# A Statistical Estimation of the Occurrence of Extraterrestrial Intelligence in the Milky Way Galaxy

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## Abstract

**:**

_{A}); (2) evolutionary timescales (T

_{evo}); and (3) probability of self-annihilation of complex life (P

_{ann}). We found P

_{ann}to be the most influential parameter determining the quantity and age of galactic intelligent life. Our model simulation also identified a peak location for ETI at an annular region approximately 4 kpc from the galactic center around 8 billion years (Gyrs), with complex life decreasing temporally and spatially from the peak point, asserting a high likelihood of intelligent life in the galactic inner disk. The simulated age distributions also suggest that most of the intelligent life in our galaxy are young, thus making observation or detection difficult.

## 1. Introduction

## 2. Methodology

- Initiated a 3D spatial hash table of Milky Way with distributed gas mass;
- Generated Sun-like stars harboring Earth-like planets and activated supernova explosion with the same distribution as observations;
- For each Earth-like planet, allow life to emerge with the Poisson process of abiogenesis;
- For each life-bearing planet free from transient events (e.g., supernova), follow life’s evolution into intelligence.

#### 2.1. Formation of Sun-Like Star Harboring Earth-Like Planet

#### 2.1.1. Prevalence of Sun-Like Star Harboring Earth-Like Planets

_{⊙}≤ M ≤ 1.2 M

_{⊙}, where M

_{⊙}= 1 denotes the mass of the Sun. We also adopted the initial mass function (IMF, the initial distribution of mass for a star population), with α = 2.35 [28], and calculated the approximate Sun-like star fraction in the Milky Way. Next, we described the Earth-like planets as planets: (1) with 1–2 Earth-radii, (2) receiving stellar energy within a factor of 4 compared to that of Earth, and (3) with Earth-like orbital period of 200 to 400 days. From these perspectives, we used recent observational analysis on the prevalence of Earth-sized planets [29], which estimated that 11% of the Earth-size planets around Sun-like stars receive Earth-like stellar energy, and 5.7% of the Earth-sized planets obtain Earth-like orbital periods. We multiplied these probabilities to acquire the fraction of Sun-like stars harboring Earth-like planets in the Galaxy that fit our four criteria described above.

#### 2.1.2. Spatial Hash Table and Distribution of Gas

^{3}. This galactic table enables the computation of large-scale objects at a real-time frame rate, and allows fast location and proximity detection queries [30]. A recent work [31] used a similar approach to implement the hierarchical density in investigating galactic formation and evolution.

_{⊙}kpc

^{−2}) and r is the radial distance from the Galactic Center (kpc). The constant ${{\displaystyle \sum}}_{\mathrm{c}}=1.4\times {10}^{8}{\text{}\mathrm{M}}_{\odot}{\mathrm{pc}}^{-2}$ is the central surface density of the Galaxy [32], and ${\mathrm{h}}_{\mathrm{R}}$ = 2.25 kpc denotes the radial disk scale length. At the time of the simulated Galaxy’s formation, this equation assigns different total surface densities of gas to each cell based on their distance from the Galactic Center.

#### 2.1.3. Upper Limit of Star Formation

_{SFR}represents the surface density of SFR (M

_{⊙}kpc

^{−2}Myr

^{−1}), and ${{\displaystyle \sum}}_{\mathrm{G}}$ is the dimensionless ${{\displaystyle \sum}}_{\mathrm{gas}}$ from Equation (1) in the unit of M

_{⊙}kpc

^{−2}. The constant A = 250 M

_{⊙}kpc

^{−2}Myr

^{−1}[34], and N = 1.4 [34,35]. For each cell within the galactic model, we first calculated its ${{\displaystyle \sum}}_{\mathrm{SFR}}$ from the initially-assigned ${{\displaystyle \sum}}_{\mathrm{gas}}$ described above, and then calculated the theoretical stellar mass of SFR (M

_{SFR}, in M

_{⊙}Myr

^{−1}) by multiplying its surface area. We estimated the M

_{SFR}for Sun-like stars harboring Earth-like planets according to the fraction from Section 2.2. For each time step (Myr), our galactic model accumulates the theoretical stellar mass available for the formation of stars (M

_{SF}, in M

_{⊙}). This means, at each location, newly available stellar mass from the collapse of gas will be added to the total available M

_{SF}according to the M

_{SFR}. We then acquired the theoretical stellar mass for the star formation and used it as an upper limit for the total stellar mass of star formation in each cell within the galactic model. This theoretical estimate is not intended for the SFR, but rather, to incorporate the relationship between gas and star formation. We utilized the SFR according to a recent chemical evolution model of star formation history (SFH), and the process of star formation will be described in detail in Section 2.1.5.

