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Essays on Gaia Gaia is a satellite mission of the European Space Agency, launched in 2013, and which should be operational until about 2023. It is measuring the distances and motions of more than two billion stars in our Galaxy and beyond. It represents an enormous advance in the understanding of our Universe. As of early 2021, several thousand scientific papers have been written on its findings. In these short 'essays', I have picked out some scientific highlights as they are emerging, or as they caught my attention. They make no attempt at a complete review of a given topic, and many will quickly become superseded by new results. But they offer a snapshot of the exciting discoveries that Gaia is making across all areas of astronomy. ​ Only a few references are included, and these are 'discreetly' hyperlinked for those who want to read more... where references appear in the form (Einstein 1908) or www.gaia.com , clicking on the text (even though not highlighted) should lead to the relevant online article. ​ Click on the "access PDF" icon to access the file, and on the audio file to listen to a short interview with one of the scientists involved. select category published 106. The remarkable cluster Westerlund 1 Resolving the puzzle of its age At a distance of about 4 kpc, the young compact star cluster Westerlund 1 contains many rare, evolved, high-mass stars, including red supergiants, yellow hypergiants, one of the largest known stars, and 24 Wolf-Rayet stars. Gaia is pinpointing its distance and its members, and resolving the puzzling question of its age. 9 January 2023 access PDF Interview 00:00 / 01:04 105. Wolf–Rayet stars Some of the hottest and brightest stars Wolf-Rayet stars are the final He-burning phase in the evolution of massive O stars, the last observable stage before core collapse. They are rare, but have an enormous influence on their environment. Distances were only poorly constrained before Gaia, which is now having a significant impact on their detailed understanding. 2 January 2023 access PDF Interview 00:00 / 01:04 104. Light deflection... by Jupiter Measuring Jupiter's effects on space-time Gravitational light-bending by the Sun during the solar eclipse of 1919, around 1.7 arcsec at the solar limb, was the first observational confirmation of general relativity. Hipparcos measured light bending over the entire celestial sphere. Gaia has now measured light bending due to Jupiter, at around 10 milli-arcsec. 26 December 2022 access PDF Interview 00:00 / 01:04 103. Stellar rotation... for 3 million stars How is Gaia measuring them? The study of stellar rotation has been transformed within the past decade. Twenty years ago, the number of stars with measured rotation periods stood at 11,000. Kepler made a major advance by characterising photometric modulation for some 60,000. With Gaia DR3, more than three million are now known. 19 December 2022 access PDF Interview 00:00 / 01:04 102. The heart of the Milky Way Hints of the earliest structures Compared to recent advances in understanding the details of our Milky Way's halo, the inner Galaxy has proven more elusive, complicated by the large distances involved. Amongst several advances being made with the Gaia data is the identification of the most ancient `proto-Galactic' component of our Galaxy. 12 December 2022 access PDF Interview 00:00 / 01:04 101. The nearest black hole The first black hole discoveries Gaia is enabling the discovery of two important classes of stellar-mass black holes in our Galaxy: isolated black holes, and those in binary systems which lack significant mass transfer. Amongst the latter, recently reported, is the nearest known black hole, at a distance of just 480 pc. 5 December 2022 access PDF Interview 00:00 / 01:04 100. The Fermi paradox Do alien civilisations exist? Following my last three essays, which looked at the historical debate about the existence of life on other worlds, and the search for anomalous stars which may be the first steps along the path for discovering alien civilisations, I look in more details at the Fermi paradox: if such civilisations exist, where are they? 28 November 2022 access PDF Interview 00:00 / 01:04 99. Searching for Dyson spheres Searches for alien civilisations I look at one specific search for alien civilisations which is being assisted by Gaia: the search for so-called Dyson spheres. These are hypothetical megastructures that might encompass a star, capturing a significant fraction of its emitted energy, and satisfying that civilisation's continuously growing energy needs. 21 November 2022 access PDF Interview 00:00 / 01:04 98. Boyajian's star(s) More ideas for SETI searches Amongst Kepler's exoplanet discoveries was the curious KIC 8462852 (Boyajian's star), which displays an unusual lightcurve whose nature is still under debate, even in the context of being an interesting SETI target. I describe a search for other similar stars, and the surprising spatial clustering of some of the new candidates. 14 November 2022 access PDF Interview 00:00 / 01:04 97. Life on other worlds? A historical perspective This week, I will review the philosophical debates that have raged since antiquity on whether ‘populated’ worlds exist beyond our own. While deviating from the topic of Gaia directly, it nonetheless provides an interesting historical background to the search for exoplanets, and life on other worlds, which are being assisted by Gaia. 7 November 2022 access PDF Interview 00:00 / 01:04 96. Is the Earth flat? A message for scientists and educators? Why do some people, in the face of overwhelming evidence to the contrary, cling vigorously to the idea that the Earth is flat? If it is because of the way today's big science is conducted and communicated, the question may hold an important message for scientists and educators. 31 October 2022 access PDF Interview 00:00 / 01:04 95. Our Galaxy's tumbling motion Big movements of our Galaxy's disk I look at two large-scale dynamical phenomena which are, today, believed to affect the bulk motion of our Galaxy's disk with respect to its dark matter halo. The first is a tumbling motion tied to their primordial origin, while the other is related to the orbit of our neighbouring Large Magellanic Cloud. 24 October 2022 access PDF Interview 00:00 / 01:04 94. The mass of the Local Group The sum of all our neighbours I look at the latest estimates of the total mass of our Local Group of galaxies. These take into account increasingly subtle effects related to their detailed dynamics, many being clarified by Gaia. And they must also be consistent with the increasingly detailed predictions of numerical models of the formation and evolution of structure in the Universe. 