M dwarfs: planet formation and long term evolution

Transcription

1 Astron. Nachr. / AN 326, No. 10, (2005) /DOI /asna M dwarfs: planet formation and long term evolution F.C. ADAMS 1,P.BODENHEIMER 2,andG.LAUGHLIN 2 1 Michigan Center for Theoretical Physics, University of Michigan, Ann Arbor, MI 48109, USA 2 Lick Observatory, University of California, Santa Cruz, CA 95064, USA Received 11 August 2005; accepted 13 October 2005; published online 15 December 2005 Abstract. The first part of this paper discusses how planet formation proceeds in the disks orbiting M dwarf stars. These environments are different from those associated with solar-type stars in several ways: The planet forming clock (set by orbits) runs slower, the disks are more prone to evaporation, the supply of raw material is lower, the snowline is closer in, and planetary systems are more easily disrupted. Because of these considerations, red dwarfs are less likely to harbor giant planets, but can readily produce smaller planets. The second part of this paper describes stellar evolution calculations for M dwarfs, which live far longer than the current age of the universe. These diminutive stellar objects remain convective over most of their lives, continue to burn hydrogen for trillions of years, and do not experience red giant phases in their old age. Instead, red dwarfs turn into blue dwarfs and finally white dwarfs. This work also shows (in part) why larger stars become red giants. Key words: planets: formation protoplanetary disks stars: formation, evolution stars: late-type (M dwarfs, red giants) 1. Introduction Red dwarfs are the most common stars in the galaxy and in the universe. In our solar neighborhood, for example, nearly all of the closest stars are red dwarfs (Henry et al. 1994), which are also known as M dwarfs (this paper considers these terms interchangable). More specifically, of the 50 nearest stars to Earth, our Sun is the fourth largest. As a result, we can conclude with confidence that the most common result of the star formation process is the production of a red dwarf. For the sake of definiteness, we consider red dwarfs to have masses that lie in the range M = M. In spite of their ubiquity, however, red dwarfs have received relatively little attention from planet searches, planet formation theories, and stellar evolution calculations. This paper seeks to correct part of this oversight. In particular, we investigate how the processes of planet formation (Sect. 2; from Laughlin, Bodenheimer & Adams 2004, hereafter LBA04) and long term stellar evolution (Sect. 3; from Laughlin, Bodenheimer & Adams 1997, hereafter LBA97) are expected to proceed differently for M dwarf stars as compared to solar-type stars. This work shows that for both planet formation and stellar evolution, M dwarfs display markedly different behavior than their solar-type counterparts. Correspondence to: fca@umich.edu 2. Giant planet formation around M dwarfs Nearly 150 planets have been detected orbiting nearby stars (e.g., Marcy et al. 2003; Udry, Mayor & Queloz 2003), but these planet searches have thus far concentrated on solar-type host stars. The leading mechanism for explaining the origin of both these extrasolar planets and the giant planets in our solar system is the so-called core-accretion process. In this paradigm, icy planetesimals collide and accumulate until they build up planetary cores with mass M c 5 15 M.These cores then accrete nebular gas and eventually reach masses comparable to Jupiter. A long-standing problem with the core-accretion hypothesis was that the estimated time required for the core to grow and subsequently accrete 1M J of gas exceeded the observed lifetimes of circumstellar disks (Pollack et al. 1996). [We note that the process of gravitational instability does not suffer from this shortcoming and has been seriously discussed as an alternate mechanism (Boss 2000).] However, updated estimates for the opacity in protoplanetary envelopes indicate that Jupiter-mass planets can readily form through the core-accretion mechanism in solar-metallicity disks around solar-mass stars, with a time scale of 2 3 Myr at orbital radii a 5 AU (Hubickyj, Bodenheimer & Lissauer 2004). To achieve this relatively short formation time, the surface density of solid material in the disk must be somewhat larger (by

