## Publications

73 results found

Kamran M, Ghara R, Majumdar S,
et al., 2022, Redshifted 21-cm bispectrum: impact of the source models on the signal and the IGM physics from the Cosmic Dawn, *JOURNAL OF COSMOLOGY AND ASTROPARTICLE PHYSICS*, ISSN: 1475-7516

- Author Web Link
- Cite
- Citations: 1

Acedo EDL, de Villiers DIL, Razavi-Ghods N,
et al., 2022, The REACH radiometer for detecting the 21-cm hydrogen signal from redshift z approximate to 7.5-28, *NATURE ASTRONOMY*, Vol: 6, Pages: 984-+, ISSN: 2397-3366

- Author Web Link
- Cite
- Citations: 2

Cumner J, Acedo EDL, de Villiers DIL,
et al., 2022, Radio Antenna Design for Sky-Averaged 21cm Cosmology Experiments: The REACH Case, *JOURNAL OF ASTRONOMICAL INSTRUMENTATION*, Vol: 11, ISSN: 2251-1717

- Author Web Link
- Cite
- Citations: 5

Gorce A, Hutter A, Pritchard JR, 2021, Using the sample variance of 21cm maps as a tracer of the ionisation topology, *Astronomy and Astrophysics: a European journal*, ISSN: 0004-6361

Intensity mapping of the 21cm signal of neutral hydrogen will yield excitinginsights into the Epoch of Reionisation and the nature of the first galaxies.However, the large amount of data that will be generated by the next generationof radio telescopes, such as the Square Kilometre Array (SKA), as well as thenumerous observational obstacles to overcome, require analysis techniques tunedto extract the reionisation history and morphology. In this context, weintroduce a one-point statistic, to which we refer as the local variance,$\sigma_\mathrm{loc}$, that describes the distribution of the mean differential21cm brightness temperatures measured in two-dimensional maps along thefrequency direction of a light-cone. The local variance takes advantage of whatis usually considered an observational bias, the sample variance. We find theredshift-evolution of the local variance to not only probe the reionisationhistory of the observed patches of the sky, but also trace the ionisationmorphology. This estimator provides a promising tool to constrain the midpointof reionisation as well as gaining insight into the ionising properties ofearly galaxies.

Koopmans LVE, Barkana R, Bentum M,
et al., 2021, Peering into the dark (ages) with low-frequency space interferometers Using the 21-cm signal of neutral hydrogen from the infant universe to probe fundamental (Astro)physics, *EXPERIMENTAL ASTRONOMY*, Vol: 51, Pages: 1641-1676, ISSN: 0922-6435

- Author Web Link
- Cite
- Citations: 1

Kamran M, Majumdar S, Ghara R, et al., 2021, Probing IGM Physics during Cosmic Dawn using the Redshifted 21-cm Bispectrum

With the advent of the first luminous sources at Cosmic Dawn (CD), theredshifted 21-cm signal, from the neutral hydrogen in the Inter-Galactic Medium(IGM), is predicted to undergo a transition from absorption to emission againstthe CMB. Using simulations, we show that the redshift evolution of the sign andthe magnitude of the 21-cm bispectrum can disentangle the contributions fromLy$\alpha$ coupling and X-ray heating of the IGM, the two most dominantprocesses which drive this transition. This opens a new avenue to probe thefirst luminous sources and the IGM physics at CD.

Kamran M, Ghara R, Majumdar S,
et al., 2021, Redshifted 21-cm bispectrum – II. Impact of the spin temperature fluctuations and redshift space distortions on the signal from the Cosmic Dawn, *Monthly Notices of the Royal Astronomical Society*, Vol: 502, Pages: 3800-3813, ISSN: 0035-8711

