arXiv subjects

J. S. B. Wyithe

Publications and source records attributed to J. S. B. Wyithe.

At least 37 records · Page 2Linked to original sources

arXiv2016

First Season MWA EoR Power Spectrum Results at Redshift 7

The Murchison Widefield Array (MWA) has collected hundreds of hours of Epoch of Reionization (EoR) data and now faces the challenge of overcoming foreground and systematic contamination to reduce the data to a cosmological measurement. We introduce several novel analysis techniques such as cable reflection calibration, hyper-resolution gridding kernels, diffuse foreground model subtraction, and quality control methods. Each change to the analysis pipeline is tested against a two dimensional power spectrum figure of merit to demonstrate improvement. We incorporate the new techniques into a deep integration of 32 hours of MWA data. This data set is used to place a systematic-limited upper limit on the cosmological power spectrum of $Δ^2 \leq 2.7 \times 10^4$ mK$^2$ at $k=0.27$ h~Mpc$^{-1}$ and $z=7.1$, consistent with other published limits, and a modest improvement (factor of 1.4) over previous MWA results. From this deep analysis we have identified a list of improvements to be made to our EoR data analysis strategies. These improvements will be implemented in the future and detailed in upcoming publications.

astro-ph.IM↗

arXiv2016

Low frequency observations of linearly polarized structures in the interstellar medium near the south Galactic pole

We present deep polarimetric observations at 154 MHz with the Murchison Widefield Array (MWA), covering 625 deg^2 centered on RA=0 h, Dec=-27 deg. The sensitivity available in our deep observations allows an in-band, frequency-dependent analysis of polarized structure for the first time at long wavelengths. Our analysis suggests that the polarized structures are dominated by intrinsic emission but may also have a foreground Faraday screen component. At these wavelengths, the compactness of the MWA baseline distribution provides excellent snapshot sensitivity to large-scale structure. The observations are sensitive to diffuse polarized emission at ~54' resolution with a sensitivity of 5.9 mJy beam^-1 and compact polarized sources at ~2.4' resolution with a sensitivity of 2.3 mJy beam^-1 for a subset (400 deg^2) of this field. The sensitivity allows the effect of ionospheric Faraday rotation to be spatially and temporally measured directly from the diffuse polarized background. Our observations reveal large-scale structures (~1 deg - 8 deg in extent) in linear polarization clearly detectable in ~2 minute snapshots, which would remain undetectable by interferometers with minimum baseline lengths >110 m at 154 MHz. The brightness temperature of these structures is on average 4 K in polarized intensity, peaking at 11 K. Rotation measure synthesis reveals that the structures have Faraday depths ranging from -2 rad m^-2 to 10 rad m^-2 with a large fraction peaking at ~+1 rad m^-2. We estimate a distance of 51+/-20 pc to the polarized emission based on measurements of the in-field pulsar J2330-2005. We detect four extragalactic linearly polarized point sources within the field in our compact source survey. Based on the known polarized source population at 1.4 GHz and non-detections at 154 MHz, we estimate an upper limit on the depolarization ratio of 0.08 from 1.4 GHz to 154 MHz.

astro-ph.GA↗

arXiv2016

A High Reliability Survey of Discrete Epoch of Reionization Foreground Sources in the MWA EoR0 Field

Detection of the Epoch of Reionization HI signal requires a precise understanding of the intervening galaxies and AGN, both for instrumental calibration and foreground removal. We present a catalogue of 7394 extragalactic sources at 182 MHz detected in the RA=0 field of the Murchison Widefield Array Epoch of Reionization observation programme. Motivated by unprecedented requirements for precision and reliability we develop new methods for source finding and selection. We apply machine learning methods to self-consistently classify the relative reliability of 9490 source candidates. A subset of 7466 are selected based on reliability class and signal-to-noise ratio criteria. These are statistically cross-matched to four other radio surveys using both position and flux density information. We find 7369 sources to have confident matches, including 90 partially resolved sources that split into a total of 192 sub-components. An additional 25 unmatched sources are included as new radio detections. The catalogue sources have a median spectral index of -0.85. Spectral flattening is seen toward lower frequencies with a median of -0.71 predicted at 182 MHz. The astrometric error is 7 arcsec. compared to a 2.3 arcmin. beam FWHM. The resulting catalogue covers approximately 1400 sq. deg. and is complete to approximately 80 mJy within half beam power. This provides the most reliable discrete source sky model available to date in the MWA EoR0 field for precision foreground subtraction.

