Search

Pulsars in the Galactic Center (GC) are important probes of General Relativity, star formation, stellar dynamics, stellar evolution, and the interstellar medium. Despite years of searching, only a handful of pulsars in the central 0.5 deg are known. The high-frequency sensitivity of ngVLA will open a new window for discovery and characterization of pulsars in the GC. A pulsar in orbit around the GC black hole, Sgr A*, will provide an unprecedented probe of black hole physics and General Relativity., Comment: To be published in the ASP Monograph Series, "Science with a Next-Generation VLA", ed. E. J. Murphy (ASP, San Francisco, CA)

It is widely accepted that dark matter contributes about a quarter of the critical mass-energy density in our Universe. The nature of dark matter is currently unknown, with the mass of possible constituents spanning nearly one hundred orders of magnitude. The ultralight scalar field dark matter, consisting of extremely light bosons with $m \sim 10^{-22}$ eV and often called "fuzzy" dark matter, provides intriguing solutions to some challenges at sub-Galactic scales for the standard cold dark matter model. As shown by Khmelnitsky and Rubakov, such a scalar field in the Galaxy would produce an oscillating gravitational potential with nanohertz frequencies, resulting in periodic variations in the times of arrival of radio pulses from pulsars. The Parkes Pulsar Timing Array (PPTA) has been monitoring 20 millisecond pulsars at two to three weeks intervals for more than a decade. In addition to the detection of nanohertz gravitational waves, PPTA offers the opportunity for direct searches for fuzzy dark matter in an astrophysically feasible range of masses. We analyze the latest PPTA data set which includes timing observations for 26 pulsars made between 2004 and 2016. We perform a search in this data set for evidence of ultralight dark matter in the Galaxy using Bayesian and Frequentist methods. No statistically significant detection has been made. We therefore place upper limits on the local dark matter density. Our limits, improving on previous searches by a factor of two to five, constrain the dark matter density of ultralight bosons with $m \leq 10^{-23}$ eV to be below $6\,\text{GeV}\,\text{cm}^{-3}$ with 95\% confidence in the Earth neighborhood. Finally, we discuss the prospect of probing the astrophysically favored mass range $m \gtrsim 10^{-22}$ eV with next-generation pulsar timing facilities., Comment: Fixed a typo in Fig. 5; Published in Phys. Rev. D as Editor's Suggestion article, 17 pages, 7 figures, 4 tables

The capability of the Event Horizon Telescope (EHT) to image the nearest supermassive black hole candidates at horizon-scale resolutions offers a novel means to study gravity in its strongest regimes and to test different models for these objects. Here, we study the observational appearance at 230 GHz of a surfaceless black hole mimicker, namely a non-rotating boson star, in a scenario consistent with the properties of the accretion flow onto Sgr A*. To this end, we perform general relativistic magnetohydrodynamic simulations followed by general relativistic radiative transfer calculations in the boson star space-time. Synthetic reconstructed images considering realistic astronomical observing conditions show that, despite qualitative similarities, the differences in the appearance of a black hole -- either rotating or not -- and a boson star of the type considered here are large enough to be detectable. These differences arise from dynamical effects directly related to the absence of an event horizon, in particular, the accumulation of matter in the form of a small torus or a spheroidal cloud in the interior of the boson star, and the absence of an evacuated high-magnetization funnel in the polar regions. The mechanism behind these effects is general enough to apply to other horizonless and surfaceless black hole mimickers, strengthening confidence in the ability of the EHT to identify such objects via radio observations., Comment: 16 pages, 12 figures. Published in MNRAS. Adding more information in the form of appendices, and a new simulation of a different boson star model. The conclusions do not change