2 914 Astron. Nachr. / AN 326, No. 10 (2005) / a factor of 3) than that of the minimum-mass solar nebula (MMSN). In one calculation, e.g., the resulting core mass was about 16 M, modestly larger than the core mass (10 M ) deduced for Jupiter (Wuchterl, Guillot & Lissauer 2000). To account for the low core mass of Jupiter, a cutoff of solid accretion beyond a certain core mass is required, and can be explained by nearby planetary embryos that compete for available solid material. In an independent calculation with similar opacities (Inaba & Ikoma 2003; Inaba, Wetherill & Ikoma 2003) and a disk with eight times the solid surface density of the MMSN, a core of 25 M can form in 1 Myr at 5 AU, so that the total formation time is 2 3 Myr. In this latter model, the fragmentation of planetesimals and the enhancement of the solid accretion rate due to the gaseous envelope (primarily from gas drag) are taken into account, although the main gas accretion phase is not calculated. If the solid surface density is reduced to four times that of the MMSN, an 8 M core can still form in 5 Myr. Taken together, these results imply that giant planets can readily form, but somewhat special circumstances are required for the core accretion model to explain the particular properties of our Jupiter. The ongoing observational surveys are shifting our view of extrasolar planets from a disorganized collection of individual systems (e.g., 51 Peg, υ And, or 47 UMa) to a more robust statistical census. Different categories and populations of planets can now be delineated (e.g., Marcy & Butler 1998; Marcy, Cochran & Mayor 2000; Udry et al. 2003; Marcy et al. 2003). This emerging statistical view is important for improving our understanding of the planet formation process, and to learn how our own solar system fits into the galactic planetary census. One of the cleanest statistical results to emerge from extant planet searches is that stars with observed extrasolar planets tend to have high metallicities, typically twice that of the average Population I star in the solar neighborhood (Fischer & Valenti 2005; Santos et al. 2003; Butler et al. 2000). In addition, low metallicity stars are observed to be deficient in currently detectable giant planets (with P<8 yr; Sozzetti et al. 2004). This connection between planets and host-star metallicity can be interpreted as evidence in favor of the core accretion hypothesis (although it can also be interpreted as evidence in favor of migration see Sigurdsson et al. 2003). Metal-rich circumstellar disks have a higher surface density of solids and growing cores can easily reach the M c 5 15M threshold required for rapid gas accretion. In this work, we assume that the core accretion model can explain the formation of Jovian planets within disks orbiting solar-mass stars with solar metallicity. We then address the question of whether or not Jovian planets can form within disks orbiting around M dwarfs (M < 0.4M ). We find that the core-accretion process makes a clear prediction for the relative frequency of Jovian-mass planets as a function of stellar mass: The circumstellar disks orbiting red dwarfs are significantly less efficient in producing Jupitermass planets than disks around solar-mass stars (Sect. 2.1), although smaller, rockier planets (like Neptune) can readily form. Moreover, this prediction is immediately testable (Sect. 2.2) Theoretical model of planet formation In the theoretical model explored here, giant planets form within a circumstellar disk with the following properties: The surface density σ(r) = σ in (r in /r) 3/2,whereσ in is the normalization factor required to obtain a total disk mass M d (t) within inner and outer disk radii, r in and r d. The time dependence of the disk surface density is given by a depletion function of the form f σ (t) =1/(1 + t/t 0 ) so that the disk mass decreases according to M d (t) =M d (0)f σ (t).observations of circumstellar disks (e.g., Briceno et al. 2001) suggest that t 0 =10 5 yr and M id (0) = 0.05 M are reasonable benchmark values. The temperature distributions for both viscously evolving accretion disks and flat, passively irradiated disks have nearly the same power-law form, T d (r) = T d (R /r) 3/4,whereT d is related to the stellar surface temperature by a geometrical factor (e.g., T d /T [2/3π] 1/4 for a flat disk see Adams & Shu 1986). This model uses disks that are flat and passive, and assumes that the disk is isothermal in the vertical direction. The effective temperature T of the star is related to the stellar radius R and luminosity L (t, M ) through T (t, M ) = [L (t, M )/4πR 2σ]1/4. We adopt T (t, M ) and L (t, M ) from published pre-mainsequence stellar evolution tracks (D Antona & Mazzitelli 1994). We use a Henyey-type code (Henyey, Forbes & Gould 1964; see also Sect. 3) to