astro-ph.IM↗

arXiv2016

The Murchison Widefield Array 21 cm Power Spectrum Analysis Methodology

We present the 21 cm power spectrum analysis approach of the Murchison Widefield Array Epoch of Reionization project. In this paper, we compare the outputs of multiple pipelines for the purpose of validating statistical limits cosmological hydrogen at redshifts between 6 and 12. Multiple, independent, data calibration and reduction pipelines are used to make power spectrum limits on a fiducial night of data. Comparing the outputs of imaging and power spectrum stages highlights differences in calibration, foreground subtraction and power spectrum calculation. The power spectra found using these different methods span a space defined by the various tradeoffs between speed, accuracy, and systematic control. Lessons learned from comparing the pipelines range from the algorithmic to the prosaically mundane; all demonstrate the many pitfalls of neglecting reproducibility. We briefly discuss the way these different methods attempt to handle the question of evaluating a significant detection in the presence of foregrounds.

astro-ph.IM↗

arXiv2016

First Limits on the 21 cm Power Spectrum during the Epoch of X-ray heating

We present first results from radio observations with the Murchison Widefield Array seeking to constrain the power spectrum of 21 cm brightness temperature fluctuations between the redshifts of 11.6 and 17.9 (113 and 75 MHz). Three hours of observations were conducted over two nights with significantly different levels of ionospheric activity. We use these data to assess the impact of systematic errors at low frequency, including the ionosphere and radio-frequency interference, on a power spectrum measurement. We find that after the 1-3 hours of integration presented here, our measurements at the Murchison Radio Observatory are not limited by RFI, even within the FM band, and that the ionosphere does not appear to affect the level of power in the modes that we expect to be sensitive to cosmology. Power spectrum detections, inconsistent with noise, due to fine spectral structure imprinted on the foregrounds by reflections in the signal-chain, occupy the spatial Fourier modes where we would otherwise be most sensitive to the cosmological signal. We are able to reduce this contamination using calibration solutions derived from autocorrelations so that we achieve an sensitivity of $10^4$ mK on comoving scales $k\lesssim 0.5 h$Mpc$^{-1}$. This represents the first upper limits on the $21$ cm power spectrum fluctuations at redshifts $12\lesssim z \lesssim 18$ but is still limited by calibration systematics. While calibration improvements may allow us to further remove this contamination, our results emphasize that future experiments should consider carefully the existence of and their ability to calibrate out any spectral structure within the EoR window.

astro-ph.CO↗

arXiv2016

The relation between star formation rate and stellar mass of galaxies at z $\sim$ 1-4

The relation between the Star Formation Rate (SFR) and stellar mass (${\rm M}_{\star}$) of galaxies represents a fundamental constraint on galaxy formation and has been studied extensively both in observations and cosmological simulations. However, the observed amplitude has not been successfully reproduced in simulations, indicating either that the halo accretion history and baryonic physics are poorly modeled or that observations contain biases. We examine the evolution of the SFR$-{\rm M}_{\star}$ relation of $z\sim1-4 $ galaxies and display the inconsistency between observed relations that are obtained using different techniques. We employ cosmological hydrodynamic simulations and compare these with a range of observed SFR$-{\rm M}_{\star}$ relations. We find that numerical results are consistent with observations that use Spectral Energy Distribution (SED) techniques to estimate star formation rates and dust corrections. On the contrary, simulations are not able to reproduce results that were obtained by combining only UV and IR luminosities. These imply SFRs at a fixed stellar mass that are larger almost by a factor of 5 than those of SED measurements for $z \sim1.5-4$. Furthermore, we find remarkable agreement between the numerical results from various authors who have employed different cosmological codes and run simulations with different resolutions. This is interesting for two reasons. A) simulations can produce realistic populations of galaxies within representative cosmological volumes even at relatively modest resolutions. B) It is likely that current numerical codes that rely on similar subgrid multiphase Inter-Stellar Medium (ISM) models and are tuned to reproduce statistical properties of galaxies, produce similar results for the SFR$-{\rm M}_{\star}$ relation by construction, regardless of resolution, box size and, to some extent, the adopted feedback prescriptions.

