A SIMPLE EVOLUTIONAL MODEL OF THE UV HABITABLE ZONE AND THE POSSIBILITY OF PERSISTENT LIFE EXISTENCE: THE EFFECTS OF MASS AND METALLICITY

From the era of Strughold (1953) and Huang (1959), there are many studies on the habitable zone (HZ; e.g., Dole 1964; Budyko 1969; Sellers 1969; North 1975; Rasool & De Bergh 1970; Hart 1979; Fogg 1992; Kasting et al. 1993; Spiegel et al. 2010; Abe et al. 2011; Danchi & Lopez 2013; Kopparapu 2013; Shchekinov et al. 2013; Vladilo et al. 2013; Zsom et al. 2013; Ramirez & Kaltenegger 2014; Safonova et al. 2016). However, detailed study of the the UV habitable zone (UV-HZ) remains to be done.

The inner and outer boundaries of the UV-HZ are defined as a region where the UV radiation field from a host star is moderate for persistent life existence (e.g., Buccino et al. 2007; Grenfell et al. 2014), whereas the inner and outer HZ boundaries are determined by the existence of liquid water on the surface of a terrestrial planet (Shapley 1953). UV radiation has both good and bad influences on the existence of life. If UV radiation is too weak, the synthesis of many biochemical compounds cannot occur. However, if it is too strong, the terrestrial biological systems are damaged (e.g., Rea 2000).

It should be noted that the supply of UV radiation does not come only from steady radiation from host stars but also from exceptional phenomena such as gamma-ray bursts and flares of magnetic active stars. Furthermore, there are factors other than UV radiation that affect the emergence of life. For example, the sources of organic molecules, primitive life, and water molecules include comets, and life can emerge in abnormal environments such as hydrothermal vents (e.g., Sreedhara et al. 2004; Furukawa et al. 2009; Callahan et al. 2011). Furthermore, there is a theory that lightning causes amino acids, which are made from methane, hydrogen, ammonia, and water in the atmosphere (see Schoph 1991). There is a probability that life emerges because of these sources in the absence of UV radiation. However, because stellar UV radiation is important, we discuss the effects of stellar UV radiation in this paper.

In their characteristic work, Buccino et al. (2006), Jones et al. (2006) and Guo et al. (2010) propose simple UV-HZ models. They construct UV-HZ models around host stars, the masses of which range from 0.08 to 4.00 M_☉, and consider stellar evolution along the main sequence at Zero-Age Main Sequence (ZAMS) and Terminal-Age Main Sequence (TMS). Similar to the HZ, they determine the inner and outer UV-HZ boundaries by fitting formulas between stellar luminosity, L, and radius, R, calculating the boundary flux, S. Using these values, they determine the inner and outer UV-HZ boundaries by using the stellar luminosity at wavelengths from 200 to 315 nm, the range of UV-B and UV-C in the electromagnetic spectrum. UV photon flux is estimated as UV radiation does not damage DNA at the inner UV-HZ boundary and supplies enough energy for the synthesis of biochemical compounds at the outer UV-HZ boundary. According to their estimate, the UV-HZ is closer than the HZ in cases with an effective temperature T_eff lower than 4600 K and is farther than the HZ in cases with T_eff higher than 7137 K.

It is notable that they study only the case in which the metallicity is Z = 0.02, like the Sun. The effect of metallicity depends on T_eff more than luminosity L and mass M (Tout et al. 1996). Hence, following our previous study (Oishi & Kamaya 2016), we consider the UV-HZ with low metallicity to study more broadly the possibility of the existence of life. The importance of metallicity is also suggested by many observations (e.g., Orosz et al. 2012; Barclay et al. 2013; Campante et al. 2015; Crossfield et al. 2015). Considering the long lifespan of low-mass stars, it is important to examine metallicity, because these stars have formed at the early period of the universe and have little metallicity. Furthermore, if metallicity is less than that of the Sun, the stellar spectrum changes because of its low opacity. So, in this work, we consider 1/10 and 1/100 metallicity of the Sun as extreme cases.

