The Astrobiological Copernican Weak and Strong Limits for Extraterrestrial Intelligent Life

We present a cosmic perspective on the search for life and examine the likely number of Communicating Extra-Terrestrial Intelligent civilizations (CETI) in our Galaxy by utilizing the latest astrophysical information. Our calculation involves Galactic star-formation histories, metallicity distributions, and the likelihood of stars hosting Earth-like planets in Habitable Zones, under specific assumptions which we describe as the Astrobiological Copernican Weak and Strong conditions. These assumptions are based on the one situation in which intelligent, communicative life is known to exist - on our own planet. This type of life has developed in a metal-rich environment and has taken roughly 5 Gyr to do so. We investigate the possible number of CETI based on different scenarios. At one extreme is the Weak Astrobiological Copernican principle - such that a planet forms intelligent life sometime after 5 Gyr, but not earlier. The other is the Strong Condition in which life must form between 4.5 to 5.5 Gyr, as on Earth. In the Strong Condition (a strict set of assumptions), there should be at least 36$_{-32}^{+175}$ civilizations within our Galaxy: this is a lower limit, based on the assumption that the average life-time, L, of a communicating civilization is 100 years (based on our own at present). If spread uniformly throughout the Galaxy this would imply that the nearest CETI is at most 17000$_{-10000}^{+33600}$ light-years away, and most likely hosted by a low-mass M-dwarf star, far surpassing our ability to detect it for the foreseeable future. Furthermore, the likelihood that the host stars for this life are solar-type stars is extremely small and most would have to be M-dwarfs, which may not be stable enough to host life over long timescales. We furthermore explore other scenarios and explain the likely number of CETI there are within our Galaxy based on variations of our assumptions.

Due to advances in astrophysics and knowledge of star formation and planetary systems we are collecting enough data to enable a new examination of the occurrence rate of CETI in the Milky Way. With new and better data on our Galaxy's star formation history and a better knowledge of the characteristics of exoplanets, we can now make a solid attempt to answer the question of the likelihood of intelligent life elsewhere.
Furthermore, we argue here that we can also invert the question of how much intelligent life there is in the Universe to one in which we ask why life has not yet been found in the Galaxy, and what this implies for our own existence on Earth. The spatial distribution of intelligent lifeforms will be related to the lifetime of intelligent civilizations, including our own, thus constraining our estimate of the former will have a bearing on the latter.
We start with a revision of the Drake equation, and we make a key assumption: since the time required for the development of communicative intelligent civilization on our own planet is of order 5 Gyr, then we propose that life will have a reasonable probability of forming on another planet such as the Earth in the habitable zone of a suitable star within our Galaxy in a similar amount of time. This idea has not been confirmed but is worth exploring as on earth we see many examples of convergent evolution, and life may in principle arise in a similar manner on a different planet. In this paper we reexamine the likely occurrence rate of CETI, under two different assumptions. The first, which we call the Weak Astrobiological Copernican scenario, is that intelligent life can only form on an Earth-like planet in a habitable zone after the star is at least 5 billion years old -which mimics the amount of time it has taken to form such life on Earth (Dalrymple, 2001) -however, intelligent life can form any time after 5 billion years: in practice, this limit is not a very strong constraint as we find that most stars in the Galaxy are older than this. The other situation we investigate -called the Strong Astrobiological Copernican scenario -whereby intelligent life forms around stars exactly in the same timescale as on Earth: between 4.5 and 5.5 billion years after formation. We investigate both scenarios using the star formation history of our Galaxy, knowledge of stellar life-times and the properties of planets derived from the Kepler mission (NASA), in order to determine how many stars in our galaxy have the appropriate age to allow for the development of CETI. This paper is a mixture of areas of contemporary astronomy, with the basic outline discussed in Section 2. Next, we discuss a variety of topics, including the star formation history of the Milky Way in Section 3. In Section 4, we investigate the metallicity distribution of stars in the Milky Way and develop a calculation of how many active CETI civilizations there are likely to be in the Galaxy using our criteria.