We present a study of the 21-cm signal bispectrum (which quantifies the non-Gaussianity in the signal) from the Cosmic Dawn (CD). For our analysis, we have simulated the 21-cm signal using radiative transfer code GRIZZLY, while considering two types of sources (mini-QSOs and HMXBs) for Ly α coupling and the X-ray heating of the IGM. Using this simulated signal, we have, for the first time, estimated the CD 21-cm bispectra for all unique k-triangles and for a range of k modes. We observe that the redshift evolution of the bispectrum magnitude and sign follow a generic trend for both source models. However, the redshifts at which the bispectrum magnitude reaches their maximum and minimum values and show their sign reversal depends on the source model. When the Ly α coupling and the X-ray heating of the IGM occur simultaneously, we observe two consecutive sign reversals in the bispectra for small k-triangles (irrespective of the source models). One arising at the beginning of the IGM heating and the other at the end of Ly α-coupling saturation. This feature can be used in principle to constrain the CD history and/or to identify the specific CD scenarios. We also quantify the impact of the spin temperature (TS) fluctuations on the bispectra. We find that TS fluctuations have maximum impact on the bispectrum magnitude for small k-triangles and at the stage when Ly α coupling reaches saturation. Furthermore, we are also the first to quantify the impact of redshift space distortions (RSD), on the CD bispectra. We find that the impact of RSD on the CD 21-cm bispectra is significant (

Hothi I, Chapman E, Pritchard JR,
et al., 2021, Comparing foreground removal techniques for recovery of the LOFAR-EoR 21 cm power spectrum, *MONTHLY NOTICES OF THE ROYAL ASTRONOMICAL SOCIETY*, Vol: 500, Pages: 2264-2277, ISSN: 0035-8711

- Author Web Link
- Cite
- Citations: 23

Majumdar S, Kamran M, Pritchard JR,
et al., 2020, Redshifted 21-cm bispectrum - I. Impact of the redshift space distortions on the signal from the Epoch of Reionization, *MONTHLY NOTICES OF THE ROYAL ASTRONOMICAL SOCIETY*, Vol: 499, Pages: 5090-5106, ISSN: 0035-8711

Bacon DJ, Battye RA, Bull P,
et al., 2020, Cosmology with Phase 1 of the Square Kilometre Array Red Book 2018: Technical specifications and performance forecasts, *PUBLICATIONS OF THE ASTRONOMICAL SOCIETY OF AUSTRALIA*, Vol: 37, ISSN: 1323-3580

- Author Web Link
- Cite
- Citations: 90

Weltman A, Bull P, Camera S,
et al., 2020, Fundamental physics with the square kilometre array, *Publications of the Astronomical Society of Australia*, Vol: 37, Pages: 1-52, ISSN: 1323-3580

The Square Kilometre Array (SKA) is a planned large radio interferometer designed to operate over a wide range of frequencies, and with an order of magnitude greater sensitivity and survey speed than any current radio telescope. The SKA will address many important topics in astronomy, ranging from planet formation to distant galaxies. However, in this work, we consider the perspective of the SKA as a facility for studying physics. We review four areas in which the SKA is expected to make major contributions to our understanding of fundamental physics: cosmic dawn and reionisation; gravity and gravitational radiation; cosmology and dark energy; and dark matter and astroparticle physics. These discussions demonstrate that the SKA will be a spectacular physics machine, which will provide many new breakthroughs and novel insights on matter, energy, and spacetime.

Gorce A, Pritchard JR, 2019, Studying the morphology of reionisation with the triangle correlation function of phases, *Monthly Notices of the Royal Astronomical Society*, Vol: 489, Pages: 1321-1337, ISSN: 0035-8711

AbstractWe present a new statistical tool, called the triangle correlation function (TCF), inspired by the earlier work of Obreschkow et al. (2013). It is derived from the 3-point correlation function and aims to probe the characteristic scale of ionised regions during the Epoch of Reionisation from 21cm interferometric observations. Unlike most works, which focus on power spectrum, i.e. amplitude information, our statistic is based on the information we can extract from the phases of the Fourier transform of the ionisation field. In this perspective, it may benefit from the well-known interferometric concept of closure phases. We find that this statistical estimator performs very well on simple ionisation fields. For example, with well-defined fully ionised disks, there is a peaking scale, which we can relate to the radius of the ionised bubbles. We also explore the robustness of the TCF when observational effects such as angular resolution and noise are considered. We also get interesting results on fields generated by more elaborate simulations such as 21CMFAST. Although the variety of sources and ionised morphologies in the early stages of the process make its interpretation more challenging, the nature of the signal can tell us about the stage of reionisation. Finally, and in contrast to other bubble size distribution algorithms, we show that the TCF can resolve two different characteristic scales in a given map.

