1. Effects of Young Clusters on Nascent Solar Systems Eva M. Proszkow (University of Michigan) ----------------------------------------------------- Philip C. Myers (Harvard Smithsonian CfA) Marco Fatuzzo (Xavier University) David Hollenbach (NASA Ames) Greg Laughlin (UC Santa Cruz) Anthony Bloch (University of Michigan) Fred C. Adams University of Michigan

2. Most stars form in clusters: What exactly are the effects of the cluster environment on the coupled processes of star and planet formation?

3. N-body Simulations of Young Clusters UV Radiation Fields in Young Clusters Photoevaporation Models for Disks Orbit Solutions in Cluster Potentials Scattering Encounters in Young Clusters NGC 1333 Case Study Constraints on Solar Birth Aggregate Outline

4. Introduction Environmental effects on planet formation: –disruptive FUV radiation –scattering interactions between star-disk systems Large (>1000 stars), dense clusters disrupt disk and planet formation Small (<100 stars) clusters don’t Intermediate sized clusters (100 < N < 1000 members) Virial and subvirial initial conditions (NGC 1333, 2068, 2264) (Lada & Lada 2003; Porras et al. 2003)

5. Simulations of Embedded Clusters Modified NBODY2 Code (S. Aarseth) Simulate evolution from embedded stage out to ages of 10 Myr Cluster evolution depends on the following: –cluster size –initial stellar and gas profiles –gas disruption history –star formation history –primordial mass segregation –initial dynamical assumptions 100 realizations are needed to provide robust statistics for output measures

6. Virial RatioQ = |K/W| virial Q = 0.5; cold Q = 0.04 Mass Segregation: largest star at center of cluster Simulation Parameters Cluster Membership N = 100, 300, 1000 Cluster Radius Initial Stellar Density Gas Distribution Star Formation Efficiency0.33 Embedded Epoch t = 0–5 Myr Star Formation t = 0-1 Myr

7. Fundamental Plane for Clusters (from Megeath, Allen et al. PPV)

8. (Walsh et al. 2006) NGC 1333 - cold start

9. Collection of SPITZER Clusters

10. Results from Simulations Evolution of cluster parameters: –bound cluster fraction f b –virial ratio Q –velocity isotropy parameter  = 1 - v  2 /v r 2 –half-mass radius R 1/2 Distribution of closest approaches Radial position probability distribution Cluster mass profiles

11. Time Evolution of Parameters Subvirial ClusterVirial Cluster 1003001000 In subvirial clusters, 50-60% of members remain bound at 10 Myr instead of 10-30% for virial clusters R 1/2 is about 70% smaller for subvirial clusters Stars in the subvirial clusters fall rapidly towards the center and then expand after t = 5 Myr

12. Mass Profiles Subvirial Virial  = r/r 0 Simulationpr0r0 a 100 Subvirial0.690.392 100 Virial0.440.703 300 Subvirial0.790.642 300 Virial0.491.193 1000 Subvirial0.821.112 300 Subvirial0.591.963 Stellar Gravitational Potential

13. Closest Approach Distributions Simulation 00  b C (AU) 100 Subvirial0.1661.50713 100 Virial0.05981.431430 300 Subvirial0.09571.711030 300 Virial0.02561.632310 1000 Subvirial0.07241.881190 1000 Virial0.01011.773650 Typical star experiences one close encounter with impact parameter b C during 10 Myr time span

14. –Photoevaporation of a circumstellar disk –Radiation from the background cluster often dominates radiation from the parent star (Johnstone et al. 1998; Adams & Myers 2001) –FUV radiation (6 eV < E < 13.6 eV) is more important in this process than EUV radiation –FUV flux of G 0 = 3000 will truncate a circumstellar disk to r d over 10 Myr, where Effects of Cluster Radiation on Forming/Young Solar Systems

15. Calculation of the Radiation Field Fundamental Assumptions –Cluster size N = N primaries (ignore binary companions) –No gas or dust attenuation of FUV radiation –Stellar FUV luminosity is only a function of mass –Meader’s models for stellar luminosity and temperature Sample IMF → L FUV (N) Sample Cluster Sizes Expected FUV Luminosity in SF Cluster →

16. FUV Flux depends on: –Cluster FUV luminosity –Location of disk within cluster Assume: –FUV point source located at center of cluster –Stellar density  ~ 1/r Photoevaporation of Circumstellar Disks G 0 = 1 corresponds to FUV flux 1.6 x 10 -3 erg s -1 cm -2 Median900 Peak1800 Mean16,500 G 0 Distribution

17. Photoevaporation Model (Adams et al. 2004)

18. Results from PDR Code

19. Solution for Fluid Fields

20. Evaporation Time vs FUV Field

21. Photoevaporation in Simulated Clusters Radial Probability Distributions Simulationr eff (pc)G 0 meanr med (pc)G 0 median 100 Subvirial0.08066,5000.323359 100 Virial0.11234,3000.387250 300 Subvirial0.12681,0000.5491,550 300 Virial0.18139,0000.687992 1000 Subvirial0.197109,6000.9553,600 1000 Virial0.34835,2001.252,060 FUV radiation does not evaporate enough disk gas to prevent giant planet formation for Solar-type stars