Background
The traditional approach towards examining whether CETI has formed in the Galaxy has been proposed through the use of the Drake equation (Drake 1962). This has remained the primary method for inferring the likely number of CETI in our Galaxy, yet it is Many, but not all, of the Drake Equation terms can be simplified and calculated using new data. We have a good understanding of the star formation rate history of our Galaxy, as well as in all nearby galaxies, and the universe as a whole (e.g. Hopkins 2004, Hopkins and Beacom 2006, Bauer et al. 2011, Madau and Dickinson 2014. From Kepler data we also have a good idea concerning the fraction of stars with planets, as well as calculations of the number of these planets per star that can host life in principle.

The CETI Equation -a New Approach
We re-derive a modern version of a Drake-like equation by first making the simple assumption that a sufficiently Earth-like planet in the habitable zone of a suitable star which exists for a sufficiently long time (henceforth referred to as a Suitable Planet, SP) will form life in a pattern similar to what has occurred on earth (i.e. in Equation 1 is assumed to be 1, for an SP). This is the Astrobiological Copernican Principle. Below we give a brief overview of this idea, and how we calculate the number of CETI in our Galaxy. Later in the paper we actually make this calculation using the latest astrophysical data.
We assume that if an SP remains in the circumstellar Habitable Zone (HZ) for a time equal to the current age of the Earth (denoted as ≈ 5 Gyr), it will develop intelligent, communicative life. This approach has the advantage of circumventing the need for Drake equation quantities such as and , which are -at presentimpossible to establish on a solid, physical basis. Our assumption is based on what we call the Principle of Mediocrity: there is no evidence to assert that the Earth should be treated as a special case, and therefore -according to the Copernican Principlewe propose that the likelihood of the development of life, and even intelligent life, should be broadly uniformly distributed amongst any suitable habitats. This would also be consistent with an idea of universal convergent evolution.
It is therefore of foremost importance to estimate the fraction, , of all stars presently within the Milky Way that are older than 5 Gyr. For this value, we take the estimate from Dalrymple (2001) to one significant figure, for -as we shall see in Section 3.1.4 -our estimated fraction is relatively insensitive to adjustments to this parameter. As we show, the results do not change significantly if we relax this criterion and allow life to form after e.g., a few Gyr, given that the star formation rate has steadily declined throughout the Galaxy's lifetime.
In the above considerations, we make the assumptions that if a planet could potentially support life, then it will inevitably develop a CETI but no earlier than ≈ 5 . To determine this, we use the star formation history of the Galaxy and the Initial Mass Function (IMF) of stars. We discuss this calculation in Section 3.1 below. Clearly, our results will therefore be upper limits on the number of planets which form intelligent life. However, in the absence of data on the other terms, this is a reasonable place to begin this calculation. It is important to realize that this is in many ways the most optimistic scenario when we later discuss the number of CETI in the Milky Way we could possibly detect.
With these assumptions, we can therefore write the CETI equation as: Where: = the number of intelligent, communicating civilizations in the Galaxy at the present time * = the total number of stars within the Galaxy = the fraction of those stars which are older than 5 Gyr = the fraction of those stars which also host a Suitable Planet in a habitable zone, which could support life ′ = the average amount of time that has been available in which life could have evolved on such a planet, orbiting such a star. In other words, ′ represents the time in which life could exist, which (based on our assumption) is given by: ′ = (average age of stars in the Galaxy / Gyr) -(5 Gyr).
= the average lifetime of an advanced civilization, or how long a civilization survives once it develops a technological ability to transmit signals.
Here, the fraction ′ is of paramount importance to our estimate. In the original approach to the SETI equations (by Drake), the relevant ratio was that of the typical civilization lifetime to the entire age of the Galaxy: which, of course, assumed a constant Star Formation Rate (SFR) throughout the Milky Way's history. However, in the present work, we are concerned with the fraction ′ , which can be considered as the probability of our observation of a stellar system coinciding with the (possibly relatively fleeting) existence of CETI: for example, if the average lifetime of CETI turns out to be ≈ 200 years, and if the average age of all stars in the Galaxy turns out to be 11 Gyr (i.e. 6 Gyr older than the critical 5 Gyr age at which we are assuming CETI can originate, hence ′ ≈ 6 Gyr) then the probability that we will detect CETI during its existence (which we may assume to be randomly distributed across the lifetime of the stellar system) would be 200 6 × 10 9 ≈ 3 × 10 −8 , in the Weak Astrobiological Copernican limit.