Radio images of the Galactic Center supermassive black hole, Sagittarius A* (Sgr A*), are dominated by interstellar scattering. Previous studies of Sgr A* have adopted an anisotropic Gaussian model for both the intrinsic source and the scattering, and they have extrapolated the scattering using a purely $\lambda^2$ scaling to estimate intrinsic properties. However, physically motivated source and scattering models break all three of these assumptions. They also predict that refractive scattering effects will be significant, which have been ignored in standard model fitting procedures. We analyze radio observations of Sgr A* using a physically motivated scattering model, and we develop a prescription to incorporate refractive scattering uncertainties when model fitting. We show that an anisotropic Gaussian scattering kernel is an excellent approximation for Sgr A* at wavelengths longer than 1cm, with an angular size of $(1.380 \pm 0.013) \lambda_{\rm cm}^2\,{\rm mas}$ along the major axis, $(0.703 \pm 0.013) \lambda_{\rm cm}^2\,{\rm mas}$ along the minor axis, and a position angle of $81.9^\circ \pm 0.2^\circ$. We estimate that the turbulent dissipation scale is at least $600\,{\rm km}$, with tentative support for $r_{\rm in} = 800 \pm 200\,{\rm km}$, suggesting that the ion Larmor radius defines the dissipation scale. We find that the power-law index for density fluctuations in the scattering material is $\beta < 3.47$, shallower than expected for a Kolmogorov spectrum ($\beta=11/3$), and we estimate $\beta = 3.38^{+0.08}_{-0.04}$ in the case of $r_{\rm in} = 800\,{\rm km}$. We find that the intrinsic structure of Sgr A* is nearly isotropic over wavelengths from 1.3mm to 1.3cm, with a size that is roughly proportional to wavelength. We discuss implications for models of Sgr A*, for theories of interstellar turbulence, and for imaging Sgr A* with the Event Horizon Telescope., Comment: 26 Pages, 17 Figures, Accepted for publication in ApJ

Physical growth traits can be naturally represented by continuous functions. In a large dataset of infancy growth patterns, we develop a practical approach to infer statistical associations between growth-trajectories and IQ performance in early childhood. The main objective of this study is to show how to assess physical growth curves and detect if particular infancy growth patterns are associated with differences in IQ (Full-scale WASI scores) in later ages using a semi-parametric functional response model. Additionally, we investigate the association between different growth measurements in terms of their cross-correlation with each other, their correlation with later IQ, as well as their time-varying dynamics. This analysis framework can easily incorporate or learn population information in a non-parametric way, rendering the existence of prior population charts partially redundant.

FRB 121102, the only repeating fast radio burst (FRB) known to date, was discovered at 1.4 GHz and shortly after the discovery of its repeating nature, detected up to 2.4 GHz. Here we present three bursts detected with the 100-m Effelsberg radio telescope at 4.85 GHz. All three bursts exhibited frequency structure on broad and narrow frequency scales. Using an autocorrelation function analysis, we measured a characteristic bandwidth of the small-scale structure of 6.4$\pm$1.6 MHz, which is consistent with the diffractive scintillation bandwidth for this line of sight through the Galactic interstellar medium (ISM) predicted by the NE2001 model. These were the only detections in a campaign totaling 22 hours in 10 observing epochs spanning five months. The observed burst detection rate within this observation was inconsistent with a Poisson process with a constant average occurrence rate; three bursts arrived in the final 0.3 hr of a 2 hr observation on 2016 August 20. We therefore observed a change in the rate of detectable bursts during this observation, and we argue that boosting by diffractive interstellar scintillations may have played a role in the detectability. Understanding whether changes in the detection rate of bursts from FRB 121102 observed at other radio frequencies and epochs are also a product of propagation effects, such as scintillation boosting by the Galactic ISM or plasma lensing in the host galaxy, or an intrinsic property of the burst emission will require further observations., Comment: Accepted to ApJ. Minor typos corrected

The grand challenges of contemporary fundamental physics---dark matter, dark energy, vacuum energy, inflation and early universe cosmology, singularities and the hierarchy problem---all involve gravity as a key component. And of all gravitational phenomena, black holes stand out in their elegant simplicity, while harbouring some of the most remarkable predictions of General Relativity: event horizons, singularities and ergoregions. The hitherto invisible landscape of the gravitational Universe is being unveiled before our eyes: the historical direct detection of gravitational waves by the LIGO-Virgo collaboration marks the dawn of a new era of scientific exploration. Gravitational-wave astronomy will allow us to test models of black hole formation, growth and evolution, as well as models of gravitational-wave generation and propagation. It will provide evidence for event horizons and ergoregions, test the theory of General Relativity itself, and may reveal the existence of new fundamental fields. The synthesis of these results has the potential to radically reshape our understanding of the cosmos and of the laws of Nature. The purpose of this work is to present a concise, yet comprehensive overview of the state of the art in the relevant fields of research, summarize important open problems, and lay out a roadmap for future progress., Comment: White Paper for the COST action "Gravitational Waves, Black Holes, and Fundamental Physics", 272 pages, 12 figures; v4: updated references and author list. Overall improvements and corrections. To appear in Classical and Quantum Gravity