astro-ph.GA↗

arXiv2016

Parametrising Epoch of Reionization foregrounds: A deep survey of low-frequency point-source spectra with the MWA

Experiments that pursue detection of signals from the Epoch of Reionization (EoR) are relying on spectral smoothness of source spectra at low frequencies. This article empirically explores the effect of foreground spectra on EoR experiments by measuring high-resolution full-polarization spectra for the 586 brightest unresolved sources in one of the MWA EoR fields using 45 h of observation. A novel peeling scheme is used to subtract 2500 sources from the visibilities with ionospheric and beam corrections, resulting in the deepest, confusion-limited MWA image so far. The resulting spectra are found to be affected by instrumental effects, which limit the constraints that can be set on source-intrinsic spectral structure. The sensitivity and power-spectrum of the spectra are analysed, and it is found that the spectra of residuals are dominated by PSF sidelobes from nearby undeconvolved sources. We release a catalogue describing the spectral parameters for each measured source.

astro-ph.IM↗

arXiv2016

The Importance of Wide-field Foreground Removal for 21 cm Cosmology: A Demonstration With Early MWA Epoch of Reionization Observations

In this paper we present observations, simulations, and analysis demonstrating the direct connection between the location of foreground emission on the sky and its location in cosmological power spectra from interferometric redshifted 21 cm experiments. We begin with a heuristic formalism for understanding the mapping of sky coordinates into the cylindrically averaged power spectra measurements used by 21 cm experiments, with a focus on the effects of the instrument beam response and the associated sidelobes. We then demonstrate this mapping by analyzing power spectra with both simulated and observed data from the Murchison Widefield Array. We find that removing a foreground model which includes sources in both the main field-of-view and the first sidelobes reduces the contamination in high k_parallel modes by several percent relative to a model which only includes sources in the main field-of-view, with the completeness of the foreground model setting the principal limitation on the amount of power removed. While small, a percent-level amount of foreground power is in itself more than enough to prevent recovery of any EoR signal from these modes. This result demonstrates that foreground subtraction for redshifted 21 cm experiments is truly a wide-field problem, and algorithms and simulations must extend beyond the main instrument field-of-view to potentially recover the full 21 cm power spectrum.

astro-ph.IM↗

arXiv2016

CHIPS: The Cosmological HI Power Spectrum Estimator

Detection of the cosmological neutral hydrogen signal from the Epoch of Reionization, and estimation of its basic physical parameters, is the principal scientific aim of many current low-frequency radio telescopes. Here we describe the Cosmological HI Power Spectrum Estimator (CHIPS), an algorithm developed and implemented with data from the Murchison Widefield Array (MWA), to compute the two-dimensional and spherically-averaged power spectrum of brightness temperature fluctuations. The principal motivations for CHIPS are the application of realistic instrumental and foreground models to form the optimal estimator, thereby maximising the likelihood of unbiased signal estimation, and allowing a full covariant understanding of the outputs. CHIPS employs an inverse-covariance weighting of the data through the maximum likelihood estimator, thereby allowing use of the full parameter space for signal estimation ("foreground suppression"). We describe the motivation for the algorithm, implementation, application to real and simulated data, and early outputs. Upon application to a set of 3 hours of data, we set a 2$σ$ upper limit on the EoR dimensionless power at $k=0.05$~h.Mpc$^{-1}$ of $Δ_k^2<7.6\times{10^4}$~mK$^2$ in the redshift range $z=[6.2-6.6]$, consistent with previous estimates.

astro-ph.IM↗

arXiv2015

Intensity Mapping Cross-Correlations: Connecting the Largest Scales to Galaxy Evolution

