1

Enrique Vázquez-SemadeniInstituto de Radioastronomía y Astrofísica, UNAM

IRyA

2

Collaborators:

Pedro ColínU (IRyA)

Marina Kounkel (WWU)

Manuel Zamora-Avilés (INAOE-

LMT)

Postdoc:

Alejandro González-Samaniego

(IRyA)

3

• Outline:

– Global hierarchical collapse (GHC) context

• Acceleration of SF

• Filament formation

• Accretion at all scales

– The simulations

• Simplified prescriptions

– Effects of feedback:

• Triggering vs. quenching

• Cluster expansion

• Indirect feedback-cluster coupling via the gas

• Regulation of the SFR and SFE.

– Young cluster evolution (time permitting)

• Age histograms

• Delayed massive-star formation

• Age-mass correlation

4

I. The Global Hierarchical

Collapse (GHC) Scenario(VS+19, MNRAS, 490, 3061)

5

• Mounting evidence of multi-scale infall flows, in

particular via filaments, in MCs.

6

• The GHC scenario (VS+09, ApJ, 707, 1023; VS+19, MNRAS, 490, 3061):

– Solar-neighborhood-type clouds form by compression-triggered phase

transition WNM CNM (Hennebelle & Perault 99; Koyama & Inutsuka 02; Heitsch+05;

VS+06).

7

• Turbulence in the diffuse ISM forms clouds as much as it shakes

them (BP+99, ApJ, 515, 286):

An SPH simulation of

decaying solenoidal

turbulence with initial

Ms = 2 in the

thermally bistable

WNM with self-gravity(Heiner+15, MNRAS, 452,

1353).

8

• The GHC scenario (VS+09, ApJ, 707, 1023; VS+19, MNRAS, 490, 3061):

– Solar-neighborhood-type clouds form by compression-triggered phase

transition WNM CNM (Hennebelle & Perault 99; Koyama & Inutsuka 02; Heitsch+05;

VS+06).

• Self-consistent moderate turbulence inside cloud driven by various instabilities.

• r 100x r; T T/100

– Jeans mass (~ r-1/2 T3/2) drops precipitously (x104) by cooling/compression

and cloud begins to collapse (Gómez & VS 14).

• As cloud contracts, average Jeans mass decreases (Hoyle 53).

As time proceeds, turbulent fluctuations of ever lower mass go into collapse.

• Cloud gradually turns molecular (Hartmann+01; Heiner+15, MNRAS, 452, 1353).

• Large-scale collapse becomes filamentary because Pth becomes negligible.

Collapse (and cloud) become strongly anisotropic (Lin+65).

– Collapse is multi-scale: small-scale collapses within and falling into larger-

scale ones.

– All scales accrete from their parent scale.

• Filaments are the accretion flow from clouds to hubs (Gómez & VS 14).

• With durations ~ free-fall time of the parent structure. ( Pamela’s talk)

• Conveyor-belt (Longmore+14) type of flow.

• For simulations: crucial to couple to the larger scale. ( Hosokawa’s talk)

9

• Filament formation:

– Due to nearly pressureless collapse (Lin+65), not to strongly supersonic turbulence.

Gómez & VS

2014, ApJ,

791, 124.

Produces

“Conveyor-belt”-

like (Longmore+14)

filamentary flow

onto hubs.

Hubs grow in

mass and density.

Secondary, low-

mass SF in

filaments.

10

• SF accelerates in a contracting cloud (Zamora-Avilés+12, ApJ, 751, 77,

ZA & VS 14, ApJ, 793, 84; VS+18, MNRAS 479, 3254. See also Hartmann+12;

Burkert & Hartmann 13; Völschow+17; Burkhart18):

– Because mass fraction of dense gas increases in time due to

gravitational contraction and accretion.

– Massive stars appear late, when the accretion rate onto a hub and

the SFR are large (~ 103 Msun Myr-1).

• When massive stars appear (a few Myr after the first stars), they

disperse the cloud (Leisawitz+89).

SFR increases first by contraction, then decreases again due to

feedback.

11

II. The simulations

12

– LAF1: Simulation of molecular cloud formation, evolution and

cluster formation by converging flows (Robi’s talk) including self-

gravity, photoionizing feedback and a realistic IMF (imposed).

• ART+HD code (Kravtsov+97; Kravtsov03)

• Box size: 256 pc; maximum resolution: 0.06 pc.

