Cosmic explosions, life in the Universe and the Cosmological Constant
Gamma-Ray Bursts (GRBs) are copious sources of gamma-rays whose interaction with a planetary atmosphere can pose a threat to complex life. Using recent determinations of their rate and probability of causing massive extinction, we explore what type of universes are most likely to harbour advanced forms of life. We use cosmological N-body simulations to determine at what time and for what value of the cosmological constant () the chances of life being unaffected by cosmic explosions are maximised. Life survival to GRBs favours -dominated universes. Within a CDM cosmology, the likelihood of life survival to GRBs is governed by the value of and the age of the Universe. We find that we seem to live in a favorable point in this parameter space that minimises the exposure to cosmic explosions, yet maximises the number of main sequence (hydrogen-burning) stars around which advanced life forms can exist.
Why the value of the cosmological constant is neither zero nor of the order of the Planck density (the Planck mass to the fourth power, ) remains one of the deepest mysteries of nature. Refs Barrow & Tipler (1986); Weinberg have argued that in order for observers (and thus cosmic structure) to exist, the value of could not be larger than . This was the first indication that the value of could not be arbitrary and that requiring the existence of observers bounded from above. Subsequent works (e.g., Efstathiou (1995); TegmarkRees ; Garriga99 ; Garriga00 ; Peacock ) have firmed up this argument. However, to this date no argument has been given to provide a lower bound to ; in particular, it is not clear why does not simply vanish111A lower bound to based on the stability of atomsBarrowSandvik , applies only in the distant future for spatially flat universes.. Interestingly, the necessity to avoid massive life extinction events by GRBs can shed a new light on this issue.
GRBs are potentially catastrophic events for biological organisms222In what follows when we refer to life we consider biological organisms which are sufficiently complex to act as observers. Our considerations will be for Earth-like planets where the UV protection provided by the atmosphere is due to an Ozone layer.. In particular, copious flux of -ray photons with energies above keV could destroy the ozone layer of a –habitable, Earth-like– planet, exposing living organisms to damaging UV radiation and compromising its habitability. This has led to the suggestion (Thorsett, 1995; Scalo & Wheeler, 2002; Melott et al., 2004) that galactic GRBs have been responsible for some mass extinction events on Earth. Yet the rate or energy of nearby GRBs were not sufficient to avoid the emergence of observers. However, such GRBs take place more frequently at the inner parts of the Milky Way and may cause a serious problem for development of life there PJ14 . On Earth and in general, in the outskirts of large galaxies, the most luminous GRBs, the ones around the knee of the luminosity function see Fig. 3 in PJ14 , pose the greatest threat for the development of complex organisms 333A small fraction of mass extinction from short-GRBs Melott (2006) won’t change our results, as it would just add a baseline that equally penalises all values of .as they could cause catastrophic damage even if located in a sufficiently nearby satellite galaxy.
The rate of GRBs within a given galaxy depends on the metallicity: most GRBs take place where metallicity solar and the stellar mass of the host galaxy is above M Savaglio ; JP13 . Such low-metallicity environments are rare within the Milky Way and the kpc region around it. Small mass, low metallicity, Magellanic Cloud (SMC and LMC)-type galaxies are the typical host of GRBs and thus the most likely location for potentially damaging nearby GRBs. We explore next the rate of such catastrophic extra-galactic events.
The observed global GRB rate is GRB/Gpc/Gyr Wanderman & Piran (2010)444We use here the rate of GRBs beamed towards a given observer. The overall rate is larger by a factor corresponding to the beaming. However, this is not relevant for this work. GRB hosts have stellar masses between and Savaglio ; JP13 . Integrating the stellar mass function of Panter in this mass range we find a stellar density of , yielding a rate of GRB//Gyr. This rate depends only on stellar physics and thus is independent of cosmology. Integrating (out to kpc from the center) the dark matter profile from CDM simulations Acquarius , the dark matter mass in satellites is 20% of the total halo mass () of the Milky Way. Since % of this mass is in stars Fukugita we obtain a stellar mass of in the satellites555This number is in excellent agreement with direct integration of the observed stellar mass in Milky Way satellites James11 . Thus, we expect GRB/Gyr in satellites. Using the observed GRB luminosity function Wanderman & Piran (2010) assuming an effective duration of , we expect: (70%) erg; (18%) erg; (1%) and (0.15%) with energy of . Ref PJ14 has shown that most likely there has been one GRB during the last Gyr with a fluence on Earth of ; this fluence is the value found by thomas ; Melott for massive life extinction to take place. This event is believed to have caused the Orvidician extinctionOrdo , which wiped out 85% of all species present on Earth at the time. Following thomas ; Melott we take a fluence of to be the threshold: higher fluence would have catastrophic consequences for having observers666The amount of ozone depletion and DNA damage scales slowly with fluence: they are reduced by factors of 2 and 2.5 respectively by reducing fluence from 100 to 10 kJ/m thomas06 .. Then the equivalent damaging distance from the center of the galaxy for a planet at 10 kpc from the center is 17kpc for erg, 27 kpc for and 50 kpc for erg. This implies, conservatively, that a region of (from the center of the host halo) should be devoid of GRB-hosting sub-halos for harbouring planets suitable to support observers. If there are no satellites in this region then there will be no damaging GRBs (of fluence ) with a rate much higher777About 8% of the satellites are within a radius of 20kpc for a cosmology. Regardless of the cosmology, almost all satellites are within a radius of kpc. than that on Earth. Since there is a non-zero probability of a GRB/Gyr in the satellites which yields a lethal fluence at a distance of kpc, we also discuss this case.