Intensity mapping of the neutral hydrogen (HI) is a new observational tool that can be used to efficiently map the large-scale structure of the Universe over wide redshift ranges. The power spectrum of the intensity maps contains cosmological information on the matter distribution and probes galaxy evolution by tracing the HI content of galaxies at different redshifts and the scale-dependence of HI clustering. The cross-correlation of intensity maps with galaxy surveys is a robust measure of the power spectrum which diminishes systematics caused by instrumental effects and foreground removal. We examine the cross-correlation signature at redshift z=0.9 using a variant of the semi-analytical galaxy formation model SAGE (Croton et al. 2016) applied to the Millennium simulation in order to model the HI gas of galaxies as well as their optical magnitudes based on their star-formation history. We determine the clustering of the cross-correlation power for different types of galaxies determined by their colours, acting as a proxy for their star-formation activity. We find that the cross-correlation coefficient for red quiescent galaxies falls off more quickly on smaller scales k>0.2h/Mpc than for blue star-forming galaxies. Additionally, we create a mock catalogue of highly star-forming galaxies using a selection function to mimic the WiggleZ survey, and use this to predict existing and future cross-correlation measurements of the GBT and Parkes telescope. We find that the cross-power of highly star-forming galaxies shows a higher clustering on small scales than any other galaxy type and that this significantly alters the power spectrum shape on scales k>0.2h/Mpc. We show that the cross-correlation coefficient is not negligible when interpreting the cosmological cross-power spectrum. On the other hand, it contains information about the HI content of the optically selected galaxies.

astro-ph.CO↗

arXiv2015

Gravitational waves from binary supermassive black holes missing in pulsar observations

Gravitational waves are expected to be radiated by supermassive black hole binaries formed during galaxy mergers. A stochastic superposition of gravitational waves from all such binary systems will modulate the arrival times of pulses from radio pulsars. Using observations of millisecond pulsars obtained with the Parkes radio telescope, we constrain the characteristic amplitude of this background, $A_{\rm c,yr}$, to be < $1.0\times10^{-15}$ with 95% confidence. This limit excludes predicted ranges for $A_{\rm c,yr}$ from current models with 91-99.7% probability. We conclude that binary evolution is either stalled or dramatically accelerated by galactic-center environments, and that higher-cadence and shorter-wavelength observations would result in an increased sensitivity to gravitational waves.

astro-ph.CO↗

arXiv2015

A spectroscopically confirmed z=1.327 galaxy-scale deflector magnifying a z~8 Lyman-Break galaxy in the Brightest of Reionizing Galaxies survey

We present a detailed analysis of an individual case of gravitational lensing of a $z\sim8$ Lyman-Break galaxy (LBG) in a blank field, identified in Hubble Space Telescope imaging obtained as part of the Brightest of Reionizing Galaxies survey. To investigate the close proximity of the bright ($m_{AB}=25.8$) $Y_{098}$-dropout to a small group of foreground galaxies, we obtained deep spectroscopy of the dropout and two foreground galaxies using VLT/X-Shooter. We detect H-$α$, H-$β$, [OIII] and [OII] emission in the brightest two foreground galaxies (unresolved at the natural seeing of $0.8$ arcsec), placing the pair at $z=1.327$. We can rule out emission lines contributing all of the observed broadband flux in $H_{160}$ band at $70σ$, allowing us to exclude the $z\sim8$ candidate as a low redshift interloper with broadband photometry dominated by strong emission lines. The foreground galaxy pair lies at the peak of the luminosity, redshift and separation distributions for deflectors of strongly lensed $z\sim8$ objects, and we make a marginal detection of a demagnified secondary image in the deepest ($J_{125}$) filter. We show that the configuration can be accurately modelled by a singular isothermal ellipsoidal deflector and a Sérsic source magnified by a factor of $μ=4.3\pm0.2$. The reconstructed source in the best-fitting model is consistent with luminosities and morphologies of $z\sim8$ LBGs in the literature. The lens model yields a group mass of $9.62\pm0.31\times10^{11} M_{\odot}$ and a stellar mass-to-light ratio for the brightest deflector galaxy of $M_{\star}/L_{B}=2.3^{+0.8}_{-0.6} M_{\odot}/L_{\odot}$ within its effective radius. The foreground galaxies' redshifts would make this one of the few strong lensing deflectors discovered at $z>1$.

