It was recently claimed httpsarxiv.orgpdf2408.10799 that solar system ephemeris data can exclude primordial black hole PBH dark matter in the mass range 10SUP18SUP10SUP22SUP g. I show that this conclusion is based on an implausible implicit assumption namely the uncertainty on the solar system mass within 50 au is as small as the uncertainty on the mass of the Sun. Correcting for this error I find that ephemeris data can only constrain PBHs with mass below 10SUP16SUP g which is already excluded by constraints on their evaporation via Hawking radiation. Correcting a further error concerning the timeaveraged rate of such fluctuations nullifies even this weaker constraint.
['Primordial black holes', '1292', 'High Energy Physics - Phenomenology', 'Astrophysics - Cosmology and Nongalactic Astrophysics', 'General Relativity and Quantum Cosmology']
Comment on Excluding Primordial Black Holes as Dark Matter Based on Solar System Ephemeris
{"Comment on 'Excluding Primordial Black Holes as Dark Matter Based on Solar System Ephemeris'": "James M. Cline ∗  \nMcGill University Department of Physics & Trottier Space Institute, 3600 Rue University, Montr'eal, QC, H3A 2T8, Canada and CERN, Theoretical Physics Department, Geneva, Switzerland  \nIt was recently claimed ( https://arxiv.org/pdf/2408.10799 ) that solar system ephemeris data can exclude primordial black hole (PBH) dark matter in the mass range 10 18 -10 22 g. We show that this conclusion is based on an implausible, implicit assumption; namely the uncertainty on the solar system mass within 50 au is as small as the uncertainty on the mass of the sun. Correcting for this error, we find that ephemeris data can only constrain PBH's with mass below 10 16 g, which is already excluded by constraints on their evaporation via Hawking radiation. Correcting a further error concerning the time-averaged rate of such fluctuations nullifies even this weaker constraint.  \nRef. [1] recently argued that if primordial black holes (PBHs) in the mass range 10 18 -10 22 g constitute the dark matter of the Universe, they would give rise to Poisson fluctuations in the total mass of the solar system contained within some assumed fiducial volume, and that observational limits on such fluctuations can be used to exclude this PBH mass range. It was claimed that fluctuations due to crossing PBHs would show up as an effective time rate of change of the solar mass M /circledot , by their perturbation of planetary orbits. These orbits have been monitored over more than 50 years, and the search for deviations was used by Ref. [2] to set strong limits on the time variation of GM /circledot , at the level of a few parts in 10 14 per year.  \nIn Ref. [1], Loeb assumed the relevant volume is the region within 50 au, the orbital radius of Pluto. However, Ref. [3] shows that the ephemeris data are vastly dominated (94 %) by measurements of the inner planets. Therefore a fiducial radius of 1.5 au (encompassing Mars) would be more appropriate for the data at hand. To have at least one PBH on average within this volume, in order to cause a fluctuation, it should have a mass no greater than 3 × 10 16 g, assuming a monochromatic spectrum of PBHs making up the total dark matter density. Such a light PBH as dark matter is already ruled out by constraints on its Hawking radiation evaporation products, namely photons and e + -e -pairs [4].  \nHowever, even this weakened limit on the PBH mass cannot be a valid inference from the ephemeris data. The limit on d/dt ( GM /circledot ) derived by Ref. [2] relies upon a long duration, ∼ 50y of data taking, in order to be so stringent. In contrast, the crossing time of the 1.5 au  \nfiducial volume by a PBH is less than a few weeks, hence any perturbation produced on planetary orbits would average to zero during the observation time. Moreover, the direct limit on the dark matter density in the solar system from ephemeris data is 14,000 times weaker than the accepted value 0 . 4 GeV/cm 3 [3], underscoring the implausibility of these data being sensitive to such a weak perturbation as a PBH crossing.  \nNot discussed in Ref. [1] is the possibility that a close encounter of a PBH could strongly perturb an inner planet. An order of magnitude estimate shows that this is highly unlikely. The ephemeris bound on the integrated perturbation to the gravitational force on a planet of mass m is of order  \nδF ∼ G ˙ M /circledot Tm R 2 , (1)  \nwhere ˙ M /circledot is the limit on the time variation of the solar mass, T is the observing time, and R ∼ 1 au is the orbital radius. The maximum force exerted by a transiting PBH is F = GM bh m/b 2 , where b is the distance of closest approach. Thus one needs  \nb /lessorsimilar R ( M bh ˙ MT ) 1 / 2 ∼ 0 . 01 au (2)  \nfor M bh = 10 18 g, to have an observable effect. On the other hand, Ref. [1] computes the rate of such crossings to be  \nΓ ∼ 1000 ( b 50 au ) 2 yr -1 < 4 × 10 -5 yr -1 . (3)  \nAcknowledgment. I thank Gabriele Franciolini for helpful discussions.  \n- [1] A. Loeb, 'Excluding Primordial Black Holes as Dark Matter Based on Solar System Ephemeris,' arXiv:2408.10799 [hep-ph] .\n- [2] E. V. Pitjeva, N. P. Pitjev, D. A. Pavlov, and C. C. Turygin, 'Estimates of the change rate of solar mass and gravitational constant based on the dynamics of the Solar System,' Astron. Astrophys. 647 (2021) A141, arXiv:2201.09804 [astro-ph.EP] .\n- [3] N. P. Pitjev and E. V. Pitjeva, 'Constraints on\n- dark matter in the solar system,' Astron. Lett. 39 (2013) 141-149, arXiv:1306.5534 [astro-ph.EP]  \n.  \n- [4] B. Carr, K. Kohri, Y. Sendouda, and J. Yokoyama, 'Constraints on primordial black holes,'\n- Rept. Prog. Phys. 84 no. 11, (2021) 116902, arXiv:2002.12778 [astro-ph.CO] ."}