Koopmans L, Barkana R, Bentum M, et al., 2019, Peering into the dark (Ages) with low-frequency space interferometers, Publisher: arXiv

Neutral hydrogen pervades the infant Universe, and its redshifted 21-cmsignal allows one to chart the Universe. This signal allows one to probeastrophysical processes such as the formation of the first stars, galaxies,(super)massive black holes and enrichment of the pristine gas from z~6 to z~30,as well as fundamental physics related to gravity, dark matter, dark energy andparticle physics at redshifts beyond that. As one enters the Dark Ages (z>30),the Universe becomes pristine. Ground-based low-frequency radio telescopes aimto detect the spatial fluctuations of the 21-cm signal. Complementary, global21-cm experiments aim to measure the sky-averaged 21-cm signal. Escaping RFIand the ionosphere has motivated space-based missions, such as theDutch-Chinese NCLE instrument (currently in lunar L2), the proposed US-drivenlunar or space-based instruments DAPPER and FARSIDE, the lunar-orbitinterferometer DSL (China), and PRATUSH (India). To push beyond the currentz~25 frontier, though, and measure both the global and spatial fluctuations(power-spectra/tomography) of the 21-cm signal, low-frequency (1-100MHz;BW~50MHz; z>13) space-based interferometers with vast scalable collecting areas(1-10-100 km2), large filling factors (~1) and large fields-of-view (4pi sr.)are needed over a mission lifetime of >5 years. In this ESA White Paper, weargue for the development of new technologies enabling interferometers to bedeployed, in space (e.g. Earth-Sun L2) or in the lunar vicinity (e.g. surface,orbit or Earth-Moon L2), to target this 21-cm signal. This places them in astable environment beyond the reach of most RFI from Earth and its ionosphericcorruptions, enabling them to probe the Dark Ages as well as the Cosmic Dawn,and allowing one to investigate new (astro)physics that is inaccessible in anyother way in the coming decades. [Abridged]

Binnie T, Pritchard JR, 2019, Bayesian model selection with future 21cm observations of the epoch of reionization, *Monthly Notices of the Royal Astronomical Society*, Vol: 487, Pages: 1160-1177, ISSN: 0035-8711

We apply Bayesian statistics to perform model selection on different reionization scenarios via the MULTINEST algorithm. Initially, we recover the results shown by 21CMMC for the parameter estimation of 21CMFAST models. We proceed to test several toy models of the epoch of reionization defined in contrasting morphology and scale. We find that LOFAR observations are unlikely to allow model selection even with long integration times. HERA would require 61 dipoles to perform the same analysis in 1080 h, and becomes comparable to the Square Kilometre Array (SKA) with 217 dipoles. We find the SKA requires only 324 h of observation to conclusively distinguish between our models. Once model selection is achievable, an analysis of observational priors is performed finding that neutral fraction checks at specific redshifts add little to no inference. We show the difficulties in model selection at the level of distinguishing fiducial parameters within a model or distinguishing galaxies with a constant versus power-law mass-to-light ratio. Finally, we explore the use of the Savage–Dickey density ratio to show the redundancy of the parameter Rmfp within 21CMFAST.

Mirocha J, Jacobs D, Dillon J, et al., 2019, Astro2020 science white paper: First stars and black holes at cosmic dawn with redshifted 21-cm observations

The "cosmic dawn" refers to the period of the Universe's history when starsand black holes first formed and began heating and ionizing hydrogen in theintergalactic medium (IGM). Though exceedingly difficult to detect directly,the first stars and black holes can be constrained indirectly throughmeasurements of the cosmic 21-cm background, which traces the ionization stateand temperature of intergalactic hydrogen gas. In this white paper, we focus onthe science case for such observations, in particular those targeting redshiftsz $\gtrsim$ 10 when the IGM is expected to be mostly neutral. 21-cmobservations provide a unique window into this epoch and are thus critical toadvancing first star and black hole science in the next decade.

