Infall rates from observations

1. Infall rates from observations Joseph Mottram

2. Why is infall relevant? • Infall must happen for star formation to proceed • The rate of infall on envelope scales is important for the timescale for envelope depletion • Balance of infall and outflow relates to local star formation efficiency • Effect disk properties including: • Stability • Heating • Chemical composition • When it forms?

3. Observing Infall • Identified through asymmetric line profiles • Commonly used: HCO+, CS, H2CO, N2H+ Myers et al., 2000

4. Extracting the mass infall rate • Skewness/asymmetry (e.g. Gregersen+ `97, Mardonnes+ `97) – doesn’t measure infall rate but can identify infall candidates. No model required. • Slab model (e.g. Myers+ `96, Di Francesco+ `01) – calculate mass infall rate at characteristic radius. No RT needed but no information on velocity variation.

5. Extracting the mass infall rate • PV diagram (e.g. Tobin+ `12, Wang+ `12) – use analytical/RT model and observed PV & moment 1 maps to constrain balance of infall and other motions • 1-D RT model to fit line profiles from multiple lines (e.g. Hogerheijde& Sandell `00, Mottram+ `13) – self-consistently constrain fit to 1-D model using line shape and intensity.

6. Mottram et al., 2013 Water line profiles • Line profiles dominated by outflow – remove with Gaussian fits • IPC observed towards 7 WISH LM sources • Mostly only in the ground-state lines • Also 202-111 line in IRAS4A

7. 1-D line modelling • Tdustand n power-law profiles from a grid of 1-D continuum model fits to the SED and SCUBA images (Kristensen+ ‘12) • Non-LTE line radiative transfer modelling using RATRAN (Hogerheijde & van der Tak ‘00) • Assume: • v = v0 (r/r0)-0.5 • Tgas = Tdust • o/p for H2 is thermal, for H2O = 3 • Water abundance profile from simple chemical network (Schmalzl+ in prep.)

8. Limit of Infall radius • Infall continues to at least ~1000AU Mottram et al., 2013

9. Limit of Infall radius • Infall must be to outer edge of model for all sources • Similar result also found by Beloche et al., ‘06 Mottram et al., 2013

10. Extent and rate of infall • Infall to ≤ 3000 AU in four other sources – mass infall rate of order few x 10-5Myr-1 • Outer edge of the model must be infalling for all sources • tff ~ 10 tinf, tinf 0.4 – 2.5 x 104yrs • Mass infall rate in IRAS4A (2×10-4 Myr-1 at 1000 AU) is an order of magnitude larger than the mass outflow and accretion rate • Profile in two source not due to envelope infall

11. Future requirements & prospects • To date, almost all analysis methods have had to impose assumptions about the velocity field, usually 1D • Few have been directly sensitive to infall on envelope-> disk scales • ALMA will be able to change this, but it requires: • Multiple transitions and/or molecules which are sensitive to different spatial scales • Observations sensitive to emission from few 1000 AU to ~100AU • Consider infall, turbulence and rotation • Self-consistent analysis which fits both line profiles and spatial variation

13. Water abundance profile Mottram et al., 2013 • Simple chemistry required to reproduce all line profiles Cloud/ISM