compute the buildup and contraction of gaseous envelopes surrounding growing protoplanetary cores embedded within the evolving disk. This method (Kornet, Bodenheimer & Różyczka 2002; Pollack et al. 1996) adopts recent models for envelope opacity (Podolak 2003) which include grain settling (see also Hubickyj et al. 2004). The calculation is simplified in that it uses a core accretion rate of the form dm c /dt = C 1 πσ s R c R h Ω (Papaloizou & Terquem 1999; compare with Pollack et al. 1996), where σ s is the surface density of solid material in the disk, Ω is the orbital frequency, R c is the effective capture radius for the accretion of solid particles, R h = a[m p /(3M )] 1/3 is the tidal radius of the protoplanet, and C 1 is a constant of order unity. An important feature of this present model is that the outer boundary conditions for the planet include the decrease in the background gas density and temperature with time. The results of this planet formation calculation are illustrated in Fig. 1. The first simulation shown here corresponds to a disk orbiting a 1 M star with an initial solid surface density σ s =11.5gcm 2 at a =5AU, about four times that of the MMSN. This value is based on an initial gas-tosolid ratio of 70 in the disk; as the disk evolves, σ s decreases with time because mass accretes onto the growing planet. A Jupiter-mass planet forms in 3.25 Myr with a core mass of 18 M (see also Hubickyj, Bodenheimer & Lissauer 2004). The second calculation is for a disk surrounding an M star with mass M =0.4M, where the initial solid surface density is σ s =4.5gcm 2 at a =5AU (the disk surface density scales with stellar mass). In this case, the disk is not able to produce a Jupiter-mass planet: The growing planet has reached a mass of only M P = 14M at t = 10 Myr. No additional growth is expected at later times because the mass of the entire disk is

3 F.C. Adams, P. Bodenheimer & G. Laughlin: M dwarfs: planet formation and long term evolution 915 Mass (Earth Masses) time (Millions of Years) Fig. 1. Growth of the core and envelopes of planets at 5.2 AU in disks orbiting stars of two different masses (from LBA04). The curves in the upper left part of the graph show the time-dependent core mass (dotted curve) and total mass (solid curve) for a planet forming in a disk surrounding a 1M star. The curves in the lower right part of the graph show the time dependence of the core mass (dotted curve) and total mass (solid curve) for a planet forming in a disk around a 0.4M star. After 10 Myr, the disk masses become extremely low, which effectively halts further planetary growth. The planet orbiting the M star gains its mass more slowly and stops its growth at a much lower mass M 14M. less than 1 M J. The resulting planet is similar in mass, size, and composition to Uranus and Neptune. The aforementioned calculation shows that the formation of giant planets is difficult at a 5 AU (for M stars). Could other locations in the disk be viable? Additional calculations (see LBA04) demonstrate that Jovian planet formation around a 0.4M star is also compromised at radii of 1 AU and 10 AU. The lower surface densities (σ s ) and longer orbital timescales (Ω = GM /a 3 ) of M-star disks more than offset the increase in tidal radius R h and lead to a greatly reduced capacity for forming Jovian-mass planets within the standard core-accretion paradigm. In addition, the reduced core mass found in the M-star disk results in much longer times for the accretion of the gaseous envelope. Although red dwarfs have a hard time forming Jupiter-mass planets, the formation of Neptune-like objects and terrestrial-type planets should be common around these low-mass stars. Indeed, our failed attempts at giant planet formation around M stars produced bodies with masses 14, 2.0, and 4.3 M after 10 Myr. Furthermore, the final sizes/masses of these objects correlates with the surface density of solids (dust and ice) in the precursor protoplanetary disk and should thus depend on the metallicity of the host star. In addition to the effects discussed above, planets forming around red dwarfs face other problems. Most stars form within groups and clusters, where external radiation from other nearby stars can efficiently drive mass loss from disks around M stars (Adams et al. 2004). M dwarfs are nearly as bright as solar-type stars in their youth, but their gravitational potential wells are less deep; this combination of properties allows the inner disks to be more readily evaporated. For M stars, photoevaporation due to both external radiation fields and