Stellar Yields of Rotating First Stars:

Y TP YUKAWA INSTITUTE FOR THEORETICAL PHYSICS NIC XIII@Debrecen 2014.07.10 Stellar Yields of Rotating First Stars: Yields of Weak Supernovae and Abundances of Carbon-enhanced Hyper Metal Poor Stars KT subm. arxiv: 1406.5305 Koh Takahashi 1, Hideyuki Umeda 1, Takashi Yoshida 2 1 Department of Astronomy, The University of Tokyo 2 Yukawa Institute for Theoretical Physics, Kyoto University

First Stars In the early universe, first stars provide high energy photons and synthesized materials, affecting the evolution of the universe.

Theoretical studies has revealed the part of the nature of the Pop III star formation. In an ab-initio cosmological simulation, gravitationally unstable primordial gas clouds of ~1000 M8 start to collapse to form a proto-stellar core of ~0.01 M8 in a small dark matter halo of 10 5-10 6 M8 at the red shift of ~20-30. Though large uncertainties exist in a later accretion phase, the initial mass range (e.g., Hirano et al. 2014) or the initial rotational property (Stacy et al. 2011) of the first stars are investigated. How can we observationally confirm characteristics of the first stars?

Fe I Ni I Fe I Fe I 3 a Fe I CD 38 245 [Fe/H] = 4.1 Relative flux 2 1 0 HE 0107 5240 [Fe/H] = 5.3 SMSS 0313 6708 [Fe/H]< 7.1 CH 385.5 386.0 386.5 387.0 1.05 b 1.00 0.95 385.8 385.9 386.0 386.1 386.2 3 c Fe I Fe I Ca II CD 38 245 Relative flux 2 1 HE 0107 5240 8 Interstellar Ca II

The Mixing-fallback Model

Aim: To find characteristic stellar yields. That is useful to constrain -the initial mass and -the rotation of first stars.

Stellar Evolution Calculation 24 massive first stars are calculated for a wide initial parameter range. - Z=0 - M ini = 12-140 M8 covering CCSNe progenitors - Moderate initial rotation (v ZAMS /v k ~ 0.15, ~200-300 km/s) log L/L 6.5 6 5.5 5 4.5 140 M 80 M 50 M 30 M 20 M - From d-burning to collapse 4 12 M non-rotating rotating 5.2 5 4.8 4.6 4.4 4.2 4 3.8 3.6 log T eff

Stellar Evolution Code Rotation affects stellar structure and evolution. Three effects are treated in 1(.5)-dimensional stellar evolution calculations. Rotation profiles are assumed to be shelluler (constant on isobars) (Zahn 92). (NOTE: Rotating stellar model has a lot of uncertainties.) 1) Deformation by centrifugal force (Meynet&Maeder97, Denissenkov&VandenBerg03) 2) Matter mixing by rotationally induced instabilities 3) Enhancement of mass-loss (Heger+00, Heger+05) (Langer98, Maeder&Meynet00, Yoon+12)

Stellar Evolution Code Calculate hydrostatic and hydrodynamic structure of a star. Basic Equations - mass conservation dr 1 = dm 4πr 2 p - hydro dynamical structure dp = - GM M d - 2 r dm 4πr 4 4πr 2 p dt 2 - energy conservation dl ds dn = -T - μ + εnuc - εν dm dt dt - energy transport dt GMT = - [ rad or conv] dm 4πr 4 p - composition evolution dxi dt dxi dxi dxi = [ ]nuc + [ ]mix, [ ]nuc = fi(x; T, ρ, Yn, Ye), dt dt dt [ dxi]mix = d dxi (D ) dt dm dm Evolution of a rotating 40 M8 first star.

Supernova Yields from Weak Supernovae Two assumptions are; log mass fraction 0-2 -4-6 -8 0-2 Fallback Eject H He C N O Ne Na Mg Al Si Ca non-rotating 1. Only gravitationally weakly bound outer distributed matter is ejected by the explosion. 2. Shock wave is too weak to modify the outer distributed matter by the explosive nucleosynthesis. -4-6 -8 rotating 0 5 10 15 20 25 30 35 40 mass coordinate [M ] M in = f in x M CO Then the explosive yields can be calculated by a simple integration, M i (M in )= Msurface M in of the ejection and X i (M)dM, is an abun

Supernova Yields from Weak Supernovae Thus our stellar yields have three parameters, 1. M ini : Initial mass 2. V rot : Stellar rotation 3. M in (or f in ) : Inner boundary of the ejection. Point: The weak supernova yields depend on the initial mass and stellar rotation of the progenitor, since the initial parameters affect the abundance distribution in helium layers and hydrogen envelopes. From now on, four yield characteristics and the dependence on the initial parameters are shown with the fixed M in.

