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As the evidence in favor of dark matter in galaxies and galaxy clusters accumulated, more and more astronomers began to contemplate what might make up this faint material. To many astronomers and astrophysicists, the most obvious possibility was that this missing mass might consist of compact objects that were much less luminous than – but otherwise qualitatively similar to – ordinary stars. Possibilities for such objects included planets, brown dwarfs, red dwarfs, white dwarfs, neutron stars, and black holes. Kim Griest would later coin the term “MACHOs” – short for massive astrophysical compact halo objects – to denote this class of dark matter candidates, in response to the leading alternative of weakly interacting massive particles, “WIMPs”.

Although there is a consensus today that MACHOs do not constitute a large fraction of the dark matter, opinions differ as to which lines of evidence played the most important role in reaching that conclusion (for an example of some of the very early arguments that had been made against MACHOs as dark matter, see Ref. [152]). That being said, two lines of investigation would ultimately prove to be particularly important in resolving this question: searches for MACHOs using gravitational microlensing surveys, and determinations of the cosmic baryon density based on measurements of the primordial light element abundances and of the cosmic microwave background.

A. Gravitational Microlensing

The possibility that light could be deflected by gravity has a long history, extending back as far as Newton. In 1915, Einstein made the correct prediction for this phenomena using the framework of general relativity (which predicts twice the degree of deflection as Newtonian gravity). An early test of general relativity was famously conducted during the solar eclipse of 1919, which provided an opportunity to measure the bending of light around the Sun. Although the measurements obtained by Arthur Eddington favored the relativistic prediction, other simultaneous observations appeared to agree with the Newtonian expectation. Despite this apparent ambiguity, Eddington's results were seen as persuasive by many astronomers, and served to elevate the status of Einstein's theory.

In 1924, the Russian physicist Orest Chwolson returned to the topic of gravitational lensing, pointing out that a massive body could deflect the light from a more distant source in such a way that would lead to the appearance of multiple images, or of a ring [80]. In 1936, Einstein himself published a paper on this topic [111], but concluded that due to the very precise alignment required, “there is no great chance of observing this phenomenon”.

The modern theory of gravitational lensing was developed in the 1960s, with contributions from Yu Klimov [180, 181, 182], Sidney Liebes [195], and Sjur Refsdal [256, 255], followed by the first observation of a lensed quasar by Dennis Walsh, Robert Carswell and Ray Weyman in 1979 [324]. In the same year, Kyongae Chang and Sjur Refsdal showed that individual stars could also act as lenses, leading to potentially observable variations over timescales of months [78]. In 1986, Bohdan Paczynski proposed that this phenomena of gravitational microlensing could be used to search for compact objects in the “dark halo” of the Milky Way [230], followed in 1987 by more detailed predictions for the probability and light curves of such events, described in the Ph.D. thesis of Robert Nemiroff [223] 12.

The strategy proposed by these authors was to simultaneously monitor large numbers of stars in a nearby galaxy (such as in the Large Magellanic Cloud), in an effort to detect variations in their brightness. If the halo consisted entirely of MACHOs, approximately one out of 2 million stars should be magnified at a given time, a ratio known as the microlensing optical depth. Furthermore, as the duration of a microlensing event is predicted to be t ∼ 130 days × (M / M)0.5, such a program would be best suited to detect objects with masses in the range of ∼ 10−7 M to ∼ 102 M, corresponding to variations over timescales of hours to a year. These factors motivated the approaches taken by the MACHO, EROS (Experience pour la Recherche d'Objets Sombres), and OGLE (Optical Gravitational Lensing Experiment) Collaborations, who each set out to conduct large microlensing surveys in order to test the hypothesis that the Milky Way's dark halo consisted of MACHOs.

Although the first claim of a microlensing event was reported in 1989, by Mike Irwin and collaborators [167], the implications of microlensing surveys for dark matter only began to take shape a few years later with the first results of the MACHO Collaboration. The MACHO Collaboration was a group of mostly American astronomers making use of the 1.27-meter telescope at the Mount Stromlo Observatory in Australia to simultaneously monitor millions of stars in the Large Magenellic Cloud. In October of 1993, they reported the detection of their first microlensing event, consistent with a 0.03 to 0.5 M MACHO [20]. In the same month, the EROS Collaboration reported the detection of two such events, favoring a similar range of masses [30]. At the time, the rate of these events appeared to be consistent with that anticipated from a halo that was dominated by MACHOs. Kim Griest (a member of the MACHO Collaboration) recalled in 2000:

After the discovery of MACHOs in 1993, some thought that the dark matter puzzle had been solved.

But alas, it was not to be.

Over a period of 5.7 years, the MACHO Collaboration measured the light curves of 40 million individual stars, identifying between 14 and 17 candidate microlensing events. This was well above their expected background rate, and lead them to conclude that between 8% and 50% of the Milky Way's halo mass consisted of compact objects, most of which had masses in the range of 0.15 to 0.9 M [21]. After collecting data for 6.7 years, however, the EROS Collaboration had identified only one microlensing candidate event, allowing them to place an upper limit of 8% on the halo mass fraction in MACHOs [193, 309]. Compact objects, at least within the mass range probed by microlensing surveys, do not appear to dominate the missing mass in the Milky Way's halo.

B. The Universe's Baryon Budget

Throughout much of the mid-twentieth century, the origin of the various nuclear species remained a subject of considerable mystery and speculation. As early as 1920, Arthur Eddington and others argued that the fusion of hydrogen into helium nuclei could be capable of providing the primary source of energy in stars, and suggested that it might also be possible to generate heavier elements in stellar interiors [104, 105]. In 1939, Hans Bethe expanded significantly upon this idea, describing the processes of the proton-proton chain and the carbon-nitrogen-oxygen cycle that are now understood to dominate the energy production in main sequence stars [52]. Fred Hoyle, in papers in 1946 and 1954, calculated that nuclei as heavy as iron could be synthesized in massive stars [160], and that even heavier nuclear species could be produced by supernovae [161].

