Dark Matter And The Habitability of Planets                                                                               ...
the universe’s hydrogen into helium. But unlike             this surface temperature may exceed trillions ofbaryonic matte...
planets with an iron core, and with a range of             periments (Ahmed et al. 2010a; Aprile et al. 2010;masses betwee...
As seen in Fig. 1, dark matter annihilations are                                                           predicted to in...
Fig. 2.— The rate (in energy-equivalent units) atwhich dark matter particles are predicted to be            Fig. 3.— The s...
ticles annihilate within a planet will be very nearly       4.   Discussion and Conclusionsequal to the rate at which they...
G. Bertone and D. Merritt.       Phys.Rev., D72:         K. C. Sahu, S. Casertano, H. E. Bond, J. Valenti,  103502, 2005a....
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Dark matter and the habitability of planets

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Dark matter and the habitability of planets

  1. 1. Dark Matter And The Habitability of Planets Dan Hooper1,2 and Jason H. Steffen1 1 Center for Particle Astrophysics, Fermi National Accelerator Laboratory, Batavia, IL 60510 2 Department of Astronomy and Astrophysics, The University of Chicago, Chicago, IL 60637arXiv:1103.5086v1 [astro-ph.EP] 25 Mar 2011 ABSTRACT In many models, dark matter particles can elastically scatter with nuclei in planets, causing those particles to become gravitationally bound. While the energy expected to be released through the subsequent annihilations of dark matter particles in the interior of the Earth is negligibly small (a few megawatts in the most optimistic models), larger planets that reside in regions with higher densities of slow moving dark matter could plausibly capture and annihilate dark matter at a rate high enough to maintain liquid water on their surfaces, even in the absence of additional energy from starlight or other sources. On these rare planets, it may be dark matter rather than light from a host star that makes it possible for life to emerge, evolve, and survive. Subject headings: dark matter — planetary systems — FERMILAB-PUB-11-149-A 1. Introduction instance, orbits at a distance of 0.72 AU and thus falls within the Sun’s nominal habitable zone, but Life, as generally imagined, is capable of evolv- maintains an average surface temperature that is ing and surviving only under a limited range of well above 700 K. Alternatively, energy sources environmental circumstances. In particular, the other than starlight could contribute to maintain- presence of liquid water to serve as a universal sol- ing a planet’s surface temperature. The decay of vent appears to be a likely requirement of carbon- radioactive elements and other sources of geother- based life. This need, in turn, implies a finite range mal energy, for example, contribute approximately of temperatures under which it will be possible for 0.025% of the total energy that goes into main- life to emerge and survive. taining the Earth’s surface temperature (Pollack The surface temperature of a typical planet is et al. 1993), but could potentially contribute more maintained primarily by light from a host star. For significantly for other planets. A different atmo- planets with an Earth-like albedo and emissivity, spheric composition and thickness may provide a and in orbit around a Sun-like star, one can cal- habitable environment even on rogue planets in culate that average surface temperatures between the interstellar medium (Stevenson 1999). On 273 and 373 K will persist for orbital distances some planets and moons, significant quantities of between approximately 0.6 and 1.1 AU. This rep- heat could also be generated by tidal flexing and resents a naive estimate for the habitable zone of other geological activity (Peale and Cassen 1978; a Sun-like star—planets in significantly larger or Murray and Dermott 2000; Abbot and Switzer smaller orbits will likely contain water in only solid 2011). or gaseous form. In this paper, we consider another possible en- Of course there are a number of caveats that ergy source for planetary heating—the annihila- can alter the boundaries of the habitable zone, tions of dark matter particles. The mass of the such as chemical cycles (Kasting et al. 1993) or the dark matter contained in our universe represents greenhouse effect. For example, a more efficient an enormous energy reservoir—a factor of approx- greenhouse effect (leading to a lesser emissivity) imately 103 times greater than the total energy than is found on the Earth could significantly in- that would be released through the fusion of all of crease a planet’s surface temperature. Venus, for 1