Schmit CJ, Heavens AF, Pritchard JR, 2019, The gravitational and lensing-ISW bispectrum of 21 cm radiation, *Monthly Notices of the Royal Astronomical Society*, Vol: 483, Pages: 4259-4275, ISSN: 0035-8711

Cosmic microwave background experiments from COBE to Planck have launched cosmology into an era of precision science, where many cosmological parameters are now determined to the per cent level. Next-generation telescopes, focusing on the cosmological 21 cm signal from neutral hydrogen, will probe enormous volumes in the low-redshift Universe, and have the potential to determine dark energy properties and test modifications of Einstein’s gravity. We study the 21 cm bispectrum due to gravitational collapse as well as the contribution by line-of-sight perturbations in the form of the lensing-ISW bispectrum at low redshifts (z ∼ 0.35−3), targeted by upcoming neutral hydrogen intensity mapping experiments. We compute the expected bispectrum amplitudes and use a Fisher forecast model to compare power spectrum and bispectrum observations of intensity mapping surveys by Canadian Hydrogen Intensity Mapping Experiment (CHIME), MeerKAT, and SKA-mid. We find that combined power spectrum and bispectrum observations have the potential to decrease errors on the cosmological parameters by an order of magnitude compared to Planck. Finally, we compute the contribution of the lensing-ISW bispectrum, and find that, unlike for the cosmic microwave background analyses, it can safely be ignored for 21 cm bispectrum observations.

Watkinson CA, Giri SK, Ross HE,
et al., 2019, The 21-cm bispectrum as a probe of non-Gaussianities due to X-ray heating, *MONTHLY NOTICES OF THE ROYAL ASTRONOMICAL SOCIETY*, Vol: 482, Pages: 2653-2669, ISSN: 0035-8711

Majumdar S, Mondal R, Pritchard JR, et al., 2019, A comprehensive study of the EoR 21-cm signal bispectrum, URSI Asia-Pacific Radio Science Conference (AP-RASC), Publisher: IEEE

Majumdar S, Pritchard JR, Mondal R,
et al., 2018, Quantifying the non-Gaussianity in the EoR 21-cm signal through bispectrum, *Monthly Notices of the Royal Astronomical Society*, Vol: 476, Pages: 4007-4024, ISSN: 0035-8711

The epoch of reionization (EoR) 21-cm signal is expected to be highly non-Gaussian in nature and this non-Gaussianity is also expected to evolve with the progressing state of reionization. Therefore the signal will be correlated between different Fourier modes (k). The power spectrum will not be able capture this correlation in the signal. We use a higher order estimator – the bispectrum – to quantify this evolving non-Gaussianity. We study the bispectrum using an ensemble of simulated 21-cm signal and with a large variety of k triangles. We observe two competing sources driving the non-Gaussianity in the signal: fluctuations in the neutral fraction (xHI) field and fluctuations in the matter density field. We find that the non-Gaussian contribution from these two sources varies, depending on the stage of reionization and on which k modes are being studied. We show that the sign of the bispectrum works as a unique marker to identify which among these two components is driving the non-Gaussianity. We propose that the sign change in the bispectrum, when plotted as a function of triangle configuration cos θ and at a certain stage of the EoR can be used as a confirmative test for the detection of the 21-cm signal. We also propose a new consolidated way to visualize the signal evolution (with evolving x¯HI or redshift), through the trajectories of the signal in a power spectrum and equilateral bispectrum i.e. P(k) − B(k, k, k) space.

Schmit CJ, Pritchard JR, 2017, Emulation of reionization simulations for Bayesian inference of astrophysics parameters using neural networks, *Monthly Notices of the Royal Astronomical Society*, Vol: 475, Pages: 1213-1223, ISSN: 0035-8711

Next generation radio experiments such as LOFAR, HERA and SKA are expected toprobe the Epoch of Reionization and claim a first direct detection of thecosmic 21cm signal within the next decade. Data volumes will be enormous andcan thus potentially revolutionize our understanding of the early Universe andgalaxy formation. However, numerical modelling of the Epoch of Reionization canbe prohibitively expensive for Bayesian parameter inference and how tooptimally extract information from incoming data is currently unclear.Emulation techniques for fast model evaluations have recently been proposed asa way to bypass costly simulations. We consider the use of artificial neuralnetworks as a blind emulation technique. We study the impact of trainingduration and training set size on the quality of the network prediction and theresulting best fit values of a parameter search. A direct comparison is drawnbetween our emulation technique and an equivalent analysis using 21CMMC. Wefind good predictive capabilities of our network using training sets of as lowas 100 model evaluations, which is within the capabilities of fully numericalradiative transfer codes.

