arXiv:1705.01297v2 [astro-ph.GA] 9 May 2017 20)adfudta h aiu ubro tr which stars of number al. maximum at the Lineweaver that in- of found were and results flows (2004) previous al. gas the radial et which confirmed Spitoni in cluded, I), particular time Paper Galactic hereafter In the (2014, distances. hab- of the functions Galactocentric studied as have Galaxy and 2014) our al. of et zones Spitoni itable 2013, al 2008, Prantzos et 2004, Carigi al. et Lineweaver 2001, (Lineweaver els Z 0.1 2012). of Li value & the Johnson at of with work fixed oretical planet et been Gonzalez has a by 2001) of al. discussed formation (firstly the in characteristics include Earth-like and would space forma- which in planetary for evolution tion, needed GHZ metallicity minimum the The key life. model time. a sustaining plays properly Galaxy of to the capable role of be evolution might chemical plan- the and terrestrial Therefore, found ele- which be as in heavy could systems of defined ets planetary abundances been form high to has sufficiently ments (GHZ) with region zone the habitable Galactic The Introduction 1. ⋆ srnm Astrophysics & Astronomy a 0 2017 10, May mi o [email protected] to: email ntels er eea ueyceia vlto mod- evolution chemical purely several years last the In ffidn at-iepaesa h ucino h S dust- ISM the words. of Key function (th center the Galactic as the from planets results. kpc Earth-like 8 finding at centred of wide kpc 2 region sol the in Conclusions. models polyn evolution order chemical ratio. sixth with dust-to-gas a found provide we relation Moreover, the stars. FGK of number 1 r ae noacut ttepeettm h oa ubro number total the Galact time the present from the kpc [Fe/H At 8 of account. at values is into supersolar planets taken for habitable are stars hosting FGK stars around of ones the from deta by ex computed will as we neighborhood time, solar first the the in Methods. for ISM of Moreover, the us evolution of stars. zone the FGK ratio habitable for and Galactic prescriptions M the recent around find most to the is adopting here aim Our systems. nwihErhlk lnt ol ebr n ih ecapabl be might and Aims. events. born explosion be supernova could nearby planets Earth-like which in 2 ats(u ogsgatpaes hc uvvdsproae supernova survived which planets) giant Results. gas no (but Earths Context. xxxx Accepted / xxxx Received h aatchbtbezn rudMadFKsaswith stars FGK and M around zone habitable Galactic The iatmnod iia ein iAtooi,Universit` Astronomia, di Sezione Fisica, di Dipartimento ....Osraoi srnmc iTise i ..Tie G.B. via Trieste, di Astronomico Osservatorio I.N.A.F. aatcceia vlto oescnb sfltosfrs for tools useful be can models evolution chemical Galactic h rbblte ffidn ersra lnt u o gas not but planets terrestrial finding of probabilities The h aatchbtbezn sdfie stergo ihhigh with region the as defined is zone habitable Galactic The tafie aatctm n aatcnrcdsac edeter we distance Galactocentric and time Galactic fixed a At aay bnacs-Glx:eouin-paesadsatell and planets - evolution Galaxy: - abundances Galaxy: h otlkl aatczn ofidtretilhbtbep habitable terrestrial find to zone Galactic likely most The hmcleouinmdl ihdust with models evolution chemical aucitn.spitoni no. manuscript .Spitoni E. 1 ⊙ ⋆ .Gioannini L. , ytethe- the by ABSTRACT iTise i ..Teoo1,I311 ret,Italy Trieste, I-34131, 11, Tiepolo G.B. via Trieste, di a utadfrtepoaiiyo nigpaeaysystems planetary finding of probability the for and dust uie a eaclrtdb lota re fmagnitude of of order formation an almost the by plan- that accelerated showed terrestrial be (2003) can the Jupiter Armitage destroy turbulent & to could Rice liter- due disc ets. the migration the in stochastic in giant accepted next fluctuations of widely the model” most and accretion the ature, Jupiters “core is hot The formation as to Jupiters. planet referred orbit- hot are When they very star matter. or host solid the other to close or ing rock of primarily posed ee olrepaes typically planets, large planet to two refer last evolution. the their during principle Earths in destroy planets could because giant types Jupiters, gas any hot which without or in found systems are planetary planets forming terrestrial of probability consid- was the it ered models), cosmological and evolution chemical formed. be galactic could to planets rise al. habitable give Vukoti´c which et can and in halos structures of (2016), & kind al. which Gobat showing et (2015), (2016) al. Zackrisson et (2016), Forgan wide. Hong by kpc (ΛCDM) 2 context and logical kpc, 8 at centered neighbor- region solar in the are i.e. planets