radiation from the central star can be more effective than for solar-type stars by a factor of , depending on the environment, so the gas supply for planet formation can be much shorter lived. Star forming regions are dynamically disruptive due to passing binary stars and background tidal forces; these influences affect circumstellar disks and planetary systems around M stars more effectively than in systems anchored by larger primaries. Because these difficulties affect not only planet formation, but also planet migration, short-period Jovian-mass planets (hot Jupiters) should be especially rare near M stars. Although large planets like Jupiter should be rare near M stars, it remains possible for small icy planets like Neptune to form around solar type stars. The existing data base on extrasolar planets now includes some examples. An interesting challenge for the future is to observationally determine the distribution of planet masses for stars of varying mass, and to theoretically account for the observed distributions Potential observational tests A number of observational programs can confirm or falsify this predicted paucity of Jovian planets orbiting M stars; these searches and can also detect Neptune-mass objects if they are present. Given an adequate time baseline, the Doppler radial velocity method (e.g., Marcy & Butler 1998) will determine whether Jupiter-mass planets are common around red dwarfs. A Neptune-mass planet in a circular orbit with semimajor axis a =3AU around a 0.4M star has a period P = 8.2 yr, and induces a stellar radial velocity half-amplitude K =1.6ms 1 (for inclination angle i =90 ). This type of planet is marginally detectable using the current RV precision of 3ms 1, provided that one can attain a high sampling rate. To date, ongoing planet searches have detected a few examples of planets orbiting M dwarf stars, and a large collection ( 100) red dwarfs are currently under surveillance. The GJ876 system (Marcy et al. 2001), with M 0.3 M, contains two Jovian planets (M c sin i = 0.6M J, M b sin i =1.9M J ) with periods P c 30 d and P b 60 d. Because of its resonant configuration, the system is thought to have undergone migration (Lee & Peale 2002), which suggests that an abundant gas supply was present when the planets formed. The calculations presented here suggest that, within the standard core-accretion paradigm, systems such as GJ 876 are intrinsically rare; such systems can form, but they must be drawn from the extreme high-mass end of the circumstellar disk mass distribution (LBA04). In the alternative formation scenario via gravitational instabilities (Boss 2000), the growth rate depends primarily on the ratio of disk mass to star mass; instabilities are not suppressed in disks surrounding low mass stars (compared to disks orbiting solar-type stars) as long as the disks are sufficiently massive. Systems like GJ 876 may turn out to be examples of giant planet formation through gravitational instability. On the other hand, gravitational fragmentation will not generally produce ice giants such as Neptune, so the discovery of ice giants in extrasolar systems provides an important confirmation of the coreaccretion hypothesis. The recent detection of a Neptune-mass

4 916 Astron. Nachr. / AN 326, No. 10 (2005) / for the lensing system. Models of the galactic disk (Han & Gould 1996) indicate a 90% a-priori probability that the optically faint lens primary is an M dwarf (in which case the planet orbiting the M star GJ 436 (Butler et al. 2004) is the first such example. Microlensing is another promising technique for determining the census of planets orbiting M dwarfs. Recent work (Bond et al. 2004) reports an unusual light-curve for a G- type source star in the direction of the galactic bulge. The observed light curve is consistent with the passage of an optically faint binary lens with mass ratio µ = planet mass M P 1.5M J )anda 10% probability that the primary is a white dwarf (implying a somewhat higher planet mass). In either case, the projected sky separation of the primary-planet system is 3 AU. Our calculations imply that M dwarfs should rarely harbor Jupiter-mass planets and favor the possibility that the lensing system has a white dwarf primary. This prediction can be tested within 10 years as proper motion separates the source star from the lens. We also predict that the mass spectrum of microlensed planets (drawn largely from M dwarf primaries) should be shifted dramatically toward Neptune-mass objects compared to the mass spectrum of planets found by the ongoing RV and Transit