#### 2.1.4. Stellar Mass and Main Sequence Lifetime

_{⊙}≤ M ≤ 1.2 M

_{⊙}and its main sequence lifetime, the star’s overall lifespan, corresponding to its mass [36]:

_{SF}at the corresponding cell, analogous to the formation of planetary nebulae.

#### 2.1.5. Star Formation Model

_{SF}(described in Section 2.1.3) from the corresponding cell at that location, and checks if there is sufficient available stellar mass for the star to form. If the criteria are met, the total M

_{SF}at that cell will be subtracted by the stellar mass of the newly formed star, resembling the conversion of gas into stars. This process of star formation will be repeated through the loop of the SFR from the SFH model, varying by different time phases of the Galaxy. By combining the theoretical approach of star formation prescription from the Schmidt–Kennicutt law with a SFH model derived from the accurate stellar observations, our model has greater power in that it respects the nature of star formation and does not rely too heavily upon a single model.

#### 2.2. Supernova

^{−2}yr

^{−1}was modeled and it concluded that 85% of these SNes are from massive progenitors. This is consistent with the theoretical estimates [44] that predicted the Type II supernova (SNII, explosion of a star with mass greater than 8 M

_{⊙}) rate to be 1.96–3.35 × 10

^{−2}yr

^{−1}. The frequency of Type Ia supernova (SNIa, explosion of a white dwarf in a binary system) events is estimated by an earlier study [45], which found the value of 2.25 to 2.9 × 10

^{−3}yr

^{−1}.

_{B}, about 435nm wavelength) to be −16.89 and σ = 1.35. In addition, a recent study [48] developed the SNIa distribution from 239 SNIa samples with K-corrections and a bias correction process, which found the mean M

_{B}of −19.25 and σ = 0.5. From these distributions of SN, we propose a simple parameterization for the sterilization distance of each SNII and SNIa, which is inspired by the approach from the previous work [15]:

_{SNe}is the distance that will result in extinction of life from a given SN to a nearby life-bearing planet, and M

_{SN}is the absolute magnitude of the given SN. The constant d

_{SNII}= 0.008 kpc denotes the extinction distance of an average SNII [46], and M

_{SNII}= –16.89 is the mean absolute magnitude M

_{B}of SNII [47]. We acknowledge that this parameterization may not be the most realistic, considering the complexity of sterilization mechanisms caused by SNe; however, it is reasonable enough to model SNe in our simulation.

_{min;}the emergence of life is defined as a Poisson process of abiogenesis, which is presented in the next subsection.

#### 2.3. Poisson Process of Abiogenesis

_{A}, with unit Myr

^{−1}) and time. In addition, we interpreted the complex and multi-path chemistry towards the accumulation of life as an ensemble, similar to previous work (e.g., [22]). Thus, the probability of life arising on a planet within time T is:

_{Poisson}[λ

_{A}, T, n = 0] is the probability of obtaining zero successful events, λ

_{A}is the rate parameter, or the probability rate of abiogenesis in an Earth-like planet per unit time (Myr), and T

_{min}is the time period when a young Earth-like planet had a severe environment that precluded life by the time of its formation, uniformly chosen from a range of 0.1 to 1 Gyr. We prefer this approach of T

_{min}over a normal distribution or a specific chosen value because it will provide a relatively unbiased value and allow different Earth-like planets to vary, as the time period that strictly precludes life in Earth remains disputed. We recognize that this range itself is an assumption; however, as we currently lack a better understanding towards the origin of life, this range is reasonable enough to put a constraint on the results while allowing some variations to occur.

_{A}may not be a uniform constant even when the planets are all Earth-like and possibly share common mechanisms for the development of life. The disparities of planetary environments over time may also influence our results. To address this problem, we include the parameter T

_{min}, which responds to one of the major changes from a severe environment to a milder one. We argue that, as most of the stark changes in Earth came from the activities of life after the first success of an abiogenesis event, those changes are irrelevant to this process of our model. Additionally, while a recent study [23] suggested that the rate of abiogenesis, λ

_{A}, is heavily dependent on specific environmental conditions, we assume that Earth-like planets are likely to have a very similar rate of abiogenesis, λ

_{A}.