Equation 2 presents two important unknowns, L and N, which -while unknown -have welldetermined lower limits of N ≥ 1 and L > 100 years, given that Earth counts as a civilization emitting radio signals and has been doing so on the order of a century. Therefore, in the most pessimistic assumption (in which we are the only intelligent communicating civilization in the Galaxy, and we are on the brink of destruction presently), N = 1 and L = 100 years. We will revisit these constraints in Section 5.
In terms of what we have referred to as a Suitable Planet, we restrict investigation to planets with a sufficiently high Earth Similarity Index (ESI), which resides within the circumstellar Habitable Zone (HZ) of a suitably old star. The fraction of stars which host such a planet -for a time sufficient to develop a communicating civilization -is referred to as fHZ.
The possibility of a so-called Galactic Habitable Zone (GHZ) -i.e. that not all stars are able to develop life in our Galaxy due to their location -has also been considered in the past. This controversial area is debated amongst astronomers but pertains to the largely radial variation of metallicity throughout the Galaxy, as well as the density of stars, and therefore the frequency of supernovae which have the potential to destroy life once it has begun to develop. In this paper, we aim to address these issue on the grounds of the most solid physical factors, thus in Section 3.3 we tackle this by assessing the Metallicity Distribution Functions (MDFs) of stars within different regions of the Galaxy, and compute the fraction of all stars with metallicities exceeding certain selected thresholds. Therefore, we add a new term into the CETI equation to account for the fraction of stars within the Galaxy with what we shall estimate to be a sufficient metallicity for the formation of advanced biology, and -of course -to enable the existence of heavy metal resources required for a communicating civilization. We call this term fM (as set out in Section 3.3).
Hence, we can replace the term fsp in Equation 2 by the product = .
, so overall, the final form of the CETI equation is then: Note that the key aspects for this paper are the determination of , L, τ ' and ; the fraction is based on findings from recent papers examining this fraction based on Kepler results.
Once the necessary estimates of the numerical quantities have been made, we consider twelve theoretical categories, based on different modelling assumptions which reflect different philosophical positions within the Astrobiological Copernican Principle. This Principle asserts that the properties and evolutionary mechanisms in operation in our Solar System is not unusual in any important way, and so we may feel justified in assuming that life, and even communicative intelligence, should stand an equal chance of evolving in any such system, given the requisite amount of time and raw materials.
Our twelve modelling categories are as shown in , and we express this to one significant figure). Clearly, this is the only time-scale we have as an example for the formation of intelligent life, and it is, perforce, a simplified first approximation: we are considering the persistence of the stability of the star's conditions, and can say nothing about the planetary environment, which may be dramatically affected by climate, orbital or geological shifts within this 5 Gyr timeframe. In fact, because of this our limits are, in many ways, upper limits due to these other conditions. However, even if we relax this assumption, we find very little difference in the following results (see Section 3.1.4), and we demonstrate that -even within this apparently severe limit -we obtain interesting results.
To carry out this calculation we need to determine the age distribution of stars within our Galaxy. To do this, we assume a form of the star formation rate history and then convert this into the number of stars formed at a given mass as a function of time, throughout the entire history of the Galaxy. To do this first part, we use an analytical fit for data on Star Formation Rate (SFR) versus redshift (z).