16 October 2022 access PDF Interview 00:00 / 01:04 93. The mass of the Milky Way Why it's so difficult to measure What is the mass of our Milky Way galaxy? Why is it important to know? Why is it so difficult to measure? And what is Gaia contributing to our knowledge? Here, I take a look at the Gaia-related papers that have been trying to tackle this problem, and see why the Galaxy halo still resists our attempts to fully characterise it. 9 October 2022 access PDF Interview 00:00 / 01:04 92. Diffuse interstellar bands A slowly advancing mystery Diffuse interstellar bands, or DIBs, comprise some 600 known absorption features widely observed in stellar spectra. Known for more than a century, only one has been securely identified. Nearly half a million sources show the 862 nm DIB in their Gaia spectra, providing new insight into interstellar absorption. 2 October 2022 access PDF Interview 00:00 / 01:04 91. Cerium and the Galaxy infall history Its use in Galactic archaeology As one of the developments in Galactic archaeology being enabled by Gaia, I will explain what cerium is, why it is relevant to astronomy, how it is measured by Gaia, and what its occurrence tells us about the formation, and in particular the complex infall history, of our Galaxy. 25 September 2022 access PDF Interview 00:00 / 01:04 90. Astrophysics of our Galaxy Examples of Gaia's astrophysical parameters I continue with the subject of my previous essay, and give some examples of the way in which the derived astrophysical data are providing new insights in understanding the structure, formation, and evolution of huge numbers of stars in our Galaxy. They give just a flavour of what Gaia is providing. 18 September 2022 access PDF Interview 00:00 / 01:04 89. A revolution in stellar astrophysics How the astrophysical parameters are derived The recently published Data Release 3 includes a wealth of `extracted' astrophysical data, of staggering extent, including stellar spectroscopic and evolutionary parameters for up to 470 million sources. A dozen refereed papers detail the underlying computations. Here, I provide a synopsis of the methods, and results. 11 September 2022 access PDF Interview 00:00 / 01:04 88. Pinpointing exoplanets Some other areas where Gaia assists Continuing with the study of exoplanets, I focus here on three areas where Gaia is helping to vet, and to pinpoint, these other worlds: rejecting false positives from transit searches, establishing masses from radial velocity minimum estimates, and identifying accelerating systems for imaging searches. 4 September 2022 access PDF Interview 00:00 / 01:04 87. Radial velocities: results from DR3 First science with RVS Gaia Data Release 3 provides radial velocities for more than 33 million stars down to about 14 mag. Here I look at some of the first scientific results from these radial velocities: their distribution across our Galaxy, their high-velocity star content, and their distribution in the globular cluster 47 Tuc. 28 August 2022 access PDF Interview 00:00 / 01:04 86. Radial velocities: their acquisition How are radial velocities measured Of the 1.8 billion sources in Gaia Data Release 3, more than 33 million have published radial velocities. More than 100 million are expected in DR4. I describe how the radial velocities are acquired on board, how they are processed, and the additional data that is being extracted from the spectra. 21 August 2022 access PDF Interview 00:00 / 01:04 85. Radial velocities: what wavelength? The wavelength choice for radial velocities I look back to the period leading up to the selection of Gaia in 2000, and recall why the decision was made to acquire radial velocity observations on-board the satellite itself. And I recall the various considerations which influenced the choice of spectral range chosen for the Gaia radial velocity spectrometer. 14 August 2022 access PDF Interview 00:00 / 01:04 84. Gaia's microlensing events A new chapter in microlensing Photometric microlensing has been responsible for the many thousands of events that have been discovered to date, including more than 350 exoplanets. Gaia is opening a new chapter in these studies, with its all-sky coverage, and its 3-colour sampling. Data Release 3 has identified 363 such events, 90 of them new. 7 August 2022 access PDF Interview 00:00 / 01:04 83. The Andromeda photometric survey A test region for epoch photometry The Gaia Andromeda Photometry Survey contains 3-colour epoch photometry for a million stars in the region of the Andromeda Galaxy. It was selected, as representative of the sky scanning and range of stellar densities, to provide a test region in advance of the full-sky epoch photometry planned for DR4. 31 July 2022 access PDF Interview 00:00 / 01:04 82. Gaia's galaxy survey First results on Gaia's galaxies Gaia Data Release 3 contains the first treatment of sources considered to be extended. Out of nearly one million galaxies, profile fitting yields robust parameter solutions for more than 900,000 mostly elliptical systems. Out of more than a million known quasars, a host galaxy has been detected around more than 60,000. 24 July 2022 access PDF Interview 00:00 / 01:04 81. Supernova remnants Furthering our knowledge of supernovae Continuing with the theme of neutron stars and pulsars, I look here at some well-known supernova remnants and the search for runaway stars escaping from them. I also look at Gaia's distance to the Crab Pulsar, to Gaia's photometry of its synchrotron-induced spin down, and to a class of stars that... disappear! 17 July 2022 access PDF Interview 00:00 / 01:04 80. Neutron stars and pulsars Invisible objects and advances with Gaia Apart from the Crab, pulsars are not bright enough to be observed by Gaia. But more than 20 binary pulsar companions have been identified in Gaia DR2. Astrometry provides crucial input to models of supernova core collapse and their equation of state, their orbital decay and spin-down rates, and their birth sites. 10 July 2022 access PDF Interview 00:00 / 01:04 79. More insights into non-single stars Insights from non-single stars Gaia DR3 was accompanied by new insights into the nature of non-single stars in the Gaia survey. In Essay 78, I looked at the first results on exoplanet companions discovered by astrometry. Here, I look at some other results on stellar masses, brown dwarf and white dwarf companions, and some of the more exotic variables. 3 July 2022 access PDF Interview 00:00 / 01:04 78. Gaia's first exoplanets The first of thousands? Pre-Gaia DR3, the NASA exoplanet archive tabulated more than 5000 exoplanets, with just one discovered from astrometry. With just over 34 months of data, Gaia DR3 is accompanied by 130,000 astrometric orbit solutions, including 1843 brown dwarf companion candidates, and 72 exoplanet candidates. 