This document summarizes a presentation on modeling the synthetic spectral signatures of hierarchically collapsing cores. It begins with background on the present understanding of cores as quasi-static, gravoturbulent structures. It then describes a simulation of hierarchical collapse, showing the development of density and velocity profiles. Radiative transfer modeling was performed on timesteps from the simulation to generate optically thick and thin spectral line profiles. The results included measurements of asymmetry in self-absorbed lines and the ratio of blue and red peak intensities, both indicators of infall motions developing prior to the prestellar stage.

1. Overview Background Radial Velocity Numerical Simulation Radiative Transfer Results Conclusions
Synthetic Spectral Signatures in Hierarchically
Collapsing Cores
Robert Loughnane
Instituto de Radioastronom´ıa y Astrof´ısica
(IRyA-UNAM)
Morelia, Michoac´an, M´exico
in collaboration with: Enrique V´azquez-Semadeni & Ra´ul Naranjo-Romero
CLOUDY: Emission Lines in Astrophysics,
from Gaseous Nebulae to Quasars,
M´exico City, M´exico
Monday 8th August, 2016
Robert Loughnane CLOUDY 2016

2. Overview Background Radial Velocity Numerical Simulation Radiative Transfer Results Conclusions
Overview
Background
Radial Velocity
Simulation Details
Radiative Transfer
Analytical Infall Analysis
Results: Tb/Tr and δv
Concluding Remarks
Robert Loughnane CLOUDY 2016

3. Overview Background Radial Velocity Numerical Simulation Radiative Transfer Results Conclusions
Overview
1 Overview
2 Background
Present Understanding of Cores I
Present Understanding of Cores II
Hierarchical Collapse I
Hierarchical Collapse II
Hierarchical Collapse III
3 Radial Velocity
Velocity Assumptions
4 Numerical Simulation
Simulation Details I
Simulation Details II
Simulation Details III
5 Radiative Transfer
Modeling Approximation
6 Results
Selected Results I
Selected Results II
Selected Results III
7 Conclusions
Robert Loughnane CLOUDY 2016

4. Overview Background Radial Velocity Numerical Simulation Radiative Transfer Results Conclusions
Present Understanding of Cores I
How are cores supported?
Figure: N2D+
emission from single massive
self-gravitating core from ALMA. [Image
courtesy of Bill Saxton & Alexandra Angelich
(NRAO/AUI/NSF); ALMA
(ESO/NAOJ/NRAO)]
Molecular clouds (MCs) are supersonically
turbulent - not magnetically supported
(Crutcher et al. 2010)
Gravoturbulent: MCs are supported
against collapse by virialized turbulence
(Heyer et al. 2009)
Magnetic support scenario →
gravoturbulent scenario
Cores evolve quasi-statically in prestellar
phase → supported by observations of
Bonnor-Ebert (BE) like density
profiles
Robert Loughnane CLOUDY 2016

5. Overview Background Radial Velocity Numerical Simulation Radiative Transfer Results Conclusions
Present Understanding of Cores II
“Quasi-static” picture
How can cores be “quasi-static”? They are produced in a
supersonically turbulent medium!
Complications:
Jeans-stable confined configurations need a confining medium
for the dense cores
How does hydrostatic configuration arise first - then accretes
quasi-statically if formed by a dynamic compression?
Evolving configurations form and acrete through shocks.
Before becoming Jeans-unstable, expands and then become
unstable. It therefore collapses and never once undergoes
quasi-static stage.
Robert Loughnane CLOUDY 2016

6. Overview Background Radial Velocity Numerical Simulation Radiative Transfer Results Conclusions
Hierarchical Collapse I
Plausible Scenario
Global hierarchical collapse of MCs (Buckert & Hartmann 2007;
V´azquez-Semadeni et al. 2007, 2009; Naranjo-Romero et al. 2015
[NR15])
MCs are turbulent - due to several instabilities during assembly
- strongly Jeans unstable (mass ≈ many Jeans masses, MJ)
Gas entering suffers phase transition: warm-diffuse atomic
phase → dense-cold phase ⇒ n↑ and T↓ by ∼102. Reduction
in MJ by 104 (G´omez & V´azquez-Semadeni 2014)
Clouds contract globally → ¯MJ goes down due to larger ¯n
(constant T) ⇒ small-scale fluctuations [from turbulence]
undergo collapse when M > MJ.
Robert Loughnane CLOUDY 2016

