1. Fitting Magnetized Molecular Cloud Collapse Models to NGC 1333 IRAS 4A Pau Frau Josep Miquel Girart Daniele Galli Institut de Ciències de l’Espai (IEEC-CSIC) Osservatorio Astrofisico di Arcetri (INAF) Fitting Magnetized Molecular Cloud Collapse Models to NGC 1333 IRAS 4A Pau FrauCC2YSO - University of Western OntarioMay 17th, 2010

2. Introduction Magnetic fields may play an important role in the SF process Fitting Magnetized Molecular Cloud Collapse Models to NGC 1333 IRAS 4A Pau FrauCC2YSO - University of Western OntarioMay 17th, 2010 -Subcritical magnetized molecular clouds form dense molecular cores through ambipolar diffusion. -The increasing mass overcomes the magnetic support and the supercritical core collapses. Magnetic fields are strengthened and warped in the core, and are expected to adopt an hourglass morphology. Grain alignment is one of the visible effects of magnetic fields. The polarization angle is perpendicular to the magnetic field. Aim To test the influence of the magnetic fields we compare high-angular resolution observations of the polarized emission in the sub-mm range with collapse models of magnetized molecular clouds. This first step in model testing will help on: -Differentiate the best suited models for this kind of sources -Better understand the importance of the physical processes involved in SF

3. Method 1- Assume a density profile and magnetic flux function from theoretical models. 2- Select the orientation of the synthetic source by two viewing angles:  : polar axis with respect to north-south direction (inside the POS)  : inclination of the meridional plane respect to north-south direction (  POS) 3- Compute a large number of Stokes I, Q and U synthetic maps exploring the model parameters and orientation angles. 4- Convolve the synthetic maps with an interferometric response. 5- Compare the synthetic maps with the observational data and select the best model. Fitting Magnetized Molecular Cloud Collapse Models to NGC 1333 IRAS 4A Pau FrauCC2YSO - University of Western OntarioMay 17th, 2010

4. Assumptions (and future work) Fitting Magnetized Molecular Cloud Collapse Models to NGC 1333 IRAS 4A Pau FrauCC2YSO - University of Western OntarioMay 17th, 2010 -Uniform T (T dependence  Gonçalves et al. 2005) -Optically thin emission, no absorption or scattering effects. Very good approximation for submm emission (Hildebrand 1983; Novak et al. 1989) -Total density proportional to number density of dust grains -Aspherical and partially aligned dust grains with uniform properties (different species  Fiege et al. 2000) -Regular grid and uniform step in LOS integration -Output maps without noise

5. Models Fitting Magnetized Molecular Cloud Collapse Models to NGC 1333 IRAS 4A Pau FrauCC2YSO - University of Western OntarioMay 17th, 2010 -Combination of a numerical solution of MHD equations plus a semi-analytical perturbative solution -Assumes an initially unstable singular isothermal non-rotating sphere with uniform B -The free parameters are the spatial scale prior to collapse and the non-dimensional time since the collapse start Allen et al. (2003) -Fully numerical solution of MHD equations -Evolution of Galli 1993 model, with an isothermal toroid and more realistic initial condition -Predicts a pseudo-disk, and the results strongly depend on the level of magnetic to thermal support and sound speed Shu et al. (2006) -Totally different approach: steady-state axisymmetric calculation of the accretion on a low-mass magnetized protostar with Ohmic dissipation -The only free parameter is the Ohm radius -The magnetic field changes from radial at large distances to asymptotically uniform approaching the origin Galli & Shu (1993)

6. NGC 1333 IRAS 4A Fitting Magnetized Molecular Cloud Collapse Models to NGC 1333 IRAS 4A Pau FrauCC2YSO - University of Western OntarioMay 17th, 2010 General properties: - Low-mass young stellar system in a very early stage of evolution. - It is embedded in an infalling dense molecular and dusty envelope. Magnetic properties: - Girart et al. 1999 detect partially resolved polarization in both dust (1.3mm) and line (CO J=2-1), showing hints of hourglass morphology - Recent dust polarimetric observations with the SMA (877  m) revealed a well defined hourglass morphology associated with the infalling envelope (Girart et al. 2006) No-ideal properties: - Multiple system. The envelope harbors at least two embedded sources, distorting the “single-source” morphology. - The embedded sources power outflows, distorting the “only-infalling” morphology.