26 June 2022 access PDF Interview 00:00 / 01:04 77. The Galactic escape velocity Constraints on the halo mass What is the total mass of our Galaxy? How far out does our Galaxy halo extend? The distribution of stellar velocities, and in particular the ‘escape’ velocity from the solar neighbourhood, holds a number of clues. Estimates from Gaia are converging on a Milky Way mass of about 10^(12) times the mass of our Sun. 19 June 2022 access PDF Interview 00:00 / 01:04 76. Data Release 3 Gaia's latest stunning data release Gaia is now almost seven years into a possible 10-year data collection phase. Today marks the latest data release, Gaia DR3. For the same stretch of time and the same set of observations as EDR3 (Early Data Release 3), DR3 presents a stunning wealth of new data products derived from this first 3 years of mission data. 12 June 2022 access PDF Interview 00:00 / 01:04 75. The local mass density Gaia as a dark matter detector Stars in the Galactic disk 'bounce' slowly up and down around its mid-plane as a result of the force exerted by the matter comprising the disk itself. The detailed stellar motions depend on the total disk mass, both visible and dark matter. The Gaia data are throwing new light on the disk structure and its dark matter content. 5 June 2022 access PDF Interview 00:00 / 01:04 74. Open clusters with Gaia More sites of recent star formation Gaia is revolutionising the study of Galactic open clusters. High-quality distances allow cluster membership to be refined, space motions convey details of their dynamics and dispersion, and its unprecedented multi-epoch multi-colour photometry further contributes to classifying membership and chemistry. 29 May 2022 access PDF Interview 00:00 / 01:04 73. White dwarf pollution and exoplanets Remarkable clues about ancient planets Heavy element pollution in white dwarf atmospheres is attributed to the accretion of rocky planetesimals which have been scattered and torn apart to form a dusty debris disk that can be accreted by the white dwarf. Deep insights into the nature of the associated planetary systems are now being assembled. 22 May 2022 access PDF Interview 00:00 / 01:04 72. The warp of our Galaxy The mystery of its origin continues Various explanations have been proposed for our Galaxy's warped structure, including infall of intergalactic material, a close encounter with a companion galaxy, or misalignment of the disk and its dark matter halo. Gaia is contributing to an improved picture of its structural complexity, but the underlying driving mechanism remains uncertain. 15 May 2022 access PDF Interview 00:00 / 01:04 71. More halo streams from Gaia The origin of the Galaxy's stellar halo Ancient signatures of tidal infall, responsible for our Galaxy's stellar halo, remain evident because orbital time-scales in the outer parts of the Milky Way extend to billions of years. As a result, the halo retains kinematic evidence of the surviving remnants of accretion. A number of these are being found and characterised by Gaia. 8 May 2022 access PDF Interview 00:00 / 01:04 70. The Local Bubble Do supernovae pose an existential threat? Our Sun lies within a low-density region of the interstellar medium known as the local cavity. This is partially filled with hot, low-density gas, about 100 pc in size, and referred to as the Local Bubble. Its detailed morphology can be probed through our knowledge of stellar distances, and these are being transformed by Gaia. 1 May 2022 access PDF Interview 00:00 / 01:04 69. HD 140283: as old as Methuselah? Our Galaxy's oldest stars Today, most astronomers would probably place their bets on the microwave background radiation providing the most secure estimate of the age of the Universe. But there are a number of nearby stars whose estimated ages push at the limits of this inferred upper bound. Accurate distances are crucial to a better understanding. 24 April 2022 access PDF Interview 00:00 / 01:04 68. Gaia photometry Background to the why and how Multi-colour photometry of stars can be carried out from the ground. But there were compelling reasons to make these observations onboard Gaia, at the multiple epochs coinciding with the astrometric measurements. I explain the reasoning, and the challenges involved in the technical implementation. 17 April 2022 access PDF Interview Carme Jordi 00:00 / 01:04 67. Where is Gaia? Choice of the L2 orbit Gaia observes from the Sun-Earth Lagrange point L2, about 1.5 million km from Earth, in the direction away from the Sun. Various interesting properties of the L2 orbit have made it a popular destination for science missions observing deep space. But a special observation programme is need to continuously monitor Gaia's position. 10 April 2022 access PDF Interview Martin Altmann 00:00 / 01:04 66. Exoplanet habitability: TESS and Gaia Advancing the search for life The number of known terrestrial-type planets in the `habitable zone' are increasing, based on transit measurements with the space missions Kepler and TESS. Gaia is fixing their distances, and characterising their properties, allowing the list of potentially habitable planets to be sharpened, and adding key targets to SETI searches. 3 April 2022 access PDF Interview 00:00 / 01:04 65. Hot Jupiters and star clustering New evidence for their formation Amongst exoplanets known today are the perplexing class of `hot Jupiters', gas giants orbiting close to their host star. What brought them to such bizarre orbits? Gaia shows that their existence correlates with ancient star clusters, and with other waves and ripples of star densities in space and space motion in our Galaxy. 27 March 2022 access PDF Interview 00:00 / 01:04 64. Solar system objects in DR2 New insights in dynamics and taxonomy Hipparcos observed around 100,000 stars, but just 48 asteroids. Gaia is expected to determine highly accurate orbits and reflectance spectra for 350,000 solar system objects, permitting profound studies of their dynamics, structure, and taxonomy. Their properties will shed new light on the formation and evolution of our solar system. 21 March 2022 access PDF Interview Paolo Tanga 00:00 / 01:04 63. Catalogue validation How confident should users be? When making the successive Gaia data releases available to the world-wide scientific community, an important question is to what extent the positions, distances, proper motions, photometry, and radial velocities can be ‘trusted’? What sort of independent validation can be made before publication? Many tests are made, and I describe a few. 14 March 2022 access PDF Interview Claus Fabricius 00:00 / 01:04 62. Variability across the HR diagram Which evolutionary states show variability? Variable stars have long been recognised as offering deep insights into stellar structure and evolution. Similarly, the Hertzsprung–Russell diagram provides a quantitative visualisation of all stages of stellar evolution. Together with its empirical analogue, the colour–magnitude diagram, it has enabled many advances in stellar astrophysics. 