• Parameterized cooling functions (Koyama & Inutsuka 2002).

• A “PMRT” (“poor man’s radiative transfer”) scheme:

– For each grid cell i compare its distance to star s, di,s to the Strömgren

radius Rsgiven by

where

– If di,s < RS, heat cell to 104 K.

Numerical simulation (Colín+2013, MNRAS, 435, 1701;

Vázquez-Semadeni+17, MNRAS, 467, 1313)

iSnnn LOS

13

– The stars have lifetimes

– Each star radiates according to its mass.

• A probabilistic SF scheme:

– When maximum refinement level has been reached, if ni > nth, have

probability p of forming a stellar particle.

– If no star forms, no further refinement accretion occurs onto cell.

– When star forms, acquires half of the cell’s mass. No accretion onto

stellar particle.

– Produces power-law, stellar-mass sink IMF, with p-dependent slope:

“Winds”

“UV radiation”

Salpeter for p = 0.003

Minimum stellar mass:

0.3 Msun

Can trust cluster

dynamics.

14

pc

x104 yr

“Cluster 2”

Self-consistent turbulence,

cloud evolution and

energy-injection locations.

15

16

Qualitative behavior consistent with full-RT FLASH 2.5

simulations (Zamora-Avilés+19, MNRAS, 487, 2200)

17

III. Effect of the

feedback on cluster

structure(González-Samaniego & VS 2020, to be subm.)

– Compare feedback run (LAF1) to a non-feedback one (LAF0).

1822.5 Myr 29.1 Myr27.5 Myr25 Myr

LAF1

LAF0

15

pc

15

pc

– Cluster is assembled hierarchically from the cloud’s hierarchical

collapse.

• Secondary subgroups appear in filaments.

– Gas dispersal dominated by the most massive star.

• Subgroup expansion and gas dispersal occurs at later times for more

distant clumps.

19

Plots of individual stars’ distances to cluster’s center of mass vs. time.

• Triggered or primordial neighboring SF?

– Most peripheral SF is primordial, from secondary collapses in

filaments.

– Only one instance of triggered SF.

20

– Gas mass increases by accretion faster than SFR.

• Keeps observed SFE low even before cloud dispersal.

• At tage = 7 Myr, SFELAF0 ~ 6.5% SFELAF1 ~ 4%

• But LAF0 keeps going, LAF1 shuts off, so final M*,LAF0 >> M*,LAF1

21

)()(

)()SFE(

*g

*

tMtM

tMt

22

• Evolution of virial parameter:

– Clouds have virial parameters a ~ 1 before SFR becomes large.

Then massive stars form and disrupt the clouds, with a >> 1:

Viria

lpara

mete

r a

Massive stars

form, unbind cloud.

Colín+13, MNRAS,

435, 1701

SFR

*max,gas

*SFEMM

M

Final SFE ~ 7%

Mcloud

Most (~90%) of

cloud’s mass

dispersed. The

“unbound” clouds?

23

– SFEff within every volume:

– Consistent with observations.

– Feedback-star coupling via the gas:

2422.5 Myr 29.1 Myr27.5 Myr25 Myr

LAF1

LAF0

15

pc

15

pc

25

– Prevents excessively large group infall speeds (Krumholz+19).

26

IV. Cluster Formation and

Structure(VS+17, MNRAS, 467, 1313)

27

28

– SFR increases by collapse, then decreases by feedback.

Stellar age histograms peak at a certain age.

Quantitatively

consistent with

observed embedded

cluster age

histograms (e.g.,

Palla & Stahler 2000;

daRio+10).

Vázquez-Semadeni+17, MNRAS, 467, 1313

1.5 Myr since

onset of SF.

3.5 Myr 5.7 Myr 6.7 Myr

29

Cluster 1 @ 11 Myr (synth)

Cluster 1 @ 11 Myr (raw))

Age histograms

Synthetic and observed age histograms for Cluster 1 (11

Myr after the formation of its first star) and Orion D from

Kounkel+18. (González-Samaniego+20, in prep.)

30

• Massive-star population builds up over time

– As clumps become denser and more massive by accretion...

Cu

mu

lative

ma

ss fra

ctio

n

Vázquez-Semadeni+17, MNRAS, 467, 1313

... and SFR is high,

> 103 Msun Myr-1

31

3. Mass-age correlations and radial gradients.

• Stars form in hub and filaments over large-scale collapse duration

(tff), not local.