_{A}(e.g., [22]), we notice the value of this parameter varies greatly. To extend previous work of quantifying λ

_{A}, we assume no particular value but simply present varying results with different values of λ

_{A}and evaluate their weights on a global scale of distributed stellar systems. We chose the range of values of the parameter to be 1 and 10

^{−6}Myr

^{−1}, the upper and lower limits obtained from the range suggested by the previous study [22].

#### 2.4. Sufficient Time for the Evolution of Intelligence

_{evo}, in Gyr). While Earth may provide a hypothetical inference for this parameter, we present the results from selected potential values. On Earth, T

_{evo}is approximately 3 to 3.5 Gyrs from the emergence of life to the current state where we start the SETI. Whether or not this is a typical timescale on other Earth-like planets is unknown, so we therefore selected three potential values: T

_{evo}± 0.2 Gyr, where T

_{evo}= 1, 3, 5.

_{evo}we described in this subsection corresponds to the time period that is free from transient events; when a nearly sterilizing SNe threatens land-based life during the evolutionary process, we simply reset the process of abiogenesis and evolution on that planet, allowing them to recur as the planet ages.

#### 2.5. Annihilation of Intelligence

_{ann}to denote the probability of self-annihilation for galactic complex life. In each time step (1 Myr), we incorporated P

_{ann}to the development of complex life with Monte Carlo methods. We assumed that this parameter remains uniformly constant over time, which lacks temporal variations or different social aspects from the civilizations and may result in a large variation. However, by no means did we attempt to estimate P

_{ann}, as this parameter serves only to provide a qualitative understanding on possible outcomes of intelligent life, that we, as complex life, can potentially annihilate ourselves. We also utilized different values of P

_{ann}to present the varying results from extreme case scenarios (e.g., when P

_{ann}is set to 0 or 0.99) as a means to examine its impact on the global prevalence of ETI in the Milky Way. We tested a range of values from 0 to 0.99, and selected the following for this parameter: 0, 0.5 and 0.99; the lower the value of P

_{ann,}the greater the maximum number of potential galactic life. For all three values, we provided their spatial and temporal variations on the galactic prevalence of intelligent life. We excluded the value of 1 for the upper limit, simply due to the fact that we are still alive; a value of 1 would mean that the level of intelligent life in the entire Galaxy would be zero. On the other hand, a value of zero cannot be ruled out, as a civilization may become immortal [56,57].

## 3. Results and Discussion

#### 3.1. Spatial–Temporal Analysis on the Occurrence of ETI

_{ETI}) with spatial and temporal profiles. Figure 1 has the current time line (13 Gyrs) and our location at the current time (8 kpc, 13 Gyrs) indicated for reference.

_{A}, 1 or 10

^{−6}Myr

^{−1}, was assigned to each vertical panel. For better comparison, we presented the results from different λ

_{A}with the same color-contour coding and found similar results. This is possibly due to the large number of Earth-like planets around the peak areas, and given enough time, life may be common there; such a significantly large sample of life resulted in little variation. Thus, we suggest that life is common elsewhere and the prevalence of ETI is not significantly dependent on the parameter λ

_{A}. Within the time range developed [22], the probability of life arising is likely not the factor behind the Fermi Paradox. Unless we speculatively assume a value for λ

_{A}far below the lower limit of the range developed by previous work, the number and prevalence of ETI is unlikely to alter significantly, which may discredit the Rare Earth hypothesis as a resolution to the Fermi Paradox.

_{ann}values from 0 to 0.99 for examining the impact of the potential of self-annihilation on the prevalence of ETI. The selected values of 0, 0.5, and 0.99 are plotted in horizontal panels (I), (II) and (III), respectively. As shown, the range of Z

_{ETI}varies significantly with different values of P

_{ann}, suggesting that the quantity of galactic intelligent life is highly dependent on the likelihood of self-annihilation. One can interpret the significance of this parameter on the related hypothesis (Great Filter theory) that the probability of self-annihilation is possibly high, resulting in an extremely small fraction of ETI. We take no position in this argument; rather, our focus is to highlight the growth propensity for potential intelligent life in the Milky Way. We note that in panel (III), P

_{ann}= 0.99 shows that some proportions of the spatial–temporal variations deviate from general patterns due to its small size resulting from an extremely high possibility of self-annihilation; however, this will not invalidate our conclusions as: (1) the probability of 0.99 is an extreme case scenario and the actual probability of self-annihilation is unlikely to be so close to 1; and (2) the general peak location and how prevalence of ETI change spatially and temporally remain consistent in their spatial–temporal profiles.