7 March 2022 access PDF Interview 00:00 / 01:04 61. Discovering variability with Gaia How is Gaia identifying variable stars There are enormous numbers of known variable stars, of dozens of different types. Some variability is 'intrinsic', being due to the luminosity of the star itself changing with time. Others are 'extrinsic', meaning that something affects the stellar light on the way from the star to us. Gaia is, again, transforming the field. 28 February 2022 access PDF Interview Laurent Eyer 00:00 / 01:04 60. Scientific project management Lessons can be passed on! In this short introduction to my own experiences, I will argue that there are skill sets that a scientific leader should possess in order to best optimise the prospects of success, and that there are lessons that can be learned from previous space projects, and indeed from wider sociological studies of how people and teams best work together. 21 February 2022 access PDF Interview 00:00 / 01:04 59. Supernovae with Gaia What they tell about stellar evolution Supernovae are dramatic and violent end-points of stellar evolution, and several thousand should be detected. But the physics of the progenitor star, and the evidence that each supernova leaves behind, are also rich in diagnostics: of neutron stars, black holes, and millisecond pulsars. We look at some of this forensic evidence being discovered by Gaia. 14 February 2022 access PDF Interview 00:00 / 01:04 58. Einstein crosses Rare new lensing discoveries Amongst the 500,000 quasars being observed by Gaia, and the several hundred showing multiple gravitationally lensed images, we take a more detailed look at the curious quadruple-imaged quasars, how they arise, how they are being discovered in the Gaia data, and what they might tell us about black holes, dark matter, and the Hubble constant. 7 February 2022 access PDF Interview 00:00 / 01:04 57. Technology preparation for Gaia Advanced technologies for Gaia Why does ESA fund the development of space science missions? Why do some of these run over budget, and over schedule? And what steps were put in place during the Concept and Technology Study in the 1990s to ensure that the advanced technologies needed for Gaia would be available consistent with its target launch date of 2012? 31 January 2022 access PDF Interview 00:00 / 01:04 Show More

Exoplanets: some contributions What is expected from Gaia? In 2000, and as part of the scientific case for Gaia, I made the first estimates of the number of giant exoplanets that the satellite should discover through the positional 'wobble' of the host star, and putting the number at somewhere between 10,000 - 50,000, depending on details of their orbital distribution. Several refinements of these estimates have been made since. My study in 2014 predicted the number of astrometric discoveries at around 20,000 for a 5-year mission duration, and perhaps up to 70,000 for a 10-year mission. Others have also estimated the additional numbers of discoveries expected from Gaia's photometric data, through the detection of their photometric transits. ​ As of mid-2021, the Gaia satellite has acquired around seven years of data. It may continue to operate until around 2023. It is an enormous number-crunching problem, currently ongoing, to process the vast amounts of data coming from the satellite. Any exoplanet discoveries (including the 'final' discovery numbers) can only be announced towards the very end of the processing chain. If some reasonably secure results will be available by around 2025, it will have been a quarter century between my first experimental predictions, and the actual discoveries. I'm sure it will be worth the wait! The Exoplanet Handbook Soon after the discovery of the first exoplanets in 1995, I looked at whether the reflex motion of the host stars of the first three discoveries was seen in the Hipparcos data (it wasn't). But this research paper led to an invitation to review the embryonic field of exoplanet science, which was published in the journal Reports on Progress in Physics in 2000 . This later developed into my book-length review of the field published by Cambridge University Press in 2011 , with a second edition in 2018 . The 'Perryman Tree' I created this diagram for my review in 2000, and have updated it annually since (as of 1 January). It shows the total number of exoplanets known at the time, sub-divided according to discovery method. ​ This gallery has the latest version, 1 January 2022, and some earlier versions, giving an idea of how the field is developing with time. These gallery images (navigate with > or < button) are all jpg format. A vector pdf of the latest version is available here . Exoplanet discoveries Status as of 1 January 2022 Exoplanet discoveries Status as of 1 January 2021 Exoplanet discoveries Status as of mid-2000 Exoplanet discoveries Status as of 1 January 2022 1/11 Exoplanet Handbook (second edition 2018): Appendixes and Updates The following files are available at the Cambridge University Press www site (under Resources/Appendixes) and included here also. ExoplanetHandbook2-AppendixC-F-end2017.pdf contains the four Appendixes C-F, which together provide a compilation of the exoplanets discovered by the stated method (radial velocity, transits, lensing and imaging respectively), and largely following the content of the NASA Exoplanet Archive as of the end of 2017 (and corresponding to 3572 known exoplanets in total). Other discoveries, notably by timing methods and astrometry, are listed in the relevant chapters of the main text. This version corresponds to the published edition, viz. listing the known planets as of the end of 2017, and the main bibliography (according to the literature survey by the author) also as of the end of 2017. In order to maintain full congruence with the published edition, the References included in this pdf version correspond to the complete bibliography for the published edition (and not only to the content of the Appendixes). Since this version has been superseded, it will be of little or no interest to most users. ExoplanetHandbook2-AppendixC-F-end2018.pdf contains the four Appendixes C-F, with system and planet content updated to the end of 2018 (according to the NASA Exoplanet Archive, and corresponding to 3869 known exoplanets in total). The bibliography