talk 1

Slide1: 

Effects of Young Clusters on Forming Solar Systems WITH: Eva M. Proszkow, Anthony Bloch (Univ. Michigan) Philip C. Myers (CfA), Marco Fatuzzo (Xavier University) David Hollenbach (NASA Ames), Greg Laughlin (UCSC) Fred C. Adams University of Michigan Nobel Symposium 135 - Stockholm

Slide2: 

Most stars form in clusters: => How does the cluster environment affect the process of planet formation?

Outline: 

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

Slide4: 

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

Simulations of Embedded Clusters: 

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

Simulation Parameters: 

Virial Ratio Q = |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 Radius Initial Stellar Density Gas Distribution Star Formation Efficiency 0.33 Embedded Epoch t = 0–5 Myr Star Formation t = 0-1 Myr

Dynamical Results : 

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

Mass Profiles: 

Mass Profiles Stellar Gravitational Potential

Closest Approach Distributions: 

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

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 Effects of Cluster Radiation on Forming/Young Solar Systems

Calculation of the Radiation Field: 

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

Photoevaporation of Circumstellar Disks: 

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

Slide13: 

Photoevaporation Model (Adams et al. 2004)

Results from PDR Code : 

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

Solution for Fluid Fields: 

Solution for Fluid Fields outer disk edge sonic surface

Evaporation Time vs FUV Field: 

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

Photoevaporation in Simulated Clusters: 

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

Slide18: 

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

Evaporation vs Accretion: 

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 . . .

Slide20: 

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

Monte Carlo Experiments: 

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

Slide22: 

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

Slide23: 

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

Cross Sections: 

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

Slide25: 

Solar System Scattering in Clusters Integrate over IMF (normalized to cluster size) 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)

Conclusions: 

Conclusions Clusters have moderate effects on planet formation: FUV flux levels leave `Jupiter’ unperturbed, but can significantly shorten total disk lifetime Disruption of planetary systems rare, bC ~ 700-4000 AU Planet ejection rates via scattering encounters are low All modes of destruction more important for M stars --------------------------------------------------------------------- Photoevaporation model for external FUV radiation Distributions of FUV flux and luminosity Distributions of radial positions and closest approaches Cross sections for solar system disruption [Orbit solutions, triaxial effects, spirographic approx.]

Time Evolution of Parameters: 

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

Orbits in Cluster Potentials: 

Orbits in Cluster Potentials

Orbits (continued): 

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

Slide31: 

Spirographic Orbits! (Adams & Bloch 2005) Orbital Elements

Slide32: 

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

Slide33: 

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.

Slide34: 

Triaxial Potentials in Clusters Box Orbit Growth of perpendicular coordinate

Slide35: 

Where did we come from?

Solar Birth Aggregate: 

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

Slide37: 

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

Constraints on the Solar Birth Aggregate: 

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

Slide39: 

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

Slide40: 

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

Probability of Supernovae: 

Probability of Supernovae

Probability of Supernovae: 

Probability of Supernovae

Probability of Scattering : 

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

Cross Section for Solar System Disruption: 

Cross Section for Solar System Disruption