astro-ph.CO↗

arXiv2015

Confirmation of Wide-Field Signatures in Redshifted 21 cm Power Spectra

We confirm our recent prediction of the "pitchfork" foreground signature in power spectra of high-redshift 21 cm measurements where the interferometer is sensitive to large-scale structure on all baselines. This is due to the inherent response of a wide-field instrument and is characterized by enhanced power from foreground emission in Fourier modes adjacent to those considered to be the most sensitive to the cosmological H I signal. In our recent paper, many signatures from the simulation that predicted this feature were validated against Murchison Widefield Array (MWA) data, but this key pitchfork signature was close to the noise level. In this paper, we improve the data sensitivity through the coherent averaging of 12 independent snapshots with identical instrument settings and provide the first confirmation of the prediction with a signal-to-noise ratio > 10. This wide-field effect can be mitigated by careful antenna designs that suppress sensitivity near the horizon. Simple models for antenna apertures that have been proposed for future instruments such as the Hydrogen Epoch of Reionization Array and the Square Kilometre Array indicate they should suppress foreground leakage from the pitchfork by ~40 dB relative to the MWA and significantly increase the likelihood of cosmological signal detection in these critical Fourier modes in the three-dimensional power spectrum.

astro-ph.CO↗

arXiv2015

Foregrounds in Wide-Field Redshifted 21 cm Power Spectra

Detection of 21~cm emission of HI from the epoch of reionization, at redshifts z>6, is limited primarily by foreground emission. We investigate the signatures of wide-field measurements and an all-sky foreground model using the delay spectrum technique that maps the measurements to foreground object locations through signal delays between antenna pairs. We demonstrate interferometric measurements are inherently sensitive to all scales, including the largest angular scales, owing to the nature of wide-field measurements. These wide-field effects are generic to all observations but antenna shapes impact their amplitudes substantially. A dish-shaped antenna yields the most desirable features from a foreground contamination viewpoint, relative to a dipole or a phased array. Comparing data from recent Murchison Widefield Array observations, we demonstrate that the foreground signatures that have the largest impact on the HI signal arise from power received far away from the primary field of view. We identify diffuse emission near the horizon as a significant contributing factor, even on wide antenna spacings that usually represent structures on small scales. For signals entering through the primary field of view, compact emission dominates the foreground contamination. These two mechanisms imprint a characteristic "pitchfork" signature on the "foreground wedge" in Fourier delay space. Based on these results, we propose that selective down-weighting of data based on antenna spacing and time can mitigate foreground contamination substantially by a factor ~100 with negligible loss of sensitivity.

astro-ph.IM↗

arXiv2015

The Murchison Widefield Array Correlator

The Murchison Widefield Array (MWA) is a Square Kilometre Array (SKA) Precursor. The telescope is located at the Murchison Radio--astronomy Observatory (MRO) in Western Australia (WA). The MWA consists of 4096 dipoles arranged into 128 dual polarisation aperture arrays forming a connected element interferometer that cross-correlates signals from all 256 inputs. A hybrid approach to the correlation task is employed, with some processing stages being performed by bespoke hardware, based on Field Programmable Gate Arrays (FPGAs), and others by Graphics Processing Units (GPUs) housed in general purpose rack mounted servers. The correlation capability required is approximately 8 TFLOPS (Tera FLoating point Operations Per Second). The MWA has commenced operations and the correlator is generating 8.3 TB/day of correlation products, that are subsequently transferred 700 km from the MRO to Perth (WA) in real-time for storage and offline processing. In this paper we outline the correlator design, signal path, and processing elements and present the data format for the internal and external interfaces.

astro-ph.IM↗

arXiv2014

Prospects for gravitational-wave detection and supermassive black hole astrophysics with pulsar timing arrays

Large-area sky surveys show that massive galaxies undergo at least one major merger in a Hubble time. Ongoing pulsar timing array (PTA) experiments are aimed at measuring the gravitational wave (GW) emission from binary supermassive black holes (SMBHs) at the centres of galaxy merger remnants. In this paper, using the latest observational estimates for a range of galaxy properties and scaling relations, we predict the amplitude of the GW background generated by the binary SMBH population. We also predict the numbers of individual binary SMBH GW sources. We predict the characteristic strain amplitude of the GW background to lie in the range $5.1\times10^{-16}<A_{\rm yr}<2.4\times10^{-15}$ at a frequency of $(1\,{\rm yr})^{-1}$, with 95% confidence. Higher values within this range, which correspond to the more commonly preferred choice of galaxy merger timescale, will fall within the expected sensitivity ranges of existing PTA projects in the next few years. In contrast, we find that a PTA consisting of at least 100 pulsars observed with next-generation radio telescopes will be required to detect continuous-wave GWs from binary SMBHs. We further suggest that GW memory bursts from coalescing SMBH pairs are not viable sources for PTAs. Both the GW background and individual GW source counts are dominated by binaries formed in mergers between early-type galaxies of masses $\gtrsim5\times10^{10}M_{\odot}$ at redshifts $\lesssim 1.5$. Uncertainties in the galaxy merger timescale and the SMBH mass - galaxy bulge mass relation dominate the uncertainty in our predictions.