• SF accelerates in hub as mass and density grow by accretion.

– Massive stars form later, when SFR is high (> 103 Msun Myr-1).

• Older stars are more scattered and less massive on average,

younger stars more concentrated and up to higher mass.

~

32

Age

Scarcity of young stars

at large distances.

Vázquez-Semadeni+17, MNRAS, 467, 1313

33

Age

A flyby.

Vázquez-Semadeni+17, MNRAS, 467, 1313

Mass gradient Mass-age relation

34

V. Conclusions

– GHC is synonymous with cloud and SFR evolution.

• Flow regime consists of multi-timescale collapses within collapses...

• ... and accretion at all scales from parent structures.

– Need to include accretion onto system at least from next larger scale.

• Accretion onto massive-SF cores via clumpy filaments. (CCCs?)

• Clumps grow in mass and density SF accelerates.

• Clumps definitely not spheroidal (important for simulation initial conditions).

– Effect of UV feedback on cluster:

• Dominated by most massive star.

• Some momentum imparted to stars via the gas they form from.

• Most peripheral star-forming clumps were pre-existing, not triggered.

• Hub’s gas mass increases by accretion faster than stellar mass.

– Keeps instantaneous apparent SFE low even without feedback for a while.

(Can’t model this without coupling to the next larger scale.)

– This structure/evolution is imprinted on forming clusters.

• Massive stars begin to form when clumps are massive and SFR is large.

• When sufficiently massive stars appear, clumps and filaments are quickly

destroyed SFR decreases again.

• Most stars have age of SFR peak. 35

• Provocative questions/food for thought:

– Having self-consistent conditions is at least as important as

extremely detailed modeling of the physical processes.

• Appropriate level of self-consistently-driven turbulence.

• Appropriate cloud geometry (flattened/filamentary rather than

spherical clumps?)

• Self-consistently-generated magnetic fields.

– How much can we learn from light simulations that capture the

essentials without extreme detail and power?

– When do we really need the full power?

• To generate the self-consistent environment? ( Aake’s question)

36

THE END

38

Fundamental fact for production of density

enhancements:

A density enhancement requires an accumulation of initially

distant material into a more compact region. A convergingflow.

(d/dt is the Lagrangian, or material, derivative)

Not optional!

udt

d r

r

39

• Filamentary flow akin to rivers funneling material from high to low

potential levels (Gómez & VS 14, ApJ, 791, 124):

40

• Flow smoothly changes

direction from perpendicular

to longitudinal (Gómez & VS

14, ApJ, 791, 124):

– No strong shocks form at

the filament’s axis.

– Strong shocks only form at

central hub if infall is

supersonic.

– Shocks in filament, if any,

are weak.

• Filaments in turn accrete

from parent cloud

– The large-scale collapse

flow.

41

Position-velocity diagram:

High velocity dispersion at

local collapse centers.

Column density

Red: n < 103 cm-3

Green: n > 103 cm-3

Gómez & VS 2014, ApJ, 791, 124

Longitudinal velocity:

Acceleration and shocks

at collapse centers.Hacar+17

Compare to

42

• In the presence of

subdominant magnetic

field (Gómez et al. 18, MNRAS, 480,

2939):

– Magnetic field lines draggedalong by the collapse.

• Not controlling the flow.

– Thus nearly perpendicular to

main filament...

– ... although with curvature

induced by flow along

filament.

43

Compare to Planck XXXV

44

Hierarchical collapse of cloud implies several properties of

cluster (Vázquez-Semadeni+17, MNRAS, 467, 1313):

1. Hierarchical-collapse structure of cloud imprinted on cluster

structure.

Groups identified by a

friends-of-friends

algorithm, varying the

linking parameter l.

l = 0.5

l = 1 l =2

45

4. Comparison with observations (González-Samaniego+19, in prep.):

– Kounkel+18 (AJ, 156, 84): spectroscopic and astrometric study of Orion.

– Discussed 5 star-forming regions: Orion A, B, C, D and l Ori.

– Process on simulation stars:

(age,mass) (color,magnitude) place in HR diagram synthetic (age,mass)

Orion D

46

Cluster 1

47

Simulation

HII region expansion test:

– Within 30% of analytic solution.

Colín +13