A Possible Solution of The Faint Young Sun Paradox from Modified Gravities with

Transcription

1 from Was the A Possible Young Sun from Ministero dell Istruzione, dell Università e della Ricerca (M.I.U.R.)-Istruzione, Fellow of the Royal Astronomical Society (F.R.A.S.) Karl Schwarzschild Meeting 2013, Frankfurt, Germany, July 22-26, 2013

2 from Was the 1 2 Was the Outline

3 from Was the According to consolidated models of the Sun s evolution history, the energy output of our star during the Archean, from 3.8 Gyr to 2.5 Gyr ago, would have been too low to keep liquid water on the s surface. Instead, there are compelling and independent evidences that, actually, our planet was mostly covered by liquid water oceans, hosting also forms of life, during that eon. It is the so-called Faint (FYSP) [Feulner 2012]. Although intense efforts in the last decades to find a satisfactory solution involving multidisciplinary investigations on deep-time paleoclimatology, greenhouse effect, ancient cosmic ray flux, solar activity and solar wind, the FYSP not only refuses to go away, but rather it becomes even more severe in view of some recent studies [Goldblatt and Zahnle 2011].

4 from Was the According to consolidated models of the Sun s evolution history, the energy output of our star during the Archean, from 3.8 Gyr to 2.5 Gyr ago, would have been too low to keep liquid water on the s surface. Instead, there are compelling and independent evidences that, actually, our planet was mostly covered by liquid water oceans, hosting also forms of life, during that eon. It is the so-called Faint (FYSP) [Feulner 2012]. Although intense efforts in the last decades to find a satisfactory solution involving multidisciplinary investigations on deep-time paleoclimatology, greenhouse effect, ancient cosmic ray flux, solar activity and solar wind, the FYSP not only refuses to go away, but rather it becomes even more severe in view of some recent studies [Goldblatt and Zahnle 2011].

5 from Was the The Evolution of the Solar Luminosity Setting the origin of the time at the Zero-Age Main Sequence (ZAMS) epoch, i.e. when the nuclear fusion ignited in the core of the Sun, a formula which accounts for the temporal evolution of the solar luminosity L(t) reasonably well over the eons, with the possible exception of the first 0.2 Gyr in the life of the young Sun, is [Gough 1981] L(t) L 0 = 1 ( ), (1) t t 0 where t 0 = 4.57 Gyr is the present epoch, and L 0 is the current Solar luminosity. The formula of eq. (1) is in good agreement with recent standard solar models.

6 from Was the The Solar Irradiance According to eq. (1), at the beginning of the Archean era 3.8 Gyr ago, corresponding to t Ar = 0.77 Gyr in our ZAMS-based temporal scale, the solar luminosity was just L Ar = 0.75L 0. (2) Thus, if the heliocentric distance of the was the same as today, eq. (2) implies that where I Ar = 0.75I 0, (3) I 0 = ± 0.5 W m 2 (4) is the present-day Solar irradiance.

7 from Was the The Solar Irradiance According to eq. (1), at the beginning of the Archean era 3.8 Gyr ago, corresponding to t Ar = 0.77 Gyr in our ZAMS-based temporal scale, the solar luminosity was just L Ar = 0.75L 0. (2) Thus, if the heliocentric distance of the was the same as today, eq. (2) implies that where I Ar = 0.75I 0, (3) I 0 = ± 0.5 W m 2 (4) is the present-day Solar irradiance.

8 from Was the A Receding? Let us assume that, at t Ar, the was closer to the Sun than now in such a way that the irradiance I Ar was equal to the minimum value [Longdoz and Francois 1997] I oc = 0.82I 0 required to keep liquid water on its surface. This implies r Ar = 0.956r 0. Let us assume that some mechanism displaced the during the Archean to its current location by keeping the irradiance basically equal to I oc. Then, ṙ(t) r(t) = 1 7t 0 (1 2 7 ) yr 1. (5) t t 0 No independent evidences of geological nature contradict such a hypothesis

9 from Was the A Receding? Let us assume that, at t Ar, the was closer to the Sun than now in such a way that the irradiance I Ar was equal to the minimum value [Longdoz and Francois 1997] I oc = 0.82I 0 required to keep liquid water on its surface. This implies r Ar = 0.956r 0. Let us assume that some mechanism displaced the during the Archean to its current location by keeping the irradiance basically equal to I oc. Then, ṙ(t) r(t) = 1 7t 0 (1 2 7 ) yr 1. (5) t t 0 No independent evidences of geological nature contradict such a hypothesis

10 from Was the A Receding? Let us assume that, at t Ar, the was closer to the Sun than now in such a way that the irradiance I Ar was equal to the minimum value [Longdoz and Francois 1997] I oc = 0.82I 0 required to keep liquid water on its surface. This implies r Ar = 0.956r 0. Let us assume that some mechanism displaced the during the Archean to its current location by keeping the irradiance basically equal to I oc. Then, ṙ(t) r(t) = 1 7t 0 (1 2 7 ) yr 1. (5) t t 0 No independent evidences of geological nature contradict such a hypothesis