What we want to use here is a function that describes the variation in SFR within the Milky Way Galaxy throughout time, however, this is difficult to know and no functional formula or derivation of this exists. We start by using established SFR data for distant galaxies throughout the Universe at large, as reported by Madau and Dickinson (2014): the data from Table 1  To do this we take the analytical form of the SFR history of the universe and adapt it as the relative star formation history of the Milky Way, which is the relevant quantity for this work. For this we use the variation of SFR with redshift which can be fitted as an analytical expression, as shown by many authors (e.g., Hopkins, 2004;Hopkins and Beacom, 2006;Hernquist et al. 2003). In this last work, observed data on SFR at , , 1 , 2 and 3 are the constants whose values may be varied to achieve the best fit to the observed data for SFR vs z. Curve-fitting techniques yield the values of the parameters which give a best fit to the observational data. This fit yields the following values for the fitting constants in Equation 4, which are shown in  We then combine this relationship of the SFR with redshift with the relationship between redshift and lookback time, (i.e. the time between the emission of the light from a distant source, and the present time at which the light is received by the observer). We then plot the cosmic history of star formation: see Figure 1, in which the raw SFR data has been combined with the analytical fitting function Equation 4, using parameters from Table 2. Note that the raw data has associated error bars, and we have shifted some points slightly to avoid overlap. Note also that in Fig  If we normalize this expression such that N = 1, this allows us to find the relative fraction of stars in the entire stellar population which formed with masses between any desired limits. To do this, we evaluate the normalization constant k, by using values for the minimum and maximum possible stellar mass as Mlower and Mupper respectively.
The minimum mass required for Hydrogen fusion is taken as 0.08M⊙ (Richer et al., 2006 -note: this choice of lower mass limit may have an impact on the final value for , see Section 3.1.4); whilst the maximum stellar mass we use is 100M⊙ (Kroupa, 2005) -there is considerable debate on this upper limit, but fortunately this value will prove far less significant at the higher end of the Salpeter distribution.
Using these values, we set the left-hand side of Equation 6 equal to unity, in order to achieve an expression for the relative fraction of all stars between the given mass limits. Therefore, we evaluate k = 0.0446. Hence, we can re-write Equation 6: which we use to evaluate the relative fraction of stars in a population with masses between the desired limits. We explore the relationship between this Survival Fraction and the time since starburst and find that the vast majority of the stars which still survive today did indeed form in starbursts more than 5 Gyr ago.

ii) Stellar Masses and Lifetimes.
We now consider the Main Sequence lifetime of stars, in order to ascertain the fraction of stars which formed at a certain time in the past and which still survive today. The first step here is to establish the relationship between stellar mass and a star's lifetime on the Main Sequence. The amount of time that a star spends burning Hydrogen will, of course, depend on its initial mass and luminosity, as: ~ ( L ). Given that the estimated Main Sequence lifetime of the Sun is of order 10 Gyr (Schroder and Smith, 2008), we may write, in terms of solar units: where is the luminosity of the star. Luminosity is also tightly dependent on stellar mass, and -taking the relationships from Salaris et al. (2005): Hence, combining the relationships from Equations 8 and 9, we find: Since we are interested in evaluating the fraction of all stars which are older than 5 Gyr, we examine only stars of spectral types F, G, K, M and lower (if we include L and T-type dwarfs in our consideration), for which we take the mass data in

The Distribution of Ages of Stars Surviving in the
Galaxy.
In this section we investigate the survival fraction of stars in the Milky Way over time and use this to arrive at the age distribution of all stars surviving in the Galaxy today. First, we use the analytical fit to the raw SFR data to calculate the total mass of stars formed per Mpc 3 , per 50Myr interval of time, as a function of the time since each star-forming event.
However, more significant for our purpose is the mass of stars per Mpc 3 that was formed during this 50Myr time step, and still survives today. We then renormalize this such that the integral of the number of these stars is equal to the total number we know exist today in the Milky Way. To achieve this, we use the Salpeter IMF to calculate the distribution of the total mass of stars made up by stars of each mass. The number of stars formed in a particular mass category, N, is given by Equation 6. Therefore, the total mass of the stars within each mass category is the number of stars of a given mass multiplied by that mass, giving: where b is another normalization constant, and again, α = -2.35 for a Salpeter IMF.
We normalize this expression to make Mtotal = 1 for the full range of masses, from Mlower = 0.08M⊙ to Mupper = 100M⊙, giving: which can be used to find the relative fraction of the grand total of stellar mass which was formed in a particular category of stars of masses between the desired limits. (Note: once more, the evaluation of the normalization constant in Equation 12 is dependent on the choice of minimum mass of 0.08M⊙ -see discussion in 3.1.4).
