Effectively modeling phenomena present in highly nonlinear dynamical systems whilst also accurately quantifying uncertainty is a challenging task, which often requires problem-specific techniques. We present a novel, domain-agnostic approach to tackl
ing this problem, using compositions of physics-informed random features, derived from ordinary differential equations. The architecture of our model leverages recent advances in approximate inference for deep Gaussian processes, such as layer-wise weight-space approximations which allow us to incorporate random Fourier features, and stochastic variational inference for approximate Bayesian inference. We provide evidence that our model is capable of capturing highly nonlinear behaviour in real-world multivariate time series data. In addition, we find that our approach achieves comparable performance to a number of other probabilistic models on benchmark regression tasks.
We present the results of a joint analysis of $Chandra$ X-ray and South Pole Telescope (SPT) SZ observations targeting the first sample of galaxy clusters at $0.3 < z < 1.3$, selected to be the progenitors of well-studied nearby clusters based on the
ir expected accretion rate. We develop a new procedure in order to tackle the analysis challenge that is estimating the intracluster medium (ICM) properties of low-mass and high-redshift clusters with ${sim}150$ X-ray counts. One of the dominant sources of uncertainty on the ICM density profile estimated with a standard X-ray analysis with such shallow X-ray data is due to the systematic uncertainty associated with the ICM temperature obtained through the analysis of the background-dominated X-ray spectrum. We show that we can decrease the uncertainty on the density profile by a factor ${sim}5$ with a joint deprojection of the X-ray surface brightness profile measured by $Chandra$ and the SZ integrated Compton parameter available in the SPT cluster catalog. We apply this technique to the whole sample of 67 clusters in order to track the evolution of the ICM core density during cluster growth. We confirm that the evolution of the gas density profile is well modeled by the combination of a fixed core and a self-similarly evolving non-cool core profile. We show that the fraction of cool-cores in this sample is remarkably stable with redshift although clusters have gained a factor ${sim}4$ in total mass over the past ${sim}9$ Gyr. This new sample combined with our new X-ray/SZ analysis procedure and extensive multi-wavelength data will allow us to address fundamental shortcomings in our current understanding of cluster formation and evolution at $z > 1$.
(Abridged) The relaxed cool-core Phoenix cluster (SPT-CL J2344-4243) features an extremely strong cooling flow, as well as a mini-halo. Strong star-formation in the brightest cluster galaxy indicates that AGN feedback has been unable to inhibit this
cooling flow. We have studied the strong cooling flow in the Phoenix cluster by determining the radio properties of the AGN and its lobes. In addition, we use spatially resolved observations to investigate the origin of the mini-halo. We present new Very Large Array 1-12 GHz observations of the Phoenix cluster which resolve the AGN and its lobes in all four frequency bands, and resolve the mini-halo in L- and S-band. Using our L-band observations, we measure the total flux density of the radio lobes at 1.5 GHz to be $7.6pm0.8$ mJy, and the flux density of the mini-halo to be $8.5pm0.9$ mJy. Using L- and X-band images, we produce the first spectral index maps of the lobes from the AGN and measure the spectral indices of the northern and southern lobes to be $-1.35pm0.07$ and $-1.30pm0.12$, respectively. Similarly, using L- and S-band data, we map the spectral index of the mini-halo, and obtain an integrated spectral index of $alpha=-0.95 pm 0.10$. We find that the mini-halo is most likely formed by turbulent re-acceleration powered by sloshing in the cool core due to a recent merger. In addition, we find that the feedback in the Phoenix cluster is consistent with the picture that stronger cooling flows are to be expected for massive clusters like the Phoenix cluster, as these may feature an underweight supermassive black hole due to their merging history. Strong time variability of the AGN on Myr-timescales may help explain the disconnection between the radio and the X-ray properties of the system. Finally, a small amount of jet precession likely contributes to the relatively low ICM re-heating efficiency of the mechanical feedback.