astro-ph.CO↗

arXiv2014

Measurement of Galaxy Clustering at z~7.2 and the Evolution of Galaxy Bias from 3.8<z<8 in the XDF, GOODS-S AND GOODS-N

Lyman-Break Galaxy (LBG) samples observed during reionization ($z\gtrsim6$) with Hubble Space Telescope's Wide Field Camera 3 are reaching sizes sufficient to characterize their clustering properties. Using a combined catalog from the Hubble eXtreme Deep Field and CANDELS surveys, containing $N=743$ LBG candidates at z>6.5 at a mean redshift of $z=7.2$, we detect a clear clustering signal in the angular correlation function (ACF) at $\sim4σ$, corresponding to a real-space correlation length $r_{0}=6.7^{+0.9}_{-1.0}h^{-1}$cMpc. The derived galaxy bias $b=8.6^{+0.9}_{-1.0}$ is that of dark-matter halos of $M=10^{11.1^{+0.2}_{-0.3}}$M$_{\odot}$ at $z=7.2$, and highlights that galaxies below the current detection limit ($M_{AB}\sim-17.7$) are expected in lower-mass halos ($M\sim10^{8}-10^{10.5}$M$_{\odot}$). We compute the ACF of LBGs at $z\sim3.8-z\sim5.9$ in the same surveys. A trend of increasing bias is found from $z=3.8$ ($b\sim3.0$) to $z=7.2$ ($b\sim8.6$), broadly consistent with galaxies at fixed luminosity being hosted in dark-matter halos of similar mass at $4<z<6$, followed by a slight rise in halo masses at $z\sim7$ ($\sim2σ$ confidence). Separating the data at the median luminosity of the $z=7.2$ sample ($M_{UV}=-19.4$) shows higher clustering at $z=5.9$ for bright galaxies ($r_{0}=5.5^{+1.4}_{-1.5}h^{-1}$cMpc, $b=6.2^{+1.2}_{-1.5}$) compared to faint galaxies ($r_{0}=1.9^{+1.1}_{-1.0}h^{-1}$cMpc, $b=2.7\pm1.2$) implying a constant mass-to-light ratio $\frac{dlogM}{dlogL}\sim1.2^{+1.8}_{-0.8}$. A similar trend is present in the $z=7.2$ sample with larger uncertainty. Finally, our bias measurements allow us to investigate the fraction of dark-matter halos hosting UV-bright galaxies (the duty-cycle, $ε_{DC}$). At $z=7.2$ values near unity are preferred, which may be explained by the shortened halo assembly time at high-redshift.

astro-ph.GA↗

arXiv2014

Binary super-massive black hole environments diminish the gravitational-wave signal in the pulsar timing band

We assess the effects of super-massive black hole (SMBH) environments on the gravitational-wave (GW) signal from binary SMBHs. To date, searches with pulsar timing arrays for GWs from binary SMBHs, in the frequency band $\sim1-100$\,nHz, include the assumptions that all binaries are circular and evolve only through GW emission. However, dynamical studies have shown that the only way that binary SMBH orbits can decay to separations where GW emission dominates the evolution is through interactions with their environments. We augment an existing galaxy and SMBH formation and evolution model with calculations of binary SMBH evolution in stellar environments, accounting for non-zero binary eccentricities. We find that coupling between binaries and their environments causes the expected GW spectral energy distribution to be reduced with respect to the standard assumption of circular, GW-driven binaries, for frequencies up to $\sim20$\,nHz. Larger eccentricities at binary formation further reduce the signal in this regime. We also find that GW bursts from individual eccentric binary SMBHs are unlikely to be detectable with current pulsar timing arrays. The uncertainties in these predictions are large, owing to observational uncertainty in SMBH-galaxy scaling relations and the galaxy stellar mass function, uncertainty in the nature of binary-environment coupling, and uncertainty in the numbers of the most massive binary SMBHs. We conclude, however, that low-frequency GWs from binary SMBHs may be more difficult to detect with pulsar timing arrays than currently thought.

astro-ph.CO↗