_{evo}. The vertical panels of Figure 1A–C correspond to a timescale of 1, 3, and 5 ($\pm $0.1) Gyrs, respectively, each plotted with the same scale for time and galactocentric radius. In panel Figure 1A, the peaks stretch a wider time period than other two panels because civilizations appeared earlier with a shorter timescale required for evolution. Results for growth propensity remain generally consistent, and the number range does not vary significantly compared to what is presented with different values for P

_{ann}.

_{ETI}varies significantly with change in parameters like P

_{ann}, peak location and spatial–temporal propensity for the prevalence of ETI remains precise throughout all scenarios. From Figure 1, we can develop a comprehensive picture of where and when potential complex life has formed: at the inner Galaxy between 2 and 8 kpc, with the center focus of the peak 4 kpc from the Galactic Center and time around 8 Gyrs, with the number decreasing monotonically outward. The Z

_{ETI}immediately dropped at the boundary of the galactic inner disk (8 kpc), and remained a low number density throughout the galactic outer disk. Interestingly, our location is not within the region where most ETI occur, as our sun is located outside of the boundary of the inner Galaxy (see the white star in Figure 1); our location may merely be too far from other potential complex life. We suggest for the SETI to be conducted further into the inner Galaxy, ideally towards the annulus 4 kpc from the galactic center.

_{ETI}over a stretch of 50 Gyrs. The parameter P

_{ann}is set to 0 in this plot, suggesting the only factors resulted in this equilibrium are star formation and death, and sterilizing SNe. Namely, this latter equilibrium state also remarks the peak point as an unusual outburst of ETI over time. In particular, Figure 2 marks the equilibrium state at around 20 Gyrs, and the prevalence of ETI remained identical throughout the next 30 Gyrs.

_{ETI}, we presented the sterilized number of ETI with a similar spatial–temporal analysis, plotted in Figure 3. We presented the results when T

_{evo}is set to 3 Gyrs, simply because one collection of plots is enough to see the correlation between the sterilizing SNe frequency and the prevalence of ETI. However, we presented results from other varying parameters as a means to compare the plots with the corresponding spatial–temporal profiles from vertical panel Figure 1B. We found the quantity of ETI increases with the frequency of sterilizing SNe. When the Z

_{ETI}reaches the maximum, the SNe event that sterilized complex life also reaches a maximum, and we can conclude that the significantly higher number density of habitable stars outweighs the impact of more frequent sterilizing SNe events.

#### 3.2. The Effect of Intelligence Annihilation Parameter on Age Distributions

_{evo}, λ

_{A}, P

_{ann}), and found that P

_{ann}observably influences the results of age distribution. Therefore, we ran the model with P

_{ann}values ranging from 0 to 0.99, and selected three resulting plots in Figure 4. We selected the value 0, 0.001, and 0.1 because each changes the age distribution greatly. When P

_{ann}is set to 0 in panel (a), the ages of ETI vary significantly from 0 to 10 Gyrs. However, this variation immediately drops when P

_{ann}is set to 0.001 in panel (b), with ages only varying from 0 to 2.5 Gyrs. This suggests that P

_{ann}must be extremely low to permit age variations to occur. More, when increasing P

_{ann}to 0.1 in panel Figure 4C, all complex life become less than 0.06 Gyr in age, and the majority stay younger than 0.01 Gyr. Since we cannot preclude the high possibility of annihilation, Figure 4 suggests that most of potential complex life within the Galaxy may still be very young.

#### 3.3. Discussion

## 4. Conclusions

_{A}, T

_{evo}, P

_{ann,}to trace the origin, evolution, and development of life in the Milky Way, and assess the spatial and temporal variations for the quantity of ETI.