The violation of the weak equivalence principle (EP) in the gravitational field of the Earth, described by the E\"otv\"os parameter $\eta_\oplus$, was recently constrained to the level $\left|\eta_\oplus\right| \lesssim 10^{-14}$ by the MICROSCOPE space mission. The E\"otv\"os parameter $\eta_{\rm DM}$, pertaining to the differential couplings of dark matter (DM) and ordinary matter, was only tested to the level $\left| \eta_{\rm DM} \right| \lesssim 10^{-5}$ by the E\"ot-Wash group and lunar laser ranging. This test is limited by the EP-violating driving force in the Solar neighborhood that is determined by the Galactic distribution of DM. Here we propose a novel celestial experiment using the orbital dynamics from radio timing of binary pulsars, and obtain a competing limit on $\eta_{\rm DM}$ from a neutron star (NS) -- white dwarf (WD) system, PSR J1713+0747. The result benefits from the large material difference between the NS and the WD, and the large gravitational binding energy of the NS. If we can discover a binary pulsar within $\sim 10$ parsecs of the Galactic center, where the driving force is much larger in the expected DM spike, precision timing will improve the test of the universality of free fall towards DM and constrain various proposed couplings of DM to the Standard Model by several orders of magnitude. Such a test probes the hypothesis that gravity is the only long-range interaction between DM and ordinary matter., Comment: 5 pages, 2 figures; accepted by PRL

Our Galactic Center, Sagittarius A* (Sgr A*), is believed to harbour a supermassive black hole (BH), as suggested by observations tracking individual orbiting stars. Upcoming sub-millimetre very-long-baseline-interferometry (VLBI) images of Sgr A* carried out by the Event-Horizon-Telescope Collaboration (EHTC) are expected to provide critical evidence for the existence of this supermassive BH. We assess our present ability to use EHTC images to determine if they correspond to a Kerr BH as predicted by Einstein's theory of general relativity (GR) or to a BH in alternative theories of gravity. To this end, we perform general-relativistic magnetohydrodynamical (GRMHD) simulations and use general-relativistic radiative transfer (GRRT) calculations to generate synthetic shadow images of a magnetised accretion flow onto a Kerr BH. In addition, and for the first time, we perform GRMHD simulations and GRRT calculations for a dilaton BH, which we take as a representative solution of an alternative theory of gravity. Adopting the VLBI configuration from the 2017 EHTC campaign, we find that it could be extremely difficult to distinguish between BHs from different theories of gravity, thus highlighting that great caution is needed when interpreting BH images as tests of GR., Comment: Published in Nature Astronomy on 16.04.18 (including supplementary information); simulations at https://blackholecam.org/telling_bhs_apart/

Observational efforts to image the immediate environment of a black hole at the scale of the event horizon benefit from the development of efficient imaging codes that are capable of producing synthetic data, which may be compared with observational data. We aim to present RAPTOR, a new public code that produces accurate images, animations, and spectra of relativistic plasmas in strong gravity by numerically integrating the equations of motion of light rays and performing time-dependent radiative transfer calculations along the rays. The code is compatible with any analytical or numerical spacetime. It is hardware-agnostic and may be compiled and run both on GPUs and CPUs. We describe the algorithms used in RAPTOR and test the code's performance. We have performed a detailed comparison of RAPTOR output with that of other radiative-transfer codes and demonstrate convergence of the results. We then applied RAPTOR to study accretion models of supermassive black holes, performing time-dependent radiative transfer through general relativistic magneto-hydrodynamical (GRMHD) simulations and investigating the expected observational differences between the so-called fast-light and slow-light paradigms. Using RAPTOR to produce synthetic images and light curves of a GRMHD model of an accreting black hole, we find that the relative difference between fast-light and slow-light light curves is less than 5%. Using two distinct radiative-transfer codes to process the same data, we find integrated flux densities with a relative difference less than 0.01%. For two-dimensional GRMHD models, such as those examined in this paper, the fast-light approximation suffices as long as errors of a few percent are acceptable. The convergence of the results of two different codes demonstrates that they are, at a minimum, consistent., Comment: 18 pages, 14 figures, 5 tables