Schmit CJ, Pritchard JR, 2017, Neural Network Emulation of Reionization Simulations, *PEERING TOWARDS COSMIC DAWN*, Vol: 12, Pages: 43-46, ISSN: 1743-9213

Watkinson CA, Majumdar S, Pritchard JR,
et al., 2017, A fast estimator for the bispectrum and beyond - a practical method for measuring non-Gaussianity in 21-cm maps, *Monthly Notices of the Royal Astronomical Society*, Vol: 472, Pages: 2436-2446, ISSN: 0035-8711

In this paper, we establish the accuracy and robustness of a fast estimator for the bispectrum – the ‘FFT-bispectrum estimator’. The implementation of the estimator presented here offers speed and simplicity benefits over a direct-measurement approach. We also generalize the derivation so it may be easily be applied to any order polyspectra, such as the trispectrum, with the cost of only a handful of Fast-Fourier Transforms (FFTs). All lower order statistics can also be calculated simultaneously for little extra cost. To test the estimator, we make use of a non-linear density field, and for a more strongly non-Gaussian test case, we use a toy-model of reionization in which ionized bubbles at a given redshift are all of equal size and are randomly distributed. Our tests find that the FFT-estimator remains accurate over a wide range of k, and so should be extremely useful for analysis of 21-cm observations. The speed of the FFT-bispectrum estimator makes it suitable for sampling applications, such as Bayesian inference. The algorithm we describe should prove valuable in the analysis of simulations and observations, and whilst, we apply it within the field of cosmology, this estimator is useful in any field that deals with non-Gaussian data.

Burns JO, Bradley R, Tauscher K,
et al., 2017, A Space-based Observational Strategy for Characterizing the First Stars and Galaxies Using the Redshifted 21cm Global Spectrum, *ASTROPHYSICAL JOURNAL*, Vol: 844, ISSN: 0004-637X

The redshifted 21 cm monopole is expected to be a powerful probe of the epoch of the first stars and galaxies ($10\lt z\lt 35$). The global 21 cm signal is sensitive to the thermal and ionization state of hydrogen gas and thus provides a tracer of sources of energetic photons—primarily hot stars and accreting black holes—which ionize and heat the high redshift intergalactic medium (IGM). This paper presents a strategy for observations of the global spectrum with a realizable instrument placed in a low-altitude lunar orbit, performing night-time 40–120 MHz spectral observations, while on the farside to avoid terrestrial radio frequency interference, ionospheric corruption, and solar radio emissions. The frequency structure, uniformity over large scales, and unpolarized state of the redshifted 21 cm spectrum are distinct from the spectrally featureless, spatially varying, and polarized emission from the bright foregrounds. This allows a clean separation between the primordial signal and foregrounds. For signal extraction, we model the foreground, instrument, and 21 cm spectrum with eigenmodes calculated via Singular Value Decomposition analyses. Using a Markov Chain Monte Carlo algorithm to explore the parameter space defined by the coefficients associated with these modes, we illustrate how the spectrum can be measured and how astrophysical parameters (e.g., IGM properties, first star characteristics) can be constrained in the presence of foregrounds using the Dark Ages Radio Explorer (DARE).

Liu A, Pritchard JR, Allison R,
et al., 2016, Eliminating the optical depth nuisance from the CMB with 21 cm cosmology, *Physical Review D*, Vol: 93, ISSN: 1550-7998

Amongst standard model parameters that are constrained by cosmic microwave background (CMB) observations, the optical depth τ stands out as a nuisance parameter. While τ provides some crude limits on reionization, it also degrades constraints on other cosmological parameters. Here we explore how 21 cm cosmology—as a direct probe of reionization—can be used to independently predict τ in an effort to improve CMB parameter constraints. We develop two complementary schemes for doing so. The first uses 21 cm power spectrum observations in conjunction with semianalytic simulations to predict τ. The other uses global 21 cm measurements to directly constrain low redshift (post-reheating) contributions to τ in a relatively model-independent way. Forecasting the performance of the upcoming hydrogen epoch of reionization array, we find that significant reductions in the errors on τ can be achieved. These results are particularly effective at breaking the CMB degeneracy between τ and the amplitude of the primordial fluctuation spectrum As, with errors on ln(1010As) reduced by up to a factor of 4. Stage 4 CMB constraints on the neutrino mass sum are also improved, with errors potentially reduced to 12 meV regardless of whether CMB experiments can precisely measure the reionization bump in polarization power spectra. Observations of the 21 cm line are therefore capable of improving not only our understanding of reionization astrophysics, but also of cosmology in general.