has been correspondingly updated for all systems. Since this version has been superseded, it will be of little or no interest to most users. ExoplanetHandbook2-AppendixC-F-end2019.pdf contains the four Appendixes C-F, with system and planet content updated to the end of 2019 (according to the NASA Exoplanet Archive, and corresponding to 4104 known exoplanets in total). The bibliography has been correspondingly updated for all systems. Exoplanets included: Content corresponds essentially to that of the NASA Exoplanet Archive at the given dates. Some additional systems of note are also included. Primary identifiers correspond to those given in the NASA Exoplanet Archive. Bibliography included: The bibliography provides a concise overview and narrative of the currently perceived importance and scientific developments associated with each system. Ordering is by year, and then by first author. Bibliographic entries are a result of my own literature survey, and claim no completeness: the CDS SIMBAD facility can be consulted for a more extensive bibliography for each system. For the version updated to the end of 2018, and because of the many new references included, the reference keys are not (necessarily) congruent with those given in the published Second Edition. Hyperlinks: These pdf versions are extensively hyperlinked as follows: * host star names (bold) are hyperlinked to the relevant NASA Exoplanet Archive 'Planet Host Overview' page * citations are hyperlinked to the relevant page of the References * each small triangular symbol following the citation is hyperlinked to the associated SAO/NASA ADS Abstract page

Essays on recreational mathematics Young men should prove theorems, old men should write books. G.H. Hardy At King Edward VII school, King's Lynn, in the early 1970s, I had the benefit of an inspiring maths teacher, Harry Thornton. The half a dozen of us with similar interests met after school in Harry's back room, where he would introduce this 'Maths Club' to a variety of mathematical problems, puzzles and games. Many were picked from the monthly column in Scientific American, written at the time by Martin Gardner, who inspired an interest in recreational mathematics in so many people over many years. ​ I went on to study mathematics and theoretical physics at Cambridge University in the mid-1970s. My PhD in radio astronomy at the Cavendish Laboratory, Cambridge, in 1980, focused on the cosmological evolution of radio sources. Shortly afterwards, as a research fellow with the European Space Agency, it was the mathematical elegance underpinning the principles of space astrometry that led to my interest in the Hipparcos mission. Returning to my curiosity in mathematics, this project started in 2018 as an informal input for a local school. Later, throughout 2020, I wrote these short weekly 'essays' on just a few of the more recreational topics that have interested or entertained me over the years. In this more structured form, I hope they may be of interest to others exploring the endlessly fascinating and beautiful world of mathematics, and that they might inspire a few young minds in the process. And I dedicate this small collection of 52 essays to the memory of Harry Thornton. 4 1. The Basel problem The 'Basel problem' was to find an exact sum for the series in which each term is the square of the corresponding term in the harmonic series. It was famously tackled by Jakob Bernoulli, professor of mathematics at Basel University in the 17th century. The answer connects pi, prime numbers, and the Euler product. 6 January 2020 access PDF For the more mathematical 2. Magic squares A magic square is an n x n square grid, filled with positive whole numbers in sequence. The sums of the integers in each row, column and diagonal are identical. This sum is referred to as the 'magic constant', or magic sum. Magic squares have many curious properties, and similar concepts also exist in more than two dimensions. 13 January 2020 access PDF Why do they exist? 3. Möbius bands and topology There is perhaps no better illustration of the seemingly abstract mathematical field of topology than the Möbius band. Take a strip of paper, and join the ends together. What would happen if you were to pierce the middle of the band with scissors, and cut around its full length? Things get more puzzling if you give the band a twist first! 20 January 2020 access PDF Fun with paper and scissors 4. Nim Games which contain a strong element of mathematics, and in which probability or chance playing a greater or lesser role, abound. These range from the trivial, such as noughts-and-crosses, to games of almost infinite complexity such as chess. Nim is one of the oldest, and one of the simplest to play whilst still being engaging. 27 January 2020 access PDF Use mathematics to win! 5. Prime numbers Carl Friedrich Gauss stated that "The problem of distinguishing prime numbers from composite numbers and of resolving the latter into their prime factors is known to be one of the most important and useful in arithmetic". Two hundred years later, prime numbers remain as mysterious and perplexing as ever. 3 February 2020 access PDF A most mysterious class 6. How many primes How many prime numbers are there less than any given number, N? This apparently straightforward question is of great importance in mathematics. Is there some law, or some expression, which predicts the number of prime numbers up to a given value? Searches for this 'law' leads to some remarkable results. 10 February 2020 access PDF For the more mathematical 7. Almost integers An 'almost integer' is, as its name suggests, a number that is not an integer, but is almost an integer. Almost integers are considered to be interesting when they arise in an unexpected context. So far, you may be thinking, this is not very interesting... But these two pages contain some beautiful results, and will convince you otherwise! 17 February 2020 access PDF For the more mathematical 8. Constrained writing Letter frequency analysis has been used for centuries to break simple cryptograms and ciphers, and became important in the 15th century with the development of movable typeface. It is a small step from here to enter the field of constrained writing, a literary technique in which a text follows some sort of algorithmic rule, usually lexical in nature. 