@rootone
I'm still not convinced that MACHOs are ruled out.
Allow me to remind you of some of the pertinent evidence which rules out MACHOs.
As noted by stefan r above, there is no doubt that some MACHO candidates exist (although
primordial black holes have not yet been observed and there is good reason to doubt that they exist), but there simply are enough of them and they aren't in the right places to account for a meaningful share of dark matter phenomena. The smallest primordial black holes are impossible:
Depending on the model, primordial black holes could have initial masses ranging from 10
−8 kg (the so-called Planck relics) to more than thousands of solar masses. However primordial black holes with a mass lower than 10
11 kg would have evaporated (due to
Hawking radiation) in a time much shorter than the age of the Universe, and so cannot have survived in the present Universe.
The constraints on non-primordial black hole (PBH) MACHOs (terrestrial planets, baby or ordinary gas giants, neutron stars, cannibalized white dwarfs that become helium or diamond planets) are severe and these candidates have been ruled out for many years. Indeed,
massive compact halo objects (MACHOs) are pretty much ruled out, in general, as dark matter candidates (citations in the original omitted and paragraph breaks added in the quotation below):
A MACHO may be detected when it passes in front of or nearly in front of a star and the MACHO's gravity bends the light, causing the star to appear brighter in an example of
gravitational lensing known as
gravitational microlensing. Several groups have searched for MACHOs by searching for the microlensing amplification of light. These groups have ruled out
dark matter being explained by MACHOs with mass in the range 1×10−8
solar masses (0.3 lunar masses) to 100 solar masses.
One group, the MACHO collaboration, claims to have found enough microlensing to predict the existence of many MACHOs with mass of about 0.5
solar masses, enough to make up perhaps 20% of the dark matter in the galaxy. This suggests that MACHOs could be white dwarfs or red dwarfs which have similar masses. However, red and white dwarfs are not completely dark; they do emit some light, and so can be searched for with the
Hubble Telescope and with
proper motion surveys. These searches have ruled out the possibility that these objects make up a significant fraction of dark matter in our galaxy.
Another group, the EROS2 collaboration, does not confirm the signal claims by the MACHO group. They did not find enough microlensing effect with a sensitivity higher by a factor 2.
Observations using the Hubble Space Telescope's
NICMOS instrument showed that less than one percent of the halo mass is composed of red dwarfs. This corresponds to a negligible fraction of the dark matter halo mass.
Therefore, the missing mass problem is not solved by MACHOs. . . .
Theoretical work simultaneously also showed that ancient MACHOs are not likely to account for the large amounts of dark matter now thought to be present in the universe. The
Big Bang as it is currently understood could not have produced enough
baryons and still be consistent with the observed elemental abundances, including the abundance of
deuterium. Furthermore, separate observations of
baryon acoustic oscillations, both in the
cosmic microwave background and large-scale structure of galaxies, set limits on the ratio of baryons to the total amount of matter. These observations show that a large fraction of non-baryonic matter is necessary regardless of the presence or absence of MACHOs.
There have been arguments that PBHs are not subject to some of the exclusions above applicable to other kinds of MACHOs. But, a the MACHO exclusion chart below (which is a few years out of date (with the left side showing the ratio of MACHOs to dark matter and the horizontal axis showing MACHO mass) is as follows:
:
In terms of MACHOs are a dark matter candidate, only the very top part matters, since 10
-2 means just 1% of dark matter can be accounted for by MACHOs of that type. You really need to be above 10
-1 (i.e. 10%) to be considered as a significant source of dark matter phenomena.
As this chart shows, there are
pretty significant observational constraints on the size of primordial black hole dark matter, however (relying mostly on
this source). The sweet spot is 10^22 kilograms, which is a bit less than the mass of the Moon (which is 7*10^22 kilograms), plus or minus, which would imply a typical primordial black hole with an event horizon radius of about 0.1 millimeters.
Another paper on PBHs was even less bullish:
We investigate constraints on primordial black holes (PBHs) as dark matter candidates that arise from their capture by neutron stars (NSs). If a PBH is captured by a NS, the star is accreted onto the PBH and gets destroyed in a very short time. Thus, mere observations of NSs put limits on the abundance of PBHs. High DM densities and low velocities are required to constrain the fraction of PBHs in DM. Such conditions may be realized in the cores of globular clusters if the latter are of a primordial origin. Assuming that cores of globular clusters possesses the DM densities exceeding several hundred GeV/cm3 would imply that PBHs are excluded as comprising all of the dark matter in the mass range 3×1018g≲mBH≲1024g. At the DM density of 2×103 GeV/cm3 that has been found in simulations in the corresponding models, less than 5% of the DM may consist of PBH for these PBH masses.
Fabio Capela, et. al, "
Constraints on primordial black holes as dark matter candidates from capture by neutron stars." Phys. Rev. D 87, 123524 (2013) (link is to open access pre-print version conformed to final print version).
Since the chart above was made the observational constraints on PBHs have further tightened. For example:
We model the accretion of gas on to a population of massive primordial black holes in the Milky Way, and compare the predicted radio and X-ray emission with observational data. We show that under conservative assumptions on the accretion process, the possibility that O(10)M⊙ primordial black holes can account for all of the dark matter in the Milky Way is excluded at 4σ by a comparison with the VLA radio catalog at 1.4 GHz, and at more than 5σ by a comparison with the NuSTAR X-ray catalog (10 - 40 keV). We also propose a new strategy to identify such a population of primordial black holes with more sensitive future radio and X-ray surveys.
Daniele Gaggero, et al., "
Searching for Primordial Black Holes in the radio and X-ray sky" (Pre-Print December 1, 2016).
Another recent paper constraining MACHOs as cluster dark matter (keeping in mind that galaxy clusters are inferred to have much more dark matter proportionately than any kind of galaxy) finds:
Galaxy clusters, employed by Zwicky to demonstrate the existence of dark matter, pose new stringent tests. If merging clusters demonstrate that dark matter is self-interacting with cross section σ/m∼2 cm2/gr, MACHOs, primordial black holes and light axions that build MACHOs are ruled out as cluster dark matter. Recent strong lensing and X-ray gas data of the quite relaxed and quite spherical cluster A1835 allow to test the cases of dark matter with Maxwell-Boltzmann, Bose-Einstein and Fermi-Dirac distribution, next to Navarro-Frenck-White profiles. Fits to all these profiles are formally rejected at over 5σ, except in the fermionic situation.
Theodorus Maria Nieuwenhuizen "
Subjecting dark matter candidates to the cluster test" (October 3, 2017) (omitting from the abstract conclusions about sterile neutrino dark matter candidates).
It also turns out that the model used in many PBH exclusion analyses is actually too lenient and that
more realistic modeling makes the exclusions even tighter.
