MARK KRUMHOLZ OPEN PROBLEMS IN STAR FORMATION
OUTLINE OUTLINE: THE BIG QUESTIONS ▸ Regulation of the star formation rate ▸ Global vs. local regulation ▸ Universal versus variable efficiency ▸ Bound clusters versus unbound associations ▸ What is special about stars that stay bound? ▸ What sets transition between bound and unbound stars? ▸ The origin of the IMF ▸ Where does it come from? ▸ Is it universal?
REGULATION OF THE SFR Figure 1. Theorist who has been asked to talk about JWST.
DEPLETION TIME ≈ 100 × FREE-FALL TIME Compilation: Krumholz (2014) TIGHT SFR-GAS CORRELATION AT ~500 PC SCALES Data: Leroy+ (2013), Bolatto+ (2010), Schruba+ (2010)
REGULATION OF THE SFR ORIGIN OF THE CORRELATION: THE TOP-DOWN VIEW ▸ One model: tight correlation comes from momentum balance between gravity and SN feedback (Ostriker+ 2010, 2011, Hopkins+ 2011, 2012; Faucher-Giguere+ 2013) ▸ If SN inject momentum per unit mass of stars formed <p/M * >, SFR obeys P mp ≈ 2 𝜌 G Σ gas ( Σ gas + Σ * ) ≈ <p/M * > Σ SFR ▸ Depletion time long and SF inefficient because each SN injects a lot of momentum ⇒ ε ff ≡ SFR / (M gas / t ff ) = t ff / t dep ≪ 1 ▸ Important point: SFR regulated in scales of order galactic scale height — on smaller scales, SF can be efficient, ε ff ≈ 1
All simulations MW_10_8_hr: ε =0.35% Low � int High � int MW_10_7_hr: ε =1.5% MW_10_9_hr: ε =6.0% 10 • yr -1 ] SFR [M O 1.0 0.1 10 − 4 10 − 3 10 − 2 10 − 1 10 0 10 1 0.0 0.2 0.4 0.6 � ff, 50 Hopkins+ 2011 Grudic+ 2018 NUMERICAL EXPERIMENTS Left: large-scale SFR independent of small-scale SF efficiency Right: huge variation in SF efficiency in ≲ 100 pc clouds
REGULATION OF THE SFR THE BOTTOM-UP VIEW ▸ Alternate model: galaxy- scale correlation is just counting the # GMCs / beam, with each GMC forming stars at ~same rate / unit mass (Krumholz+ 2005, 2012, 2018, Padoan+ 2011, 2012; Federrath+ 2012, 2015) ▸ ε ff ≈ 0.01 within clouds due to turbulence, B-fields, jets Federrath 2015
REGULATION OF THE SFR OBVIOUS TEST: IS THE CLOUD-SCALE SF EFFICIENCY UNIFORMLY LOW? σ ≈ 0.3 DEX Cloud-to-cloud variation in ε ff (Krumholz 2014) Intra-cloud variation in ε ff (Pokhrel+ in prep)
� - � S º p a º s ▸ Mean value and dispersion of ε ff depend on method and targets: a = + � 20 ) ▸ Nearby clouds, SFR from YSO � counting: ε ff ≈ 0.01, σ ≈ 0.3 dex ▸ Distant clouds, SFR from matching HII regions to clouds: ε ff ≈ 0.1, σ ≈ 1 dex YSO counting Cloud matching O+17 � O+17 log ✏ ff = − 1 . 7 +0 . 45 log ✏ ff = − 1 . 3 +0 . 61 − 0 . 33 S µ S t PDF [arbitrary units] − 0 . 44 � H+16 log ✏ ff = − 1 . 8 +0 . 40 LMDM16 − 0 . 44 log ✏ ff = − 1 . 7 +0 . 77 − 0 . 92 log ✏ ff = − 2 . 1 +0 . 37 EHV14 S − 0 . 33 � S µ S t � log ✏ ff = − 2 . 5 +0 . 46 VEH16 − 0 . 70 log ✏ ff = − 2 . 2 +0 . 30 L+13 � − 0 . 33 − 4 . 0 − 3 . 5 − 3 . 0 − 2 . 5 − 2 . 0 − 1 . 5 − 1 . 0 − 0 . 5 0 . 0 − 4 . 0 − 3 . 5 − 3 . 0 − 2 . 5 − 2 . 0 − 1 . 5 − 1 . 0 − 0 . 5 0 . 0 log ✏ ff log ✏ ff � OBSERVERS CAN’T AGREE! Top: Lee+ 2016 Bottom: Krumholz+ 2019, ARA&A S �
REGULATION OF THE SFR THIS IS WHERE JWST COMES IN ▸ Right now can only count ~1 M ⨀ YSOs within ~1 kpc of Earth; JWST will push this out to the Magellanic Clouds ▸ Two possible explanations for discrepancy: ▸ Nearby cloud sample missing efficient star-formers that account for most of SF budget of galaxy ▸ Assigning clouds to HII regions based on proximity doesn’t work well, and returns bogus SFRs sometimes ▸ JWST test: count YSOs in more distant sources, particularly those proposed to have very high ε ff
ORIGIN OF STAR CLUSTERS Figure 2. Epicycles: simpler and cleaner than most models of star cluster formation.
NGC 1313 M > 20 M ⨀ , t life < 5 Myr M = 8-20 M ⨀ , t life = 5-25 Myr M < 8 M ⨀ , t life > 25 Myr MOST STARS DISPERSE FROM BIRTH SITE BY ~20 MYR Pellerin+ 2007
ORIGIN OF STAR CLUSTERS CASE STUDY: ORION ▸ Most stars form in a diffuse, extended (~30 pc) dynamically-unrelaxed region ▸ Bound cluster formation sites (e.g. the ONC) are the densest parts of these regions, distinguished by: ▸ Extended age distribution (t 90 ≳ 5 t ff ) (da Rio+ 2014, Krumholz+ 2019) ▸ Little sub-structure (Hillenbrand+ 1998, da Rio+ 2017) ▸ Velocities close to virial equilibrium (Kim+ 2019) Data: Kounkel+ 2018 Figure: Krumholz+ 2019
ORIGIN OF STAR CLUSTERS FORMATION SCENARIOS ONC, Kounkel+ (2018) 1 . 0 t 90 ≈ 10 t ff ▸ “Conveyor belt”: mass accretes onto a 0 . 8 dp ∗ /d log t ∗ quasi-static star-forming clump for several 0 . 6 t ff (e.g., Longmore+ 2014, Lee + t ff = 0 . 6 Myr 0 . 4 Hennebelle 2016) 0 . 2 ▸ “Global hierarchical collapse”: large 0 . 0 structure collapses on its (longer) t ff , bound CB NGC 6530, Prisinzano+ (2019) stuff fell to current position (e.g., GHC 1 . 0 IE t 90 ≈ 6 t ff Kuznetsova+ 2018, Vazquez-Semadeni+ 0 . 8 2019) dp ∗ /d log t ∗ 0 . 6 ▸ “Increasing efficiency”: ε ff rises over time — t ff = 0 . 5 Myr 0 . 4 slow start allows long SF history, but then most stars form late (e.g., Murray & Chang 0 . 2 2015, Caldwell & Chang 2018) 0 . 0 − 1 . 0 − 0 . 5 0 . 0 0 . 5 1 . 0 log t ∗ [Myr]
ORIGIN OF STAR CLUSTERS FORMATION SCENARIOS: OTHER CONSTRAINTS ▸ IE: hard to reconcile model with variable ε ff with observed narrow distribution from YSO counting ▸ GHC: possible budget problem — ATLASGAL found ~10 7 M ⊙ in proto-ONC-like dense clumps with t ff ≈ 0.5 Myr; if these collapse in ~t ff , MW SFR should be ~20 M ⊙ yr − 1 ▸ CB: no obvious problems, but needs testing: in still- embedded clusters, younger stars (t ≲ t ff ) should be non- virialized, while older stars are virialized: can test with JWST proper motions