In For example, Fig 2 shows that -during a 50Myr time step, at a time 5 Gyr ago -a total of 1.26 x 10 6 stars were formed throughout the Milky Way Galaxy as a whole, of which 97% survive today. In fact, we find that most stars formed still exist today, even if a larger fraction of stellar mass has been recycled. This is due to our assumption of the Salpeter IMF.
Note also that the red and blue curves in Fig 2 demonstrate an important point about the calculation of : the total mass of stars formed in starbursts in the past has decreased today by a substantial fraction, but -since the vast majority of stars are low-mass, and these have the greatest Main Sequence lifetimes -the actual number of stars which still survive today has decreased by a small amount. Therefore, the fraction of stars surviving today which are older than 5 Gyr, , should be close to 100%. However, this calculation also allows us to determine the average age of the stars, which we use in Section 3.2. This estimate is based on using the central values of the fitting constants, given in In this section, we calculate the value of by an independent method using the Chabrier IMF for comparison. We consider the Chabrier IMF for individual (non-multiple) stars (Chabrier 2003), described in the following way: (10 ) ) exp (− ( where γ = 2.3 ± 0.3, and k is chosen to provide a smooth transition between the two regions.
According to our calculation, the value of , based on the Chabrier IMF, is approximately: , ℎ ≈ 97%. Hence, we conclude that the choice of the Initial Mass Function has a low impact on our overall accuracy in . This is due to the number of stars being dominated by the lowest mass systems -the M dwarfs in particular.
It is worth discussing some of the implications concerning the result that 97% of the stars in the Milky Way are older than 5 Gyr. Firstly, we find that the somewhat arbitrary assumption that CETI becomes established when the star is 5 Gyr old will not Note: in this method, we have worked out the mean age of all stars in the Galaxy.
However, we require the average age of all of the stars which have survived beyond 5 Gyr. But since the fraction of stars older than 5 Gyr, fL, is found from Section 3 to be so large (97%), the difference will be minimal. We calculate that the average age of all of the stars which have survived beyond 5 Gyr is 9.80 Gyr (which matches the throughout the Galaxy, so that we may evaluate an estimate of : that is to say, the fraction of all Milky Way stars with a metallicity greater than some reference value.
Using this as part of our criteria is an important aspect and again relates to the Copernican principle: life on Earth has formed in a very metal-rich environment, thus it is seems likely that life would normally form in a metal-rich environment on other planets. One could argue -a priori -that having a stellar environment with metallicity which exceeds a certain reference value could be a prerequisite for the formation of habitable planets and even life itself. This is an assumption we make hereafter, but later discuss other possibilities.
According to Johnson and Li (2012), a suitable minimum stellar metallicity required for the formation of planets with Earth-like characteristics has been posited as 0.1 Z⊙.
However, for the present work, we employ three reference values in the investigation: 0.1Z⊙, 0.5Z⊙ and 1.0Z⊙ and explore how the results would vary within these assumptions.
Hayden et al (2015)  with particular values of mean, standard deviation and skewness, as recalculated for our purposes in Table 6-8, below. These are used to generate a distribution, and then the required percentages of stars above the three reference values of metallicity are determined.
Hence -for example -by using these measurements, it is possible to arrive at the following estimates for the Galactic region which contains the Sun (which we refer to as Region D -see Table 6): Fraction of stars with metallicity, Z > 1.0 Z ⊙ , at different vertical distances from midplane (z / kpc), and radial distance from Galactic centre (R / kpc). Note: data unavailable for inner region (R < 3 kpc). Error bars similar size to line width.
1.00 < |z / kpc| < 2.00 0.50 < |z / kpc| < 1.00 0 < |z / kpc| < 0.50 In order to calculate an estimate of the overall percentage of stars in the Galaxy with metallicities exceeding the Reference Values, we require an estimate of the proportion of all stars which are located within the different regions analysed in the last section. To express this, we create simple exponential models for the decrease in number density of stars throughout the Galaxy, with increasing Galactic radius and increasing vertical distance from the mid-plane: ( ) and ( ) respectively.