The current model is an extension of our previous work (Oishi & Kamaya 2016). A simple model of HZ is useful. Indeed, Guo et al. (2009) developed a model including the effect of stellar evolution. Consequently, they can discuss HZ according to the mass spectrum of host stars. In another context, a simple UV-HZ is modeled by Buccino et al. (2006). Coupling Guo et al. (2009) and Buccino et al. (2006), Guo et al. (2010) constructed a simple UV-HZ model with stellar evolution. After that, Oishi & Kamaya (2016) discussed the effect of metallicities of host stars with various masses and their evolution, and they found that the possibility of persistent life existence decreases if the metallicity becomes lower. However, the UV-HZ problem remains to be discussed. Thus, this paper proposes a model coupling Guo et al. (2010) and Oishi & Kamaya (2016). It is notable that the stellar evolution effect is ineffective if stellar mass is smaller than about 0.8 M_☉ (e.g., Oishi & Kamaya 2016). So we focus our attention on the mass range larger than about 0.8 M_☉.

On this basis, in this paper, we construct simple models of the inner and outer UV-HZ boundaries, considering the effect of metallicity in addition to the formulas of Guo et al. (2010). The outline of the paper is as follows: we introduce the HZ model with the metallicity effect and present our formula of UV-HZ in Section 2 and present our numerical results in Section 3. A discussion is provided in Section 4, followed by a summary of our paper.

This section describes our formulation for studying the UV-HZ affected by stellar evolution and metallicity, following Buccino et al. (2007). That is, our formula is an extension of Guo et al. (2010). Using the formulas and values in Oishi & Kamaya (2016), we determine the distance of the inner and outer UV-HZ boundaries at each evolutional phase at ZAMS and TMS. In this work, we do not consider masses, M_planet, and sizes, R_planet, of planets. This is because the effect of size is nearly canceled, as found from the most simple case (heating by stellar radiation is ∼blackbody radiation cooling): $\pi {R}_{\mathrm{planet}}^{2}S\sim 4\pi {R}_{\mathrm{planet}}^{2}\sigma {T}^{4}$. Then, in this work and previous works (e.g., Guo et al. 2009, 2010 and Oishi & Kamaya 2016), we mainly discuss the greenhouse effect. In the following, we adopt typical models of Z = 0.0002, 0.002, and 0.02 for clear discussions. For the reader's convenience, we present our previous formulation of HZ in the Appendix. In this paper, the inner and outer boundaries of HZ at each evolutional phase are denoted as ${d}_{\mathrm{out},\mathrm{HZZAMS}}$, ${d}_{\mathrm{in},\mathrm{HZZAMS}}$, ${d}_{\mathrm{out},\mathrm{HZTMS}}$, and ${d}_{\mathrm{in},\mathrm{HZTMS}}$, respectively.

In addition to HZ models, we determine the inner and outer UV-HZ boundaries. The inner UV-HZ boundaries are defined by UV radiation that should not damage DNA, and the outer UV-HZ boundaries are defined by UV radiation that nicely supplies enough energy for the synthesis of biochemical compounds. We calculate stellar luminosity, L_λ, at wavelength, λ, and UV photons, N, at both the inner and outer UV-HZ boundaries using stellar radius, R, and effective temperature, T_eff. The expression of L_λ is

$$\begin{eqnarray}&&{L}_{\lambda }=4\pi {R}^{2}\pi \displaystyle \frac{2\mathrm{hc}}{{\lambda }^{3}}\displaystyle \frac{1}{{e}^{\displaystyle \frac{\mathrm{hc}}{{{kT}}_{\mathrm{eff}}\lambda }}-1},\end{eqnarray} \tag{ 1 }$$

and those of UV photons at both inner and outer UV-HZ boundaries are

$$\begin{eqnarray}&&{N}_{\mathrm{in}}={\int }_{200\,\mathrm{nm}}^{315\,\mathrm{nm}}B(\lambda )\displaystyle \frac{\lambda }{\mathrm{hc}}\displaystyle \frac{{L}_{\lambda }}{4\pi {d}^{2}}d\lambda ,\end{eqnarray} \tag{ 2 }$$

$$\begin{eqnarray}&&{N}_{\mathrm{out}}={\int }_{200\,\mathrm{nm}}^{315\,\mathrm{nm}}\displaystyle \frac{\lambda }{\mathrm{hc}}\displaystyle \frac{{L}_{\lambda }}{4\pi {d}^{2}}d\lambda ,\end{eqnarray} \tag{ 3 }$$

where B(λ) is the probability of a UV photon of energy hc/λ to dissociate free DNA and its expression is

$$\begin{eqnarray}&&\mathrm{log}B(\lambda )\simeq \displaystyle \frac{6.113}{1+\exp \tfrac{\lambda -310.9}{8.8}}-4.6.\end{eqnarray} \tag{ 4 }$$

