1. Infall rates from observations Joseph Mottram 1

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? 2

3. Observing Infall Identified through asymmetric line profiles Commonly used: HCO +, CS, H 2 CO, N 2 H + 3 Myers et al., 2000

4. Extracting the mass infall rate 4 1.Skewness/asymmetry (e.g. Gregersen+ `97, Mardonnes+ `97) – doesn’t measure infall rate but can identify infall candidates. No model required. 2.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 3.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 4.1-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. 5

6. 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 2 02 -1 11 line in IRAS4A 6 Mottram et al., 2013

7. 1-D line modelling T dust and 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 = v 0 (r/r 0 ) -0.5 – T gas = T dust – o/p for H 2 is thermal, for H 2 O = 3 Water abundance profile from simple chemical network (Schmalzl+ in prep.) 7

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

9. Limit of Infall radius 9 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 10 Infall to ≤ 3000 AU in four other sources – mass infall rate of order few x 10 -5 M  yr -1 Outer edge of the model must be infalling for all sources t ff ~ 10 t inf, t inf 0.4 – 2.5 x 10 4 yrs 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 11

12. 12

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