7. Overview Background Radial Velocity Numerical Simulation Radiative Transfer Results Conclusions
Hierarchical Collapse II
NR15 Simulation
NR15: Numerical simulation of collapse of local, near-MJ
fluctuation in a uniform, multi-MJ spherical background medium.
NOTE: Collapse is until prestellar stage with center outside box.
Similar to Larson (1969) - but it sits on a uniform, Jeans unstable
background
Features of simulation:
Develops BE-like density profile - not in equilibrium
Characterized by “outside-in” velocity profile
Core develops supersonic infall speeds before singularity.
Contradicts notion that low-mass starless cores exhibit subsonic
infall speeds (Lee et al. 2001)
Robert Loughnane CLOUDY 2016

8. Overview Background Radial Velocity Numerical Simulation Radiative Transfer Results Conclusions
Hierarchical Collapse III
Density & Velocity Profiles
−1.5 −1.0 −0.5 0.0 0.5 1.0 1.5
x/LJ
10
4
10
5
10
6
10
7
n[cm
−3
]
−0.3 −0.2 −0.1 0.0 0.1 0.2 0.3
r [pc]
−1.5 −1.0 −0.5 0.0 0.5 1.0 1.5
x/LJ
−3
−2
−1
0
1
2
3
v/cs
−0.3 −0.2 −0.1 0.0 0.1 0.2 0.3
r [pc]
Simulation develops radial velocity profile from fluctuation in
background flow. Core with amplitude 50% more than mean
density of unstable “cloud”.
“Core” defined at radius it merges into background. Grows in
mass & radius over time - dissimilar to other numerical setups.
Robert Loughnane CLOUDY 2016

9. Overview Background Radial Velocity Numerical Simulation Radiative Transfer Results Conclusions
Overview
1 Overview
2 Background
Present Understanding of Cores I
Present Understanding of Cores II
Hierarchical Collapse I
Hierarchical Collapse II
Hierarchical Collapse III
3 Radial Velocity
Velocity Assumptions
4 Numerical Simulation
Simulation Details I
Simulation Details II
Simulation Details III
5 Radiative Transfer
Modeling Approximation
6 Results
Selected Results I
Selected Results II
Selected Results III
7 Conclusions
Robert Loughnane CLOUDY 2016

10. Overview Background Radial Velocity Numerical Simulation Radiative Transfer Results Conclusions
Velocity Assumptions
Velocity Assumptions
Optically-thick lines of non-homologously collapsing cores show
blue-skewed, self-absorbed profiles.
Plausible collapse: Blue-skewed, self-absorbed optically-thick line
and gaussian-like optically thin line at the self-absorption dip.
Earliest assumptions on radial velocity profiles:
Inside-out collapse (Snell & Loren 1977, Zhou et al. 1993) -
collapse of initially static SIS (Shu 1977). Unrealistic since
SIS is unstable!
Other suggestions: Simple two-layer model (Myers et al.
1996) and initially unstable BE-like sphere (e.g. Keto et al.
2015). Latter ⇒ QE-BE model is most likely for
Taurus-Auriga core L1544!
Robert Loughnane CLOUDY 2016

11. Overview Background Radial Velocity Numerical Simulation Radiative Transfer Results Conclusions
Overview
1 Overview
2 Background
Present Understanding of Cores I
Present Understanding of Cores II
Hierarchical Collapse I
Hierarchical Collapse II
Hierarchical Collapse III
3 Radial Velocity
Velocity Assumptions
4 Numerical Simulation
Simulation Details I
Simulation Details II
Simulation Details III
5 Radiative Transfer
Modeling Approximation
6 Results
Selected Results I
Selected Results II
Selected Results III
7 Conclusions
Robert Loughnane CLOUDY 2016

12. Overview Background Radial Velocity Numerical Simulation Radiative Transfer Results Conclusions
Simulation Details I
Numerical Setup
Isothermal (T=11.4K) gas starting at rest with a uniform density
n=104cm−3 ⇒ cs=0.2km s−1
The Jeans length LJ= πc2
s
Gρ
1/2
≈ 0.22pc, where µmol=2.36
Lb=
√
10LJ ≈ 0.71pc per side with total mass
M ≈ 207M ≈ 31.6MJ. Grid resolution is 5123 cells.
Robert Loughnane CLOUDY 2016

13. Overview Background Radial Velocity Numerical Simulation Radiative Transfer Results Conclusions
Simulation Details II
Modeled Sub-box
For synthetic spectra generation:
Central half-length sub-box of grid with V=0.047pc3 = Lb
2
3
centered on highest density voxel.
⇒ Sub-box resolution is 2563 grid cells with spatial resolution of
1.387×10−3pc
x, LOS y
z
Robert Loughnane CLOUDY 2016