The first gravitational wave detections of mergers between black holes and neutron stars represent a remarkable new regime of high-energy transient astrophysics. The signals observed with LIGO-Virgo detectors come from mergers of extreme physical objects which are the end products of stellar evolution in close binary systems. To better understand their origin and merger rates, we have performed binary population syntheses at different metallicities using the new grid-based binary population synthesis code ComBinE. Starting from newborn pairs of stars, we follow their evolution including mass loss, mass transfer and accretion, common envelopes and supernova explosions. We apply the binding energies of common envelopes based on dense grids of detailed stellar structure models, make use of improved investigations of the subsequent Case BB Roche-lobe overflow and scale supernova kicks according to the stripping of the exploding stars. We demonstrate that all the double black hole mergers, GW150914, LVT151012, GW151226, GW170104, GW170608 and GW170814, as well as the double neutron star merger GW170817, are accounted for in our models in the appropriate metallicity regime. Our binary interaction parameters are calibrated to match the accurately determined properties of Galactic double neutron star systems, and we discuss their masses and types of supernova origin. Using our default values for the input physics parameters, we find a double neutron star merger rate of about 3.0 Myr^-1 for Milky-Way equivalent galaxies. Our upper limit to the merger-rate density of double neutron stars is R=400 yr^-1 Gpc^-3 in the local Universe (z=0)., Comment: 36 pages, 26 figures, 8 tables, plus 9 pages appendix. Accepted 2018 August 6 by MNRAS after revision according to referee report (in particular, including further discussions on the progenitor binary of GW170817)

We apply the algorithm published by Liang et al. (2014) to describe the Double Pulsar system J0737$-$3039 and extract the sense of rotation of first born recycled pulsar PSR J0737$-$3039A. We find that this pulsar is rotating prograde in its orbit. This is the first direct measurement of the sense of rotation of a pulsar with respect to its orbit and a direct confirmation of the rotating lighthouse model for pulsars. This result confirms that the spin angular momentum vector is closely aligned with the orbital angular momentum, suggesting that kick of the supernova producing the second born pulsar J0737$-$3039B was small., Comment: Accepted for publication in ApJ

Polarised radio emission from PSR J1745-2900 has already been used to investigate the strength of the magnetic field in the Galactic Centre, close to Sagittarius A*. Here we report how persistent radio emission from this magnetar, for over four years since its discovery, has revealed large changes in the observed Faraday rotation measure, by up to 3500 rad m$^{-2}$ (a five per cent fractional change). From simultaneous analysis of the dispersion measure, we determine that these fluctuations are dominated by variations in the projected magnetic field, rather than the integrated free electron density, along the changing line of sight to the rapidly moving magnetar. From a structure function analysis of rotation measure variations, and a recent epoch of rapid change of rotation measure, we determine a minimum scale of magnetic fluctuations of size ~ 2 au at the Galactic Centre distance, inferring PSR J1745-2900 is just ~ 0.1 pc behind an additional scattering screen., Comment: 7 pages, 5 figures, submitted to ApJ Letters

Fast radio bursts are a new class of transient radio phenomena currently detected as millisecond radio pulses with very high dispersion measures. As new radio surveys begin searching for FRBs a large population is expected to be detected in real-time, triggering a range of multi-wavelength and multi-messenger telescopes to search for repeating bursts and/or associated emission. Here we propose a method for disseminating FRB triggers using Virtual Observatory Events (VOEvents). This format was developed and is used successfully for transient alerts across the electromagnetic spectrum and for multi-messenger signals such as gravitational waves. In this paper we outline a proposed VOEvent standard for FRBs that includes the essential parameters of the event and where these parameters should be specified within the structure of the event. An additional advantage to the use of VOEvents for FRBs is that the events can automatically be ingested into the FRB Catalogue (FRBCAT) enabling real-time updates for public use. We welcome feedback from the community on the proposed standard outlined below and encourage those interested to join the nascent working group forming around this topic., Comment: 11 pages, 2 figures, parameter definition table in appendix