  2. 2. the universe’s hydrogen into helium. But unlike this surface temperature may exceed trillions ofbaryonic matter, dark matter does not generally years—outliving even the smallest, and longest-interact at rates sufficient to produce ecologically lived, main sequence stars (Laughlin et al. 1997).relevant quantities of energy. An exception to In this rather special and rare class of planets, thethis conclusion, however, could possibly be found annihilations of dark matter could provide the en-for dark matter particles that have become grav- ergy necessary for liquid water, and thus life, toitationally captured in a planet’s interior. Dark exist.matter, in the form of weakly interacting massive The remainder of this article is structured asparticles (WIMPs), is generally predicted to inter- follows. In Sec. 2 we discuss the capture ofact with nuclei, enabling them to lose momentum dark matter particles in Earth-like and super-and become gravitationally bound and captured Earth planets. In Sec. 3, we calculate the result-by stars or planets (Silk et al. 1985; Krauss et al. ing surface temperature of planets in regions such1985). After accumulating in a planet’s interior, as dwarf spheroidal galaxies and the inner Milkythese dark matter particles can, in many models, Way, finding that liquid water could plausibly besubsequently annihilate to produce energetic par- maintained on planets in these regions, even in theticles that are then absorbed by the surrounding absence of light from a host star. In Sec. 4 we dis-material. cuss some of the implications of these results and In the case of the Earth, dark matter anni- summarize our conclusions.hilations are not expected to meaningfully com-pete with the total energy absorbed from sun- 2. The Capture Of Dark Matter Particleslight. Even for the most optimistic of the hypothe- In Earth-like and Super-Earth Planetssized dark matter candidates, we estimate that theEarth would gravitationally capture less than one As dark matter particles move through thebillionth of the dark matter required to match the Galaxy, they can occasionally scatter elasticallyenergy input from the Sun. This conclusion, how- with nuclei within stars or planets. In some ofever, could be very different for planets in other these collisions, enough momentum can be trans-galactic environments. In particular, the density ferred as to leave the dark matter particle grav-of dark matter is expected to be hundreds or thou- itationally bound to the object. The subsequentsands of times larger in the inner tens of parsecs of orbits of such particles, which pass through thethe Milky Way and in the cores of dwarf spheroidal volume of the star or planet, lead to further scat-galaxies than it is in our solar system. This fact, tering and eventually cause the dark matter to ac-combined with much lower velocities of dark mat- cumulate in the object’s interior. Once a sufficientter particles in such environments (which helps to quantity of dark matter is captured, it can beginfacilitate dark matter capture), could enable dark to annihilate efficiently, converting its mass intomatter particles to accumulate in planetary ob- kinetic energy in the form of relativistic particlesjects at rates that would provide the dominant en- that are then absorbed by the surrounding mate-ergy source for planets, potentially enabling their rial. To calculate the rate at which dark mattersurfaces to maintain liquid water without the aid particles are expected to be captured by a planet,of light from a stellar host. We find that rocky we follow the standard approach of Gould (1992,super-Earths in the inner region of the Milky Way 1987) (see also Griest and Seckel (1987)). As re-could capture dark matter at a rate sufficient to peating the details of this calculation here wouldmaintain liquid water on their surfaces through not be particularly enlightening, we leave it to thethe annihilations of dark matter alone. Thus, interested reader to pursue these references if sorocky planets on large, cold orbits—whether scat- inclined.tered from the interior regions of a system or dis- As we are most interested in those planets withtant cores that failed to accrete a large envelope chemistry, surface gravity, and other character-of light elements (Laughlin et al. 2004)—or rogue istics similar to the Earth (as such features areplanets with no stellar host could potentially be likely to be related to the likelihood of a planethabitable through this mechanism. Moreover, the being able to support life), we focus on broadlytimescale over which such an object can maintain Earth-like planets. Specifically, we consider rocky 2