14. Overview Background Radial Velocity Numerical Simulation Radiative Transfer Results Conclusions
Simulation Details III
Analysed Timesteps
Robert Loughnane CLOUDY 2016

15. Overview Background Radial Velocity Numerical Simulation Radiative Transfer Results Conclusions
Overview
1 Overview
2 Background
Present Understanding of Cores I
Present Understanding of Cores II
Hierarchical Collapse I
Hierarchical Collapse II
Hierarchical Collapse III
3 Radial Velocity
Velocity Assumptions
4 Numerical Simulation
Simulation Details I
Simulation Details II
Simulation Details III
5 Radiative Transfer
Modeling Approximation
6 Results
Selected Results I
Selected Results II
Selected Results III
7 Conclusions
Robert Loughnane CLOUDY 2016

16. Overview Background Radial Velocity Numerical Simulation Radiative Transfer Results Conclusions
Modeling Approximation
Modeling Approximation
MOLLIE (Keto et al. 2004, 2010)
High-τ: HCO+
more opaque than CS
& H2CO - µHCO+ > µCS
χHCO+ =3×10−9
Low-τ: N2H+
JF1F=101→012 -
gaussian
χN2H+ =3×10−10
Beam convolution:
θb = 0.015, 0.03, 0.06pc
Robert Loughnane CLOUDY 2016

17. Overview Background Radial Velocity Numerical Simulation Radiative Transfer Results Conclusions
Overview
1 Overview
2 Background
Present Understanding of Cores I
Present Understanding of Cores II
Hierarchical Collapse I
Hierarchical Collapse II
Hierarchical Collapse III
3 Radial Velocity
Velocity Assumptions
4 Numerical Simulation
Simulation Details I
Simulation Details II
Simulation Details III
5 Radiative Transfer
Modeling Approximation
6 Results
Selected Results I
Selected Results II
Selected Results III
7 Conclusions
Robert Loughnane CLOUDY 2016

18. Overview Background Radial Velocity Numerical Simulation Radiative Transfer Results Conclusions
Selected Results I
Analytical Infall
Infall velocities derived using “Hill5hybrid”-model from De Vries
& Myers (2005). Fits σ, vlsr, τ0, TP & vin
Loughnane et al. (in prep)
Robert Loughnane CLOUDY 2016

19. Overview Background Radial Velocity Numerical Simulation Radiative Transfer Results Conclusions
Selected Results II
Mardones Parameter - δv
δv = Vthick−Vthin
∆vthin
δv-parameter (Mardones et al. 1997): Skewness of blue peak
De Vries & Myers (2005).
Loughnane et al. (in prep)
Robert Loughnane CLOUDY 2016

20. Overview Background Radial Velocity Numerical Simulation Radiative Transfer Results Conclusions
Selected Results III
Degree of Asymmetry: Tb/Tr-ratio
Another measure of the degree of infall δv-parameter
(Mardones et al. 1997): Skewness of blue peak
Stahler & Yen (2010): Current numerical models cannot
reproduce observed Tb/Tr-ratio
Loughnane et al. (in prep)
Robert Loughnane CLOUDY 2016

21. Overview Background Radial Velocity Numerical Simulation Radiative Transfer Results Conclusions
Overview
1 Overview
2 Background
Present Understanding of Cores I
Present Understanding of Cores II
Hierarchical Collapse I
Hierarchical Collapse II
Hierarchical Collapse III
3 Radial Velocity
Velocity Assumptions
4 Numerical Simulation
Simulation Details I
Simulation Details II
Simulation Details III
5 Radiative Transfer
Modeling Approximation
6 Results
Selected Results I
Selected Results II
Selected Results III
7 Conclusions
Robert Loughnane CLOUDY 2016

22. Overview Background Radial Velocity Numerical Simulation Radiative Transfer Results Conclusions
Concluding Remarks
Apparently subsonic velocities - artifact of assumed radial
velocity profile
Core collapses outside-in with maximum speed at envelope -
not in the center, as in inside-out picture of Shu.
Line profiles are density-weighted LOS velocity histograms -
Vmax at lower densities
Core displays well-publicized values of δv and can reproduce
observed Tb/Tr
Robert Loughnane CLOUDY 2016

23. Overview Background Radial Velocity Numerical Simulation Radiative Transfer Results Conclusions
Gracias por su atenci´on!
r.loughnane@crya.unam.mx
Robert Loughnane CLOUDY 2016