hood, terrestrial habitable host can rnihoho ewe h F/]audne n the and abundances [Fe/H] the between neighborhood ar oo1,I311 ret,Italy Trieste, I-34131, 11, polo poin,uigtefraimo u ae I. Paper our of formalism the using xplosions, 1 cCnr,i etutv ffcsb uenv explosions supernova by effects destructive if Centre, ic fssann iesriigt h etutv ffcsof effects destructive the to surviving life sustaining of e oa egbrod.W lopoieteprobabilities the provide also We neighborhood). solar e n .Matteucci F. and , n hmcleouinmdl o h ik a disc, Way Milky the for models evolution chemical ing ogsrtouigdtie hmcleouinmodels evolution chemical detailed using ratio to-gas ma t(n ieroebtmr prxmtd for approximated) more but one linear a (and fit omial ldceia vlto models. evolution chemical iled h em in lnt,gsgat,o ipyJupiters, simply or giants, gas planets, giant terms The purely for (both above mentioned models the of most In cosmo- the in studied also been has GHZ the Recently, .Frbt G n tr h aiu number maximum the stars M and FGK both For ]. tr ihhbtbepaesare planets habitable with stars M f rs hs rbblte ntrso h dust-to-gas the of terms in probabilities those press in lnt rudMsasdvaesubstantially deviate stars M around planets giant uyn h aatchbtbeznsi different in zones habitable galactic the tudying yeog ealct ofr lntr systems planetary form to metallicity enough ly ts eea S:general ISM: - general ites: aesaon n G tr steannular the is stars FGK and M around lanets ietenme fMadFKsashaving stars FGK and M of number the mine 1 , 2 > 0M 10 ⊕ ≃ htaentcom- not are that , 0tmsthe times 10
c S 2017 ESO 1 Spitoni et al.: The Galactic habitable zone in presence of dust if the growing core executes a random walk with an ampli- ratio of the protoplanetary discs (the dust-to-gas ratio of tude of ≈ 0.5 AU. Nowadays, about 3 thousands of planets the ISM at the instant of the protoplanetary disc forma- have been discovered and the statistics is good enough to tion). confirm that most of planetary systems host planets which The paper is organized as follows: in Section 2 we are not present in our solar system, such as hot Jupiters or present the probabilities of terrestrial planets around M and super-Earths. FGK stars. In Section 3 we describe the Milky Way chem- In this paper we retain the assumption that gas gi- ical evolution model with dust and we present the main ant planets could destroy, during their evolution, terrestrial results in Section 4. Finally, our conclusions are summa- ones (we are aware that the real effects are still uncertain). rized in Section 5. On this basis we study the GHZ using the most updated probabilities related to the formation of gas giant planets as functions of [Fe/H] abundance values as well as the stellar 2. The probabilities of terrestrial planets around M mass for FGK and M stars. It is recent the discovery of a and FGK stars planetary system around the M star Trappist-1 (Gillon at Buchhave et al. (2012) who analyzed the mission Kepler, al. 2016, 2017) composed by seven terrestrial planets char- found that the frequencies of the planets with earth-like acterized by equilibrium temperature low enough to make sizes are almost independent of the metallicity of the host possible the presence of liquid water. This detection makes star up to [Fe/H] abundance values smaller than 0.5 dex. the habitability around M stars even more interesting. In agreement with these observations, Prantzos (2008) In this paper we also compute the probabilities related fixed the probability of forming Earth-like planets (PFE, to the formation of gas giant planets as functions of [Fe/H] where F E stands for Forming Earths) at value of 0.4 for abundance values and the stellar mass for FGK and M stars [Fe/H] ≥ -1 dex, otherwise PFE = 0 for smaller values with a detailed chemical evolution model for the Milky Way of [Fe/H]. This assumption was also adopted by Carigi et with dust evolution. al. (2013) and Paper I. The value of PFE= 0.4 was cho- Even though, we know very little about the formation of sen to reproduce the metallicity integrated probability of planetary systems: in particular, it is not well understood Lineweaver et al. (2001). the transition from a protoplanetary disc to a planetary In Paper I it was considered the case in which gaseous system. In this transition, dust and gas rapidly evolve in giant planets with same host star can destroy terrestrial very different ways due to many processes (Armitage 2013) planets (i.e. during their migration path). Armitage (2003) such as dust growth, gas photoevaporization (Alexander