And according to Buccino et al. (2006), a terrestrial planet needs to receive from half to twice of the UV radiation received by the Archean Earth for biological evolution. So, the expressions are simply estimated as

$$\begin{eqnarray}&&{N}_{\mathrm{in}}\sim 2{N}_{\mathrm{in}}(\mathrm{Arc}),\end{eqnarray} \tag{ 5 }$$

$$\begin{eqnarray}&&{N}_{\mathrm{out}}\sim 0.5{N}_{\mathrm{out}}(\mathrm{Arc}).\end{eqnarray} \tag{ 6 }$$

Combining Equations (1)–(6), we can obtain the distance of the inner and the outer UV-HZ boundaries from a host star

$$\begin{eqnarray}&&{d}_{\mathrm{uvin}}=\displaystyle \frac{\sqrt{2}}{2}\displaystyle \frac{R}{{R}_{\mathrm{Arc}}}\sqrt{\displaystyle \frac{{F}_{1}({T}_{\mathrm{eff}})}{{F}_{1}({T}_{\mathrm{Arc}})}},\end{eqnarray} \tag{ 7 }$$

$$\begin{eqnarray}&&{d}_{\mathrm{uvout}}=\sqrt{2}\displaystyle \frac{R}{{R}_{\mathrm{Arc}}}\sqrt{\displaystyle \frac{{F}_{2}({T}_{\mathrm{eff}})}{{F}_{2}({T}_{\mathrm{Arc}})}}.\end{eqnarray} \tag{ 8 }$$

And the expressions of F₁ and F₂ are

$$\begin{eqnarray}&&{F}_{1}(T)={\int }_{200\,\mathrm{nm}}^{315\,\mathrm{nm}}\displaystyle \frac{\tfrac{B(\lambda )}{{\lambda }^{2}}d\lambda }{{e}^{\displaystyle \frac{\mathrm{hc}}{{kT}\lambda }}-1},\end{eqnarray} \tag{ 9 }$$

$$\begin{eqnarray}&&{F}_{2}(T)={\int }_{200\,\mathrm{nm}}^{315\,\mathrm{nm}}\displaystyle \frac{\tfrac{1}{{\lambda }^{2}}d\lambda }{{e}^{\displaystyle \frac{\mathrm{hc}}{{kT}\lambda }}-1}.\end{eqnarray} \tag{ 10 }$$

In these equations, R is in solar units, T_eff is in Kelvin, and d is in units of au. R_Arc is 0.9113 R_☉ and T_Arc is 5603 K, which are quantities at the Archean Earth (about 3.8 Gyr ago). In the following, the inner and outer boundaries of the UV-HZ at each evolutional phase are denoted as ${d}_{\mathrm{out},\mathrm{UVZAMS}}$, ${d}_{\mathrm{in},\mathrm{UVZAMS}}$, ${d}_{\mathrm{out},\mathrm{UVTMS}}$, and ${d}_{\mathrm{in},\mathrm{UVTMS}}$, respectively.

In this section, we present our numerical results for the UV-HZ. Because we are interested in main-sequence stars with low and intermediate mass, the mass range is selected from 0.08 to 4.00 M_☉ since we are interested in planets like Earth. Furthermore, we adopt various metallicities, since long-lived stars can be detected in future observational surveys. Then, we select 1/10 and 1/100 metallicity of the Sun as extreme cases (Guo et al. 2010 and Oishi & Kamaya 2016). Thus, we determine the inner and outer UV-HZ boundaries at ZAMS and TMS by means of Equations (7) and (8). Results are presented in the following figures.