Take M in = M CO, f in = 1 to show features of the outer abundance distributions. M i (M in )= Msurface M in X i (M)dM, of the ejection and is an abun 30M8 models 80M8 models log mass fraction 0-2 -4-6 -8 0 H He C N O Ne Na Mg Al Si Ca non-rotating log mass fraction 0-2 -4-6 -8 0 H He C N O Ne Na Mg Al Si Ca non-rotating -2-2 -4-4 -6-6 -8 rotating -8 rotating 0 5 10 15 20 25 30 mass coordinate [M ] 0 10 20 30 40 50 60 70 80 mass coordinate [M ]

2. Nitrogen During core helium burning phase, carbon and oxygen are transported from the core convective zone to the base of the hydrogen envelope. The CNO cycle initiates owing to the transport of the seed materials, producing nitrogen around the region.

2. Sodium and Aluminum Alpha capture reactions by nitrogen synthesizes 22 Ne. 14 N(α, γ) 18 F(β + νe) 18 O(α, γ) 22 Ne And alpha capture reaction by 22 Ne emits neutron. 22 Ne (α, n) 25 Mg Z Al 27 Free neutron is captured by 22 Ne and 26(25) Mg, producing 23 Na and 27 Al respectively. Mg Na Ne 20 24 23 22 Ne (n) 23 Ne(β - νe) 23 Na 26 Mg (n) 27 Mg(β - νe) 27 Al F O N 14 16 19 N

4. Calcium Non-rotating >80 M8 models produce calcium by the break-out reactions from the CNO cycle. The reactions take place at the base of the hydrogen envelope. log mass fraction 0-2 -4-6 -8 H He C N O Ne Na Mg Al Si Ca non-rotating 40 Ca 0 20 40 60 80 100 120 140 mass coordinate [M ]

Summary: 1. Weak SN yields have a small O/C ratio 2. Rotating models yield N, Na and Al. 3. Massive models yield Mg and Si. 4. Non-rotating massive models yield Ca.

Abundance Profiling [X/H] -2-3 -4-5 -6-7 SMSS 0313-6708 3D/nLTE correction m30-rot-0.95 m40-rot-0.95 m50-rot-1.00 m60-rot-1.00 m70-rot-1.00 m80-rot-1.00 SMSS 0313-6708 ([Fe/H] < -7) This star has C, Mg but no Na, Al. Rotating models overproduce Na and Al by the rotationally induced reactions. [X/H] -8-9 -2-3 -4-5 -6 C N O F Ne Na Mg Al Si P S Cl Ar K Ca 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 Z SMSS 0313-6708 3D/nLTE correction m30-nrot-0.94 m40-nrot-0.95 m100-nrot-1.00 m120-nrot-1.00 Massive models of >100M8 fail to explain the small [Mg/C]. Less massive models of <40M8 produce Na and Al besides Mg, since the Mg production is attributed to carbon burning. -7-8 -9 C N O F Ne Na Mg Al Si P S Cl Ar K Ca 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 Z

Abundance Profiling [X/H] -2-3 -4-5 -6-7 SMSS 0313-6708 3D/nLTE correction m50-nrot-0.97 m60-nrot-0.96 m70-nrot-0.97 m80-nrot-0.97 SMSS 0310-6708 ([Fe/H] < -7) Only non-rotating 50-80 M8 models can fit the abundance. The progenitor should be massive but do not rotate fast. The 60 M8 model consistently explains the abundance pattern from C to Si. -8-9 C N O F Ne Na Mg Al Si P S Cl Ar K Ca 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 Calcium in the star may be explained by the 80M8 model. Z

Abundance Profiling HE1327-2326 Abundance pattern from Na to Al can match with carbon burning products in 15-40 Msun stars. 5 4 HE 1327-2326 3D/nLTE correction m30-nrot-he-0.96 m40-nrot-he-0.96 5 4 HE 1327-2326 3D/nLTE correction m15-rot-he-0.92 m20-rot-he-0.93 m30-rot-he-0.96 3 3 [X/Fe] 2 [X/Fe] 2 1 1 0 0-1 C N O F Ne Na Mg Al Si P S Cl Ar K Ca 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20-1 C N O F Ne Na Mg Al Si P S Cl Ar K Ca 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 Z Z

Abundance Profiling HE0107-5240 enhancement of Na can be explained by efficient internal mixing in the progenitor. [X/Fe] 4 3 2 1 HE 0107-5240 3D/nLTE correction m30-rot-1.07 m30-hrot-1.02 m40-qrot-1.02 m40-hrot-1.00 0-1 C N O F Ne Na Mg Al Si P S Cl Ar K Ca 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 Z