pointed out the potentially hazardous effects of the gas gi- et al. 2014), gas accretion onto the star (Gammie 1996). ant planet migration on the formation of Earth-like ones, Dust plays a fundamental role in the formation of the first and suggested that these planets preferentially exist in sys- planetesimals, as it represents the solid compounds of the tems where massive giants did not migrate significantly. matter which can form rocky planetesimals and therefore Matsumura et al. (2013) studying the orbital evolution of planets. terrestrial planets when gas giant planets become dynami- The first fundamental step to understand and explain cally unstable, showed that Earth-like planets far away from the origin of the observed diversity of exoplanetary systems, giants can also be removed. is to measure the stellar disc properties, especially the disc On the other hand, various numerical simulations found mass. Dust grains of µm are directly observed in protoplan- that the formation of earths is not necessarily prevented by etary discs and then, dust coagulation increase their size up the gas giant planet migration, when eccentricity excitation to mm (Dullemond & Dominik 2005). On the other hand, timescales for (proto-)terrestrial planets are long compared observations of the gas are almost forbidden, because it is to migration timescales of giant planets (e.g., Mandell & relatively cool and in molecular form. Sigurdsson 2003; Lufkin et al. 2006; Raymond et al. 2006). In most cases, the mass of the gas is set starting from the The adopted probability of formation of a gaseous giant one of the dust and by assuming a value for the dust-to-gas planet as the function of the iron abundance in the host ratio. Unfortunately, this practice has several uncertainties star is taken by Fischer & Valenti (2005) as: (Williams & Best 2014). Usually, models of planetary for- −2 mation use an average value of 10 for the initial condition P ([Fe/H]) = 0.03 × 102.0[Fe/H]. (1) of the dust-to-gas ratio in the protoplanetary disc (Bohlin GGP et al. 1978). A possible theoretical explanation is that the high Furthermore, the formation rate of gas giant planets metallicity observed in some stars hosting giant planets rep- seems to be related to the metallicity of the hosting stars resent the original composition that protostellar and pro- (Fisher & Valenti 2005, Johnson et al. 2010, Mortier et al. toplanetary molecular clouds were formed. In this scenario, 2012, Gaidos & Mann 2014). Moreover, even if Buhhave et the higher the metallicity of the primordial cloud, the pro- al. (2012) showed that planets with radii smaller than 4 R⊕ portion of dust to gas in the protoplanetary disc. This facil- do not present any metallicity correlation, the theoretical itates the condensation and accelerates the protoplanetary work of Johnson & Li (2012) predicted that first Earth-like accretion before the disc gas is lost (Pollack et al. 1996). planets likely formed from circumstellar discs with metal- Giant planets are subsequently formed by runaway accre- licities Z ≥ 0.1 Z⊙. tion of gas onto such rocky cores with M ≈ 10M⊕, rather With this work, providing the time evolution of the dust, than by gravitational instabilities in a gaseous disk which we discuss the connection between the metallicity of the predicts formation much less sensitive to metallicity (Boss, D ISM and the dust-to-gas ( G ) ratio (especially for the solar 2002). neighborhood). In this way, we can link the metallicity of The novelty of this work is to consider the following stars, which is observationally related to the probability of new probabilities for gas giant planets formation found by the presence of hosted planets, with the initial dust-to-gas Gaidos & Mann (2014) and used by Zackrisson et al. (2016)
2 Spitoni et al.: The Galactic habitable zone in presence of dust
20 20 30 A) 0.4 B) 18 18 0.2 25 16 16
] 0 -1 14 14 Gyr 20 -0.2 -2
12 -0.4 12 sun pc
15 [Fe/H] R [kpc] R [kpc] 10 -0.6 10
SFR [M 10 8 -0.8 8
5 -1 6 6 -1.2 0 4 4 0 2 4 6 8 10 12 14 0 2 4 6 8 10 12 14 t [Gyr] t [Gyr]
0.14 20 0.4 20 C) D) 0.12 18 0.35 18 ]
16 ] 0.3 16 -1
0.1 -2 pc Gyr 14 0.25 14 -2 0.08 sun 12 0.2 12 R [kpc] 0.06 R [kpc] 10 0.15 10 Total Dust [M SNII+SNIa [pc 0.04 8 0.1 8
0.02 6 0.05 6
0 4 0 4 0 2 4 6 8 10 12 14 0 2 4 6 8 10 12 14 t [Gyr] t [Gyr]
