• Therefore, the rate of change in the metal content of the gas mass is
dM
h/dt = p dM
s/dt - Z dM
s/dt (1)
dM
h/dt = (p - Z) dM
s/dt
• Mass conservation implies: dM
g/dt + dM
s/dt = 0, (2)
• The metallicity of the gas changes by
dZ/dt = d(M
h/M
g)/dt ! dZ/dt = -p/M
gdM
g/dt
• If the yield p does not depend on Z, we integrate to obtain the metallicity at time t
Z(t) = Z(0) - p * ln[M
g(t)/M
g(0)]
The metallicity of the gas grows with time, as stars are formed and the
• We can also predict the metallicity distribution of the stars. The mass of the stars that have a metallicity less than Z(t) is
M
s[< Z(t)] = M
s(t) = M
g(0) - M
g(t) = M
g(0) * [1 - e
- (Z(t)- Z(0))/p]
• A closed box model seems to reproduce well the metallicity distribution of stars in the bulge of our Galaxy
Rich (1990), ApJ, 362, 604
1990ApJ. . .362. .604R
K GIANTS IN NUCLEAR BULGE OF GALAXY 615
No. 2, 1990
[Fe/H]
Fig. 7.—Abundance distribution function of bulge K giants derived in R88.
All stars have (J — K)0 > 0.45 with abundances derived using solution (1), and tabulated in Table 11 of R88. All subsequent work with the abundance dis- tribution draws on this sample.
Fig. 8.—Differential abundance distribution of bulge giants compared to two limiting cases of the simple model of chemical evolution. Solid line : simple
“closed box” model with complete gas consumption; <z> = 2.0z/zQ. Dashed line : Simple model, in the limiting case where a small fraction of the initial volume of gas is converted to stars, the remainder being lost from the system.
tion, which we now use to probe the history of chemical evolu- tion in the bulge. Figure 7 illustrates the abundance distribution function, which ranges from — 1 to +1 dex; note that 37 of the 88 stars have more than twice the solar abun- dance, and that <z> = 2.0 ± 0.3zo.
Even if we consider the bulge to comprise only the central component within 1 kpc, its mass of ~1010 M0 exceeds the mass of any Galactic globular cluster by more than four orders of magnitude. This massive stellar subsystem resides in the center of the Galaxy’s 1011 M0 potential. Therefore, in con- trast to the globular clusters, outer halo, and dwarf spher- oidals, the escape velocity from the bulge is probably large enough to arrest the outflow of gas heated by supernova explo- sions, which we shall see is the key reason the bulge abun- dances are relatively high.
If the bulge lost none of its gas and experienced no signifi- cant inflow of gas, acting, in effect, as a closed system, then the chemical evolution of the bulge would satisfy the principal requirements of the “closed box” simple model of chemical evolution (Searle and Sargent 1972). Searle and Zinn (1978) derive two limiting forms of the abundance distribution of long-lived stars resulting from complete exhaustion of gas according to the simple model. If only a small fraction of gas has been turned into stars, with the remainder lost from the system (as would happen if supernova-driven winds swept the gas from a low-mass system) then the mean metal abundance
<z> is much smaller than the yield y, and the distribution of metal abundances follows :
W = ^7X'’ 0<z< 2
<z> ¡ 2<z>
/(z) = 0 ; z > 2<z> . (6) If, as may be more appropriate for the nuclear bulge, all the initial gas has been turned into stars, then
(-<!>)' <7) In this case, the mean abundance <z> tends toward the yield, y.
In Figure 8, we fit the above extreme cases to the differential abundance distribution function derived using solution (1) (Fe and Mg lines) in R88. For both extremes of negligible and complete evolution of the gas into stars, <z> is the only free parameter. The data are much better represented by the simple model of chemical evolution in the case of complete gas con- sumption than in the case of significant gas loss. The striking feature of the bulge abundance distribution is the large numbers of stars at low abundance relative to the highest abundance observed.
