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|"Energetic constraints to chemo-photometric evolution
of spiral galaxies",|
2011, MNRAS, 415, 1155
The problem of chemo-photometric evolution of late-type galaxies is dealt with relying on prime physical arguments of energetic self-consistency between chemical enhancement of galaxy mass, through nuclear processing inside stars, and luminosity evolution of the system. Our analysis makes use of the Buzzoni (2002, 2005) template galaxy models along the Hubble morphological sequence. The contribution of TypeII and Ia SNe is also accounted for in our scenario. Chemical enhancement is assessed in terms of the so-called "yield metallicity" (Z), that is the metal abundance of processed mass inside stars, as constrained by the galaxy photometric history. For a Salpeter IMF, Z ∝ t0.23 being nearly insensitive to the galaxy star formation history. The ISM metallicity can be set in terms of Z, and just modulated by the gas fraction and the net fraction of returned stellar mass (f). For the latter, a safe upper limit can be placed, such as f ≤ 0.3 at any age. The comparison with the observed age-metallicity relation allows us to to set a firm upper limit to the Galaxy birthrate, such as b ≤ 0.5, and to the chemical enrichment ratio ΔY/ΔZ ≤ 5. About four out of five stars in the solar vicinity are found to match the expected Z figure within a factor of two, a feature that leads us to conclude that star formation in the Galaxy must have proceeded, all the time, in a highly contaminated environment where returned stellar mass is in fact the prevailing component to gas density. The possible implication of the Milky Way scenario for the more general picture of late-type galaxy evolution is dicussed moving from three relevant relationships, as suggested by the observations. Namely, i) the down-sizing mechanism appears to govern star formation in the local Universe; ii) the "delayed" star formation among low-mass galaxies, as implied by the inverse b-Mgal dependence, naturally leads to a more copious gas fraction when moving from giant to dwarf galaxies; iii) although lower-mass galaxies tend more likely to take the look of later-type spirals, it is mass, not morphology, that drives galaxy chemical properties. Facing the relatively flat trend of Z vs. galaxy type, the increasingly poorer gas metallicity, as traced by the [O/H] abundance of HII regions along the Sa → Im Hubble sequence, seems to be mainly the result of the softening process, that dilute enriched stellar mass within a larger fraction of residual gas. The problem of the residual lifetime for spiral galaxies as active star-forming systems has been investigated. If returned mass is left as the main (or unique) gas supplier to the ISM, as implied by the Roberts timescale, then star formation might continue only at a maximum birthrate bmax << f/(1-f) ≤ 0.45, for a Salpeter IMF. As a result, only massive (Mgal ≥ 1011 Msun) Sa/Sb spirals may have some chance to survive ~30% or more beyond a Hubble time. Things may be worse, on the contrary, for dwarf systems, that seem currently on the verge of ceasing their star formation activity unless to drastically reduce their apparent birthrate below the bmax threshold.
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|Figure 1 - |
The expected fraction of enriched stellar mass provided by the SNII events according to three different IMF power-law indices (Salpeter case is for s = 2.35), and for a different value of the SN triggering mass, Mup. The consensus case is marked by the big dot on the Salpeter curve. Vertical error bars derive from eq. (14).
|Figure 2 - |
The chemical enrichment from SN contribution according to the different components. Note the prevailing role of core-collapsed objects (i.e. SNII) along the early stages of galaxy evolution (t ≤ 50 Myr, see labels to the right axis). The total SNIa component adds then a further 0.2 dex to galaxy metallicity, mostly within the first Gyr of life.
|Figure 3 - |
Yield chemical abundance for the CSP set of Table 3. Theoretical output is from eq. (24), assuming a range for the enrichment ratio R = ΔY/ΔZ = 3 ±1, according to the label in each panel. Note the nearly insensitive response of both Y and Z to the SFR details.
|Figure 4 - |
The solar-neighbourhood AMR, according to different observing surveys, as labelled in the plot. In particular, the works of Twarog (1980) (dots), Carlberg et al. (1985) (triangles), Meusinger, Stecklum & Reimann (1991) (squares), Edvardsson et al. (1993) (diamonds), and Rocha-Pinto et al. (2000) (pentagons) have been considered. Observations are compared with model predictions from several theoretical codes (the shelf of thin curves; see Fig. 5 for a detailed source list). The expected evolution of yield metallicity, according to eq. (27), is also displayed, assuming [Fe/H] = log(Z/Zsun), and a birthrate b = 0.5±0.5, as labelled on the curve. A current age of 13 Gyr is adopted for the Milky Way. See text for a full discussion.