Fig. 1. Panel A): The SFR as the function of the Galactic time; Panel B): The time evolution of the [Fe/H] abundances with the two-infall chemical evolution model for the Milky Way disc (the “age-metallicity” relation); Panel C): The evolution in time of the Type II SN rates plus the Type Ia SN rates. With the red line we label the quantity 2× < RSNSV > which represents the minimum SN rate value (adopted in this work and in Paper I) to have destruction effects from SN explosions; Panel D): The time evolution of the total dust surface mass density. The color code in the four panels indicates the different Galactocentric distances. around FGK and M stars which are functions also of the FGK stars. On the other hand, Zackrisson et al. (2016) masses of the hosting stars: presented results where PFE =0.4 around FGK stars, and PFE = 1 around M stars. The possibility of finding habitable planets around M- 1.8[Fe/H] M⋆ PGGP/F GK ([Fe/H],M⋆)=0.07×10 , (2) dwarf has long been debated, due to differences between M⊙ the unique stellar and planetary environments around these low-mass stars, as compared to hotter, more luminous Sun- for the FGK stars, and like stars (Shields et al. 2016). The presence of multiple rocky planets (Howard et al. 2012), with roughly a third 1.06[Fe/H] M⋆ of these rocky M-dwarf planets orbiting within the habit- PGGP/M ([Fe/H],M⋆)=0.07 × 10 , (3) able zone, supports the hypothesis of the presence of liquid M⊙ water on their surfaces. On the other hand, flare activity, and for M stars, where M⋆ is the mass of the host star in synchronous rotation, and the likelihood of photosynthesis units of solar masses. could have a severe inpact on the habitability of planets We assume that the range of masses spanned by M type hosted by M dwarf stars (Tarter et al., 2007). stars is the following one: 0.08 ≤ M⋆ ≤ 0.45. For the F GK We define P (FGK/M,R,t) as the fraction of all M⊙ GHZ the range is: 0.45 ≤ M⋆ ≤ 1.40. FGK/M stars having around Earths (but no gas giant plan- M⊙ ets) which survived supernova explosions as a function of The probability of forming terrestrial planets around the Galactic radius and time: FGK/M stars but not gaseous giant planets is given by:
PGHZ (FGK/M,R,t)= PE/F GK,M = PFE × (1 − PGGP/F GK,M ). (4)
Here, we make the conservative assumption of Prantzos t ′ ′ ′ ′ SF R(R,t )P (R,t )PSN (R,t )dt (2008) and Paper I that the PFE probability is constant = 0 E/F GK,M (5) at the value of 0.4 for all stellar types, including M and R t ′ ′ 0 SF R(R,t )dt . R 3 Spitoni et al.: The Galactic habitable zone in presence of dust
This quantity must be interpreted as the relative prob- 0.45 20 ability to have complex life around one star at a given po- sition, as suggested by Prantzos (2008). 0.4 18 ′ In eq. (5) SF R(R,t ) is the star formation rate (SFR) at 0.35 ′ ′ 16 the time t and Galactocentric distance R, and PSN (R,t ) 0.3
IMF 0.25 We know that hard radiation originated by close-by SN > explosions could lead to the depletion of the ozone layer 12 GGP 0.2
in terrestrial atmosphere. At this point, the ultraviolet ra-
IMF For this quantity we refer to the “case 2” model of Paper 0.05 6 I in which the SN destruction is effective if the SN rate at 0 4 any time and at any radius has been higher than twice the -0.6 -0.4 -0.2 0 0.2 0.4 average SN rate in the solar neighborhood during the last [Fe/H] 4.5 Gyr of the Milky Way life (we call it < RSNSV >). Therefore, we impose that if SN rate is larger than 2× < Fig. 2. The probabilities
where τH is the typical timescale for the formation of the 3. The Milky Way chemical evolution model with halo and thick disc and it is fixed to the value of 0.8 Gyr, dust while tmax = 1 Gyr is the time for the maximum infall onto the thin disc. The coefficients a(r) and b(r) are obtained by To trace the chemical evolution of the Milky Way we adopt imposing a fit to the observed current total surface mass an updated version of the two-infall model of Paper I in density in the thin disc as a function of Galactocentric dis- which we consider the dust evolution using the new pre- tance given by: −R/RD scriptions of Gioannini et al. (2017). Σ(r)=Σ0e , (9) −2 where Σ0 = 531 M⊙ pc is the central total surface mass 3.1. The two infall model of Paper I density and RD = 3.5 kpc is the scale length. Moreover, the formation timescale of the thin disc τ (r) is assumed The chemical evolution model of Paper I is based on the D to be a function of the Galactocentric distance, leading to classical two-infall model of Chiappini et al. (2001). We an inside-out scenario for the Galaxy disc build-up. In par- describe here the main characteristics of the model. ticular, we assume that: We define Gi(t) = G(t)Xi(t) as the fractional mass of the element i at the time t in the ISM, where Xi(t) repre- τD(r)=1.033 R (kpc) − 1.267 Gyr. (10) sents the abundance of