We model the variations in stellar number density with the following functions:  Table 4 are estimated from measurements on these plots.
The results for the fraction of the number density of stars within each region of the Galaxy (according to the exponential decay models of number density, Equations 18) are shown in Tables 5 and 6. Error bounds are generated from further plots of the functions which acknowledge the uncertainty range in the exponential scale-length and scaleheight. Note, in order to create fairly weighted fractions of the absolute numbers of stars within each region (given in Table 11), we need to take into account the fact that these regions have unequal sizes. Table 5 covers the radial variations across the Galaxy. Table 5 contains the calculated disk area fraction, which represents the proportion of the surface area of each annular region out of the total disk area (taken out to a radius of 15 kpc, in accordance with the data used).   Table 11), the disk area fraction will also be required, which is calculated (without associated uncertainties) as follows: = Area of annulus between radii identified Area of MW disk of radius 15 kpc  As we have seen, the entire Galaxy is divided into 28 annular regions (labelled A to £, see Table 4), and the disk area fraction and disk thickness fraction which each region occupies are used in conjunction with the number density proportions (n) to calculate the fraction of the absolute number of stars (N) which reside within each region, which is shown (together with error bounds) in Table 7. 1.3% ± 0.9% TOTALS R < 3 3 < R < 5 5 < R < 7 7 < R < 9 9 < R < 11 11 < R < 13 13 < R < 15 Radial Distance from Galactic Centre, R / kpc The data from Table 4, Tables 13 and 14 in Appendix 1 and Table 7 Table 9 below presents a summary of the values calculated throughout this work, together with their uncertainties. These values will be utilized in Equation 3, to consider the number and likely spatial distribution of CETI, under each of our modelling assumptions.

110%
Note that the calculation of the terms is explained in Section 3.1. The uncertainties in these values (19%) are mainly due to the range of values used for the fitting constants in Equation 4, as explained in Table 2, in order to encompass the error bars in the SFR data at different redshifts (Fig 1). This also gives a good error on the uncertainty in the star formation history of the Milky Way which is otherwise unknown.
However, the major source of uncertainty remains in the estimate of (110%), which will likely improve with increasing data on exoplanet discoveries. Likewise, the range of values used in * yield an uncertainty of 60%, which stems from the considerable debate on the distribution of stellar masses throughout the Galaxy.
In the next section, we present our findings based on using the new CETI equation (Equation 3) with the calculated values stated in Table 9.
It will be useful to define the quantity, such that the number of CETI, , is related to the average lifetime of a civilization, , by: = (Equation 20) and the values of , for each Modelling Category, are given below, in Table 10, together with the associated uncertainties.

The Possible Lifetime and Spatial Distribution of Communicating Intelligent Civilizations in the Galaxy
In this section, we estimate the number and spatial distribution of communicating intelligent civilizations in the Galaxy, based on the assumption that around 5 Gyr is required for the development of such a civilization (i.e. according to the modelling assumptions of the Weak Astrobiological Copernican Principle, Categories 4, 5 and 6).
To sum up, we revisit the terms of the CETI Equation 3. We illustrate our results for the categories Weak 4, 5 and 6 (in which life is assumed to become established any time after 5 Gyr) and we use the values of all of the estimated quantities, as summarised in Section 3.5.
Therefore, we can express Equation 3 such that the number of CETI, , is related to the average lifetime of a civilization, , by Equation 20 (in which we are defining the quantity / −1 in Equation 19).
In the Weak Categories (4,5 and 6), we have: The simple statement (Equation 20) at least allows a lower limit to be made, given the communicating civilization on Earth has persisted for of order 100 years, which implies that a minimum value for can be estimated (within our assumptions) by setting Once again, the estimate of the minimum value of the lifetime of a CETI civilization, > 100 (based on our own example) can then be used to express the upper limit on .