We present first results from pilot observations using a phased array feed (PAF) mounted on the Parkes 64-m radio telescope. The observations presented here cover a frequency range from 1150 to 1480 MHz and are used to show the ability of PAFs to suppress standing wave problems by a factor of $\sim10$ which afflict normal feeds. We also compare our results with previous HIPASS observations and with previous HI images of the Large Magellanic Cloud. Drift scan observations of the GAMA G23 field resulted in direct HI detections at $z=0.0043$ and $z=0.0055$ of HIPASS galaxies J2242-30 and J2309-30. Our new measurements generally agree with archival data in spectral shape and flux density, with small differences being due to differing beam patterns. We also detect signal in the stacked HI data of 1094 individually undetected galaxies in the GAMA G23 field in the redshift range $0.05 \leq z \leq 0.075$. Finally, we use the low standing wave ripple and wide bandwidth of the PAF to set a $3\sigma$ upper limit to any positronium recombination line emission from the Galactic Centre of $<0.09$ K, corresponding to a recombination rate of $<3.0\times10^{45}\,\mathrm{s}^{-1}$., Comment: 14 pages, 13 figures, accepted for publication by PASA

We present a search for optical bursts from the repeating fast radio burst FRB 121102 using simultaneous observations with the high-speed optical camera ULTRASPEC on the 2.4-m Thai National Telescope and radio observations with the 100-m Effelsberg Radio Telescope. A total of 13 radio bursts were detected, but we found no evidence for corresponding optical bursts in our 70.7-ms frames. The 5-sigma upper limit to the optical flux density during our observations is 0.33 mJy at 767nm. This gives an upper limit for the optical burst fluence of 0.046 Jy ms, which constrains the broadband spectral index of the burst emission to alpha < -0.2. Two of the radio pulses are separated by just 34 ms, which may represent an upper limit on a possible underlying periodicity (a rotation period typical of pulsars), or these pulses may have come from a single emission window that is a small fraction of a possible period., Comment: 8 pages, 4 figures, accepted for publication in MNRAS

We report on the results of a 4-year timing campaign of PSR~J2222$-0137$, a 2.44-day binary pulsar with a massive white dwarf (WD) companion, with the Nan\c{c}ay, Effelsberg and Lovell radio telescopes. Using the Shapiro delay for this system, we find a pulsar mass $m_{p}=1.76,\pm\,0.06,M_\odot$ and a WD mass $m_{c}\,=\,1.293\,\pm\,0.025\, M_\odot$. We also measure the rate of advance of periastron for this system, which is marginally consistent with the GR prediction for these masses. The short lifetime of the massive WD progenitor star led to a rapid X-ray binary phase with little ($< \, 10^{-2} \, M_\odot$) mass accretion onto the neutron star (NS); hence, the current pulsar mass is, within uncertainties, its birth mass; the largest measured to date. We discuss the discrepancy with previous mass measurements for this system; we conclude that the measurements presented here are likely to be more accurate. Finally, we highlight the usefulness of this system for testing alternative theories of gravity by tightly constraining the presence of dipolar radiation. This is of particular importance for certain aspects of strong-field gravity, like spontaneous scalarization, since the mass of PSR~J2222$-0137$ puts that system into a poorly tested parameter range., Comment: 17 pages in journal format, 3 figures, 2 tables, accepted for publication in the Astrophysical Journal. Some references fixed and updated

We measure the effects of interstellar scattering on average pulse profiles from 13 radio pulsars with simple pulse shapes. We use data from the LOFAR High Band Antennas, at frequencies between 110 and 190~MHz. We apply a forward fitting technique, and simultaneously determine the intrinsic pulse shape, assuming single Gaussian component profiles. We find that the constant $\tau$, associated with scattering by a single thin screen, has a power-law dependence on frequency $\tau \propto \nu^{-\alpha}$, with indices ranging from $\alpha = 1.50$ to $4.0$, despite simplest theoretical models predicting $\alpha = 4.0$ or $4.4$. Modelling the screen as an isotropic or extremely anisotropic scatterer, we find anisotropic scattering fits lead to larger power-law indices, often in better agreement with theoretically expected values. We compare the scattering models based on the inferred, frequency dependent parameters of the intrinsic pulse, and the resulting correction to the dispersion measure (DM). We highlight the cases in which fits of extreme anisotropic scattering are appealing, while stressing that the data do not strictly favour either model for any of the 13 pulsars. The pulsars show anomalous scattering properties that are consistent with finite scattering screens and/or anisotropy, but these data alone do not provide the means for an unambiguous characterization of the screens. We revisit the empirical $\tau$ versus DM relation and consider how our results support a frequency dependence of $\alpha$. Very long baseline interferometry, and observations of the scattering and scintillation properties of these sources at higher frequencies, will provide further evidence., Comment: 24 pages, 23 figures, supplementary appendix