Results of the abundance profiling SMSS 0310-6708 mass range: 50-80 Msun rotation : only non-rotating models : 0.96+-0.04 (for 60 Msun) fin HE 1327-2326 mass range: 15-40 Msun rotation : both rotating and non-rotating models : 0.96+-0.01 (for non-rot 20 Msun) fin HE 0107-5240 mass range: 30-40 Msun rotation : only rotating models : 1.07+-0.06 (for 30 Msun) fin

Conclusion: We find characteristic stellar yields. Examples are Mg, Si enhancement by massive progenitors and Na, Al enhancement by rotating progenitors. We constrain the progenitor initial parameters for the three most iron-deficient stars. The presented analysis will be applicable to other carbonenhanced hyper metal poor stars observed in the future, and will give valuable information about the characteristics of the first stars. KT subm. arxiv: 1406.5305 See also the poster by Chiaki (#20). Object [Fe/H] M ini f in rotation SMSS 0313-6708 < -7.1 50-80 0.96 ± 0.04 (60 M ) non-rotating HE 1327-2326 -5.7 20-40 0.96 ± 0.01 (40 M ) non-rotating 15-30 0.93 ± 0.01 (20 M ) rotating HE 0107-5240 -5.3 30-40 1.07 ± 0.06 (30 M ) rotating

Comparison with other works Model in Keller et al. (2014) log(element number fraction relative to the solar value) 2 4 6 8 C O N Na Al Mg Si Ca Ti Sc Cr Fe Ni Zn Sr Mn Co Cu 10 20 30 40 Atomic number Model in Ishigaki et al. (2014) V SMSS 0310-6708 mass range: 50-80 Msun rotation : only non-rotating models Min : 0.96+-0.04 (for 60 Msun) v.s. [X/H] -2-3 -4-5 -6 SMSS 0313-6708 3D/nLTE correction m50-nrot-0.97 m60-nrot-0.96 m70-nrot-0.97 m80-nrot-0.97-7 -8-9 C N O F Ne Na Mg Al Si P S Cl Ar K Ca 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 Z

Model in Keller et al. (2014) log(element number fraction relative to the solar value) 2 4 6 8 C O N Na Al Mg Si Ca Ti Sc V Cr Fe Ni Zn Sr Mn Co Cu The progenitor is a non-rotating 60 M8 star with an explosion of 1.8x10 51 erg. They attribute the calcium production to the CNO break-out during the stable hydrogen burning phase. 10 20 30 40 Atomic number Model in Ishigaki et al. (2014) Accrete(f=10-5.8 ) Eject Among the models, a non-rotating 25 M8 star with an explosion of 1.0x10 52 erg reproduces observed abundances [(Na, Mg, Al)/C]. They attribute magnesium production to explosive nucleosynthesis at the base of the helium layer.

Explosion energy will be important for second generation star formation. Ritter et al. (2012) calculates a Pop III supernova of 1. x 10 51 erg, showing that the only half of the supernova ejecta is trapped into the host halo. Using the results of Ritter et al, carbon abundance of the polluted host gas may be deduced as X(C) = (1 f esc) (f C 10 1 ) f pol 2 10 5 ), ( )( ( 0.2 )( 1 = 1.25 10 6 fesc f C f pol 0.5 3 28 + log[ (0 2 )(1 and this is equivalent to ) 0 5] (Ritter+12) o [C/H] = 3.28 + log[f C (0.2/f pol )(1 f esc )/0.5]. To account for the observed abundance of [C/H]~-2.6 for SMSS 0313, the weak supernova model may be more plausible than a highly energetic model.

HE 0107-5240 mass range: 30-40 Msun rotation : only rotating models f in : 1.07+-0.06 (for 30 Msun) Model in Limongi et al. (2003) The abundance pattern is explained by a superposition of two supernovae, a typical 15 M8 explosion (M Fe = 0.056M8 ) and a less energetic 35 M8 explosion (Min = 9.6M8 ). Sodium production is attributed to proton ingestion in the 35 M8 model. [X/Fe] 4 3 2 1 0-1 HE 0107-5240 3D/nLTE correction m30-rot-1.07 m30-hrot-1.02 m40-qrot-1.02 m40-hrot-1.00 C N O F Ne Na Mg Al Si P S Cl Ar K Ca 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 Z Model in Iwamoto et al. (2005) Mixed(f=1.2x10-4 ) Eject The progenitor is a 25 M8 star with mass cut of 6.2 M8. They attribute the sodium production to ejection of the inner material in the carbon burning region.