The existence of many nearby satellites will have an additional effect. Many of these satellites in-fall into the main galaxy, bringing low metallicity material and triggering further star formation that will increase GRB production. We do not consider this enhanced rate in this work but it clearly makes development of intelligent life in cosmologies with numerous nearby satellites even more difficult than considered here.
Any inference of cosmological parameters ought to take into account the selection effects which have led us to observe the Universe from this particular vantage point Simpson (2015). Of particular interest is the value of , which can govern the growth of regions around large galaxies devoid of LMC-type satellites. The accelerated expansion induced by a cosmological constant slows the growth of cosmic structures, and increases the mean inter-galaxy separation. This reduces the number of nearby satellites likely to host catastrophic GRBs. Below we quantify this effect.
Using -body simulations, we search for halos with dark matter masses that have no satellites of dark matter mass within a radius of 20 (50) kpc (proper); we refer to these halos as isolated. In particular, we use the Millennium-II Boylan-Kolchin et al. (2009) publicly available dark-matter-only simulation 888http://www.mpa-garching.mpg.de/galform/millennium-II/ through the Millennium Database portal created by the Virgo Consortium Lemson et al. (2006). We search for these isolated halos over all 37 available snapshots from to to determine the redshift evolution. We determine the number of subhalos inside the search radius for each host halo (identified with a Friends-of-Friends ID number), which can be either empty (, isolated host halo) or not empty (, non-isolated host).
The Millenium-II simulation is performed for a flat CDM cosmology with parameters999Unless otherwise stated, cosmological parameters are at .: , , , , , . The size of the box is Mpc (comoving) on a side. The spatial resolution is kpc, so the search radius for subhalos is not affected by resolution effects. The mass resolution of the simulation is , so effectively our threshold on the mass of the satellite halo is verified by all subhalos resolved in the simulation, regardless of their mass. The host halo is required to have 30,000 to 100,000 particles, which corresponds to the halo mass bin stated above.
No public N-body simulations with the required mass resolution exist for other models than the “vanilla” CDM. Fortunately, numerical simulations of one cosmology can be re-mapped into a different one accurately both for the dark matter field and the corresponding halos Angulo ; MeadPeacock . Using this algorithm we have re-mapped the results of the Millennium-II CDM simulation to cosmologies with other values of . Note that by keeping the geometry fixed () and the early universe quantities (such as the physical matter density , the amplitude of primordial perturbations, and the baryon fraction) fixed the current value of specifies the cosmology.
It is challenging to keep track of changes of all other cosmological parameters and it is clear that other changes could mimic some of the effects that we emphasise here, for example significant amount of massive neutrinos would also suppress the growth of structure. However, it has been shown Tegmark05 that even modest modifications to a range of cosmological parameters leads to adverse consequences for the abundance of life. As such, we focus on changing only the value of the cosmological constant, while keeping the conditions of the early universe fixed.
Fig. 1 shows the number of isolated halos per comoving Mpc for four relevant flat cosmologies spanning the range : 1) , 2) (fiducial CDM) , 3) , and 4) (Einstein de Sitter) , . In the dominated models, only fairly recently, on a cosmological time scale, the number of GRB-protected halos grew significantly. In fact, a large number101010For a MW-like halo in the concordance CDM model, of the halos fulfil the 50 kp isolation criterion, so our MW is not a very special halo of isolated halos appear only below . This corresponds to a lookback-time of about Gyr, not dissimilar from the age of Earth. As structure formation proceeds faster in the universe, the amount of sub-structure grows faster and earlier: the number of isolated halos is much smaller than in the case of a dominated universe.
In order for a particular galaxy to harbour life, it must reside within a habitable region of the parameter space. The halo mass should be in the range as to give rise to a large galaxy like the Milky Way so that it has significant outer regions in which the GRB rate is low but there are sufficient number of stars. Additionally the galaxy should undergo sufficient chemical evolution so that its average metallicity is relatively large thereby reducing the GRB rate. Furthermore, the halo should be young enough that stars with mass have not left the main sequence. For stars this corresponds to ( Gyr), for this corresponds to Gyr. For example for the model with the age of the Universe is Gyr, by the time takes over the expansion, the universe is already too old and out of the habitable epoch for all main sequence stars above . For we estimate this to correspond instead to ().