An alternative to stellar nucleosynthesis was proposed in 1946 by George Gamow [131], and followed up upon two years later in a paper by Gamow and Hermann Alpher [22]. The author list of this later paper also famously included Hans Bethe (who reportedly did not contribute to the research) in order to facilitate the pun that enabled it to become known as the “alpha-beta-gamma” paper. In this pair of papers, it was proposed that all nuclear species (both light and heavy) may have been produced in the early Universe through the process of neutron capture. While of historic significance, there were considerable technical problems with the calculations presented in these early papers, some of which were pointed out by Enrico Fermi, Chushiro Hayaski, and Anthony Turkevich in the years to follow. Among other flaws, Alpher and Gamow did not correctly account for Coulomb barriers in estimating the rates for nuclear fusion. Perhaps more importantly, they did not appreciate that the lack of stable nuclei with atomic numbers in the range of 5-8 would effectively prevent any significant nucleosynthesis from occurring beyond 4He. After accounting for these issues, Alpher, along with Robert Herman and James Follin, correctly predicted the abundance of helium produced in the early Universe, and reported in 1953 that the heavier elements could not be accounted for by this mechanism [23]. For these and other reasons, stellar nucleosynthesis remained the predominant theory throughout the 1950s and into the 1960s. That being said, by the late 1950s, it was becoming increasingly clear that stellar nucleosynthesis could not generate enough helium to accommodate the observed abundance, as summarized in the classic 1957 review paper by Margaret Burbidge, Geoffrey Burbidge, William Fowler, and Fred Hoyle [66].

The discovery of the cosmic microwave background in 1965 lead to increased interest in Big Bang nucleosynthesis, and made it possible to further refine the predictions for the light element abundances. In particular, the temperature of this newly detected background favored a primordial helium fraction in the range of 26-28% [236, 323], consistent with observations. In 1973, a paper by Hubert Reeves, Jean Audouze, William Fowler and David Schramm focused on the production of deuterium in the early Universe [254]. As deuterium had been detected in the interstellar medium, but is not generated in stars, these authors argued that Big Bang nucleosynthesis offered the most plausible origin for the observed deuterium. In the same paper, the authors also used the measured light element abundances to derive an upper limit on the cosmological baryon density that was about one tenth of the critical density, Ωb ≲ 0.1 Ωcrit.

Constraints on the cosmological baryon density became increasingly stringent over the decades to follow. Of particular importance were the first high-precision measurements of the primordial deuterium abundance, which were carried out in the late 1990s by Scott Burles, David Tytler, and others [70, 69, 225]. These measurements were used to determine the baryonic abundance with roughly 10% precision, Ωb h2 = 0.020 ± 0.002 (95% CL) [68]; leaving little room for baryonic MACHOs [129]. At around the same time, measurements of the angular power spectrum of the cosmic microwave background were also becoming sensitive to this quantity. In particular, the ratio of the heights of the odd and even peaks in this power spectrum is primarily set by the baryonic density. Although limited measurements of the second peak were made by ground- and balloon-based experiments in the late 1990s, it was not until the satellite-based WMAP experiment that these determinations became competitive with (and superior to) those based on the measured light element abundances. WMAP ultimately achieved a measurement of Ωb h2 = 0.02264 ± 0.00050 (68% CL) [154], while the most recent analysis from the Planck Collaboration arrives at a constraint of Ωb h2 = 0.02225 ± 0.00016, corresponding to a fractional uncertainty of less than one percent [245]. When this is compared to the total matter density as inferred by these and other experiments, one is forced to the conclusion that less than 20% of the matter in the Universe is baryonic.

C. Primordial Black Holes

By the late 1990s, it had become clear that baryonic dark matter does not constitute a large fraction of the Universe's dark matter. Although these results seem to imply that the dark matter must consist of one or more new particle species, there remains a caveat to this conclusion: the dark matter might instead consist of black holes that formed before the epoch of Big Bang nucleosynthesis and with masses below the sensitivity range of microlensing surveys.

The possibility that black holes may have formed in the early Universe was discussed by Barnard Carr and Stephen Hawking as early as 1974 [74]. Such primordial black holes exhibit a characteristic mass that is on the order of the mass contained within the horizon at the time of formation, Mhorizon ∼ 1015 kg × (107 GeV / T)2, allowing for a very large range of possible masses. A lower limit on this mass range can be placed, however, from the lack of Hawking-radiated gamma-rays from a primordial black hole population [231, 205]. Combining gamma-ray constraints [343, 178] with the null results of microlensing surveys yields an acceptable mass range of 1014 kg to 1023 kg for dark matter in the form of primordial black holes.

A major factor that has tempered the enthusiasm for primordial black hole dark matter pertains to the number of such objects that are expected to have formed in the early Universe. If one assumes an approximately scale-invariant spectrum of density fluctuations (normalized to that observed at large scales), the predicted formation rate is cosmologically negligible. To generate a relevant abundance of such black holes, one must postulate a large degree of non-gaussianity or other such features in the primordial power spectrum.

12 The possibility that objects in the Milky Way's dark halo could be detected through gravitational lensing was also discussed earlier, in a chapter of the 1981 Ph.D. thesis of Maria Petrou. On the advice of her supervisor, Petrou did not otherwise attempt to publish this work [315]. Back.

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