The findings for Weak Category 6 are presented in Table 11. A summary of the values for all twelve modelling categories, including their uncertainties, is given in

Discussion
Our findings also provide a fresh perspective on the search for CETI -according to the expressions for the average distance between CETI (from Equation 24) of the form: Figure 5 shows a set of plots of ℎ ⁄ vs. / for each of the modelling categories (as detailed in Table 1). The points at which the curves cut the diagonal ( = ) represent the condition that the average lifetime of civilizations is just long enough to make speed of light communication between neighbouring CETI a possibility. In other words, these points on the diagonal allow an estimate of the minimum expected time required before the Search for Extra-terrestrial Intelligence (SETI) yields positive results -these times are recorded in then it is expected that we will not live long enough to make a positive SETI detection; or -if that civilization mirrors our own -they will not live long enough to receive our return signal. If our survival time can be taken as indicative of the average lifetime of all CETI, then we may imagine a Galaxy in which intelligent life is widespread, but communication unlikely. Extinction events are very hard to predict, but they do seem to occur on Earth on a regular basis throughout geological time, due to events such as asteroid collisions.
For example, a massive extinction event occurred for dinosaurs after they had existed for 350 million years, but -of course -they were not a communicating intelligence.
Part of the issue with our thinking about the lifetime of CETI is that it may be argued (rightly or wrongly) that a civilization's self-destruction is more likely to occur than a natural extinction. Perhaps the key aspect of intelligent life, at least as we know it, is the ability to self-destroy. As far as we can tell, when a civilization develops the technology to communicate over large distances it also has the technology to destroy itself and this is unfortunately likely universal. On Earth, two immediately obvious possibilities are destruction by weapons and through climate change creating an uninhabitable environment. There is, however, another factor that we do not consider here: namely, that the lifetime of an average CETI may be much longer due to spacetravel, with civilizations moving off one planet and onto another. This is of course a very difficult thing to do and has not yet been achieved by humans. This would, of course, require that the lifetime of a civilization is long enough such that that event could occur before self-destruction.
Our results also relate in some ways to the so-called Fermi Paradox (i.e. the supposedly surprising failure to detect evidence of extra-terrestrial intelligence after decades of searching) which is often used as an argument against the possibility of the existence of CETI. As detailed by Wright, Kanodia and Lubar (2018), the amount of active SETI carried out to date could hardly be expected to have produced copious positive evidence: they describe the search region as an n-Dimensional Cosmic Haystack (a function of spatial dimensions, time of transmission, sensitivity of receiver, frequency and bandwidth of signal etc) and estimate that active searches thus far have only surveyed a miniscule fraction of this region -some 5.8 x 10 -18 -which is said to be equivalent to 7700 litres out of the entire Earth's oceans. We may conclude thatwhilst a Galaxy-wide CETI in the Milky Way (with an associated large lifetime, L) may be unlikely -CETI with a shorter lifetime is certainly plausible. However, a shorter L would necessarily mean that our closest CETI would be quite distant from Earth and therefore unlikely to be detected for some time, if ever.

Summary
In this paper we calculate with known uncertainties the number of possible Communicating Extra-Terrestrial Intelligent (CETI) civilizations within our own Galaxy at the present time. We carry out this calculation using the reasonable assumption that life on other planets within the Galaxy develops in broadly similar ways in terms of timescales to life on Earth, although we allow for a range of host star properties and masses. This is the Astrobiological Copernican principle, which asserts that the development of our own intelligent life is not unique or special and similar conditions will produce similar results.
We are able to examine the number of likely communicating advanced civilizations throughout our Galaxy, based on a range of modelling categories (see Table 1). The least strict set of assumptions belong to the Ultra-Weak categories (1, 2 and 3), in which we explore the possibility that primitive life exists wherever stable conditions establish themselves, in the Habitable Zones around stars with sufficient age and metallicity. Such generous assumptions lead to estimated numbers of habitats for primitive life in the Milky Way which reach into the tens of billions.