One can imagine waiting for a long time for the GRB rate to be sufficiently low. The current decrease of the GRB rate with time Wanderman & Piran (2010) at is much flatter than the decrease in star formation rate (see their Fig. 9); extrapolating this rate implies that the star formation will be exhausted sooner than GRBs. By – when flat universes with a cosmological constant that is 0.3-0.6 of that in the vanilla model become similar to the present Universe with , the GRB rate will be down by a factor , while the star formation rate will be down by a factor . Since the decrease in star formation rate is the dominant effect, for simplicity in what follows we assume that the GRB rate remains constant. This approximation does not change qualitatively our argument.
In the range of that we have explored, and for , we find that the number density of habitable and isolated halos can be approximated by111111For 50 kpc radius and for in . For 20 kpc radius we find that a broken power law is a slightly better fit: , ; , respectively at low and high values of .
The coefficients of the fit may change for different values of or different radii but the qualitative behaviour remains with a sharp decrease for . For larger values of this relation must flatten since virtually all MW-size halos are isolated for . We also note that, always in the range of explored, the number of MW-sized halos in the same volume is roughly constant, implying that is roughly proportional to the fraction of isolated halos (for larger values of when this fraction reaches unity it is assumed to become a constant). If we assume that, for the values of we considered so far, is proportional to the probability , to infer the posterior probability for having a cosmological constant we must define a prior distribution . Previous studies take a flat prior on based on the premise that its value may arise from the cancellation of much larger terms. However given the large uncertainty regarding the nature of dark energy, this might not be the case. A more conservative approach is to select an uninformative prior such that (see also Garriga00 ). In this case one shall not consider negative values of the cosmological constant, although they are likely to generate even more inhospitable consequences.
The other mechanism by which influences the habitability of the Universe is the suppression of galaxy formation. This was studied in detail in Tegmark05 who used the fraction of baryons residing in halos of mass , where is the matter density per photon, as a proxy for the habitability of the universe. They present the following prescription for the late time solution
Here and can be considered fixed quantities, and ; we take and following Tegmark05 (see e.g., their Fig 7.). It is clear from Eq. 2 and e.g., Fig. 7 of Tegmark05 that this imposes a sharp suppression for M.
where gives the number of suitable MW-size halos and describes the sharp upper cut-off imposed by eq. 2, and imposes a much slower suppression towards 0. In Fig. 2 we sketch the probability distribution function for , normalised to the Einstein-de-Sitter case, using the computed abundance of isolated Milky Way-size halos from Fig. 1. The low-end suppression is described by Eq. 1. For high values of the suppression discussed in Tegmark05 ; Barrow & Tipler (1986); Weinberg , effectively due to the requirement of cosmic structure to form, becomes relevant. It is not surprising then that our universe has a value of (). It is instructive to compare to Fig.7 of Tegmark05 and notice that the allowed region for is now greatly reduced.
Since on average there is one isolated region in a patch of 10 Mpc radius (which, incidentally, is the mean inter galaxy cluster separation today), to ensure (at ) that there is at least one habitable galaxy in the observable universe, the horizon size should be at least 40 Mpc i.e. not more than times smaller than the current horizon size. Given our specifications for galactic habitability, both in terms of the required separations between galaxies, and the minimum age of the Universe which permits the formation of planets, a large universe is necessary for life to emerge. A loitering model with a finely tuned cosmological constant could satisfy the age requirement, but does not provide adequate inter-galactic spacing.
If our location in the Universe, and potentially the multiverse, is preferentially selected by the absence of nearby, GRB-hosting small halos, then we will expect to find that most Milky-Way sized galaxies beyond the Local Group possess a heightened number of LMC-like satellites. To some extent this has already been observed Côté, West, & Marzke (2002). The reduced number of observed Milky-Way satellites compared to predictions derived from simulations is often attributed to the inefficiency of star formation within low mass halos. Yet this puzzle may also be partially resolved by our proposed selection effect.
Another interesting implication is that if the amplitude of fluctuations is increased, then halos of a given mass form earlier, but they do so in a very crowded environment. In previous investigations is one of the few cosmological parameters which could be enlarged by an order of magnitude without any clearly adverse effects (e.g., Fig.12 in Tegmark05 ). Within the context of GRBs-limited habitability, there is likely to be much less freedom in this parameter.
In summary, we have shown that plays a crucial role at creating habitable regions for galaxies in a habitable epoch. These considerations may be used to disfavour very low values for . Negative values of will yield even more satellites and hence these arguments strongly disfavour such values.
Acknowledgements.We thank R. Angulo for help with interpreting the simulation outputs. This research was supported by the ISF I-Core center of excellence and by an Israel-China grant (TP), by Mineco grant AYA2014-58747-P (RJ,LV), FP7-IDEAS-Phys.LSS 240117 (LV, AJC,FS) and the Spanish MINECO under project MDM-2014-0369 of ICCUB (Unidad de Excelencia ‘María de Maeztu’).
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