surveys (which draw predominantly from primaries of roughly solar-mass). Transits provide yet another method for detecting planets. A Neptune-mass object in central transit around a 0.3 M M dwarf produces a photometric dip of approximately 1.5%. Such events are easily observed from the ground using telescopes of modest aperture (Henry et al. 2000; Seagroves et al. 2003). The forthcoming Kepler mission (Koch et al. 1998) will monitor 3600 M dwarf stars with m V < 16 over its 4-year lifetime, and will easily detect transits of objects of Earth size or larger in orbit around M dwarf stars. Assuming that icy core masses of M 1M can accrete at a 1 AU, the Kepler sample size will be large enough to provide a statistical test of our hypothesis. 3. Long term evolution of M dwarfs Solar-type stars have main sequence lifetimes that are comparable to the current age of the universe, with the latter age now known to be approximately 13.7 Gyr, and their long term (post-main-sequence) development is well-studied (Iben 1974). In contrast, smaller stars live much longer than their larger brethren, and hence red dwarfs live much longer than a Hubble time. As a result, the post-main-sequence development of these small stars had not been previously calculated. This section describes stellar evolution calculations that follow the post-main-sequence development of M dwarfs (Sect. 3.1). Since the smallest stars do not become red giants at the end of their lives, this work also shed light on the question of why larger stars do become red giants (Sect. 3.2) Stellar evolution calculations To follow the long term evolution of red dwarfs, we use not only the now-standard Henyey method, but also the actual Henyey code. After making updates of the opacities (Weiss et al. 1990; Alexander et al. 1983; Pollack et al. 1985) and equations of state (Saumon et al. 1995), we have carried out a study of the long term development of red dwarfs (LBA97; see also Adams & Laughlin 1997, hereafter AL97). The basic trend for M dwarf evolution is illustrated in Fig. 2, which shows evolutionary tracks in the H-R diagram for stars in the mass range M = M. Although it has long been known that these small stars will live for much longer than the current age of the universe, these stellar evolution calculations reveal some surprises. For example, the star with initial mass M =0.1M remains nearly fully convective for 5.74 trillion years. As a result, the star has access to almost all of its nuclear fuel for almost all of its lifetime. Whereas a 1.0 M star only burns about 10 percent of its hydrogen on the main sequence, this star, with 10 percent of a solar mass, burns nearly all of its hydrogen and thus has about the same main sequence fuel supply as the Sun. One of the most interesting findings of this work is that small red dwarfs do not become red giants in their post-mainsequence phases. Instead they remain physically small and grow hotter to become blue dwarfs. Eventually, of course, they run out of nuclear fuel and are destined to slowly fade away as white dwarfs. As shown by the evolutionary tracks in Fig. 2, the smallest star (in mass) that becomes a red giant has M =0.25M. We return to this issue in Sect The inset diagram in Fig. 2 shows that the stellar lifetimes for these small stars measure in the trillions of years. A red dwarf with mass M =0.25M has a main sequence lifetime of about 1 trillion years, whereas the smallest stars with M = 0.08 M last for 12 trillion years. Note that all of these calculations are performed using solar metallicities. The metals in stellar atmospheres act to keep a lid on the star and impede the loss of radiation. As metallicity levels rise in the future, these small stars can live even longer (AL97). Given that most stars are red dwarfs, and that these small stars can live for trillions upon trillions of years, the galaxy (and indeed the universe) has only experienced a tiny fraction f of its stelliferous lifetime. Most of the stellar evolution that will occur is yet to come. Another interesting feature in Fig. 2 is the track of the star with M =0.16M. Near the end of its life, such a star experiences a long period of nearly constant luminosity, about one third of the solar value. This epoch of constant power lasts for 5 Gyr, roughly the current age of the solar system and hence the time required for life to develop on Earth. Any planets in orbit about these small stars can, in principle, come out of cold storage at this late epoch and can, again in principle, provide another opportunity for life to flourish. The galaxy continues to make new stars until it runs out of gas, both literally and figuratively. With the current rate of star formation, and the current supply of hydrogen gas, the galaxy would run of gas in only a Hubble time or two. Fortunately, this time scale can be extended by several conservation practices, including recycling of gas due to mass loss from evolved stars, infall onto the galactic disk, and the reduction of the star formation rate as the gas supply dwindles. With these effects included, the longest time over which