The main focus of this work, however, is on the possibility of advanced intelligent civilizations, with the ability to communicate over large distances. The Weak categories (4, 5 and 6) are based on the assumption that any suitable habitat which has persisted with stable conditions and adequate chemical richness for at least 5 Gyr should -by comparison with our own example on Earth -have had the same likelihood of developing CETI. The Moderate categories (7, 8 and 9) place this estimate in a tighter framework: namely, we assume that intelligent communicating life can only exist within a 2-billion-year window of opportunity, in stellar systems of age 4 to 6 billion years.
The strictest set of scenarios are covered by the Strong categories (10, 11 and 12), in which the window of opportunity for CETI narrows to habitats between the ages of 4.5 and 5.5 billion years.
The starting point in our calculations is the Star Formation Rate (SFR) history, which was at its maximum some 10 Gyr ago. Therefore, we may assume that the peak epoch of life in our Galaxy (and others) would have been around 5 billion years after the peak of the SFR history -which would have been about 5 billion years ago, or at a redshift of z ~ 0.5. Hence, our own existence is likely to be somewhat later than the most populous period in Galactic history, assuming CETI has a life-time < 1 Gyr, which could be interpreted as a counterpoint to the Copernican Principle (of the mediocrity of the conditions for our own existence). Indeed, the fact that our Solar System has arrived later than this time of peak formation is intrinsically linked to its high metallicity (since the Sun's parent star must have had sufficient mass to form the heaviest elements in its supernova), so there is potential for future work to explore the concept of apparent anomalies within the Copernican Principle: as time evolves, those systems forming later than the typical time may have a greater propensity for higher metallicity and therefore our own existence -albeit late in time -may still be regarded as a typical occurrence. Cirhovic and Balbi (2019) Table 12, Category 12). That is to say, our communicating civilization here on Earth will need to persist for 6120 −2740 +6560 years beyond the advent of long-range radio technology (approximately 100 years ago) before we can expect a SETI two-way communication.
If we relax the assumptions to the Weak Copernican case, we find that there would be a minimum of 928 −818 +1980 civilizations communicating in our galaxy today (again, based on a 100 year estimate of average lifetime) with the nearest within a distance of 3320 −1440 +6300 light-years away. Under these less strict assumptions, SETI is expected to yield positive findings if the average lifespan of civilizations is 1030 −327 +1070 years (as seen in Table 12, Category 4).
Therefore -according to our most limiting set of assumptions and uncertainty boundsthe minimum number of CETI is ~8, with our nearest neighbour at a maximum distance of ~50,000 light-years, which will require ~6300 years of SETI to detect. According to our most generous set of assumptions and uncertainty bounds -the minimum number of CETI is ~2900, with our nearest neighbour at a maximum distance of ~1880 light-years, which will require ~700 years of SETI to detect.
We find that in the much more generous case, in which the lifetime of an average CETI in the Galaxy is a million years -we expect our nearest neighbouring civilization to lie at a distance between 20 and 300 lightyears away. For a perhaps more realistic lifespan of 2000 years we would expect to find a CETI between 400 and 7000 lightyears away. It is clear that the lifetime of a communicating civilization is the key aspect within this problem, and very long lifetimes are needed for those within the Galaxy to contain even a few possible active contemporary civilizations.
If we do not find intelligent life within approximately 7000 lightyears it would indicate one of two things. The first is that the lifetime of civilizations is much shorter than 2000 years, implying that our own may be quite short-lived. The second is that life on Earth is very unique, and intelligent life does not automatically form after 5 Gyr on a suitable planet but is a more random process. It would also imply that intelligences such as 'Life 3.0' artificial life-forms (e.g., Tegmark 2017) created by less robust but intelligent designers (such as ourselves) are unlikely to exist. This type III 'life' can in many ways replicated a 'biological' CETI pattern and are one logical possibility for how a planetary civilization can live for perhaps millions or billions of years without the constraints of 'natural' biological fragility (limited life span, sensitivity to space travel, self-destruction, etc).
The search for intelligent life is therefore a scientific and probabilistic way to determine how long the civilization on Earth is likely to last, or the methods by which life develops. If we do not find life within 10,000 light years for instance, this would be a bad sign for the lifetimes of civilizations, assuming that exo-intelligence is similar to our own or in other words, that the Astrobiological Copernican principle holds.