the element i in the ISM at the time t. The temporal evolution of Gi(t) in the ISM is described The Galactic thin disc is approximated by several inde- by the following expression: pendent rings, 2 kpc wide, without exchange of matter −2 between them. A threshold gas density of 7 M⊙ pc in G˙ i(t)= −ψ(t)Xi(t)+ Ri(t)+ G˙ i,inf (t). (7) the SF process (Kennicutt 1989, 1998; Martin & Kennicutt 2001; Schaye 2004) is also adopted for the disc. The halo The first term in the right side of eq. (7) represents the has a constant surface mass density as a function of the rate at which the fraction of the element i is subtracted Galactocentric distance at the present time equal to 17 −2 by the ISM due to the SFR process. Ri(t) is the returned M⊙ pc and a threshold for the star formation in the −2 mass fraction of the element i injected into the ISM from halo phase of 4 M⊙ pc , as assumed for the model B of stars thanks to stellar winds and SN explosions. This term Chiappini et al. (2001).
4 Spitoni et al.: The Galactic habitable zone in presence of dust
20 20
0.4 0.4 18 18
> 12 E 0.3 -0.2 12
0.25
=P (1-
) 8 E/M,FGK IMF FE GGP/M,FGK IMF -0.6 8 6 -0.8 6 0.2 4 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 -1 4 [Fe/H] 0 0.005 0.01 0.015 0.02 (D/G) Fig. 3. The probabilities < PE/F GK >IMF and < PE/M >IMF to find terrestrial planets but not gas giant planets around FGK and M stars, respectively, as functions 0.2 of the abundance ratio [Fe/H] using our chemical evolution model for the Milky Way disc and adopting the prescrip- 0 tions given by Gaidos & Mann (2014) and Paper I. The color code indicates the Galactocentric distance. -0.2
The assumed IMF is the one of Scalo (1986), which is [Fe/H] -0.4 assumed constant in time and space. The adopted law for the SFR is a Schmidt (1959) like -0.6 one: MW at 8 kpc k -0.8 6th order polynomial fit at 8 kpc Ψ ∝ νΣgas(r, t), (11) Linear fit at 8 kpc here Σgas(r, t) is the surface gas density with the expo- -1 nent k equal to 1.5 (see Kennicutt 1998; and Chiappini et 0 0.002 0.004 0.006 0.008 0.01 0.012 al. 1997). The quantity ν is the efficiency of the star for- (D/G) mation process, and is constant and fixed to be equal to −1 Fig. 4. Upper panel: The evolution of the abundance ra- 1 Gyr . The chemical abundances are normalized to the tio [Fe/H] as the function of the dust-to-gas ratio D Asplund et al. (2009) solar values. G predicted by our chemical evolution model of the Milky Way disc. As in Fig. 1 the color code indicates different 3.2. Evolution of dust Galactocentric distances. Lower panel With the black solid D line we report the [Fe/H] ratio vs G computed at 8 kpc Our chemical evolution model also traces the dust evolution (solar neighborhood) using the chemical evolution model of in the interstellar medium (ISM). Defining Gi,dust(t), we the Milky Way. With the green solid line we show the fit can thus write the equation for dust evolution as follows: obtained by mean of a sixth order polynomial fit. With the red dashed line we report the linear fit at 8 kpc. In both panels with the orange triangle we label the value of the ˙ Gi,dust(t) Gi,dust(t)= −ψ(t)Xi,dust(t)+ δiRi(t)+ [Fe/H] as a function of the dust-to-gas ratio D for the τaccr G model computed in the solar neighborhood at the Galactic G (t) − i,dust . time of 9.5 Gyr (i.e. model solar value). τdestr (12) The right hand of this equation contains all the pro- cesses which govern the so called “dust cycle” : the first term represents the amount of dust removed from the ISM due to star formation, the second takes into account dust The dust yields δ R (t) are not only metallicity de- pollution by stars while the third and fourth terms rep- i i pendent but also depend on the mass of the progenitor resent dust accretion and destruction in the ISM, respec- star. In this work we consider as dust producers Type tively. In this work, we used the same prescriptions used in II SNe (M > 8M⊙) and low-intermediate mass stars Gioannini et al. (2017). Dust production are provided by ⋆ (1.0M⊙ < M < 8.0M⊙). Concerning dust accretion and taking into account condensation efficiencies δ 1, as pro- ⋆ i destruction we calculated the metallicity dependent time- vided by Piovan et al. (2011). scales for these processes (τaccr and τdestr) as described in 1 The condensation efficiency (δi) represents the fraction of an Asano et al. (2013). For a more detailed explanation on dust element i expelled from a star which goes into the dust phase of prescriptions or dust chemical evolution model we address the ISM. the reader to Gioannini et al. (2017).