11 from Was the Possible Orbital Mechanisms Gravitational billiard during the Archean involving planet-planet scattering between the itself and a rogue rocky protoplanetesimal X, with m X 0.75m, which would have impacted on Venus [Minton 2012]. Isotropic Sun s mass loss due to strong stellar winds during the Archean. Both the timescale and the magnitude itself of the Solar mass loss rate at the early stages of its life are controversial [Wood 2004, Minton and Malhotra 2007]. Non-isotropic s mass loss due to possible erosion of the hydrosphere driven by the stellar wind. It implies that, at t Ar, the should have been more massive than now by 2%. If its solid part stayed unchanged, its fluid part should have been larger than now by m fl 0.02m0 tot [Iorio 2013].

12 from Was the Possible Orbital Mechanisms Gravitational billiard during the Archean involving planet-planet scattering between the itself and a rogue rocky protoplanetesimal X, with m X 0.75m, which would have impacted on Venus [Minton 2012]. Isotropic Sun s mass loss due to strong stellar winds during the Archean. Both the timescale and the magnitude itself of the Solar mass loss rate at the early stages of its life are controversial [Wood 2004, Minton and Malhotra 2007]. Non-isotropic s mass loss due to possible erosion of the hydrosphere driven by the stellar wind. It implies that, at t Ar, the should have been more massive than now by 2%. If its solid part stayed unchanged, its fluid part should have been larger than now by m fl 0.02m0 tot [Iorio 2013].

13 from Was the Possible Orbital Mechanisms Gravitational billiard during the Archean involving planet-planet scattering between the itself and a rogue rocky protoplanetesimal X, with m X 0.75m, which would have impacted on Venus [Minton 2012]. Isotropic Sun s mass loss due to strong stellar winds during the Archean. Both the timescale and the magnitude itself of the Solar mass loss rate at the early stages of its life are controversial [Wood 2004, Minton and Malhotra 2007]. Non-isotropic s mass loss due to possible erosion of the hydrosphere driven by the stellar wind. It implies that, at t Ar, the should have been more massive than now by 2%. If its solid part stayed unchanged, its fluid part should have been larger than now by m fl 0.02m0 tot [Iorio 2013].

14 from Was the The 4-Acceleration The non-geodesic 4-acceleration of a test particle is [Puetzfeld and Obukhov 2013] A µ = cξ ( δ ν µ v µ ) v ν m c 2 K ν, µ = 0, 1, 2, 3. (6) In eq. (6), m is the test particle s mass as defined in multipolar schemes within the GR framework, ξ is an integrated quantity depending on the system s matter distribution, K µ. = µ ln F, where the nonminimal function F depends arbitrarily on the spacetime metric and on the Riemann curvature tensor. In general, ξ would contain contributions from both a background source and the test particle. However, in a multipolar context, in particular in eq. (6), one would consider only test particles in source-free regions; thus, ξ would correspond to the test particle only.

15 from Was the The 3-Acceleration In the weak-field and slow-motion approximation, eq. (6) yields the test particle s 3-acceleration ξ [c 2 ( K ) ] v K ck 0 v + v A =, (7) cm written in the usual three-vector notation. In calculating perturbatively the orbital effects of eq. (7), we make the assumption that m, ξ, K µ can be considered as constant during the system s characteristic timescale set by the orbital period P b. In general, m, ξ, K µ are not constant for the very general class of theories covered in [Puetzfeld and Obukhov 2013]; thus, in principle, assuming their constancy, even over one orbital period of the test particle, would need further justification.

16 from Was the The 3-Acceleration In the weak-field and slow-motion approximation, eq. (6) yields the test particle s 3-acceleration ξ [c 2 ( K ) ] v K ck 0 v + v A =, (7) cm written in the usual three-vector notation. In calculating perturbatively the orbital effects of eq. (7), we make the assumption that m, ξ, K µ can be considered as constant during the system s characteristic timescale set by the orbital period P b. In general, m, ξ, K µ are not constant for the very general class of theories covered in [Puetzfeld and Obukhov 2013]; thus, in principle, assuming their constancy, even over one orbital period of the test particle, would need further justification.

17 from Was the The Long-Term Orbital Perturbations The standard Gauss equations for the variation of the Keplerian orbital elements a, e, I, Ω, ω are adopted No a-priori assumptions on either the orbital configuration of the test particle or the spatial orientation of K are made. All the Keplerian orbital elements undergo long-term perturbations. Among them, it is interesting to note that the semimajor axis a secularly changes according to da dt = 2ξK 0 a + O (e). (8) m Also the eccentricity e undergoes secular changes of order O ( e 0). Since r = a ( 1 + e 2 /2 ), this represents a potential mechanism to explain the FYSP [Iorio 2013].