In Figure 1, the case of metallicity Z = 0.0002, diamonds represent ZAMS cases and triangles are TMS ones. All units are the same as in Figures 1–3 of Oishi & Kamaya (2016). Here, we find bumps at about M = 0.6 M_☉ and 1.6 M_☉ for both the inner and outer UV-HZ boundaries at TMS. And we also find that the overlapped region of UV-HZ (M ≥ 1.0 M_☉), at which the outer UV-HZ boundary of ZAMS overtakes the inner UV-HZ boundary of TMS (${d}_{\mathrm{out},\mathrm{UVZAMS}}\gt {d}_{\mathrm{in},\mathrm{UVTMS}}$), is wider than that of the HZ whose overlapped region (${d}_{\mathrm{out},\mathrm{HZZAMS}}\gt {d}_{\mathrm{in},\mathrm{HZTMS}}$) is limited to more than about M ≥ 1.8 M_☉. It is notable that although the bump at about M = 1.6 M_☉ in the case of the TMS of Figure 1 is not as clear as that in the case of the HZ, we find strong undulation at M ≤ 1.0 M_☉ of Figure 1. In other words, the effect of metallicity for UV-HZ at TMS is weaker than HZ at M ≥ 1.0 M_☉, whereas it is stronger than HZ at M ≤ 1.0 M_☉.

Zoom In Zoom Out Reset image size

In Figure 2, we present the Z = 0.002 case, which is larger than the Z of Figure 1. All units are the same as in Figure 1. The shapes of graphs, the overlapped region, and the positions of bumps are almost the same as those depicted in Figure 1. In this case, the effect of metallicity is also weaker than HZ at M ≥ 1.0 M_☉ and stronger than HZ at M ≤ 1.0 M_☉. Even in Figure 3, in which we present the case of Z = 0.02, the overlapped region is almost the same as that in cases of Z = 0.0002 and Z = 0.002. Although there is no bump at M = 1.6 M_☉, we can find undulation at around M = 0.6 M_☉, resembling the cases of low metallicity.

Zoom In Zoom Out Reset image size

Zoom In Zoom Out Reset image size

4.1. The Effect of Metallicity

4.2. Possibility of Life Existence

In our study, we calculate the distances of HZ boundaries (${d}_{\mathrm{out},\mathrm{HZZAMS}}$, ${d}_{\mathrm{in},\mathrm{HZZAMS}}$, ${d}_{\mathrm{out},\mathrm{HZTMS}}$, and ${d}_{\mathrm{in},\mathrm{HZTMS}}$ ) and UV-HZ boundaries (${d}_{\mathrm{out},\mathrm{UVZAMS}}$, ${d}_{\mathrm{in},\mathrm{UVZAMS}}$, ${d}_{\mathrm{out},\mathrm{UVTMS}}$, and ${d}_{\mathrm{in},\mathrm{UVTMS}}$) by using simple and obvious models. Here, we compare the overlapped regions of HZ and UV-HZ. To have persistent life existence, the region where the area defined as the outer boundary of HZ at ZAMS overtakes the outer boundary of HZ at TMS (${d}_{\mathrm{out},\mathrm{HZZAMS}}\gt {d}_{\mathrm{in},\mathrm{HZTMS}}$) must overlap with the area defined as the outer boundary of UV-HZ at ZAMS overtakes the outer boundary of UV-HZ at TMS (${d}_{\mathrm{out},\mathrm{UVZAMS}}\gt {d}_{\mathrm{in},\mathrm{UVTMS}}$). In other words, we need any one of the following conditions of d_out,UVZAMS > d_out,HZZAMS > d_in,UVTMS > d_in,HZTMS, d_out,HZZAMS > d_out,UVZAMS > d_in,HZTMS > d_in,UVTMS, d_out,UVZAMS > d_out,HZZAMS > d_in,HZTMS > d_in,UVTMS, and d_out,HZZAMS > d_out,UVZAMS > d_in,UVTMS > d_in,HZTMS. Here, we call it the coexisting region.