The characterization of the Intra-Cluster Medium (ICM) properties of high-redshift galaxy clusters is fundamental to our understanding of large-scale structure formation processes. We present the results of a multi-wavelength analysis of the very mas
sive cluster MOO J1142$+$1527 at a redshift $z = 1.2$ discovered as part of the Massive and Distant Clusters of WISE Survey (MaDCoWS). This analysis is based on high angular resolution $Chandra$ X-ray and NIKA2 Sunyaev-Zeldovich (SZ) data. Although the X-ray data have only about 1700 counts, we are able to determine the ICM thermodynamic radial profiles, namely temperature, entropy, and hydrostatic mass. These have been obtained with unprecedented precision at this redshift and up to $0.7R_{500}$, thanks to the combination of high-resolution X-ray and SZ data. The comparison between the galaxy distribution mapped in infrared by $Spitzer$ and the morphological properties of the ICM derived from the combined analysis of the $Chandra$ and NIKA2 data leads us to the conclusion that the cluster is an on-going merger. We measure the hydrostatic mass profile of the cluster in four angular sectors centered on the large-scale X-ray centroid. This allows us to estimate a systematic uncertainty on the cluster total mass that characterizes both the impact of the observed deviations from spherical symmetry and of the core dynamics on the mass profile. We further combine the X-ray and SZ data at the pixel level to obtain maps of the temperature and entropy distributions averaged along the line of sight. We find a relatively low entropy core at the position of the X-ray peak and high temperature regions located on its south and west sides. The increase in ICM temperature at the location of the SZ peak is expected given the merger dynamics. (abridged)
In the past decade, our understanding of how stars and galaxies formed during the first 5 billion years after the Big Bang has been revolutionized by observations that leverage gravitational lensing by intervening masses, which act as natural cosmic
telescopes to magnify background sources. Previous studies have harnessed this effect to probe the distant universe at ultraviolet, optical, infrared and millimeter wavelengths. However, strong lensing studies of young, star-forming galaxies have never extended into X-ray wavelengths, which uniquely trace high-energy phenomena. Here we report an X-ray detection of star formation in a highly magnified, strongly lensed galaxy. This lensed galaxy, seen during the first third of the history of the Universe, is a low--mass, low--metallicity starburst with elevated X-ray emission, and is a likely analog to the first generation of galaxies. Our measurements yield insight into the role that X-ray emission from stellar populations in the first generation of galaxies may play in re-ionizing the Universe. This observation paves the way for future strong lensing-assisted X-ray studies of distant galaxies reaching orders of magnitude below the detection limits of current deep fields, and previews the depths that will be attainable with future X-ray observatories.
We present new, deep observations of the Phoenix cluster from the Chandra X-ray Observatory, the Hubble Space Telescope, and the Karl Jansky Very Large Array. These data provide an order of magnitude improvement in depth and/or angular resolution at
X-ray, optical, and radio wavelengths, yielding an unprecedented view of the core of the Phoenix cluster. We find that the one-dimensional temperature and entropy profiles are consistent with expectations for pure-cooling hydrodynamic simulations and analytic descriptions of homogeneous, steady-state cooling flow models. In the inner ~10 kpc, the cooling time is shorter by an order of magnitude than any other known cluster, while the ratio of the cooling time to freefall time approaches unity, signaling that the ICM is unable to resist multiphase condensation on kpc scales. When we consider the thermodynamic profiles in two dimensions, we find that the cooling is highly asymmetric. The bulk of the cooling in the inner ~20 kpc is confined to a low-entropy filament extending northward from the central galaxy. We detect a substantial reservoir of cool (10^4 K) gas (as traced by the [OII] doublet), which is coincident with the low-entropy filament. The bulk of this cool gas is draped around and behind a pair of X-ray cavities, presumably bubbles that have been inflated by radio jets, which are detected for the first time on kpc scales. These data support a picture in which AGN feedback is promoting the formation of a multiphase medium via a combination of ordered buoyant uplift and locally enhanced turbulence. These processes ought to counteract the tendency for buoyancy to suppress condensation, leading to rapid cooling along the jet axis. The recent mechanical outburst has sufficient energy to offset cooling, and appears to be coupling to the ICM via a cocoon shock, raising the entropy in the direction orthogonal to the radio jets.
We present a multi-wavelength analysis of the four most relaxed clusters in the South Pole Telescope 2500 deg^2 survey, which lie at 0.55 < z < 0.75. This study, which utilizes new, deep data from Chandra and Hubble, along with ground-based spectrosc
opy from Gemini and Magellan, improves significantly on previous studies in both depth and angular resolution, allowing us to directly compare to clusters at z~0. We find that the temperature, density, and entropy profiles of the intracluster medium (ICM) are very similar among the four clusters, and share similar shapes to clusters at z~0. Specifically, we find no evidence for deviations from self similarity in the temperature profile over the radial range 10kpc < r < 1Mpc, implying that the processes responsible for preventing runaway cooling over the past >6 Gyr are, at least roughly, preserving self similarity. We find typical metallicities of ~0.3 Zsun in the bulk of the ICM, rising to ~0.5 Zsun in the inner ~100 kpc, and reaching ~1 Zsun at r < 10kpc. This central excess is similar in magnitude to what is observed in the most relaxed clusters at z~0, suggesting that both the global metallicity and the central excess that we see in cool core clusters at z~0 were in place very early in the cluster lifetime and, specifically, that the central excess is not due to late-time enrichment by the central galaxy. Consistent with observations at z~0, we measure a diversity of stellar populations in the central brightest cluster galaxies of these four clusters, with star formation rates spanning a factor of ~500, despite the similarity in cooling time, cooling rate, and central entropy. These data suggest that, while the details vary dramatically from system to system, runaway cooling has been broadly regulated in relaxed clusters over the past 6 Gyr.