24 February 2020 access PDF Playing with letters and words 9. Integer sequences A sequence is an ordered list of numbers whose terms can be described in some well-defined way. Well-known examples abound, including powers of two, the prime numbers, the Fibonacci sequence, and many others. Indeed, as of 2020, the Online Encyclopaedia of Integer Sequences includes more than 300,000 of them. 2 March 2020 access PDF For those that like order 10. Pierre de Fermat Pierre de Fermat, 1607-1665, was a trained lawyer at the Parlement de Toulouse in France, for whom mathematics was more of a hobby than a profession. He is best known for his principle of light propagation (that light travels between two given points along the path of shortest time), and for the celebrated Fermat's Last Theorem in number theory. 9 March 2020 access PDF The life of a mathematician 11. The number pi The most common and widely known definition of pi is as the ratio of the circumference of a circle to its diameter, independent of the circle's size. This simple definition of pi gives little clue as to its appearance as one of the most important, ubiquitous and surprising numbers in all of mathematics. 16 March 2020 access PDF A very important number 12. Calculating pi There are two main challenges in calculating the digits of pi to ever-increasing accuracy. One is formulating a defining series which converges rapidly. The other is in the computational power, storage, and organisation required to perform the calculations. But these efforts also have numerous practical benefits. 23 March 2020 access PDF More useful than you might think 13. Memorising numbers Individuals who can recall large quantities of information seem to possess superior memories. And while some people display this even in the apparent absence of an encoding strategy, evidence suggests that a key component of a superior memory is the development of mnemonic skills. 29 March 2020 access PDF Impress your friends 4

Talks Future talks: 13 Nov 2023 Shaw Prize Laureate Forum, Hong Kong: The origin and evolution of our Milky Way Galaxy 07 Dec 2023 Nanjing University: Advances in understanding our Galaxy through space astrometry 19 Apr 2024 Swindon Star Gazers : Gaia: Advances in our Understanding of the Galaxy Recent talks: 06 Jul 2023 18th Patras Workshop on Axions, WIMPs, and WISPs: Latest insights on cosmology from Gaia 04 Jul 2023 Heidelberg Joint Astronomy Colloquium: Advances in astrometry: from Hipparchus to Gaia 13 Jun 2023 Warsaw University: Measuring star positions from space: Hipparcos and Gaia 12 Jun 2023 Toruń University: Measuring star positions from space: Hipparcos and Gaia 25 May 2023 University College Dublin: Measuring star positions: giant strides in understanding the Universe 20 Feb 2023 Copernican Congress, Toruń: Is the Earth flat? 04 Feb 2023 Eastbourne Astronomical Society: Latest results from Gaia 04 Feb 2023 Astrofest, London: Gaia: Mapping our Galaxy from space 02 Dec 2022 Bath Royal Literary and Scientific Society, BRLSI: The Fermi Paradox 01 Oct 2022 Herschel Society: A Celebration of William Herschel: Giant Strides from Herschel to Gaia 04 Aug 2022 JPL, Pasadena : Gaia: Advances in Our Understanding of the Galaxy 25 July 2022 Sagan Summer Workshop, Caltech : Exoplanet Science in the Gaia Era

Gaia: science essays NEW I have added a "subscribe" page. Enter your email, and you will receive an email (usually Monday morning) when each new essay is published Read more In these short weekly 'essays', I have picked out some of the scientific highlights of the Gaia mission as they are emerging, or as they caught my attention. They are not necessarily the most important. They do not follow any specific sequence. They are not a complete review of a given topic. Many will be quickly superseded by new results. But they offer a snapshot of some of the discoveries that Gaia is making across all of astronomy. I've also included some essays on related topics, including the history of astrometry, and some more technical, managerial, or developmental aspects of both the Hipparcos and Gaia missions. In each, I have included a footnote DR1, DR2, EDR3, DR3, etc to indicate which of the (latest) data releases the essay refers to (described in essays #10 and #76), with DR0 signifying technical or historical material not connected with any specific data release. Who are they written for? Anyone who might have a general interest in science and astronomy, including amateur astronomers, young scientists starting out on their careers, mid-career scientists looking in on Gaia for the first time to get a feeling of what is possible, and even specialists looking in from different areas of astronomy, or physics more generally. My thanks go to many people: to all those I worked with on the Hipparcos and Gaia projects over almost 30 years, to those now dedicating huge reserves of their time, energy, and skill to the ongoing data processing, and to those who have entered into the Gaia catalogue and published the results described here. Click on the access PDF icon to access the file. Only a few references are included, and these are 'discreetly' hyperlinked for those who want to read more... where references appear in the form (Einstein 1908) or www.gaia.com, clicking on the text (even though generally not highlighted!) should lead to the relevant online article. In a few cases, I've recorded an interview on the subject (see science interview page). The compilation of all 52 essays from 2021 (143 pp) is available here The compilation of all 52 essays from 2022 (111 pp) is available here All essays (or select category) 16 153. The solar motion New approaches to measuring this fundamental quantity Gaia represents a major advance in understanding our Galaxy's disk and halo kinematics. Here, I will look at the specific problem of determining the 'solar motion'. I explain what it is, why it is important, and how it is determined. As well as the more classical approach, methods are being developed to measure all three components with respect to the halo. 4 December 2023 access PDF 152. M dwarfs and the Jao gap Subtle but important clues in the HR diagram In essay 42, I described some new features in the Hertzsprung-Russell diagram, including a narrow gap in the M dwarf sequence, first reported in the DR2 data. Here I look at further details of this interesting feature. As Baraffe & Chabrier wrote in 2018: "Just a small gap in a colour-magnitude diagram could provide a deep insight into the interior structure of low-mass stars." 27 November 2023 access PDF 151. The Hyades main sequence How Gaia is tightening our knowledge of the Hyades main sequence The Hyades is the nearest open cluster. Even so, distance uncertainties have limited the definition of its main sequence, and hence its ability to constrain evolutionary models. It has nevertheless been used as the basic observational material for various fundamental relationships in astrophysics. Gaia DR3 astrometry and photometry is transforming its understanding. 