Current cosmological constraints allow primordial black holes to constitute dark matter in the mass range of 10SUP18SUP10SUP22SUP g. I show that a major portion of this logarithmic window can be ruledout based on the solar system ephemeris given that the external mass enclosed within 50 au from the Sun did not change by more than 5  10SUP14SUP M SUBSUB yrSUP1SUP in recent decades.
['Black holes', 'Dark matter', 'Solar system', '162', '353', '1528', 'High Energy Physics - Phenomenology', 'Astrophysics - Cosmology and Nongalactic Astrophysics', 'General Relativity and Quantum Cosmology']
Excluding Primordial Black Holes as Dark Matter Based on Solar System Ephemeris
{'No Header': 'Draft version August 27, 2024  \nTypeset using L A T E X modern style in AASTeX61', 'Abraham Loeb 1': '1 Astronomy Department, Harvard University, 60 Garden St., Cambridge, MA 02138, USA', 'ABSTRACT': 'Current cosmological constraints allow primordial black holes (PBHs) to constitute dark matter in the mass range of 10 18 -10 22 g. I show that a major portion of this logarithmic window can be ruled-out based on the Solar System ephemeris, given that the external mass enclosed within 50 au from the Sun did not change by more than ∼ 5 × 10 -14 M /circledot yr -1 in recent decades.', '1. INTRODUCTION': "Current cosmological constraints allow for the possibility that dark matter is made of primordial black holes (PBHs) in the mass range of ∼ 10 18 -10 22 g (Carr & Hawking 1974; Carr & Kuhnel 2021; Green 2024; Carr & Green 2024).  \nRecently, Pitjeva et al. (2021) used data in the Solar System ephemeris EPM2019 to constrain the change in the mass of the Sun based on the dynamics of Solar System objects out to ∼ 500 au. EPM2019 incorporates full 3D position and velocity vectors of the Sun, the Moon, the eight major planets, Pluto, the three largest asteroids (Ceres, Pallas, and Vesta) and four transneptunian objects (Eris, Haumea, Makemake, and Sedna), covering data over more than 400 yr.  \nAccounting for the known components of mass loss from the Sun in radiation or solar wind and the small mass gain from infall, Pitjeva et al. (2021) derived the following 3 σ limits on the rate of unaccounted-for mass change,  \n-2 . 9 × 10 -14 < ˙ δM M /circledot < +4 . 6 × 10 -14 per yr , (1)  \nwhere δM = ( M -M /circledot ) corresponds to any mass deficit or excess relative to the known mass budget of the Sun.  \nIf dark matter is made of PBHs, then the temporary passage of a PBH through the inner Solar System would introduce a transient δM in the gravitational mass affecting all objects orbiting the Sun outside of the PBH-Sun separation. Here, I study the constraints set by equation (1) on the abundance of PBHs in the mass range of 10 18 -10 22 g. In our analysis, I ignore the possibility of a time dependent Newton's constant, because it is unlikely that such variations would compensate random δM fluctuations introduced by PBHs as they enter and exit a perihelion distance of ∼ 50 au over timescales of years. Other recent papers addressed complementary ways for constraining PBHs from dynamical data in the Solar System (Tran et al. 2023; Bertrand et al. 2023; Cuadrat-Grzybowski et al. 2024).", '2. NEW SOLAR SYSTEM CONSTRAINTS': "Based on the latest Galactic data, the dark-matter near the Sun has a massdensity (Sivertsson et al. 2022; Staudt et al. 2024),  \nρ dm = 7( ± 1) × 10 -25 g cm -3 , (2)  \na 3D velocity dispersion of 280( ± 19) km s -1 , and a most probable speed relative to the Sun of,  \nv = 257( ± 11) km s -1 , (3)  \nwith a sharp truncation above 470 km s -1 . If PBHs of a given mass, m = m 20 × 10 20 g, make the dark matter, then their local number density is derived from equation (2),  \nn = ( ρ dm m ) ≈ 2 . 4 × 10 -5 au -3 m -1 20 . (4)  \nThe rate by which PBHs of mass m enter a volume of radius r around the Sun is given by,  \nΓ = n × ( πr 2 ) × v . (5)  \nSubstituting v from equation (3) and n from equation (4) yields an entry rate,  \nΓ = 10 . 2 m -1 20 ( r 50 au ) 2 yr -1 . (6)  \nFor our fiducial detection volume, I consider a sphere defined by transneptunian objects around r ∼ 50 au in the EPM2019 data which was used to derive equation (1). For generality, I also express our PBH constraints as a function of the bounding value of r .  \nMultiplying the PBH entry rate in equation (6) by the PBH mass m yields the rate by which the mass interior to a radius r changes as a result of the crossing of a single PBH within that radius from the Sun,  \n˙ m ≡ m Γ = 5 × 10 -13 ( r 50 au ) 2 M /circledot yr -1 , (7)  \nimplying that for r ∼ 50 au a single PBH with m 20 > 0 . 1 can violate the limits in equation (1).  \nThe crossing time of a radius r by a PBH is given by,  \nδt = ( r v ) = 0 . 93 yr ( r 50 au ) , (8)  \nintroducing a fluctuation δM on a relevant timescale to be detectable in the EMP2019 data.  \nAt any given time, the number of PBHs within the sphere of radius r is,  \nN = n × ( 4 πr 3 3 ) = 12 . 6 m -1 20 ( r 50 au ) 3 . (9)  \nPoisson fluctuations over a time δt in the enclosed mass of PBHs yield,  \n˙ δM = √ Nm δt = 1 . 9 × 10 -13 m 1 / 2 20 ( r 50 au ) 1 / 2 M /circledot yr -1 , (10)  \nwith a weak square-root dependence on m and r . Equation (10) holds for N > 1, namely r > 22 m 1 / 3 20 au.  \nEquations (7-10) imply that the 3 σ limits in equation (1) exclude PBHs as dark matter in the previously allowed mass range of 6 × 10 18 g < m < 10 22 g for r ∼ 50 au and the entire range of 10 18 -10 22 g for Sedna's semimajor axis at r ∼ 500 au . At the upper end of this mass range, a PBH with m ∼ 10 22 g is expected to get within 50 au from the Sun once per decade and within ∼ 8 au once per 400 years. At the lower mass end, there are ∼ 210 PBHs with m ∼ 6 × 10 18 g within 50 au from the Sun at any given time. The nearest is ∼ 8 . 4 au from the Sun at any given time, but during 400 years the nearest arrives as close as ∼ 0 . 2 au at perihelion.", '3. DISCUSSION': 'I have found that the dynamical constraints from the Solar System ephemeris EPM2019 exclude a substantial portion of the allowed logarithmic window for PBHs as dark matter, 10 18 -10 22 g, depending on the choice of the boundary radius r out to which the interior mass is not allowed to change by more than 5 × 10 -14 M /circledot yr -1 . Detailed simulations of how PBHs with a broad mass distribution across this range affect the specific details of the EMP2019 data, are required to refine these constraints.', 'ACKNOWLEDGEMENTS': "This work was supported in part by Harvard's Black Hole Initiative , which is funded by grants from JFT and GBMF.", 'REFERENCES': 'Bertrand, B., Cuadrat-Grzybowski, M., Defraigne, P., Van Camp, M., & Clesse, S. 2023, arXiv e-prints, arXiv:2312.14520, doi: 10.48550/arXiv.2312.14520 Carr, B., & Kuhnel, F. 2021, arXiv e-prints, arXiv:2110.02821, doi: 10.48550/arXiv.2110.02821 Carr, B. J., & Green, A. 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