  3. 3. planets with an iron core, and with a range of periments (Ahmed et al. 2010a; Aprile et al. 2010;masses between roughly 1 and 10 times that of Ahmed et al. 2010b). In the calculation of the dif-the Earth. To describe the mass density of such ferential scattering cross sections, we adopt formplanets, we adopt the models described in Valen- factors based on those described by Duda et al.cia et al. (2005, 2007). In particular, we use these (2007).models to set the overall radius, core radius, and For these dark matter models and the locallyaverage core density of a given planet. For sim- inferred distribution, we calculate that dark mat-plicity, we assume a constant density for the core ter will be captured by the Earth at a rate given byand mantle of each planet (this assumption leads approximately 3×1012 (5×1015 ) particles per sec-to a modest underestimate of the capture rate of ond in the case of dark matter model A (model B).dark matter particles). We adopt a core composi- These rates are in good agreement with those cal-tion that is similar to that of the Earth: 89% iron, culated elsewhere (see Lundberg and Edsjo (2004),6% nickel, and 5% sulfur. The remaining volume for example). While these numbers may seemof each planet is assumed to be made up of mostly large at first glance, they do not represent nearlyoxygen (45%), magnesium (23%), silicon (22%), enough energy to contribute significantly to theiron (6%), aluminium (2%), and calcium (2%). Earth’s temperature. Even if dark matter parti- The dark matter capture rate of a given planet cles were to annihilate at the same rate at whichdepends on a number of environmental factors, they are captured, they would contribute a totalas well as on the properties of the dark mat- input power of 1.4 × 105 Watts (5.6 × 106 W). Inter particles themselves. In the case of the local contrast, 1.74 × 1017 W reach the Earth’s atmo-galactic neighborhood, the average density of dark sphere from the Sun (of which about 1.2 × 1017 Wmatter is inferred from galactic rotation curves is absorbed). Furthermore, the dark matter anni-to be approximately 0.4 GeV/cm3 —roughly 7 × hilation rate will come into equilibrium with the10−25 g/cm3 or half of a proton mass per cu- capture rate only if the combined capture rate andbic centimeter—(see, for example, Catena and Ul- annihilation cross sections are sufficiently large;lio (2010)). The velocity distribution can be ap- in many models this equilibrium is not expectedproximated by a Maxwell-Boltzmann distribution to be realized, further suppressing the power con-with a velocity dispersion of roughly 250 km/s and tributed through dark matter annihilation.shifted to account for the planet’s motion relative The predicted capture rates of dark matter canto the frame of the dark matter halo. be considerably higher, however, if one considers For the properties of the dark matter parti- somewhat larger planets. A ten Earth-mass planetcles themselves, we adopt two phenomenologi- in our galactic neighborhood, for example, wouldcal models: a particle with a mass of 300 GeV capture up to 5 × 1014 (8 × 1017 ) dark matterand a spin-independent elastic scattering cross particles per second—more than a factor of 100section with nucleons of σ0 = 8 × 10−44 cm2 higher. Even when considering the larger surface(Model A), and a much lighter dark matter area over which the resulting energy will be dis-candidate with a mass of 7 GeV and a spin- tributed, this represents considerably more powerindependent elastic scattering cross section with per square meter than is produced by dark matternucleons of σ0 = 2 × 10−40 cm2 (Model B). Model inside of an Earth-like planet, although still farA can be taken as a somewhat typical example too little to meaningfully contribute to the tem-of a dark matter candidate that might appear peratures required to maintain liquid water.in electroweak-scale extensions of the standard In Fig. 1, we show the capture rate (in energy-model of particle physics—supersymmetry, for equivalent units) of dark matter particles ontoexample. Model B is motivated by the signals an Earth-like planet in the local neighborhoodreported by the CoGeNT (Aalseth et al. 2010) of the Milky Way, as a function of the planet’sand DAMA/LIBRA (Bernabei et al. 2010) collab- mass. We explicitly carry out the calculation fororations (Hooper et al. 2010). In each of these masses of 1, 3 and 10 Earth masses, and interpo-models, the dark matter particles interact with late/extrapolate (as shown as a dashed line) fornuclei at approximately the maximal degree con- other masses. For this case, we assume a relativesistent with constraints from direct detection ex- motion of the Solar System relative to the dark 3