|Figure 5 - |
Representative parameters for the observed (dots) and predicted (squares) AMR for the solar neighborhood. The theoretical works by Matteucci & Fracois (1989) (labelled as "MF" on the plot), Wyse & Silk (1989) (WS1 and WS2, respectively for a Schmidt law with n = 1 and 2), Carigi (1994} (C), Pardi & Ferrini (1994) (PF), Prantzos & Aubert (1995) (PA), Timmes, Woosley & Weaver (1995) (TWW), Giovagnoli & Tosi (1995) (GT), Pilyugin & Edmunds (1996) (PE), Mihara & Takahara (1996) (MT), Chiappini, Matteucci & Gratton (1997) (CMG), Portinari, Chiosi & Bressan (1998} (PCB), Boissier & Prantzos (1999) (BP), and Alibes, Labay & Canal (2001) (ALC) have been acounted for, including the expected output from the Z law of eq. (27) (square marker labelled as "B"). The Milky Way is assumed to be 13 Gyr old for every model. The theoretical data set is also compared with the observations, according to the surveys of Twarog (1980) (dot number "1"), Carlberg et al. (1985) ("2"), Meusinger et al. (1991) ("3"), Edvardsson et al. (1993) ("4"), Rocha-Pinto et al. (2000) ("5"), and Holmberg et al. (2007) ("6"). An AMR in the form [Fe/H] = ζ log t9 + ω, is assumed, throughout. The displayed quantities are therefore the slope coefficient ζ, vs. the expected metallicity at t = 10 Gyr, namely [Fe/H]10 = ζ+ω. Note that models tend, on average, to predict a sharper chemical evolution with respect to the observations. This leads, in most cases, to a steeper slope ζ and a slightly higher value for [Fe/H]10. See the text for a discussion of the implied evolutionary scenario.
|Figure 6 - |
The expected fraction FSSP = Mret/Mtot of stellar mass returned to the ISM for a set of SSPs, with changing the IMF power-law index (s), as labelled to the right. The evolution is traced both vs. SSP age and the main-sequence Turn Off stellar mass (mTO), the latter via eq. (3) of Buzzoni (2002). The relevant case for a Salpeter IMF (s = 2.35) and two indicative variants for giant- (s = 1.35) and dwarf-dominated (s = 3.35) SSPs are singled out in both panels, while the thin dotted curves account for the intermediate cases, by steps of Δs = 0.05 in the IMF index.
|Figure 7 - |
The output of eq. (29) is displayed vs. the mass fraction of fresh primordial gas (G). The two shelves of curves assume the fraction f of returned stellar mass as a free parameter. The lower shelf (dashed curves) is for f = 0.01 → 0.09 by steps of Δf = 0.02, while the upper shelf of curves (solid lines) cover the f range from 0.1 to 0.3, by steps of Δf = 0.1. The shaded area within −0.3 ≤ log (Zgas/Z≤ 0 single out the allowed f-G combinations that may account for the observed metallicity spread of stars in the solar neighborhood.
|Figure 8 - |
The observed metallicity distribution of stars in the solar neighbourhood. The displayed quantity is Δ[Fe/H] = [Fe/H]* − [Fe/H]yield ≡ log (Zgas/Z). Different stellar samples have been considered from the work of Edvardsson et al. (1993), Rocha-Pinto et al. (2000), and Holmberg et al. (2007), from top to bottom, as labelled in each panel. The lower panel displays the same trend for a sample of open stellar clusters, after Carraro et al. (1998). The different Galacticentric distance for these systems is indicatively marked by the dot size (i.e. the smallest the dot, the largest the distance from the Galaxy center). For each distribution, the relative fraction of stars within a −0.3 and −0.5 dex Δ[Fe/H] residual is reported in each panel. A cumulative histogram of the data is also displayed, along the right axis, in arbitrary linear units.
|Figure 9 - |
The [Fe/H] distribution of G-dwarf stellar samples in the solar neighborhood (shaded histograms), according to Rocha-Pinto et al. (2000) (upper panel), and Nordstrom (2004) (lower panel), is compared with the expected yield-metallicity distribution accounting for the different star-formation histories as for the disk stellar population of Buzzoni (2005) template galaxies along the Hubble sequence (solid curves, as labelled on the plot). A roughly constant stellar distribution in the Z domain leads to an implied birthrate of the order of b~0.6, as pertinent to Sbc galaxies (see Table 2 for a reference).
|Figure 10 - |
The [O/Fe] distribution of stars in the Milky Way is displayed acording to the Jonsell et al. (2005) (diamonds) and Edvardsson et al. (1993) (dots) data samples, respectively for the halo and disk stellar populations. Our model output, according to eq. (46) is superposed (solid lines), for a representative birthrate b = 0.4, and for a range of SNIa delay time Δ from ~50 Myr to ~1 Gyr, as discussed in Sec. 2.2.
|Figure 11 - |
The gas metallicity of 15 Gyr disk stellar populations according to the Arimoto & Jablonka (1991) (AJ91) models (solid line with diamonds) is displayed together with the expected predictions from eq. (31) (shaded area) for a range of returned mass fraction f between 0.07 and 0.3, as labelled on the plot. For tighter self-consistency in our comparison, the adopted gas fraction Gtot for our model sequence matches the corresponding figures of AJ91 models, while yield metallicity derives from eq. (27) for the relevant birthrate values of the Buzzoni (2005) template models along the Sa → Im morphological sequence (solid line with dots).
