Solar Hegemony: M-Dwarfs Are Unlikely to Host Observers Such as Ourselves

TL;DR

This work investigates why observers like ourselves do not appear to inhabit M-dwarfs despite their numerical dominance, and why we occur early in the stelliferous era. It combines astrophysical modeling of star formation history and stellar lifetimes with a Bayesian framework to jointly test two explanatory mechanisms: a desolate-M-dwarf cutoff at $M_{\text{crit}}$ and a truncated window for observers with $T_{\text{win}}$. The analysis finds that mere luck is decisively unlikely ($\mathcal{Z}_{\text{luck}}/\mathcal{Z}_{\text{desolate}} \approx 1597$) and that some degree of mass truncation is necessary, with a geophysically motivated prior (e.g., $T_{\text{win}}=10$ Gyr) yielding the most conservative $M_{\text{crit}}$ bounds ($M_{\text{crit}} > 0.34\,M_\odot$ at $2\sigma$). The results imply that M-dwarfs are unlikely seats for observers and motivate focusing SETI efforts on higher-mass stars, while illustrating how Bayesian model comparison can quantify observer-selection effects in astrobiology.

Abstract

With no firm evidence for life beyond our solar system, inferences about the population observers such as ourselves rests upon the Earth as a single input, at least for now. Whilst the narrative of our home as a 'humdrum' system has become ingrained in the public psyche via Sagan, there are at least two striking facts about our existence which we know are certainly unusual. First, the stelliferous period spans ~10Tyr - yet here we are living in the first 0.1% of that volume. Second, over three-quarters of all stars are low-mass M-dwarfs, stars with no shortage of rocky habitable-zone planets - and yet, again, our existence defies this trend, previously dubbed the Red Sky Paradox. Two plausible resolutions are that a) stars below a certain mass, $M_{crit}$, do not produce observers, and, b) planets have a truncated temporal window for observers, $T_{win}$, negating the longevity advantage of M-dwarfs. We develop a Bayesian model that encompasses both datums and jointly explores the two resolutions covariantly. Our analysis reveals that 1) the hypothesis that these observations are mere luck is disfavored with an overwhelming Bayes factor of ~1600; 2) some truncation of low-mass stars is indispensable, lowering $T_{win}$ alone cannot well-explain the observations; and, 3) the most conservative limit on $M_{crit}$ occurs when fixing $T_{win}=10$Gyr, yielding $M_{crit}>0.34 M_{\odot}$ [$0.74 M_{\odot}$] to 2$σ$ [1$σ$]. Our work challenges the tacit assumption of M-dwarfs being viable seats for observers and, indirectly, even life.

Figures (3)

• Figure 1: Number of stars capable of hosting observers (amongst a sample of $10^6$) as a function of time. The darkest track assumes that all stars are equally capable of hosting life during their MS lifetime. Each lighter track sequentially truncates the lowest mass star capable of hosting observers in 0.02 $M_{\odot}$ steps. One can see that removing low-mass stars gradually relaxes the tension as to why we live so early in the stelliferous period.
• Figure 2: Number of stars capable of hosting observers (amongst a sample of $10^6$) as a function of time. The yellow track assumes that planets remain hospitable to observers during the entire main sequence lifetime of a star (effectively $T_{\mathrm{win}}=10$ Tyr). Stepping to progressively bluer tracks, we truncate this time window $T_{\mathrm{win}}$ down to 4.5 Gyr (bluest line).
• Figure 3: Corner plot of the joint posterior distribution $\mathrm{Pr}(M_{\mathrm{crit}},T_{\mathrm{win}}|t=t_0,M_{\star}=M_{\odot})$. The lower-left panel shows the joint posterior, whereas the other two panels shows the respective marginalized 1D distributions (black lines). The $T_{\mathrm{win}}$ posterior peaks at 10 Gyr, which has good physical justification oneill:2016. We thus show a second 1D posterior for $M_{\mathrm{crit}}$ where $T_{\mathrm{win}}$ is held fixed at this value in red.