5 Spitoni et al.: The Galactic habitable zone in presence of dust
4. Results is higher because of the large production by Type II SNe, during the initial burst of star formation, as visible in panel First, in this Section we present the main results of our A). On the other hand, dust accretion becomes important Milky Way chemical evolution model in presence of dust. at later epochs, and the dust mass tends to increase at all Moreover, the PE/F GK,M probabilities of finding Earth- Galactocentric distances. The observed oscillation of the like planets but not gas giant ones around FGK and M model occurs when the rates of dust accretion and dust de- stars of Gaidos & Mann (2014) computed with detailed struction are comparable. In fact, in this case there is a gain chemical evolution models for the Galactic disc at differ- of the total mass surface density of dust provoked by the ent Galactocentric distances are shown. We express those D dust growth, rapidly followed by a decreasing due to the probabilities in terms of the dust-to-gas ratio G obtained dust destruction rate, which exceeds dust accretion. This by our ISM chemical evolution models. Finally, we present turnover between those processes occurs especially in the the maps of habitability of our Galaxy as functions of the quiescent phases of the Galactic evolution. galactic time and Galactocentric distances in terms of the total number of FGK and M stars which could host habit- able Earth like planets and not gas giant planets. 4.2. The computed probabilities PGGP/F GK,M with the two infall chemical evolution model
4.1. The Milky Way disc in presence of dust To compute the probabilities PGGP/F GK,M presented in eqs. (2) and (3) with our chemical evolution model we con- In Fig. 1 we show the time evolution of the star formation sider the weighted values on the IMF using the following rate (SFR) (panel A), of [Fe/H] abundances (panel B), of expressions: SN rates (panel C), and finally of the total dust (panel D) as functions of the Galactocentric distance. In panel A) < PGGP/F GK (R,t) >IMF = we see the effect of the inside-out formation on the SFR in the thin disc phase. During the halo-thick disc phase (up to 1 Gyr since the beginning of the star formation) all 1.8[Fe/H](R,t)model M⋆,F GK the Galactocentric distances show the same star formation 0.07 × 10 < >IMF , (13) history (for all radii we assume the same surface gas den- M⊙ sity and same formation time-scales in the halo-thick disk phase, for details see Section 3). for the FGK stars, and In the inner regions the SFR in the thin disc phase < PGGP/M (R,t) >IMF = is higher because of the larger gas density and shorter time-scales of gas accretion compared to the outer regions. Indeed, in the outer regions it is more evident the effect of the threshold in the gas density: the SFR goes to zero 1.06[Fe/H](R,t)model M⋆,M 0.07 × 10 < >IMF , (14) when the gas density is below the threshold. We notice also M⊙ that the in the halo-thick disc phase we have the same SFR history at all Galactocentric distances. for M stars. In panel B) it is shown the “age-metallicity” relation in The [Fe/H](R,t)model quantity is the computed iron terms of [Fe/H] ratio vs Galactic time. It is clear also in abundance with our chemical evolution model adopting the this case the effects of the inside-out formation: the inner Scalo (1986) IMF at the Galactic time t and Galactocentric regions exhibit a faster and more efficient chemical enrich- distance R. ment with higher values of [Fe/H]. Actually, at early times, Therefore, to compute < PGGP/M >IMF and in correspondence of the beginning of the second infall of
6 Spitoni et al.: The Galactic habitable zone in presence of dust
0.4 0.4 A) B) 0.38 12 0.38 12
0.36 0.36 10 10
IMF 0.34 0.34 IMF > > 0.32 8 0.32 8 t [Gyr] t [Gyr] GHZ, M GHZ, FGK
0.3
0.28 0.28 4 4 0.26 0.26
0.24 2 0.24 2 4 6 8 10 12 14 16 18 20 4 6 8 10 12 14 16 18 20 R [kpc] R [kpc]
0.3 C) 0.3 D) 12 12 0.25 0.25 10 10