Because differential distributions are affected by the choice of bins, we also fitted the cumulative abundance distribution with the integral forms of equations (6) and (7); the simple model with complete gas consumption now becomes
F(z) = 1 - exp . (8) Figure 9 illustrates that both the cumulative and differential distribution functions are fitted by the simple model with com- plete gas consumption and are in conflict with the limiting case of total gas loss after the first burst of star formation. Note that we do not specify why the gas is lost; this fit to the data rules out early loss of most of the gas due to dissipation into a disk just as strongly as it excludes loss of gas due to a supernova-
driven wind.
The observed abundance distribution in the bulge has important implications for various models of galaxy forma- tion, some of which we explore below.
The high abundance of the bulge population relative to the globular clusters is consistent with the concept of galaxy for- mation presented by Fall and Rees (1985), in which globular cluster formation is inhibited after the gas reaches an abun- dance of æ0.1zo. If this was indeed the case, the primordial bulge would have commenced with an initial abundance of z0 = 1/10 solar. Bond (1981) illustrates that in this case the functional form of the simple model remains the same but effectively undergoes a coordinate translation from z to z — z0. The observations do not rule out a low initial abundance, but
© American Astronomical Society • Provided by the NASA Astrophysics Data System
More considerations
• This model has its limitations and e.g. fails to reproduce the MDF of stars in the disk
• The equations can be modified to include gas accretion and outflows
• One can compute not just a single metallicity Z, but also take into account the production of different elements on different timescales
• Note that chemical enrichment/abundance depends on the SFR and
on the IMF (through the yields), as well as on age (time)
The location of the knee depends on the intensity of SF burst (or star formation rate/timescale)
α & Fe by SNII
Fe by SNII and SNI time arrow
Onset SNI
Stellar Abundances
in the Milky Way
Stellar Abundances
in the Milky Way
compilation by Venn et al. 2004
Stellar Abundances
in the Milky Way
compilation by Venn et al. 2004
Stellar Abundances
in the Milky Way
compilation by Venn et al. 2004
Stellar Abundances
in the Milky Way
Fulbright 2000, 2002, McWilliam 1995, 1998, Hanson 1998, Nissen & Schuster 1997, Prochaska 2000, Ivans et al. 2003, Stephens & Boesgaard 2002, Ryan et al. 1996, Johnson 2002, Burris et al. 2000, Gratton & Sneden 1988, 1991, 1994,
Bensby et al. 2003, Edvardsson et al. 1993, Reddy et al. 2003
compilation by Venn et al. 2004
Stellar Abundances
in the Milky Way
compilation by Venn et al. 2004
Stellar Abundances
in the Milky Way
compilation by Venn et al. 2004
“The Knee”
Stellar Abundances
in the Milky Way
compilation by Venn et al. 2004
“The Knee”
Stellar Abundances
in the Milky Way
compilation by Venn et al. 2004
“The Knee”
Stellar Abundances
in the Milky Way
compilation by Venn et al. 2004 Leceurer et al. 2007
“The Knee”
Stellar Abundances
in the Milky Way
compilation by Venn et al. 2004
“The Knee”
Stellar Abundances
in the Milky Way
compilation by Venn et al. 2004
“The Knee”
Stellar Abundances
in the Milky Way
compilation by Venn et al. 2004
“The Knee”
Stellar Abundances
in the Milky Way
Venn et al. 2004
The Milky Way
Alpha-Elements:
Comparison to a dwarf galaxy
“The Knee”
Venn et al. 2004
The Milky Way
SNII SNIa
McWilliam 1997
Alpha-Elements:
Comparison to a dwarf galaxy
“The Knee”
Venn et al. 2004
The Milky Way
SNII SNIa
McWilliam 1997
Alpha-Elements:
Comparison to a dwarf galaxy
“The Knee”
SNII SNIa
McWilliam 1997
Alpha-Elements:
Comparison to a dwarf galaxy
“The Knee”
Tolstoy et al. 2009; Starkenburg et al. 2013
Sculptor dSph
SNII SNIa