5 F.C. Adams, P. Bodenheimer & G. Laughlin: M dwarfs: planet formation and long term evolution 917 Fig. 2. The H-R diagram for red dwarfs with masses in the range M = M (from LBA97). Stars with mass M =0.25M are the least massive stars that can become red giants. The inset diagram shows the hydrogen burning lifetime as a function of stellar mass. Note that these small stars live for trillions of years. the galaxy can sustain normal star formation measures in the trillions of years (AL97). As the stellar population ages, the more massive stars die off. Their contribution to the galactic luminosity is nearly compensated by the increase in luminosity of the smaller stars. The resulting late-time light curve for a large galaxy is thus remarkably constant (Adams, Graves & Laughlin 2004) Why stars become red giants All astronomers know that our Sun is destined to become a red giant (e.g., Iben 1974). On the other hand, a simple first principles description of why stars become red giants is notable in its absence (see also Renzini et al. 1992; Whitworth 1989). Through this study of low mass stars, which do not become red giants, we can gain insight into this issue. The details are provided in LBA97; here we present a simplified argument that captures the essence of why stars become red giants at the end of their lives. This analytic argument begins with the standard relation connecting the stellar luminosity L,radiusR, and photospheric temperature T, i.e., L =4πR 2 σt 4. (1) Stars become more luminous as they age. This power increase represents a luminosity problem, which can be solved in one of two ways: The star can either become large in size, so that R increases and the star becomes giant. Alternately, the star can remain small and increase its temperature, thereby becoming a blue dwarf. The mass of the star determines the enormity of the luminosity problem that it faces near the end of its life. Which one of the two evolutionary paths the star follows is determined by the remaining stellar properties such as metallicity, composition gradients, and opacity. For the case of solar metallicity, the effects of composition gradients are relatively modest (LBA97), so we focus here on the role of opacity. Near the stellar surface, convection shuts down and stars have no choice but to radiate from their photospheres (LBA97). The opacity in the stellar photosphere increases at sufficiently high temperatures due to H and hydrogen ionization. On the other hand, the opacity also increases at sufficiently low temperatures due to molecules and grains. The stellar photosphere adjusts itself to reside in the intermediate region. When the stellar luminosity problem outlined above is sufficiently severe, the photospheric temperature cannot increase because of the sharply increasing opacity with increasing temperature, i.e., the photosphere encounters an opacity wall. As a result, the photospheric temperature remains (nearly) constant and the star ascends the red giant branch. For stars with photospheres that do not live close to this opacity wall red dwarfs have this behavior the surface temperature can increase enough to solve the luminosity problem and the star becomes a blue dwarf (instead of a red giant). The equations of stellar structure illustrate the argument outlined above. In the outer regions of the star, energy must

6 918 Astron. Nachr. / AN 326, No. 10 (2005) / be transported outwards as described by the radiation conduction equation L = 4πr 2 4acT 3 dt 3κρ dr, (2) where the symbols have their usual meanings. The star must remain in hydrostatic equilibrium, so the temperature gradient must also obey the hydrostatic force equation dt dr = 1 µgm r 1+n r 2, (3) R g where R g is the gas constant, n is the effective polytropic index (see LBA97), and µ is the mean molecular weight of the gas. Eliminating the temperature gradient from these two equations, we derive an expression for the stellar luminosity L = 16π acg µm T 3 3 R g 1+n κρ. (4) The opacity can be written in a power-law form and the density can be