IMF 0.2 0.2 IMF > > 8 8 0.15 0.15 t [Gyr] t [Gyr] GHZ, M GHZ, FGK 0.05 4 0.05 4 0 2 0 2 4 6 8 10 12 14 16 18 20 4 6 8 10 12 14 16 18 20 R [kpc] R [kpc] Fig. 5. Upper panels: The probability 7 Spitoni et al.: The Galactic habitable zone in presence of dust The solar dust-to-gas ratio D value predicted by our G ⊙ NUMBER OF FGK STARS WITH HABITABLE PLANETS model (model value computed in the solar neighborhood at 3.33e+08 9.5 Gyr) is 0.01066. D In the lower panel of Fig. 4 we show the G as a function 2.664e+08 of the [Fe/H] values only for the shell centered at 8 kpc and 2 kpc wide (the solar neighborhood). In the same plot the 1.998e+08 sixth degree polynomial fit which follows exactly the [Fe/H] D 1.332e+08 vs G in the range of [Fe/H] between -1 dex and 0.5 dex is presented. The expression of this fit is the following one: 6.66e+07 6 n D 013 [Fe/H] = αn (17) G 10.4 nX=0 7.8 3 t [Gyr] All the coefficients αn and n are reported in the footnote . 5.2 We found that for [Fe/H] values higher than -0.6 dex 2.6 0 a linear fit is able to reproduce pretty well the computed 4 8 D 12 16 20 R [kpc] [Fe/H] vs G relation in the solar vicinity. The equation of the linear fit reported in the lower panel of Fig. 4 is: NUMBER OF M STARS WITH HABITABLE PLANETS 3.53e+09 D [Fe/H] = 96.49 − 0.92. (18) G 2.824e+09 This relation is important to connect the dust-to-gas 2.118e+09 ratio with the [Fe/H] abundance. If we combine it with eq. (4) we obtain the probability of having terrestrial planets 1.412e+09 but not gas giant ones depending on the amount of dust in the ISM. 7.06e+08 013 4.4. The PGHZ values around FGK and M stars 10.4 7.8 In the upper panels of Fig. 5 (A and B) we show the evo- t [Gyr] 5.2 lution in time of the P values for FGK and M stars as GHZ 2.6 functions of the Galactocentric distance in the case where 4 0 8 12 SN destruction effects are not taken into account. 16 20 R [kpc] We notice that the < PGHZ/M >IMF and < PGHZ/F GK >IMF probabilities are identical at large Fig. 6. The total number of FGK stars (Upper panel) and Galactocentric distances. This is due to the fact that, as M stars (Lower panel) having habitable terrestrial planets shown in Fig. 3, the < PE/F GK >IMF and < PE/M >IMF but not gas giant ones as functions of the Galactocentric probabilities are similar for sub-solar values of [Fe/H]. The distance and the Galactic time (the N⋆ life quantity in eq. chemical evolution in the outer parts of the Galaxy, be- 6) where SN destructive effects are taken into account. The cause of the inside-out formation, is slow and with longer number of stars are computed within concentric rings, 2 time scales. The maximum values of [Fe/H] are smaller than kpc wide. in the inner region and sub-solar (see the “age-metallicity” relation reported in panel B of Fig. 1). Moreover, in the inner regions < PGHZ,M >IMF and stated above, the PE.FGK and PE.M values are almost the < PGHZ,FGK >IMF probabilities become to be different same. This is the reason why the two PGHZ probabilities only for Galactic times larger than 8 Gyr. As expected the are similar even at late time in the inner regions. higher probabilities are related to the M stars. Even if the In the lower panels of Fig.5 (C and D) we show that, the < PE/F GK >IMF and < PE/M >IMF probabilities are PGHZ probabilities for FGK and M stars as functions of the substantially different for [Fe/H]> 0.2 (see Fig. 3), the two Galactocentric distances and time, when the SN destruction associated PGHZ probabilities are similar. effects have been taken into account, are almost identical. This is due to the definition of PGHZ (t): at each Galactic As found in Paper I the Galactocentric distance with the time the SFR × PE quantity is integrated from 0 to t. In highest probability that a star (FGK or M type) hosts a other words, we are weighting the PE quantity on the SFR. terrestrial planet but not gas giant ones is 10 kpc. From panel C) of Fig. 1 it is clear that the peak of the SFR in the inner regions (annular region between 3 and 7 4.5. THE GHZ maps for FGK and M stars kpc) is around 3 Gyr. From the “age-metallicity” relation reported in panel B) of Fig. 1, we derive that at this age In order to recover the total number of stars at the Galactic the mean Galactic [Fe/H] is -0.5 dex. At this metallicity, as time t and Galactocentric distance R hosting habitable planets, it is required the total number of stars created 3 − . . 