As described in Figure 4(b), we find that the overlapped region of HZ and UV-HZ coexists at the mass range from 1.0 to 1.5 M_☉ when Z = 0.02. Hypothesizing for the solar system, UV-HZ exists from about 0.6–1.1 au at ZAMS and from about 0.9 to 1.9 au at TMS. According to these estimates, the coexisting region of UV-HZ is from about 0.9 to 1.1 au. The distance from the Sun to Venus is about 0.7 au, and that from Mars is about 1.5 au. Namely, these planets exist outside of the coexisting region at the moment. Once, Venus existed in UV-HZ, but was excluded from this area owing to the evolution of the Sun. In the case of Mars, the reverse will occur.

Zoom In Zoom Out Reset image size

When Z = 0.002, the coexisting region is limited at only around 1.2 M_☉ (Figure 5(b)). Of interest, when Z = 0.0002, there are no coexisting regions (Figures 6(a) and (b)). Considering this trend, the possibility of life existence extremely decreases as the metallicity decreases. This is because the lack of UV radiation lets the coexisting region disappear when metallicity is low. If we expect life emergence at low metallicity stars, we need increments of bolometric luminosity and UV radiation. For example, exceptional phenomena like the Coronal Mass Ejection (CME) may make the coexisting region wider. If the CME occurs in magnetically active low mass stars, the luminosity and UV radiation momentarily increase when it collides with planets, so we expect the coexisting region to become wider and life emergence to be possible even around low-mass and low-metallicity stars.

Zoom In Zoom Out Reset image size

Zoom In Zoom Out Reset image size

In the future, the observational technique for surveying stars with low mass and low metallicity in the infrared band will be possible. For example, the Transiting Exoplanet Survey Satellite (Ricker et al. 2014) project will be useful, and will attempt to discover thousands of exoplanets, monitoring more than 200,000 stars for temporary drops in brightness. It is important to note that red dwarfs and K-type main-sequence stars are also the targets. When this project is launched in the future, we will be able to study low-mass and low-metallicity stars as targets for life emergence.

4.3. The Importance of the Ocean

4.4. Life Emergence on Exo-moons

Confirming the previous results for HZs, this paper examines the effect of metallicity on the inner and outer UV-HZ boundaries in which the main sequence stellar mass range is from 0.08 to 4.00 M_☉. To obtain clear results, we proposed runaway greenhouse and maximum greenhouse models. Then, we found that the overlapped regions of the UV-HZ at ZAMS and TMS are little affected by the effect of metallicity. The possibility of minimally persistent life existence at the relatively wide mass range is discussed, comparing the HZ and UV-HZ. That is, considering the coexisting area of the HZ and UV-HZ, we find the possibility decreases significantly. The possibility is limited to the mass range of host stars only from 1.0 to 1.5 M_☉ with at most Z = 0.02, whereas when Z = 0.0002, we cannot find the possibility at any masses. If we expect life in cases of low-mass and low-metallicity host stars, we must consider the effect of a sea and/or increments of UV radiation.

The authors would like to thank the anonymous referee for useful and fruitful suggestions that helped to improve the original manuscript very much. We also thank Dr. Kyoko Watanabe for her encouragement.

Herein we present the formulation of the HZ in the previous paper (Oishi & Kamaya 2016). This is the extension of Guo et al. (2009) according to the detailed studies of Tout et al. (1996) and Hurley et al. (2000). All of the coefficients can be found in Oishi and Kamaya. In the case of ZAMS,

$$\begin{eqnarray}&&{L}_{\mathrm{ZAMS}}=\displaystyle \frac{({a}_{1}{M}^{5.5}+{a}_{2}{M}^{11})}{({a}_{3}+{M}^{3}+{a}_{4}{M}^{5}+{a}_{5}{M}^{7}+{a}_{6}{M}^{8}+{a}_{7}{M}^{9.5})},\end{eqnarray} \tag{ 11 }$$

$$\begin{eqnarray}&&{R}_{\mathrm{ZAMS}}=\displaystyle \frac{{a}_{8}{M}^{2.5}+{a}_{9}{M}^{6.5}+{a}_{10}{M}^{11}+{a}_{11}{M}^{19}+{a}_{12}{M}^{19.5}}{{a}_{13}+{a}_{14}{M}^{2}+{a}_{15}{M}^{8.5}+{M}^{18.5}+{a}_{16}{M}^{19.5}},\end{eqnarray} \tag{ 12 }$$