7.  FWHM =1.4”x1.1”=420x330 AU NGC 1333 IRAS 4A Fitting Magnetized Molecular Cloud Collapse Models to NGC 1333 IRAS 4A Pau FrauCC2YSO - University of Western OntarioMay 17th, 2010  FWHM =1.6”x1.4”=480x420 AU

8. Results I  Shu06 Fitting Magnetized Molecular Cloud Collapse Models to NGC 1333 IRAS 4A Pau FrauCC2YSO - University of Western OntarioMay 17th, 2010 R Ohm ~50 AU  FWHM =1.6”x1.4”=480x420 AU

9. Results II  Galli93 Fitting Magnetized Molecular Cloud Collapse Models to NGC 1333 IRAS 4A Pau FrauCC2YSO - University of Western OntarioMay 17th, 2010 R Colapse ~ 5300 AU  t Colapse ~ 7x10 4 yr x limit = 0.2 = 1000 AU  FWHM = 1.6”x1.4” = 480x420 AU R in =2” R out =18”

10. Results III  Allen03 Fitting Magnetized Molecular Cloud Collapse Models to NGC 1333 IRAS 4A Pau FrauCC2YSO - University of Western OntarioMay 17th, 2010 R Colapse ~ 2400 AU  t Colapse ~ 3x10 4 yr  FWHM = 1.6”x1.4” = 480x420 AU R out =8”

11. What about ALMA?  Allen03 Fitting Magnetized Molecular Cloud Collapse Models to NGC 1333 IRAS 4A Pau FrauCC2YSO - University of Western OntarioMay 17th, 2010 Observed map  Allen03 synthetic map  SMA convolved ALMA convolved SMA convolvedALMA convolved

12. What about ALMA?  Shu06 Fitting Magnetized Molecular Cloud Collapse Models to NGC 1333 IRAS 4A Pau FrauCC2YSO - University of Western OntarioMay 17th, 2010 SMA convolved ALMA convolved

13. Pushing the models with ALMA Fitting Magnetized Molecular Cloud Collapse Models to NGC 1333 IRAS 4A Pau FrauCC2YSO - University of Western OntarioMay 17th, 2010 Convolution with early-ALMA, configuration 15  FWHM = 0.4”x0.3” = 120x90 AU Shu06Allen03 600x600 AU

14. Summary Fitting Magnetized Molecular Cloud Collapse Models to NGC 1333 IRAS 4A Pau FrauCC2YSO - University of Western OntarioMay 17th, 2010 -The UV plane must be well sampled to have a reliable multi-scale observational map -The theoretical models used match the observations  Plausible scenario -With the current resolution we are not able to distinguish among the models -ALMA resolution and sensitivity will provide real power to distinguish among the models -This technique is a powerful tool to compare models with observations and better understand the physics involved in the process  ARTIST (LIME + B)

15. Thank you for your attention Fitting Magnetized Molecular Cloud Collapse Models to NGC 1333 IRAS 4A Pau FrauCC2YSO - University of Western OntarioMay 17th, 2010

16. References Fitting Magnetized Molecular Cloud Collapse Models to NGC 1333 IRAS 4A Pau FrauCC2YSO - University of Western OntarioMay 17th, 2010 Allen, A., Shu, F.H., & Li, Z.-Y. 2003, ApJ, 599, 351 Allen, A., Li, Z.-Y., & Shu, F.H. 2003, ApJ, 599, 363 Galli, D., & Shu, F. H. 1993, ApJ, 417, 220 Galli, D., & Shu, F. H. 1993, ApJ, 417, 243 Girart, J. M., Rao, R., & Marrone, D. P. 2006, Science, 313, 812 Gonçalves, J., Galli, D., & Walmsley, M. 2005, A&A, 430, 979 Gonçalves, J., Galli, D., & Girart, J. M. 2008, A&A, 490, L39 Shu, F. H., Galli, D., Lizano, S., & Cai, M. 2006, ApJ, 647, 382