Effects of Young Clusters on Forming Solar Systems

1. Effects of Young Clusters on Forming Solar Systems Fred C. Adams University of Michigan Stars to Planets, Univ. Florida WITH: Eva M. Proszkow, Anthony Bloch (Univ. Michigan) Philip C. Myers (CfA), Marco Fatuzzo (Xavier University) David Hollenbach (NASA Ames), Greg Laughlin (UCSC)

2. Most stars form in clusters: In quantitative detail: What effects does the cluster environment have on solar system formation?

3. Outline • N-body Simulations of Clusters • UV Radiation Fields in Clusters • Disk Photoevaporation Model • Scattering Encounters

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

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. Simulation Parameters Virial Ratio Q = |K/W| virial Q = 0.5; cold Q = 0.04 Mass Segregation: largest star at center of cluster Cluster Membership N = 100, 300, 1000 Cluster Radius Initial Stellar Density Gas Distribution Star Formation Efficiency 0.33 Embedded Epoch t = 0–5 Myr Star Formation t = 0-1 Myr

7. Dynamical Results Evolution of clusters as astrophysical objects Effects of clusters on forming solar systems • Distribution of closest approaches • Radial position probability distribution (given by cluster mass profiles)

8. x = r/r0 Subvirial Virial Mass Profiles Stellar Gravitational Potential

9. Closest Approach Distributions Typical star experiences one close encounter with impact parameter bC during 10 Myr time span

10. Effects of Cluster Radiation on Forming/Young Solar Systems 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 G0 = 3000 will truncate a circumstellar disk to rd over 10 Myr, where

11. Expected FUV Luminosity in SF Cluster Sample Cluster Sizes → Sample IMF → LFUV(N) 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

12. Photoevaporation of Circumstellar Disks FUV Fluxdepends on: • Cluster FUV luminosity • Location of disk within cluster Assume: • FUV point source located at center of cluster • Stellar density r ~ 1/r G0 Distribution G0 = 1 corresponds to FUV flux 1.6 x 10-3 erg s-1 cm-2

13. Photoevaporation Model (Adams et al. 2004)

14. Results from PDR Code Lots of chemistry and many heating/cooling lines determine the temperature as a function of G, n, A

15. Solution for Fluid Fields sonic surface outer disk edge

16. Evaporation Time vs FUV Field ----------------------- (for disks around solar mass stars)

17. Radial Probability Distributions Photoevaporation in Simulated Clusters FUV radiation does not evaporate enough disk gas to prevent giant planet formation for Solar-type stars

18. Evaporation Time vs Stellar Mass Evaporation is much more effective for disks around low-mass stars: Giant planet formation can be compromised G=3000

19. Evaporation vs Accretion Disk accretion aids and abets the disk destruction process by draining gas from the inside, while evaporation removes gas from the outside . . .

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

21. 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

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

23. Scattering Results for our Solar System Eccentricity e Saturn Uranus Jupiter Neptune Semi-major axis a

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

25. Ejection Rate per Star (for a given mass) Solar System Scattering in Clusters Subvirial N=300 Cluster G0 = 0.096, g = 1.7 GJ = 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) Integrate over IMF (normalized to cluster size)

26. Conclusions • N-Body simulations of young embedded clusters • Distributions of radial positions and closest approaches • Subvirial clusters more concentrated & longer lived • Clusters have modest effects on star and planet formation • FUV flux levels are low & leave disks unperturbed • Disruption of planetary systems rare, bC ~ 700-4000 AU • Planet ejection rates via scattering encounters are low --------------------------------------------------------------------- • Photoevaporation model for external FUV radiation • Distributions of FUV flux and luminosity • Cross sections for solar system disruption • [Orbit solutions, triaxial effects, spirographic approx.]

28. Time Evolution of Parameters Subvirial Cluster Virial Cluster 100 300 1000 • In subvirial clusters, 50-60% of members remain bound at 10 Myr instead of 10-30% for virial clusters • R1/2 is about 70% smaller for subvirial clusters • Stars in the subvirial clusters fall rapidly towards the center and then expand after t = 5 Myr

29. Orbits in Cluster Potentials

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

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

32. Allowed Parameter Space Spirographic approximation is valid over most of the plane

33. 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.

34. Triaxial Potentials in Clusters Box Orbit Growth of perpendicular coordinate

35. Where did we come from?

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

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

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

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

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

41. Probability of Supernovae

42. Probability of Supernovae

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

44. Cross Section for Solar System Disruption