20 November 2023 access PDF 150. Convection - and the mixing length How Gaia is contributing to the understanding of convection inside stars Convection represents one of the dominant sources of uncertainty in current stellar evolutionary models, propagating through to substantial uncertainties in ages and, in turn, understanding of the chemical evolution of the Galaxy. I outline the `mixing length theory' of convection, and Gaia's contribution to characterising the associated `mixing length parameter'. 13 November 2023 access PDF 149. Gravito-inertial asteroseismology Gaia compares favourably with Kepler I look at some other recent results on the non-radial pulsators in the SPB and Gamma Dor classes. These stars show periodic variations as a result of the usual restoring force of gravity (or buoyancy), as well as due to Coriolis forces resulting from stellar rotation. Many astrophysical results from Gaia compare favourably with the much denser sampling from Kepler. 6 November 2023 access PDF 148. Non-radial pulsators More than 10,000 SPB and Gamma Dor pulsators I have discussed Gaia variables in several essays, focusing on Cepheids (43), on RR~Lyrae (45), their detection and classification (61), their distribution across the Hertzsprung--Russell diagram (62), and in the context of citizen science (132). Here I look at some new insights into the non-radial g-mode pulsators in the SPB and Gamma Dor class. 30 October 2023 access PDF 147. Videos and visualisations: part 2 Some of the latest video animations for Gaia In essay 54, in January 2022, I gave links to some of the videos, animations, visualisations, and `fly-throughs' made to illustrate the science that Gaia is addressing. DR3 was released in June 2022, and many new explanatory videos have been made since. This is an introduction to some of the many video animations and illustrations that now exist. 23 October 2023 access PDF 146. Benford's law - and astrometry A curious mathematical property A curious property of many collections of numbers, including naturally occurring data, is that the leading digits are not uniformly distributed, but are skewed toward smaller values. As Benford's law, it has been considered in many contexts, including identifying suspicious accounting. I consider it here in the context of the Gaia DR2 parallaxes. 16 October 2023 access PDF 145. Spectroscopic binaries New insights in orbit circularisation Included in the DR3 data release are some 180,000 single-lined spectroscopic binaries, a colossal increase in numbers enabling the study of many aspects of short-period binaries. I look here at some new insights into orbit circularisation, where the Gaia data point to the process operating most efficiently in the pre-main sequence evolutionary phase. 9 October 2023 access PDF 144. How many open clusters? An explosion of new discoveries with Gaia Gaia is transforming the study of open clusters. Pre-2016, some 3000 clusters had been identified. But Gaia has shown that more than half of these are unreal, being simply asterisms. In their place, from nearly 25,000 new discoveries reported with Gaia (some duplicated), there are today nearly 14,000 unique clusters known in our Galaxy. 2 October 2023 access PDF 16

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Gaia/Hipparcos: project interviews Hipparcos is the first time since Sputnik in 1957 that a major new development in space science has come from outside the United States. ​ Freeman Dyson (Infinite in All Directions, 1988) Starting in 2021, I have been recording interviews with some of the people that played a part in shaping the developments of space astrometry. ​ These include some of the engineers and managers from the European Space Agency and its industrial teams involved in the Hipparcos and Gaia projects, some of the leading scientists, and just a few of the individuals at the forefront of ground-based astrometry in the years leading up to the move to space. Several others are planned. Amongst these, it is interesting to hear that two senior people, with key roles in the development of Gaia, both initially considered that the measurement goals targeted by the mission were not achievable! My thanks to all those who have taken part, and to Moby for the use of his unreleased track Morning Span in their introduction (https://mobygratis.com ). The order below follows the date of the interview. Enjoy! 3 PPM, Hipparcos-Tycho, and Gaia Ulrich Bastian (Haardt, Palatinate, Germany, 1951) started his long career in astrometry with his involvement in the ground-based activities of the Astronomisches Rechen-Institut (ARI, Heidelberg) in the early 1980s. He made leading contributions to the Hipparcos-Tycho project in the 1980s and 1990s and, since the earliest days of the Gaia mission 30 years ago, has played a central role in a number of critical activities, which continue to this day. We look back over this period of major advances in astrometry. Ulrich Bastian 2 Nov 2023 Interview: 00:00 / 1:05:14 Gaia: industrial system engineering: part 2 Frédéric Faye (Dijon, 1963) joins me for a second time. In an earlier conversation we talked about the earliest phases of the Gaia project in industry, 10 years or so before launch, and looked at the complexities that were lying ahead when he took over responsibility for the systems engineering in 2005. In this second part, Frédéric describes the organisation of his system engineering group, and some of the management and organisational challenges that his team had to deal with. Frédéric Faye 12 Jul 2023 Interview: 00:00 / 48:40 Gaia: industrial system engineering: part 1 Frédéric Faye (Dijon, 1963) was the System Engineering Manager for the Gaia satellite. Within the industrial prime contractor team, Airbus Defence & Space, he was in charge of the satellite design, integration and verification, from 2005, all the way through to the in-orbit commissioning review that took place a few months after the successful spacecraft insertion around L2 in 2014. Today, we're talking about his central role in the design, manufacture, assembly, testing, and launch of Gaia. Frédéric Faye 12 Jul 2023 Interview: 00:00 / 1:00:42 The Hipparcos mission Lennart Lindegren (Svalöv, Sweden, 1950) joins me for a second time. In an earlier conversation we talked about the period leading up to the adoption of Hipparcos in 1980. Today (as in my second conversation with Erik Høg), we discuss the Hipparcos mission, from its acceptance in 1980 to its completion in 1997. We talk about his role in the mission development, and in the preparation for - and the analysis of - the data sent down from the satellite. We also talk about his memories of the satellite launch in 1989, and of finalising the Hipparcos Catalogue. Lennart Lindegren 13 Oct 2022 Interview: 00:00 / 1:01:15 Validation of