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Oort Cloud Evolu,on in a Long-‐Lived Stellar Cluster Thomas Nordlander, Hans Rickman, Bengt Gustafsson Uppsala Astron. Observatory • When did the Oort Cloud form? − Very early or very late? − Nice Model (B&M-‐13) or independent? • What size was the Sun’s Birth Cluster? − Low mass or high mass? − OC formaHon inside or outside the BC? Embedded clusters • Solar-‐type stars are born in embedded clusters • These clusters span a range of at least from 102 to 104 stars • Those of low mass dissolve quickly like their parent GMC, while the high mass ones develop into typical GalacHc clusters with lifeHmes from 108 to 1010 years • About equal numbers of stars are born in clusters with 102, 103 and 104 members (Lada & Lada 2003) Constraints on “our” cluster size (Adams 2010) SN rate ⇒ ⇐ Save the planetary orbits • Adams (2010): likelihood distribuHon peaks at 2500 • Gounelle & Meynet (2012): the Sun is a 3rd generaHon star of a smaller daughter cluster (102-‐103 stars) that separated from a huge iniHal assembly Our scope and strategy • Assume very early OC formaGon; find out if the cloud survives unGl the LHB • Assume a solar birth cluster with N0 = 2000 or N0 = 24000 (M67) • Trace 103 OC comets for 400 My (100-‐500 My) in a staGc cluster potenGal + random stellar encounters (select the strongest) • Perform 103 such simulaHons per model for staHsHcal robustness The high-‐mass cluster AssumpGons: Spherically symmetric Collisionally relaxed (King model) No mass segregaHon, no binaries No Hme evoluHon Tidal radius for current Galactocentric distance (Rt = 28.8 pc) • M67 parameters from Hurley et al. (2005) • • • • • The low-‐mass cluster AssumpGons: • Sequence of King models, 25 My each for the interval 100-‐500 My, adapted to basic data computed with EMACSS (Alexander & Gieles 2012) • N decreases from about 1700 to 300 with constant relaHve mass distribuHon • Rt decreases from about 13 to 7 pc • No mass segregaHon, no binaries Density profiles M67 Gal. midplane Stellar encounter velocity • For each distance r from the cluster center: • From the energy (E) and angular momentum (L) distribuHons of the cluster, pick two random pairs (E,L); compute the two pairs (vr,vt) • Combine these into the relaHve velocity vrel • Repeat many Hmes! M67 Rh The Sun’s encounters • Treat one star at a Gme! • Follow the Sun’s orbit but use the mean encounter flux n<vrel>(r) at each posiHon • For ΔT = 40 My, generate random encounters with b < 20,000 AU (~100) • Pick random M, vrel and b for each of those • Realize the one with the largest S = M/(vrelb) • Repeat over 400 My (~20) Gal. midplane M67 SimulaHons • IniHalize three groups of comets with a = 5000, 10000 and 20000 AU and thermalized eccentriciHes • Each group has 1000 comets • Start the Sun with random E and L defining the iniHal roseje orbit • Integrate the effects of the ~20 stellar encounters on the Sun and comets, and the cluster Gde all the Hme • Derive staHsHcal results for 1000 simulaVons Solar orbit, high-‐mass case 6% ejecGons of the Sun Start at half-‐mass radius Ejected Surviving Solar orbit, low-‐mass case 94% ejecGons of the Sun Ejected Surviving Comet escape • Unlinked − comets reach distances > 1 pc from the Sun − Mechanism: impulse imparted by a stellar encounter, or energy perturbaHon by a non-‐ integrable cluster Hde • Loss cone entry − comets enter within 5 AU of the Sun − Mechanism: angular momentum drain by the cluster Hde, or by impulse imparted by a stellar encounter Comet loss, high-‐mass case • In more than half the simulaHons, only 0.1-‐0.2% of comets survive • Unlinked comets dominate the losses, mostly due to stellar encounters • Without stars, energy diffusion by the cluster Hde would unlink the outer cloud comets; some others enter the loss cone a0 = 5000 AU a0 = 10000 AU a0 = 20000 AU Comet loss, low-‐mass case • In more than half the simulaHons, only 0.1-‐0.2% of comets survive • Significant comet survival occurs, but only if the Sun is ejected by a distant, massive star encounter • The loss of comets is mainly due to unlinking via both mechanisms a0 = 5000 AU a0 = 10000 AU a0 = 20000 AU Survivor characterisHcs Normalized frequency distribuGons High mass cluster Low mass cluster Comets have diffused in both direcGons An inner core gets populated A sharp energy cutoff forms in the low-‐mass cluster Shortcomings, arHfacts • If the Sun formed in a rich cluster, a primordial OC would likely have a massive inner core, which we have not modeled • By preferring massive encounter partners, we drive the Sun outward in the model cluster (lower encounter rate) • NeglecHng mass segregaHon, the Sun may meet massive stars also in the model cluster outskirts • Comet loss is conservaGvely esGmated! Conclusions • With an intermediate to large mass of the Sun’s birth cluster, a primordial OC would likely lose almost all its members, most of the survivors forming a Vght inner core • For the large mass, the cluster Hde would send many OC comets into the inner solar system (~1%) • For the lower range of cluster mass, there is a reasonable chance to save a significant OC inner core if the Sun is ejected early on (10% of comets with a0 = 5000 AU survive in 1/3 of cases) Summary • A primordial OC may occur in any Birth Cluster • In a small BC, a primordial OC will likely survive • In an intermediate BC, probably, only a bleak shadow will typically survive; however, survival of a large fracVon is possible under favorable condiVons • In a very rich BC, a primordial OC gets almost completely wiped out; hence, the current OC would have to be of late origin