Pulsars are natural cosmic clocks. On long timescales they rival the precision of terrestrial atomic clocks. Using a technique called pulsar timing, the exact measurement of pulse arrival times allows a number of applications, ranging from testing theories of gravity to detecting gravitational waves. Also an external reference system suitable for autonomous space navigation can be defined by pulsars, using them as natural navigation beacons, not unlike the use of GPS satellites for navigation on Earth. By comparing pulse arrival times measured on-board a spacecraft with predicted pulse arrivals at a reference location (e.g. the solar system barycenter), the spacecraft position can be determined autonomously and with high accuracy everywhere in the solar system and beyond. We describe the unique properties of pulsars that suggest that such a navigation system will certainly have its application in future astronautics. We also describe the on-going experiments to use the clock-like nature of pulsars to "construct" a galactic-sized gravitational wave detector for low-frequency (f_GW ~1E-9 - 1E-7 Hz) gravitational waves. We present the current status and provide an outlook for the future., Comment: 30 pages, 9 figures. To appear in Vol 63: High Performance Clocks, Springer Space Science Reviews

Pulsar timing and gravitational-wave (GW) detectors are superb laboratories to study gravity theories in the strong-field regime. Here we combine those tools to test the mono-scalar-tensor theory of Damour and Esposito-Far{\`e}se (DEF), which predicts nonperturbative scalarization phenomena for neutron stars (NSs). First, applying Markov-chain Monte Carlo techniques, we use the absence of dipolar radiation in the pulsar-timing observations of five binary systems composed of a NS and a white dwarf, and eleven equations of state (EOSs) for NSs, to derive the most stringent constraints on the two free parameters of the DEF scalar-tensor theory. Since the binary-pulsar bounds depend on the NS mass and the EOS, we find that current pulsar-timing observations leave scalarization windows, i.e., regions of parameter space where scalarization can still be prominent. Then, we investigate if these scalarization windows could be closed and if pulsar-timing constraints could be improved by laser-interferometer GW detectors, when spontaneous (or dynamical) scalarization sets in during the early (or late) stages of a binary NS (BNS) evolution. For the early inspiral of a BNS carrying constant scalar charge, we employ a Fisher matrix analysis to show that Advanced LIGO can improve pulsar-timing constraints for some EOSs, and next-generation detectors, such as the Cosmic Explorer and Einstein Telescope, will be able to improve those bounds for all eleven EOSs. Using the late inspiral of a BNS, we estimate that for some of the EOSs under consideration the onset of dynamical scalarization can happen early enough to improve the constraints on the DEF parameters obtained by combining the five binary pulsars. Thus, in the near future the complementarity of pulsar timing and direct observations of GWs on the ground will be extremely valuable in probing gravity theories in the strong-field regime., Comment: 19 pages, 11 figures; accepted by Physical Review X

We present the black hole accretion code (BHAC), a new multidimensional general-relativistic magnetohydrodynamics module for the MPI-AMRVAC framework. BHAC has been designed to solve the equations of ideal general-relativistic magnetohydrodynamics in arbitrary spacetimes and exploits adaptive mesh refinement techniques with an efficient block-based approach. Several spacetimes have already been implemented and tested. We demonstrate the validity of BHAC by means of various one-, two-, and three-dimensional test problems, as well as through a close comparison with the HARM3D code in the case of a torus accreting onto a black hole. The convergence of a turbulent accretion scenario is investigated with several diagnostics and we find accretion rates and horizon-penetrating fluxes to be convergent to within a few percent when the problem is run in three dimensions. Our analysis also involves the study of the corresponding thermal synchrotron emission, which is performed by means of a new general-relativistic radiative transfer code, BHOSS. The resulting synthetic intensity maps of accretion onto black holes are found to be convergent with increasing resolution and are anticipated to play a crucial role in the interpretation of horizon-scale images resulting from upcoming radio observations of the source at the Galactic Center., Comment: revised version accepted for publication by Computational Astrophysics and Cosmology. Some figures have been down-sampled