expressed in terms of the stellar radius via κ = Cρ α T ω and ρ R γ. (5) Keep in mind that κ is the photospheric opacity, even though we have written its parametric form using similar notation to that often used for opacities in stellar interiors. The index γ = 3 for a uniform density star; real stars are centrally concentrated so that γ<3, and, for simplicity, we take γ =2toevaluate our result below. Both equations (1) and (4) can be used to express ( L )/L in terms of ( R )/R and ( T )/T. Solving the resulting two equations for two unknowns, we find T = T and R = R α L, (6) ω +1+4α L ω +1 L. (7) 2(ω +1+4α) L The answer to the red giant problem is thus embedded in these two equations: The aging star has a luminosity problem to solve, which manifests itself as a large value of ( L )/L. To overcome this problem, the star can vary its size R and/or its temperature T. If the stellar photosphere is at or near an opacity wall, where the opacity is a rapidly increasing function of temperature, then the index ω is large, T 0,and ( R )/R ( L )/2L. In other words, the temperature change is minimal, the stellar radius grows in proportion to the luminosity change, and the star becomes a red giant. 4. Summary and conclusion This contribution considers the formation of planets in disks orbiting M dwarfs and the long term evolution of the central stars. In both of these subproblems, M dwarfs have significantly different properties than stars of higher mass. Within the context of the core-accretion process, we find that the production of Jovian planets is seriously inhibited in circumstellar disks associated with M dwarfs. Our main conclusion is that Jovian planets should be rare in solar systems orbiting red dwarfs, but Neptune-like objects and terrestrial planets should be common around these low-mass stars (Fig. 1). Because disks orbiting solar-type stars more readily produce giant planets, we predict that planet properties should vary with the stellar mass. This result is straightforward to understand: Giant planet formation must take place before the disk gas is dispersed, and the dynamical time scales in M dwarf systems are longer the Keplerian orbit time scales like (M /M ) 1/2. Giant planets form in the outer solar system where ices are frozen onto the rocky building blocks, but the disks around M dwarfs have a much lower surface density in the realm of the nebula beyond the snowline. The mass supply is smaller by a factor of M /M,the growth rate for planetesimal formation is smaller by a factor (M /M ) 2, and the late stages of planetesimal accumulation are slower by a factor of M /M. These effects all conspire to impede giant planet formation, which must take place before the gas in the nebula is removed. This paper also presents the post-main-sequence development of red dwarfs, the most common stars in the universe (Fig. 2). These stars remain convective over most of their main sequence lifetimes and shine much longer than previously expected. Red dwarfs have only just begun to evolve and will continue to burn hydrogen for trillions of years into the future. As a result, our galaxy is only a small fraction (about 0.001) of the way into its Stelliferous Era. Because all stars increase their luminosity as they age, the total luminosity of the galaxy will remain nearly constant for trillions of years, even as more massive stars die off and are not replaced. At the end of their lives, these red dwarf stars do not become red giants, but rather become blue dwarfs instead. This feature sheds light on the question of why stars become red giants and allows us to construct a simple analytic argument that explains parts of the red giant phenomenon (Sect. 3.2). To conclude this discussion, let s take a step back to consider the larger context: M dwarfs are the most common stars in the galaxy. We find that M dwarfs readily produce Neptune-mass planets and large terrestrial planets, and that M dwarfs grow brighter as they age (like all stars) but do not become red giants (like solar-type stars). Taken together, these considerations suggest that solar systems associated with M stars may be interesting places to investigate in terms of their potential habitability, especially in the long term future. Acknowledgements. It is a pleasure to thank the organizers for a wonderful conference. This work was supported by the University of Michigan through The Michigan Center for Theoretical Physics and by NASA through the Terrestrial Planet Finder Mission and the Astrophysics Theory Program. 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