4 D − . 5 D 2 [Fe/H]= 1 48 + 1 05 10 G 4 91 10 G + up to time t at the Galactocentric distance R (the N⋆tot . 8 D 3 − . 10 D 4 . 11 D 5 − . 13 D 6 1 1410 G 1 32 10 G + 7 57 10 G 1 69 10 G quantity in eq. 6). 8 Spitoni et al.: The Galactic habitable zone in presence of dust Our chemical evolution model very well reproduces the to express the Gaidos & Mann (2014) probabilities of observed total local stellar surface mass density of 35 ± 5 finding gaseous giant planets around FGK or M stars in −2 D M⊙ pc (Gilmore et al. 1989, Spitoni et al. 2015). In fact, terms of the gas to dust ratio G . our predicted value for the total surface mass density of – We provide a useful theoretical tool to set the proper −2 stars is 35.039 M⊙ pc . Morever, we find that this value initial condition for the formation of protoplanetary disc −2 concerning only to M stars is 24.923 M⊙ pc and the one connecting the evolution of the dust-to-gas ratios at dif- −2 for FGK stars is 9.579 M⊙ pc . ferent Galactocentric distances with the chemical en- In Fig. 6 we show the number of FGK stars (upper richment expressed in terms of [Fe/H]. panel) and M stars (lower panel) hosting habitable ter- – The probabilities that a FGK or M star could host hab- restrial planets but not gas giant planets as functions of itable planets are roughly identical. Slightly differences the Galactic time and Galactocentric radius (the quantity arise only at Galactic times larger than 9 Gyr where the N⋆ life of eq. 6). probability of finding gas giant planets around FGK be- We notice that for both FGK and M stars, the GHZ comes substantially different from the one associated to maps, in terms of the total number of stars hosting planets M stars. with life, peaks at 8 kpc. On the other hand, as we have – As found by Paper I, adopting the same prescriptions seen above the maximum fraction of stars which can host for the destructive effect from close-by SN explosions, habitable terrestrial planets peaks at 10 kpc (see panels C the larger number of FGK and M stars with habitable and D of Fig. 5). planets are in the solar neighborhood. The reason why the GHZ peaks at galactocentric dis- – At the present time the total number of M stars with tances smaller than in the case when it is expressed in terms habitable terrestrial planets without gas giant ones are of fraction of stars is the following one: in the external re- ≃ 10 times the number of FGK stars. This result is gions the number of stars formed at any time is smaller consistent with the Scalo (1986) IMF adopted here. than in the inner regions because of the the smaller SFR. This is in agreement with the results of Prantzos (2008) The Gaia mission with its global astrometry, will be and Paper I. crucial for the study of exoplanets. We recall the relation We see that, at the present time, in the solar neighbor- used in this work between the frequency of gas giant planets and the metallicity of the host star was obtained by means hood the number N⋆,M,life/N⋆,F GK,life=10.60. This ratio is consistent with the IMF we adopt in our model. In fact, of the Doppler effect with the method of radial velocity, and the ratio between the fraction of M stars over FGK stars it will be possible with Gaia to test whether this result is an observational bias or is related to real physical processes. (by number) in a newborn population adopting a Scalo IMF 4 is: It is estimated that Gaia will be able to find out up to 10 giant planets in the solar vicinity with its global astrometry 0.45 M⊙ −2.35 M m dm with distances spanning the range between 0.5 and 4.5 AU number = 0.08 M⊙ = 11.85. from the host star. R 1.4 M⊙ F GKnumber m−2.35dm Scalo IMF 0.45 M⊙ R (19) Finally, the predicted local surface mass density of M Acknowledgments stars hosting habitable planets predicted by our model is We thank the anonymous referee for the suggestions that −2 5.446 M⊙ pc , and the value for FGK stars is 2.40 M⊙ improved the paper. The work was supported by PRIN − pc 2. 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