- 2 Smoothed Particle Hydrodynamics 2.1 Self-Gravitating Compressible F l o w ........................................................... 2.2 The concept of S P H ......................................................................................... 2.3 K e r n e l s ........................................................................................................... 2.4 SPH equations................................................................................................... 2.5 Smoothing L e n g th s ......................................................................................... 2.6 Artificial V is c o s ity ......................................................................................... 2.6.1 Time-dependent viscosity ..............................................................
- 7 Summary 163 7.1 Numerical diffusion and numerical dissipation instar formation codes . 163 7.2 Treatment of the thermodynamics in collapsing c o r e s ................................ 164 7.3 Prestellar cores in the Ophiuchus Main C l o u d ............................................. 165 7.4 The effect of metallicity on the core co llap se.................................................166 7.5 Future w o r k ........................................................................................................ 167
- 1.1 Taurus molecular cloud seen in extinction, taken from Dobashi et al. (2005) and modified by Nutter (private communication). The contour levels are Av= l, 2 ,4 .........................................................................................
- 2.1 The structure of a 2-dimensional tree constructed for a simple distribution. Depending on the value of 9, we can determine whether to calculate the gravitational accelerations directly or approximate the particles as a clu ster................................................................................................................
- 2.2 Graphical representation of MPT for when n = 5. Arrows indicate the steps that are allowed. By enforcing this, all particles will remain synchronised at the end of A t ...........................................................................
- 3.1 Solution to the Lane Emden equation for n = 3 / 2 ....................................
- 3.2 The two-dimensional lattice with inter-particle separation s......................
- 3.3 2-D plot of the isentropic monatomic sphere, constructed as described in section 3.2.3..................................................................................................
- 3.4 Density profile of sphere before settling. Red line represents the analytical solution; green points represent the actual particle densities............... 46
- 3.5 Density profile of the settled distribution......................................................
- 3.6 Radial components of the gravitational accelerations (red open squares) . and hydrostatic accelerations (filled green circles) of the particles in a settled sphere, as a function of radius............................................................
- 4.1 Schematic representation of the pseudo-cloud around an SPH particle.The location of the SPH particle inside its pseudo-cloud is not specified. Taken from Stamatellos et al. (2007a)...........................................................
- 4.3 The variation with density and temperature of the pseudo-mean opacity. Isopycnic curves are plotted as in Fig. 4.2. For comparison the local opacity at density p = 10-6 g cm-3 is also plotted (dashed line). Taken from Stamatellos et al. (2007)......................................................................... 73
- 4.4 Simulation of the collapse and fragmentation of a 5 .4 M© core, first evolved with the barotropic equation of state (top row) and then with the new treatment of the energy equation (bottom row), using identical initial conditions. Each snapshot shows the logarithm of the column density................................................................................................................
- 4.5 Stellar masses as a function of time, for a selection of simulations. Note (i) the delay between the formation of the primary and the formation of a clutch of secondaries (this is the time during which the circumprimary disc accumulates, until it becomes Toomre unstable); and (ii) the rapid decline in the accretion rate onto the primary once the secondaries start to condense out.................................................................................................
- 4.13 The distribution of eccentricities, e, for multiple protostars: (a) using the barotropic equation of state; (b) using the new treatment of the energy equation.............................................................................................................
- 4.14 The distribution of mass ratios, q, for multiple protostars: (a) using the barotropic equation of state; (b) using the new treatment of the energy equation.............................................................................................................
- 13CO map of Ophiuchus, taken from Loren (1989) and modified by Nut
- ter et al. (2006). The contour levels give antenna temperatures of 4, 5,
- 6 ,7 ,8 ,1 0 , 12,14, 18, 20K.................................................................................. 109
- Millimeter continuum mosaic of the 6 major clumps in the Ophiuchus
- main cloud, from Motte et al. (1998)............................................................. 110
- 5.3 Logarithm of the total mass of a core ( M ^ ) plotted against the number of stars formed, N *...............................................................................................121
- 5.11 For each multiple system we plot the orbital eccentricity, e against the period, P .................................................................................................................129
- 5.12 The distribution of mass ratios, q, for multiple protostars at the end of the simulations...................................................................................................... 130
- 6.1 Stellar masses as a function of time, for simulationswith Z = Z0
- 5.1 Estimated temperatures for each clump............................................................. 113
- 5.3 Sample of recalculated values of 0 4 ^ /a THESM..........................................132
- 6.1 Results of the simulations performed with metallicities Z = ZQ, Z = 0.1 ZQand Z = 0.01 ZQ, at time t = 0.3 Myr. See text for a description of each column.......................................................................................................... 145
- Bromm V., Coppi P. S., Larson R. B., 2002, ApJ, 564, 23
- Bromm V., Ferrara A., Coppi P. S., Larson R. B., 2001, MNRAS, 328, 969
- Burgasser A. J., Reid I. N., Siegler N., Close L., Allen P., Lowrance P., Gizis J., 2007, in Reipurth B., Jewitt D., Keil K., ed, Protostars and Planets V, p. 427
- Burkert A., Bodenheimer P., 1993, MNRAS, 264, 798
- Burkert A., Bodenheimer P., 2000, ApJ, 543, 822
- Caselli P., Walmsley C. M., Terzieva R., Herbst E., 1998, ApJ, 499, 234
- Chapman S., Pongracic H., Disney M., Nelson A., Turner J., Whitworth A., 1992, Nature, 359, 207
- Christlieb N., Wisotzki L., Reimers D., Homeier D., Koester D., Heber U., 2001, A&A, 366, 898
- Hubber D. A., Goodwin S. P., Whitworth A. P., 2006, A&A, 450, 881
- Hubber D. A., Whitworth A. P., 2005, A&A, 437, 113
- Jappsen A.-K., Glover S. C. O., Klessen R. S., Mac Low M.-M., 2007, ApJ, 660, 1332
- Jeans J. H., 1928, Astronomy and cosmogony. Cambridge [Eng.] The University press, 1928.
- Jijina J., Myers P. C., Adams F. C., 1999, ApJS, 125, 161