_{A}and extreme case scenarios of P

_{ann}(0 and 0.99), our conclusion of the precise location and time for the peak is not altered. Our results suggest that the quantity of intelligent life does not always increase with time; in fact, our model predicts that after the peak occurs, the number of ETI starts to decrease monotonically with time, and this propensity remains throughout the next 6.5 Gyrs. More, our results show that the level of ETI will eventually reach an equilibrium between birth and death of intelligent life at approximately 20 Gyrs. Further investigation for the number of sterilizing SNe events suggests that the prevalence of ETI reaches its maximum despite having the highest frequency of sterilizing SNe events by the location of the peak.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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**Figure 1.**Spatial–temporal profiles for Z

_{ETI}(

**A**) T

_{evo}= 1 Gyr, (

**B**) T

_{evo}= 3 Gyrs, (

**C**) T

_{evo}= 5 Gyrs; (

**I**) P

_{ann}= 0, (

**II**) P

_{ann}= 0.5, (

**III**) P

_{ann}= 0.99, over 20 Gyrs. Each vertical individual panel corresponds to a specific value of λ

_{A}, as shown in the title above. The white star marks the current location of our sun at 8 kpc, and 13.5 Gyrs, and the white dashed line represents our current time line of 13.5 Gyrs.

**Figure 2.**Normalized spatial–temporal profile for Z

_{ETI}over 50 Gyrs, when λ

_{A}= 10

^{−6}Gyr

^{−1}, P

_{ann}= 0 and T

_{evo}= 5 Gyrs.

**Figure 3.**The sterilizing SNe spatial–temporal profiles (

**I**) P

_{ann}= 0, (

**II**) P

_{ann}= 0.5, (

**III**) P

_{ann}= 0.99. Color bar represents the number of sterilized ETI from SNe.

**Figure 4.**Age distributions (

**A**) P

_{ann}= 0, (

**B**) P

_{ann}= 0.001, (

**C**) P

_{ann}= 0.1. The range of each bin for panels (

**A**) and (

**B**) are 0.5 Gyr, and the range of bin for panel (

**C**) is 0.01 Gyr. The numbers in the x-axis ticks represent the starting value of its bin range. All panels share the same legend of color coding on top.

**Table 1.**Each numerical value represents the maximum Z

_{ETI}of its spatial–temporal profile in Figure 1.

T_{evo} = 1 Gyr | T_{evo} = 3 Gyr | T_{evo} = 5 Gyr | ||||
---|---|---|---|---|---|---|

${\mathit{\lambda}}_{\mathbf{A}}\mathbf{=}{\mathbf{10}}^{\mathbf{-}\mathbf{6}}$ | ${\mathit{\lambda}}_{\mathbf{A}}\mathbf{=}\mathbf{1}$ | ${\mathit{\lambda}}_{\mathbf{A}}\mathbf{=}{\mathbf{10}}^{-\mathbf{6}}$ | ${\mathit{\lambda}}_{\mathbf{A}}\mathbf{=}\mathbf{1}$ | ${\mathit{\lambda}}_{\mathbf{A}}\mathbf{=}{\mathbf{10}}^{\mathbf{-}\mathbf{6}}$ | ${\mathit{\lambda}}_{\mathbf{A}}\mathbf{=}\mathbf{1}$ | |

P_{ann} = 0 | 7,811,780 | 8,729,415 | 4,566,340 | 5,362,915 | 2,832,970 | 3,598,260 |

P_{ann} = 0.5 | 7805 | 10,455 | 2159 | 2880 | 1117 | 1510 |

P_{ann} = 0.99 | 80 | 105 | 30 | 40 | 25 | 25 |

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## Share and Cite

**MDPI and ACS Style**

Cai, X.; Jiang, J.H.; Fahy, K.A.; Yung, Y.L. A Statistical Estimation of the Occurrence of Extraterrestrial Intelligence in the Milky Way Galaxy. *Galaxies* **2021**, *9*, 5.
https://doi.org/10.3390/galaxies9010005

**AMA Style**

Cai X, Jiang JH, Fahy KA, Yung YL. A Statistical Estimation of the Occurrence of Extraterrestrial Intelligence in the Milky Way Galaxy. *Galaxies*. 2021; 9(1):5.
https://doi.org/10.3390/galaxies9010005

**Chicago/Turabian Style**

Cai, Xiang, Jonathan H. Jiang, Kristen A. Fahy, and Yuk L. Yung. 2021. "A Statistical Estimation of the Occurrence of Extraterrestrial Intelligence in the Milky Way Galaxy" *Galaxies* 9, no. 1: 5.
https://doi.org/10.3390/galaxies9010005