  4. 4. As seen in Fig. 1, dark matter annihilations are predicted to inject only on the order of 107 to 109 Watts or less into the surface region of an Earth- mass planet located in the local neighborhood of the Milky Way, even in the most optimistic mod- els. While the temperature that results from this energy input depends on the planet’s emissivity, for Earth-like values ( ≈ 0.6) this falls at least a factor of 107 short of that needed to maintain liquid water in the absence of starlight. A very different conclusion can be reached, however, if one considers planets in regions with much higher densities of slow moving dark matter. As an ex- ample, we consider planets in the innermost tens of parsecs of a dwarf spheroidal galaxy. DwarfFig. 1.— The rate at which dark matter parti- spheroidals are highly dense, and dark mattercles are predicted to be captured by an Earth-like dominated systems. Walker et al. (2007), for ex-planet in the local neighborhood of the Milky Way ample, describes seven dwarf spheroidals (Carina,(in energy-equivalent units), as a function of the Draco, Fornax, Leo I, Leo II, Sculptor, and Sex-planet’s mass. We show results for two optimistic tans) which have dark matter densities of 40-150dark matter models. In no case does the quantity GeV/cm3 and velocity dispersions of ∼10-20 km/sof energy in dark matter captured remotely com- within their inner 10-20 parsecs. The lower veloci-pete with the energy absorbed from the Earth by ties of these dark matter particles lead to a highersunlight. See text for more details. capture rate for two reasons: 1) They are more ef- ficiently focused gravitationally toward the planet, and 2) They can become gravitationally bound tomatter frame of 250 km/s, a velocity dispersion of the planet after collisions in which they lose even250 km/s, and a local density of 0.4 GeV/cm3 . a small amount of momentum. In such an envi- ronment, planets will be capable of capturing dark3. Maintaining Liquid Water With Anni- matter at much higher rates than are possible in hilating Dark Matter our local neighborhood. The surface temperature of a planet can be de- In addition to planets in dwarf spheroidal galax-termined by equating the energy it absorbs to that ies, we also consider planets that are located veryit emits as an approximate blackbody: near the center of the Milky Way. According to the frequently used Navarro-Frenk-White (NFW) 4 2 Pstar + Pgeo + PDM + ... = σTPl 4πRPl , (1) profile (Navarro et al. 1996, 1997), for example, the smooth component of the dark matter densitywhere σ is the Stefan-Boltzmann constant, TPl is in the Milky Way can be parametrized bythe surface temperature of the planet, RPl is theradius of the planet, is the emissivity of the 1planet’s atmosphere, and the subscripts “star”, ρDM ∝ , (3) r[1 + (r/Rs )]2“geo”, and “DM” correspond to the various con-tributions from the host star, planetary geologi- where r is the distance to the Galactic Center, andcal processes, and dark matter annihilations, etc. Rs ≈ 20 kpc is the scale radius. Furthermore, theIn the case of energy from starlight, the incoming density in the innermost kiloparsecs of the Milkypower is given by Way is generally expected to be higher than de- 2 scribed by NFW due to baryonic adiabatic con- 4 2 πRPl traction (Prada et al. 2004; Bertone and Merritt Pstar = σTstar 4πRstar (1 − a), (2) 4πD2 2005b,a; Levine et al. 2008). To account for this,where D is the distance between the star and we alter the inner slope of the NFW halo profileplanet, and a is the planet’s albedo. such that ρDM ∝ r−1.35 (instead of ρDM ∝ r−1.0 ) 4
  5. 5. Fig. 2.— The rate (in energy-equivalent units) atwhich dark matter particles are predicted to be Fig. 3.— The surface temperature of an Earth-captured by an Earth-like planet in the inner 10 like-planet that is located in the inner 10 parsecsparsecs of a dwarf spheroidal galaxy (top) and 10 of a dwarf spheroidal galaxy (top) and 10 parsecsparsecs from the center of the Milky Way (bot- from the center of the Milky Way (bottom), as atom), as a function of the planet’s mass. We show function of the planet’s mass. It is assumed thatresults for two optimistic dark matter models. See no significant starlight or other non-dark mattertext for more details. sources of energy contribute. We show results for two optimistic dark matter models and for threeinside of 3 kpc of the Galactic Center. In addition, values of the planets’ emissivity, . In the cases ofthe velocity dispersion is predicted to decrease ac- heavy planets with low emissivities, we find thatcording to σv ∝ (r/Rs )1/2 . surface temperatures can be high enough to sus- tain liquid water. See text for more details. In Fig. 2, we plot the capture rate of dark mat-ter by an Earth-like planet, 10 parsecs from thecenter of a dwarf spheroidal galaxy (ρDM = 150 matter at dramatically higher rates than are pos-GeV/cm3 , σv = 10 km/s) and 10 parsecs from the sible near our solar system. If the dark mattercenter of the Milky Way (ρDM = 825 GeV/cm3 , can annihilate into standard model particles withσv = 8.6 km/s). Comparing these results to those a roughly weak-scale cross section, capture ratesshown in Fig. 1, it is clear that planets in these this large will easily lead to capture-annihilationenvironments are capable of accumulating dark equilibrium, ie. the rate at which dark matter par- 5