18 from Was the The Long-Term Orbital Perturbations The standard Gauss equations for the variation of the Keplerian orbital elements a, e, I, Ω, ω are adopted No a-priori assumptions on either the orbital configuration of the test particle or the spatial orientation of K are made. All the Keplerian orbital elements undergo long-term perturbations. Among them, it is interesting to note that the semimajor axis a secularly changes according to da dt = 2ξK 0 a + O (e). (8) m Also the eccentricity e undergoes secular changes of order O ( e 0). Since r = a ( 1 + e 2 /2 ), this represents a potential mechanism to explain the FYSP [Iorio 2013].

19 from Was the The Long-Term Orbital Perturbations The standard Gauss equations for the variation of the Keplerian orbital elements a, e, I, Ω, ω are adopted No a-priori assumptions on either the orbital configuration of the test particle or the spatial orientation of K are made. All the Keplerian orbital elements undergo long-term perturbations. Among them, it is interesting to note that the semimajor axis a secularly changes according to da dt = 2ξK 0 a + O (e). (8) m Also the eccentricity e undergoes secular changes of order O ( e 0). Since r = a ( 1 + e 2 /2 ), this represents a potential mechanism to explain the FYSP [Iorio 2013].

20 from Was the Traditional mechanisms to explain the FYSP in terms of non-orbital effects (atmospheric greenhouse, etc.) are still not entirely satisfactory. In principle, the FYSP could be explained by postulating a slowly receding which, at t Ar, was closer to the Sun than now. orbital mechanisms (gravitational billiard, isotropic Sun s mass loss, non-isotropic s mass loss due to hydrosphere s erosion by the Solar wind) proposed to explain such a putative recession of the have more or less serious drawbacks. A general class of modified theories of gravitation with nonminimal coupling is potentially able to yield a mechanism for the expansion of the s orbit. Indeed, it predicts secular variations of both a and e.

21 from Was the Traditional mechanisms to explain the FYSP in terms of non-orbital effects (atmospheric greenhouse, etc.) are still not entirely satisfactory. In principle, the FYSP could be explained by postulating a slowly receding which, at t Ar, was closer to the Sun than now. orbital mechanisms (gravitational billiard, isotropic Sun s mass loss, non-isotropic s mass loss due to hydrosphere s erosion by the Solar wind) proposed to explain such a putative recession of the have more or less serious drawbacks. A general class of modified theories of gravitation with nonminimal coupling is potentially able to yield a mechanism for the expansion of the s orbit. Indeed, it predicts secular variations of both a and e.

22 from Was the Traditional mechanisms to explain the FYSP in terms of non-orbital effects (atmospheric greenhouse, etc.) are still not entirely satisfactory. In principle, the FYSP could be explained by postulating a slowly receding which, at t Ar, was closer to the Sun than now. orbital mechanisms (gravitational billiard, isotropic Sun s mass loss, non-isotropic s mass loss due to hydrosphere s erosion by the Solar wind) proposed to explain such a putative recession of the have more or less serious drawbacks. A general class of modified theories of gravitation with nonminimal coupling is potentially able to yield a mechanism for the expansion of the s orbit. Indeed, it predicts secular variations of both a and e.

23 from Was the Traditional mechanisms to explain the FYSP in terms of non-orbital effects (atmospheric greenhouse, etc.) are still not entirely satisfactory. In principle, the FYSP could be explained by postulating a slowly receding which, at t Ar, was closer to the Sun than now. orbital mechanisms (gravitational billiard, isotropic Sun s mass loss, non-isotropic s mass loss due to hydrosphere s erosion by the Solar wind) proposed to explain such a putative recession of the have more or less serious drawbacks. A general class of modified theories of gravitation with nonminimal coupling is potentially able to yield a mechanism for the expansion of the s orbit. Indeed, it predicts secular variations of both a and e.

24 from Was the G. Feulner, Rev. of Geophys., 50, RG2006, 2012 C. Goldblatt, K.J. Zahnle, Nature, 474, E1, 2011 D.O. Gough, Sol. Phys., 74, 21, 1981 B. Longdoz, L.M. Francois, Global and Planetary Change, 14, 97, 1997 I D. Minton, D. Talk delivered at the conference 2012 The Faint Early Sun at the Space Telescope Science Institute in Baltimore on 10 April 2012 D.A. Minton, R. Malhotra, Astrophys. J., 660, 1700, 2007

25 from II Was the B.E. Wood, Liv. Rev. Sol. Phys., 1, 2, 2004, arxiv: [gr-qc], 2013 D. Puetzfeld, Y.N. Obukhov, Phys. Rev. D, 87, , 2013