22. Evaporation Time vs Stellar Mass Evaporation is much more effective for disks around M-type stars: Giant planet formation is compromised

23. Evaporation vs Accretion

24. Orbits in Cluster Potentials

25. Orbits (continued) (effective semi-major axis) (angular momentum of the circular orbit) (circular orbits do not close)

26. Spirographic Orbits! (Adams & Bloch 2005) Orbital Elements

27. Allowed Parameter Space

28. Application to LMC Orbit Spirographic approximation reproduces the orbital shape with 7 percent accuracy & conserves angular momentum with 1 percent accuracy. Compare with observational uncertainties of 10-20 percent.

29. Solar System Scattering Many Parameters + Chaotic Behavior Many Simulations Monte Carlo

30. Monte Carlo Experiments Jupiter only, v = 1 km/s, N=40,000 realizations 4 giant planets, v = 1 km/s, N=50,000 realizations KB Objects, v = 1 km/s, N=30,000 realizations Earth only, v = 40 km/s, N=100,000 realizations 4 giant planets, v = 40 km/s, Solar mass, N=100,000 realizations 4 giant planets, v = 1 km/s, varying stellar mass, N=100,000 realizations

31. Red Dwarf saves the Earth sun red dwarf earth

32. Red Dwarf captures the Earth Sun exits with one red dwarf as a binary companion Earth exits with the other red dwarf Sun and Earth encounter binary pair of red dwarfs 9000 year interaction

33. Eccentricity e Semi-major axis a Jupiter SaturnUranus Neptune Scattering Results for our Solar System

34. Cross Sections 2.0 M  1.0 M  0.5 M  0.25 M 

35. Solar System Scattering in Clusters Ejection Rate per Star (for a given mass) Integrate over IMF (normalized to cluster size) Subvirial N=300 Cluster  0 = 0.096,  = 1.7  J = 0.15 per Myr 1-2 Jupiters are ejected in 10 Myr Less than number of ejections from internal solar system scattering (Moorhead & Adams 2005)

36. NGC 1333: A Case Study

37. Observations of NGC 1333 provide position, line of sight velocities, and mass estimates for 93 N 2 H + clumps (Walsh et al. 2005) Reconstruct positions and velocities of the clumps Simulate the evolution of this cluster for 10 Myr more centrally condensed –R 1/2 is about 2 times smaller –69% of cluster remains bound instead of 54% more interactive –G 0 is 5 times larger –b C ≈ 238 AU → disk truncation to r d ~ 80 AU NGC 1333 is very much like our ‘100 Subvirial’ cluster, except…

38. Where did we come from?

39. Solar Birth Aggregate Supernova enrichment requires large N Well ordered solar system requires small N

40. Probability of Supernovae

42. Probability of Scattering Scattering rate: Survival probability: Known results provide n, v, t as function of N (BT87) need to calculate the interaction cross sections

43. Basic Cluster Considerations Velocity: Density and time:

44. Cross Section for Solar System Disruption

45. Stellar number N Probability P(N) Expected Size of the Stellar Birth Aggregate survival supernova Adams & Laughlin, 2001, Icarus, 150, 151

46. Cumulative Distribution: Fraction of stars that form in stellar aggregates with N < N as function of N Lada/Lada Porras Median point: N=300

47. Constraints on the Solar Birth Aggregate (1 out of 60) (Adams & Laughlin 2001 - updated)

48. Probability as function of system size N (Adams & Myers 2001)

49. Conclusions NBody simulations of young embedded clusters –Distributions of radial position and closest approach –Subvirial clusters are more centrally concentrated, retain more stars, and have more radial velocities (compare with virial) Clusters have modest effects on star and planet formation –most interactive system, NGC 1333, truncates disks to r d ~ 80 AU –FUV flux levels are low enough to leave disks unperturbed –disruption of planetary systems is small effect, b C ~ 700-4000 AU and disruption requires at least 250 AU approach –ejection rates for encounters with passing cluster members are lower than ejection rates from planets within the system Photoevaporation models from external FUV radiation Central concentration and mass segregation can play important role in increasing the interaction rate

50. Conclusions (continued) Spirographic approximation scheme for orbits –high accuracy and analytic results –new orbital elements Half a million Monte Carlo scattering simulations provides us with cross sections for solar system disruption Constraints on the birth aggregate of the solar system –Solar system formed in clusters with N = 2000 +/- 1000 –A priori odds of solar system conditions about 2 percent alf a million monte carlo scattering simulations)

52. Future Code Development –Mass segregation (primordial/evolutionary) –Non-spherical star and gas distributions –Primordial filamentary structure –Exponential decay of gas potential –Close encounter binary formation –Primordial binaries Parameter Space Study –Stellar membership, N & Virial ratio –Gas potentials (mass, shape) & expulsion –Stellar densities –IMF –Star formation epoch