZ signal, saying little about how the magnitude of the signal correlates with the halo masses. This is known as the mass-observable relation, and is traditionally derived by relating the tSZ signal integrated within an aperture surrounding a cluster (the “observable”) with a measure of mass from e.g. weak lensing or X-ray emission. These are indirect, relying on their own set of approximations including assumptions about projection and hydrostatic equilibrium. BORG however infers halo masses directly, affording a novel and less assumption-prone calibration of the mass-observable relation.

We show this for the CBM reconstruction in Fig 3. This is consistent with a linear relation between the tSZ signal and halo mass within the uncertainties, with a slope in agreement with the self-similar theory expectation of 5/3. CB2 yields a slope only marginally consistent with 5/3, while SLOW produces a very poor correlation as would be expected from Fig 1.

Alternative to normal image A new calibration of the relation between tSZ signal and total cluster mass afforded by CBM. The fitted slope agrees well with the theoretical expectation of 5/3.

Promise for the future

We have demonstrated that local Universe reconstructions within the BORG programme have reached the level of maturity required for meaningful comparison with the CMB. This opens the door to a wide range of future opportunities at the intersection of LSS and CMB studies. This includes modelling other secondaries along similar lines (e.g. the kinetic SZ effect, the late-time integrated Sachs-Wolfe effect and CMB lensing), but also affords more ambitious longer-term possibilities.

The first is to use BORG in conjunction with the CMB to provide new information on astrophysical objects. This may be done by forward-modelling Compton-y maps using BORG-based cluster catalogues plus a “baryonification” scheme to connect their dark matter distributions to the free electron properties that set the tSZ effect. This would afford for the first time field-level (i.e. pixel-by-pixel) constraints on the baryonification parameters, retaining more information than the purely statistical cross-correlation studies done traditionally.

More ambitious however would be to use the CMB as an additional constraint on the local density field within BORG, allowing it to be inferred simultaneously with cosmological parameters. This would involve forward-modelling both the observed LSS and the CMB (with a covariance term describing CMB primary) and running an inference with a field-level likelihood. In the future this will enable the study of LSS and the CMB to be integrated by modelling them fully self-consistently within a single framework, extracting the maximum amount of information on each.

References