|Figure 12 - |
[Fe/H] metallicity for the two galaxy samples of Perez et al. (2009) (triangles) and Zaritsky et al. (1994) (squares), compared with the yield and gas metallicity figures (solid line with dots and shaded area) as from Fig. 11. While the Perez et al. (2009) estimates derive from Lick indices tracing the galaxy stellar population, in case of Zaritsky et al. (1994) the [Fe/H] derives from the Oxygen abundance of galaxy HII regions, by adopting log (O/H)sun = 8.83 for the Sun (Grevesse & Sauval 1998). Two cases are envisaged, in this regard, assuming that Oxygen straightly traces Iron (and the full metallicity), as in lower panel or, more realistically, that a scale conversion does exist such as [O/H] = 0.6 [Fe/H], as suggested by the observation of disk stars in the Milky Way (Clegg et al. 1981, Bessell et al. 1991, Edvardsson et al. 1993). A little random scatter has been added to the morphological T class of the points in each panel for better reading.
|Figure 13 - |
The inferred star-formation properties of the spiral-galaxy sample by Marino et al. (2010), referring to three Local-Group Analogs from the LGG catalog Garcia (1993), as marked and labelled on the plot. Marker size indicates galaxy morphology along the RC3 T-class sequence (the biggest markers are for Sd/Im galaxies with T~10, while the smallest are for Sa systems with T~1). Current SFR derives from GALEX NUV fluxes, dereddened as discussed in the text, and calibrated according to Buzzoni (2002). On the contrary, Galaxy stellar mass is computed from the relevant M/LB ratio, as from the Buzzoni (2005) template galaxy models. The birthrate assumes for all galaxies a current age of 13 Gyr. The small ellipses in each panel report the typical uncertainty figures, as discussed in the text. All the relevant data for this sample are summarized in Table 5. Note the inverse relationship between b and M*gal, as in the down-sizing scenario for galaxy formation.
|Figure 14 - |
The observed relationship between morphological RC3 class T and galaxy stellar mass according to four different galaxy samples from the work of Garnett (2002) (dots), Marino et al. (2010) (diamonds), Kuzio de Naray et al. (2004) (triangles) and Saviane et al. (2008) (pentagons) (see Table 5 and 6 for details). The value of M*gal derives from B photometry for the Garnett (2002), Kuzio de Naray et al. (2004) and Marino et al. (2010) galaxies, and from H absolute magnitudes for the Saviane et al. (2008) sample, throught the appropriate M/L ratio, according to Buzzoni (2005). Equation (49) provides a fair representation of the data, as displayed by the dashed curve. As already pointed out also by Roberts & Haynes (1994) one has to remark, however, the notable dispersion in mass among Sbc galaxies.
|Figure 15 - |
Mass fraction of gas and Oxygen abundance of HII regions for the Garnett (2002) (dots) and Kuzio de Naray et al. (2004) (triangles) galaxy samples of Table 6. Marker size is propotional to the galaxy morphological class T (the biggest markers are for Sd/Im galaxies with T~10, while the smallest are for Sa systems with T~1). Gas fraction accounts for both atomic and molecular phase. Note the inverse relationships of the data versus galaxy stellar mass, the latter as derived from the relevant M/L ratio (see, again, Table 6 for details).
|Figure 16 - |
Upper panel: Oxygen abundance from HII regions for the galaxy samples of Garnett (2002) (dots), Kuzio de Naray et al. (2004) (triangles) and Saviane et al. (2008) (diamonds). A nice correlation is in place with galaxy stellar mass, where low-mass systems appear richer in gas (see Fig. 15) and poorer in metals. Once accounting for the different gas fraction among the galaxies, and rescale Oxygen abundance to the same gas fraction (Gtot = 0.2, as in the indicative example displayed in the lower panel), note that most of the [O/H] vs. M*gal trend is recovered, leaving a nearly flat [O/H] distribution along the entire galaxy mass range, as predicted by the nearly constant yield-metallicity of the systems.
|Figure 17 - |
The lifetime of spiral galaxies as active star-forming systems, better recognized as the Roberts & Haynes (1963) time, is computed along the full mass range of the systems. The definite consumption of the primordial gas reservoir, as in the original definition of the timescale, tR, derives from eq. (54), by parameterizing with the current fraction of returned stellar mass, f. Present-day galaxies are assumed to be one Hubble time old (tH ~13 Gyr, see the left scale on the vertical axis). If returned stellar mass is also included in the fuel budget, to further extend star formation, the the "extended" Roberts time, tRe derives from eq. (55). In both equations, the distinctive birthrate relies on the observed down-sizing relationship of eq. (47), while the gas fraction available to present-day galaxies is assumed to obey eq. (50), eventually extrapolated for very-low mass systems (i.e. M*gal ≤ 109Msun) (dashed curves in the plot). Note, for the latter, that they seem on the verge of definitely ceasing their star formation activity, while only high-mass galaxies (M*gal ≥ 1011Msun) may still have chance to extend their active life for a supplementary 30-40% lapse of tH. See text for a full discussion.
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