and in the case of TMS,

$$\begin{eqnarray}&&{L}_{\mathrm{TMS}}=\displaystyle \frac{{a}_{17}{M}^{3}+{a}_{18}{M}^{4}+{a}_{19}{M}^{{a}_{22}+1.8}}{{a}_{20}+{a}_{21}{M}^{5}+{M}^{{a}_{22}}},\end{eqnarray} \tag{ 13 }$$

$$\begin{eqnarray}&&{R}_{\mathrm{TMS}}=\displaystyle \frac{{a}_{23}+{a}_{24}{M}^{{a}_{26}}}{{a}_{25}+{M}^{{a}_{27}}}(M\leqslant 1.5),\end{eqnarray} \tag{ 14 }$$

$$\begin{eqnarray}&&{R}_{\mathrm{TMS}}=\displaystyle \frac{{a}_{28}{M}^{3}+{a}_{29}{M}^{{a}_{32}}+{a}_{30}{M}^{{a}_{32}+1.5}}{{a}_{31}+{M}^{5}}(M\gt 1.5),\end{eqnarray} \tag{ 15 }$$

are adopted by us. Coefficients and indexes in the above equations are denoted by means of metallicity, Z, as

$$\begin{eqnarray}{a}_{n} & = & \alpha +\beta \,{\mathrm{log}}_{10}\displaystyle \frac{Z}{{Z}_{\odot }}+\gamma {\left[{\mathrm{log}}_{10}\displaystyle \frac{Z}{{Z}_{\odot }}\right]}^{2}+\delta {\left[{\mathrm{log}}_{10}\displaystyle \frac{Z}{{Z}_{\odot }}\right]}^{3}\\ & & +\varepsilon {\left[{\mathrm{log}}_{10}\displaystyle \frac{Z}{{Z}_{\odot }}\right]}^{4}(1\leqslant n\leqslant 32),\end{eqnarray} \tag{ 16 }$$

in which the five Greek characters are summarized in Table 1 of Oishi & Kamaya (2016). The inner HZ boundary is determined by the runaway greenhouse in the broad sense and the withdrawal of water in the narrow sense. We calculate flux, S, of the inner and outer HZ boundaries by using Equations (11)–(15) and $L=4\pi {R}^{2}\sigma {{T}_{\mathrm{eff}}}^{4}$. Our effective stellar fluxes are

$$\begin{eqnarray}&&\displaystyle \frac{{S}_{\mathrm{in}}}{{S}_{\odot }}=4.190\times {10}^{-8}\,{{T}_{\mathrm{eff}}}^{2}-2.139\times {10}^{-4}\,{T}_{\mathrm{eff}}+1.296,\end{eqnarray} \tag{ 17 }$$

$$\begin{eqnarray}&&\displaystyle \frac{{S}_{\mathrm{out}}}{{S}_{\odot }}=6.190\times {10}^{-9}\,{{T}_{\mathrm{eff}}}^{2}-1.319\times {10}^{-5}\,{T}_{\mathrm{eff}}+0.2341,\end{eqnarray} \tag{ 18 }$$

where S_☉ is the solar constant and T_eff is in units of Kelvin. Equations (17) and (18) are determined on the basis of the greenhouse effect, following Underwood et al. (2003) and Jones et al. (2006). Using these equations and $L=4\pi {d}^{2}S$, we determine distances at both the inner and outer HZ boundaries, d, as follows,

$$\begin{eqnarray}&&\displaystyle \frac{{d}_{\mathrm{in}}}{\mathrm{au}}={\left[\displaystyle \frac{L}{{L}_{\odot }}\displaystyle \frac{{S}_{\odot }}{{S}_{\mathrm{in}}}\right]}^{0.5},\end{eqnarray} \tag{ 19 }$$

$$\begin{eqnarray}&&\displaystyle \frac{{d}_{\mathrm{out}}}{\mathrm{au}}={\left[\displaystyle \frac{L}{{L}_{\odot }}\displaystyle \frac{{S}_{\odot }}{{S}_{\mathrm{out}}}\right]}^{0.5}.\end{eqnarray} \tag{ 20 }$$