What Would Happen If We Were About 1 pc Away from a Supermassive Black Hole?

Abstract

We consider a hypothetical planet with the same mass $m$, radius $R$, angular momentum $\mathbf{S}$, oblateness $J_2$, semimajor axis $a$, eccentricity $e$, inclination $I$, and obliquity $\epsilon$ of the Earth orbiting a main-sequence star with the same mass $M_{\star }$ and radius $R_{\star }$ of the Sun at a distance $r_{\bullet }\simeq 1\mathrm{parsec}\left(\mathrm{pc}\right)$ from a supermassive black hole in the center of the hosting galaxy with the same mass $M_{\bullet }$ of, say, ${M87}^{\ast }$. We preliminarily investigate some dynamical consequences of its presence in the neighborhood of such a stellar system on the planet's possibility of sustaining complex life over time. In particular, we obtain general analytic expressions for the long-term rates of change, doubly averaged over both the planetary and the galactocentric orbital periods $P_{\mathrm{b}}$ and $P_{\bullet }$, of $e,I,\epsilon$, which are the main quantities directly linked to the stellar insolation. We find that, for certain orbital configurations, the planet's perihelion distance $q=a\left(1-e\right)$ may greatly shrink and lead to, in some cases, an impact with the star. $I$ may also notably change, with variations even of the order of tens of degrees. On the other hand, $\epsilon$ does not seem to be particularly affected, being shifted, at most, by $\simeq 0^{\circ }.02$ over 1 Myr. Our results strongly depend on the eccentricity $e_{\bullet }$ of the galactocentric motion.

arXiv commentLaTex2e, 17 pages, no tables, 3 figures. Version matching the one published in The Astrophysical Journal (ApJ)

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• Effects of the general relativistic spin precessions on the habitability of rogue planets orbiting supermassive black holes
• Post-Newtonian orbital effects induced by the mass quadrupole and spin octupole moments of an axisymmetric body