  6. 6. ticles annihilate within a planet will be very nearly 4. Discussion and Conclusionsequal to the rate at which they are captured. In this paper, we have calculated the capture In Fig. 3, we show the surface temperature of rate of dark matter particles in Earth-like andthe planets described in Fig. 2, in the absence of super-Earth planets, and determined the resultingstarlight or other non-dark matter sources of en- surface temperature of those planets that wouldergy. Here we assume that all of the annihilation result from dark matter annihilations. While plan-products of the dark matter are absorbed by the ets in the local region of our galaxy receive onlysurrounding planet. If the dark matter annihi- a negligible quantity of energy from dark mat-lates significantly to neutrinos (which escape the ter annihilations, we find that planets in dwarfplanet without being absorbed), the resulting sur- spheroidal galaxies and in the innermost volumeface temperature will be reduced accordingly. We of the Milky Way could plausibly accumulate andshow results for three values of the emissivity, = annihilate enough dark matter to heat their sur-0.6, 0.1 and 0.01. A value of =0.6 represents faces to temperatures capable of sustaining liquidthe value associated with the Earth’s atmosphere. water, even in the absence of energy from starlightMore massive planets are generally expected to or other standard sources.have denser atmospheres and thus lower emissiv-ities. With this in mind, we consider =0.1–0.01 Although we expect ecologically relevant quan-to be a reasonable range for super-Earth plan- tities of energy to be released through dark matterets. None of the values we have considered rep- annihilations only within the interiors of planetsresent an emissivity as low as that found on Venus that reside in very special environments (such as( ≈ 0.004), for example. near the Galactic Center, or near the center of a dwarf spheroidal galaxy), and only in the case Notably, from these calculations we see that of dark matter models which feature large elas-planets in the innermost volume of the Milky Way tic scattering cross sections with nuclei (near thewith masses of a few times that of the Earth current upper limits), we expect that within suchor more could plausibly possess surface temper- models planets will exist which derive enough heatatures capable of sustaining liquid water. Alter- from dark matter to almost indefinitely sustainnatively, somewhat more massive planets in dwarf surface temperatures sufficient to yield liquid wa-spheroidal galaxies could also have surface tem- ter. Even in the absence of starlight, such planetsperatures that allow the presence of liquid water. could plausibly contain life. And, given their ex-Other environments, such as near the core of the tremely long lifetimes, such planets may prove toLarge Magellenic Cloud (which is 10 times more be the ultimate bastion of life in our universe.massive than typical dwarf spheroidals), and otherplanets with particularly large masses of rocky ma-terial, such as a stripped-down version of the high Acknowledgements: The authors are supporteddensity planet HD 149026 which has a rocky core by the US Department of Energy, including grantof several tens of Earth-masses (Sato et al. 2005), DE-FG02-95ER40896. DH is also supported byare also promising possibilities for high rates of NASA grant NAG5-10842.planetary dark matter capture. REFERENCES To date, the planets observed closest to theGalactic Center have been those identified by the C. E. Aalseth et al. arXiv:1002.4703, 2010.SWEEPS survey (Sahu et al. 2006), although at adistance of ∼500 pc from the Galactic Center, we D. S. Abbot and E. R. Switzer. arXiv:1102.1108,do not anticipate dark matter to provide a signifi- 2011.cant amount of energy to these planets—possibly Z. Ahmed et al. Science, 327:1619–1621, 2010a.comparable to the amount that the Earth receivesfrom geothermal processes. Z. Ahmed et al. Phys.Rev.Lett., 2010b. E. Aprile et al. Phys.Rev.Lett., 105:131302, 2010. R. Bernabei et al. Eur. Phys. J., C67:39–49, 2010. 6
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