Table 1.
Input parameters and computation results of our best-fit chemical evolution models assuming the different IGIMF formulations introduced in Sect. 3.1 (lines 3 to 6) compared with the observational values (first line) and Lacchin et al. (2020) (second line).
| Label | DTD | ω | τg (Gyr) | Mini (106 M⊙) | twind (Gyr) | NSNIa, gal | [α/Fe] | M*, final (104 M⊙) | [Fe/H]mean |
|---|---|---|---|---|---|---|---|---|---|
| Observation (a) | – | – |
 |
– | – | (2 ± 0.7) | – | 3.4 ± 0.3 | −2.35 ± 0.08 |
| Lacchin19 (b) | PL | – (c) | 10 | 10 | 0.19 | – | N (d) | 17 | −2.5 |
| IGIMF-R14 | PL | 100 | 5.9 | 4.02 | 0.05 | 3.04 | Y (d) | 3.15 | −2.18 |
| IGIMF-R14-SD | SD | 100 | 6.7 | 4.33 | 0.06 | 3.65 | Y (d) | 3.56 | −2.50 |
| IGIMF(A2) | PL | 100 | 2.2 | 2.31 | 0.05 | 1.96 | Y (d) | 3.66 | −2.70 |
| IGIMF(A3) | PL | 100 | 5.0 | 5.63 | 0.06 | 4.87 | Y (d) | 2.61 | −1.93 |
| IGIMF(A4) | PL | 100 | 2.86 | 3.25 | 0.05 | 3.30 | Y (d) | 3.40 | −2.36 |
Notes. Columns: (1) gwIMF assumption, (2) assumed DTD model, where PL stands for the power-law DTD given by Maoz & Mannucci (2012) and SD stands for the single-degenerate DTD given by Matteucci & Recchi (2001), (3) wind efficiency, (4) gas-depletion timescale, and the observational value from an ensemble of dwarf galaxies (Pflamm-Altenburg & Kroupa 2009) in parentheses, (5) initial gas mass, (6) starting time of the galactic wind, (7) number of SNIa that exploded per 1000 M⊙ of stars formed when the age of the galaxy is 10 Gyr and the observational estimate for a single-age stellar population from an ensemble of stellar systems (Maoz & Mannucci 2012) in parentheses, (8) whether the model-predicted metal enrichment history fits the observed [α/Fe]–[Fe/H] relation reasonably well, (9) total mass of living stars at 14 Gyr and observational value for Boötes I (Martin et al. 2008), and (10) stellar-mass-weighted [Fe/H] for the living stars at 14 Gyr and observational (number-averaged) value for Boötes I (Lacchin et al. 2020). Other parameters are stated in the text. The columns are divided by the vertical lines into five regions. From left to right, the regions indicate the fixed assumptions or parameters of the model, variable parameters to obtain a better fit, results (by-products) of the model that cannot be well constrained by observation, target parameters that we tried to fit, and the additional observable that provides a test to a model.
The parentheses indicate that the quantity inside is estimated for an ensemble of stellar systems.
Here we list only the 3BooI model of Lacchin et al. (2020) that assumes the IGIMF theory. Lacchin et al. (2020) listed a grid of model results instead of a best-fit model. Their different models fit different observations well, but not all observations simultaneously.
The ω stated in Lacchin et al. (2020) should not be applied (see Sect. 7.2 below).
“N” stands for “does not fit”, and “Y” stands for “acceptable fit”. The resulting [α/Fe]–[Fe/H] relation of the 3BooI model assuming IGIMF-R14 in Lacchin et al. (2020) is shown by the dashed line in Fig. 7. The results from our model IGIMF-R14 and IGIMF-R14-SD are shown in Figs. 7 and A.7, respectively. The results from model IGIMF(Ai) are not shown but fit the data as well as model IGIMF-R14.
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