Harker GJA, Mirocha J, Burns JO,
et al., 2015, Parametrizations of the 21-cm global signal and parameter estimation from single-dipole experiments, *Monthly Notices of the Royal Astronomical Society*, Vol: 455, Pages: 3829-3840, ISSN: 0035-8711

One approach to extracting the global 21-cm signal from total-power measurements at low radio frequencies is to parametrize the different contributions to the data and then fit for these parameters. We examine parametrizations of the 21-cm signal itself, and propose one based on modelling the Ly α background, intergalactic medium temperature and hydrogen ionized fraction using tanh functions. This captures the shape of the signal from a physical modelling code better than an earlier parametrization based on interpolating between maxima and minima of the signal, and imposes a greater level of physical plausibility. This allows less biased constraints on the turning points of the signal, even though these are not explicitly fit for. Biases can also be alleviated by discarding information which is less robustly described by the parametrization, for example by ignoring detailed shape information coming from the covariances between turning points or from the high-frequency parts of the signal, or by marginalizing over the high-frequency parts of the signal by fitting a more complex foreground model. The fits are sufficiently accurate to be usable for experiments gathering 1000 h of data, though in this case it may be important to choose observing windows which do not include the brightest areas of the foregrounds. Our assumption of pointed, single-antenna observations and very broad-band fitting makes these results particularly applicable to experiments such as the Dark Ages Radio Explorer, which would study the global 21-cm signal from the clean environment of a low lunar orbit, taking data from the far side.

Watkinson CA, Pritchard JR, 2015, The impact of spin-temperature fluctuations on the 21-cm moments, *Monthly Notices of the Royal Astronomical Society*, Vol: 454, Pages: 1416-1431, ISSN: 0035-8711

This paper considers the impact of Lyman α coupling and X-ray heating on the 21-cm brightness-temperature one-point statistics (as predicted by seminumerical simulations). The X-ray production efficiency is varied over four orders of magnitude and the hardness of the X-ray spectrum is varied from that predicted for high-mass X-ray binaries, to the softer spectrum expected from the hot interstellar medium. We find peaks in the redshift evolution of both the variance and skewness associated with the efficiency of X-ray production. The amplitude of the variance is also sensitive to the hardness of the X-ray spectral energy distribution. We find that the relative timing of the coupling and heating phases can be inferred from the redshift extent of a plateau that connects a peak in the variance's evolution associated with Lyman α coupling to the heating peak. Importantly, we find that late X-ray heating would seriously hamper our ability to constrain reionization with the variance. Late X-ray heating also qualitatively alters the evolution of the skewness, providing a clean way to constrain such models. If foregrounds can be removed, we find that LOFAR, MWA and PAPER could constrain reionization and late X-ray heating models with the variance. We find that HERA and SKA (phase 1) will be able to constrain both reionization and heating by measuring the variance using foreground-avoidance techniques. If foregrounds can be removed they will also be able to constrain the nature of Lyman α coupling.

Pritchard J, 2015, Reionization and the SKA, *Astronomy & Geophysics*, Vol: 56, Pages: 3.25-3.30, ISSN: 1468-4004

Watkinson CA, Mesinger A, Pritchard JR,
et al., 2015, 21-cm signatures of residual H I inside cosmic H II regions during reionization, *MONTHLY NOTICES OF THE ROYAL ASTRONOMICAL SOCIETY*, Vol: 449, Pages: 3202-3211, ISSN: 0035-8711

- Author Web Link
- Open Access Link
- Cite
- Citations: 13

Koopmans L, Pritchard J, Mellema G,
et al., 2015, The Cosmic Dawn and Epoch of Reionisation with SKA, *Advancing Astrophysics with the Square Kilometre Array (AASKA14)*, Pages: 1-1

Watkinson CA, Pritchard JR, Mesinger A,
et al., 2015, The impact of small absorbers, galactic neutral hydrogen & X-rays on 1-point statistics of the 21-cm line., *STATISTICAL CHALLENGES IN 21ST CENTURY COSMOLOGY*, Vol: 10, Pages: 189-191, ISSN: 1743-9213

This data is extracted from the Web of Science and reproduced under a licence from Thomson Reuters. You may not copy or re-distribute this data in whole or in part without the written consent of the Science business of Thomson Reuters.