We present the first spatially-resolved observations of molecular gas in a sample of cluster galaxies beyond z>0.1. Using ALMA, we detect CO (2-1) in 8 z~1.6 cluster galaxies, all within a single 70 primary beam, in under 3 hours of integration time.
The cluster, SpARCS-J0225, is replete with gas-rich galaxies in close proximity. It thus affords an efficient multiplexing strategy to build up the first sample of resolved CO in distant galaxy clusters. Mapping out the kinematic structure and morphology of the molecular gas on 3.5 kpc scales reveals rotating gas disks in the majority of the galaxies, as evidenced by smooth velocity gradients. Detailed velocity maps also uncover kinematic peculiarities, including a central gas void, a merger, and a few one-sided gas tails. We compare the extent of the molecular gas component to that of the optical stellar component, measured with rest-frame optical HST imaging. We find that the cluster galaxies, while broadly consistent with a ratio of unity for stellar-to-gas effective radii, have a moderately larger ratio compared to the coeval field; this is consistent with the more pronounced trend in the low-redshift Universe. Thus, at first glance, the z~1.6 cluster galaxies generally look like galaxies infalling from the field, with typical main-sequence star formation rates and massive molecular gas reservoirs situated in rotating disks. However, there are potentially important differences from their field counterparts, including elevated gas fractions, slightly smaller CO disks, and possible asymmetric gas tails. Taken in tandem, these signatures are tentative evidence for gas-stripping in the z~1.6 cluster. However, the current sample size of spatially-resolved molecular gas in galaxies at high redshift is small, and verification of these trends will require much larger samples of both cluster and field galaxies.
Processes that break molecular bonds are typically observed with molecules occupying a mixture of quantum states and successfully described with quasiclassical models, while a few studies have explored the distinctly quantum mechanical low-energy reg
ime. Here we use photodissociation of diatomic strontium molecules to demonstrate the crossover from the ultracold, quantum regime where the photofragment angular distributions strongly depend on the kinetic energy, to the energy-independent quasiclassical regime. Using time-of-flight velocity map imaging for photodissociation channels with millikelvin reaction barriers, we explore photofragment energies in the 0.1-300 mK range experimentally and up to 3 K theoretically, and discuss the energy scale at which the crossover occurs. Furthermore, we find that the effects of quantum statistics can unexpectedly persist to high photodissociation energies.
We estimate total mass ($M_{500}$), intracluster medium (ICM) mass ($M_{mathrm{ICM}}$) and stellar mass ($M_{star}$) in a Sunyaev-Zeldovich effect (SZE) selected sample of 91 galaxy clusters with masses $M_{500}gtrsim2.5times10^{14}M_{odot}$ and reds
hift $0.2 < z < 1.25$ from the 2500 deg$^2$ South Pole Telescope SPT-SZ survey. The total masses $M_{500}$ are estimated from the SZE observable, the ICM masses $M_{mathrm{ICM}}$ are obtained from the analysis of $Chandra$ X-ray observations, and the stellar masses $M_{star}$ are derived by fitting spectral energy distribution templates to Dark Energy Survey (DES) $griz$ optical photometry and $WISE$ or $Spitzer$ near-infrared photometry. We study trends in the stellar mass, the ICM mass, the total baryonic mass and the cold baryonic fraction with cluster mass and redshift. We find significant departures from self-similarity in the mass scaling for all quantities, while the redshift trends are all statistically consistent with zero, indicating that the baryon content of clusters at fixed mass has changed remarkably little over the past $approx9$ Gyr. We compare our results to the mean baryon fraction (and the stellar mass fraction) in the field, finding that these values lie above (below) those in cluster virial regions in all but the most massive clusters at low redshift. Using a simple model of the matter assembly of clusters from infalling groups with lower masses and from infalling material from the low density environment or field surrounding the parent halos, we show that the measured mass trends without strong redshift trends in the stellar mass scaling relation could be explained by a mass and redshift dependent fractional contribution from field material. Similar analyses of the ICM and baryon mass scaling relations provide evidence for the so-called missing baryons outside cluster virial regions.