the Gaia catalogue data releases In the second of our two-part interview, Claus Fabricius talks about his activities after Hipparcos. With astrometry no longer supported financially in Denmark, Claus moved to the University of Barcelona in 2005, joining the active Gaia team there to work on the initial data treatment and on the photometry. Later, he took over responsibility for the validation of the successive versions of the Gaia Data Releases, and here he talks about the many tests that are made, pre-publication, on the astrometric and photometric results. Claus Fabricius 5 Sept 2022 Interview: 00:00 / 28:54 Astrometry in Copenhagen pre-Hipparcos Claus Fabricius (Copenhagen, 1954) spent the first part of his career at the Copenhagen University Observatory in Denmark, where he worked on one of the main instruments contributing to ground-based astrometry in the years preceding Hipparcos. In the first of this two-part interview, Claus talks about his involvement in the development and operation of the Brorfelde transit circle, later as the Carlsberg Automatic Meridian Circle in La Palma, and in the creation of the Tycho Catalogue and its associated initiatives. Claus Fabricius 5 Sept 2022 Interview: 00:00 / 54:25 Gaia satellite operations: part 1 David Milligan (Blackpool, UK, 1971) joined ESA, at its operations centre, ESOC in Germany, in 2000. There, from 2008 to the end of 2020, he was the Spacecraft Operations Manager for Gaia, the leader of the team responsible for its operation, health, and safety. In the first of this two-part interview, David talks about the preparations for the satellite operations in the years leading up to launch, and the major tasks involved in sending it on its way to its intended L2 orbit, 1.5 million km from Earth. David Milligan 7 Jul 2022 Interview: 00:00 / 46:06 Gaia satellite operations: part 2 In the second of our two-part interview, David Milligan, Spacecraft Operations Manager for Gaia, describes the challenges involved in the spacecraft commissioning, including the problems of 'icing' and 'straylight'. And he talks about keeping the satellite operational and optimised over almost a decade, including optimisation to allow the downlink of significantly more data, and the various tiny effects that can be detected, including bubbles in the propulsion system, micro-meteorites, and the effects of sunspots. David Milligan 7 Jul 2022 Interview: 00:00 / 56:52 The design of the Gaia photometric system Carme Jordi (Barcelona, 1958) is a senior research scientist at the University of Barcelona. She played a key part in designing the photometric measurements that could - and should - be made with Gaia, and played a key role in the preparation for the photometric data analysis. We talk about the scientific rationale for making photometric observations from the satellite itself, the considerations underlying the design of the photometric system, and how the photometric measurements compare with the original plans. Carme Jordi 8 Jun 2022 Interview: 00:00 / 58:21 Gaia... and beyond Erik Høg (Lolland, Denmark, 1932) joins me for a third time. In our first conversation we talked about his early involvement in ground-based astrometry, and his part in getting Hipparcos optimised and adopted by ESA in the 1970s–1980s. In the second, we talked about his involvement in Hipparcos, from its acceptance in 1980 to completion in 1997, including his ideas for the Tycho experiment. Today, we talk about his contributions to Gaia [recorded 9 February]. Erik's transcripts are at https://arxiv.org/abs/2208.09332 Erik Høg 2 Jun 2022 Interview: 00:00 / 51:31 3

Gaia is a satellite mission of the European Space Agency, launched in 2013. It is operating today (mid-2022), and it should remain operational until about 2024–25. Because of the enormous amount of data processing involved, improved catalogues will continue to be released well after the end of satellite operations, probably until around 2030. Gaia's goal is to measure the distances and motions of more than two billion stars in our Galaxy and beyond, all with unprecedented accuracy, barely imaginable even 25 years ago. These observations are enabling an enormous advance in our understanding of the Universe. As of mid-2022, several thousand scientific papers have been written on its findings. The ESA Gaia www pages include many topical news highlights. ​ Gaia builds on the success of ESA's pioneering Hipparcos mission, which was operated in orbit between 1989–1993. The Hipparcos Catalogue of nearly 120,000 star positions, distances, and space motions was published in 1997.

Michael Perryman Some contributions related to star positions, exoplanets, and recreational mathematics My career has been as a scientist with the European Space Agency, leading the development of astrometry (the measurement of accurate star positions) from space. I was Project Scientist for the pioneering Hipparcos space astrometry mission, from its adoption by ESA in 1980 to its completion and catalogue publication in 1997, including overall responsibility for the project after launch. As one of the co-originators of the Gaia mission in 1993, I was the mission's study scientist until its acceptance by ESA in 2000, and subsequently its Project Scientist until my retirement from ESA in 2008. ​ ​ Today, I am taking great pleasure in seeing the spectacular progress of the Gaia mission as it unfolds, and reading about its remarkable scientific results. Starting in 2021, I have been writing these summaries of some of the advances in astronomy flowing from it. They are a look back at what this long journey of space astrometry has achieved, and written in a form that I hope will be reasonably accessible to those not so deeply involved. And I have been interviewing some of the scientists and project leaders involved in these two space missions... ​ Since 2013 I have held a position as adjunct professor in the School of Physics, University College Dublin ( UCD-hosted CV). A more recent CV is also included here . Most recent essays (weekly) [see the Gaia essays page for the article link]: 04 Dec 2023 Gaia e ssay 153. The solar motion 27 Nov 2023 Gaia e ssay 152. M dwarfs and the Jao gap 20 Nov 2023 Gaia e ssay 151. The Hyades main sequence 13 Nov 2023 Gaia e ssay 150. Convection - and the mixing length Most recent interviews (irregular) [see the project/science interview pages for the audio link]: 02 Nov 2023 Ulrich Bastian talks about "PPM, Hipparcos-Tycho, and Gaia" 12 Jul 2023 Frédéric Faye talks about "Gaia: industrial system engineering" [in two parts] 13 Oct 2022 Lennart Lindegren talks about "The Hipparcos mission" 05 Sep 2022 Claus Fabricius talks about pre-Hipparcos astrometry, and Gaia validation [in two parts]