ORIGIN OF STAR CLUSTERS WHAT UNBINDS THE REMAINING STARS? ▸ To understand cluster formation, need to understand what clears the remaining gas, so that star formation stops before lower density regions have a chance to virialize ▸ Candidate mechanisms ▸ Photoionization ▸ Radiation pressure (direct or indirect) ▸ Massive star winds ▸ Supernovae
ORIGIN OF STAR CLUSTERS PHOTOIONIZATION ▸ Ionization heats gas to 10 4 K, producing pressure-driven wind ▸ Able to eject ~70% of the mass in clouds with v esc ≲ 10 km s − 1 Kim, Kim, & Ostriker 2018
ORIGIN OF STAR CLUSTERS DIRECT RADIATION PRESSURE ▸ Radiation force > gravitational force on any gas column with Σ < Σ crit = (L/M) / 4 𝛒 Gc ~ 300 M ⨀ pc − 2 (Fall+ 2010) ▸ In a turbulent medium with a PDF of Σ ’s, low Σ regions ejected even if mean Σ > Σ crit (Thompson & Krumholz 2016) ▸ Net effect is to eject ~50% of mass for Σ ≲ 10 Σ crit Wibking+ 2018
ORIGIN OF STAR CLUSTERS 30 Dor (Lopez+ 2011) Blue = x-ray, green = Ha, red = 8 μ m MASSIVE STAR WINDS Contours = CO ▸ Key issue with winds is leakage: how much hot gas escapes without exerting significant forces? ▸ Can measure directly by x-rays ▸ Compare to other pressures: P dir − 7 P IR photoionized gas (from radio free- P HII free), direct radiation (from log P (dyn cm − 2 ) − 8 P X bolometric luminosity), IR radiation (from dust SED) − 9 ▸ Winds not observed to be dominant − 10 1 2 10 10 R (pc) Figure 11. All pressures vs. radius from the center of R136. Regions with
ORIGIN OF STAR CLUSTERS SUPERNOVA FEEDBACK ▸ First SNe do not explode until ≳ 4 Myr after star formation ▸ Dynamical time is 4 Myr for densities n ≈ 100 cm − 3 ; at ε ff = 1%, 50% of gas used before first SN if n ≳ 3 x 10 5 cm − 3 ▸ Thus SNe probably only important for SF regulation in low- density regions — this may provide the boundary between clustered and non-clustered SF (Kruijssen 2012)
ORIGIN OF STAR CLUSTERS UNBINDING THE STARS: SUMMARY AND PROSPECTS ▸ Different feedback mechanisms suggest different thresholds separating bound and unbound stars: ▸ Photoionization : escape speed, v esc ≈ 10 km s − 1 ▸ Radiation pressure : surface density, Σ ≈ 3000 M ⊙ pc − 2 ▸ Winds : ??? ▸ Supernovae : density (free-fall time), n ≈ 10 5 cm − 3 ▸ At present not clear how to differentiate between these mechanisms; dependence of cluster demographics on environment may provide a clue (c.f. Adamo’s talk)
THE IMF Figure 3. Theorist who has been asked to explain the IMF.
ORIGIN OF THE IMF THE OBSERVED IMF ▸ In all resolved stellar populations, IMF is a power law at high mass with a turnover at lower mass ▸ Some evidence that the turnover may vary weakly with environment: ▸ Near Galactic center (Hosek+ 2019) ▸ In early-type galaxies (van Dokkum & Conroy+ 2010, Cappellari +2012) ▸ Other claims (IMHO) mostly unconvincing Data: Bastian+ 2010 Plot: Krumholz 2015
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