Metallicity

Stellar composition is often simply defined by the parameters X, Y and Z. Here X is the mass fraction of hydrogen, Y is the mass fraction of helium, and Z is the mass fraction of all the remaining chemical elements. Thus

${\displaystyle X+Y+Z=1}$

In most stars, nebulae, H II regions, and other astronomical sources, hydrogen and helium are the two dominant elements. The hydrogen mass fraction is generally expressed as ${\displaystyle X\equiv m_{\text{H}}/M}$, where ${\displaystyle M}$ is the total mass of the system, and ${\displaystyle m_{\text{H}}}$ is the mass of the hydrogen it contains. Similarly, the helium mass fraction is denoted as ${\displaystyle Y\equiv m_{\text{He}}/M}$. The remainder of the elements are collectively referred to as "metals", and the metallicity—the mass fraction of elements heavier than helium—can be calculated as

${\displaystyle Z=\sum _{i>{\text{He}}}{\frac {m_{i}}{M}}=1-X-Y.}$

For the surface of the Sun, these parameters are measured to have the following values:[5]

Description	Solar value
Hydrogen mass fraction	${\displaystyle X_{\text{sun}}=0.7381}$
Helium mass fraction	${\displaystyle Y_{\text{sun}}=0.2485}$
Metallicity	${\displaystyle Z_{\text{sun}}=0.0134}$

Due to the effects of stellar evolution, neither the initial composition nor the present day bulk composition of the Sun is the same as its present-day surface composition.

The overall stellar metallicity is conventionally defined using the total hydrogen content, since its abundance is considered to be relatively constant in the Universe, or the iron content of the star, which has an abundance that is generally linearly increasing in time in the Universe.[6] Hence, iron can be used as a chronological indicator of nucleosynthesis. Iron is relatively easy to measure with spectral observations in the star's spectrum given the large number of iron lines in the star's spectra (even though oxygen is the most abundant heavy element – see metallicities in HII regions below). The abundance ratio is the common logarithm of the ratio of a star's iron abundance compared to that of the Sun and is calculated thus:[7]

${\displaystyle [{\text{Fe}}/{\text{H}}]=\log _{10}{\left({\frac {N_{\text{Fe}}}{N_{\text{H}}}}\right)_{\text{star}}}-\log _{10}{\left({\frac {N_{\text{Fe}}}{N_{\text{H}}}}\right)_{\text{sun}}},}$

where ${\displaystyle N_{\text{Fe}}}$ and ${\displaystyle N_{\text{H}}}$ are the number of iron and hydrogen atoms per unit of volume respectively. The unit often used for metallicity is the dex, contraction of "decimal exponent". By this formulation, stars with a higher metallicity than the Sun have a positive common logarithm, whereas those more dominated by hydrogen have a corresponding negative value. For example, stars with a [Fe/H] value of +1 have 10 times the metallicity of the Sun (10¹); conversely, those with a [Fe/H] value of −1 have 1⁄10, while those with a [Fe/H] value of 0 have the same metallicity as the Sun, and so on.[8] Young Population I stars have significantly higher iron-to-hydrogen ratios than older Population II stars. Primordial Population III stars are estimated to have metallicity less than −6, a millionth of the abundance of iron in the Sun.[9][10] The same notation is used to express variations in abundances between other individual elements as compared to solar proportions. For example, the notation "[O/Fe]" represents the difference in the logarithm of the star's oxygen abundance versus its iron content compared to that of the Sun. In general, a given stellar nucleosynthetic process alters the proportions of only a few elements or isotopes, so a star or gas sample with certain [/Fe] values may well be indicative of an associated, studied nuclear process.

Astronomers can estimate metallicities through measured and calibrated systems that correlate photometric measurements and spectroscopic measurements (see also Spectrophotometry). For example, the Johnson UVB filters can be used to detect an ultraviolet (UV) excess in stars,[11] where a smaller UV excess indicates a larger presence of metals that absorb the UV radiation, thereby making the star appear "redder".[12][13][14] The UV excess, δ(U−B), is defined as the difference between a star's U and B band magnitudes, compared to the difference between U and B band magnitudes of metal-rich stars in the Hyades cluster.[15] Unfortunately, δ(U−B) is sensitive to both metallicity and temperature: if two stars are equally metal-rich, but one is cooler than the other, they will likely have different δ(U−B) values[15] (see also Blanketing effect[16][17]). To help mitigate this degeneracy, a star's B−V color can be used as an indicator for temperature. Furthermore, the UV excess and B−V color can be corrected to relate the δ(U−B) value to iron abundances.[18][19][20]

Other photometric systems that can be used to determine metallicities of certain astrophysical objects include the Strӧmgren system,[21][22] the Geneva system,[23][24] the Washington system,[25][26] and the DDO system.[27][28]

At a given mass and age, a metal-poor star will be slightly warmer. Population II stars' metallicities are roughly 1/1000 to 1/10 of the Sun's ([Z/H] = −3.0 to −1.0), but the group appears cooler than Population I overall, as heavy Population II stars have long since died. Above 40 solar masses, metallicity influences how a star will die: outside the pair-instability window, lower metallicity stars will collapse directly to a black hole, while higher metallicity stars undergo a Type Ib/c supernova and may leave a neutron star.

A star's metallicity measurement is one parameter that helps determine whether a star may have a giant planet, as there is a direct correlation between metallicity and the presence of a giant planet. Measurements have demonstrated the connection between a star's metallicity and gas giant planets, like Jupiter and Saturn. The more metals in a star and thus its planetary system and proplyd, the more likely the system may have gas giant planets. Current models show that the metallicity along with the correct planetary system temperature and distance from the star are key to planet and planetesimal formation. For two stars that have equal age and mass but different metallicity, the less metallic star is bluer. Among stars of the same color, less metallic stars emit more ultraviolet radiation. The Sun, with 8 planets and 5 known dwarf planets, is used as the reference, with a [Fe/H] of 0.00.[29][30][31][32][33]

Young, massive and hot stars (typically of spectral types O and B) in H II regions emit UV photons that ionize ground-state hydrogen atoms, knocking electrons and protons free; this process is known as photoionization. The free electrons can strike other atoms nearby, exciting bound metallic electrons into a metastable state, which eventually decay back into a ground state, emitting photons with energies that correspond to forbidden lines. Through these transitions, astronomers have developed several observational methods to estimate metal abundances in HII regions, where the stronger the forbidden lines in spectroscopic observations, the higher the metallicity.[34][35] These methods are dependent on one or more of the following: the variety of asymmetrical densities inside HII regions, the varied temperatures of the embedded stars, and/or the electron density within the ionized region.[36][37][38][39]

Theoretically, to determine the total abundance of a single element in an HII region, all transition lines should be observed and summed. However, this can be observationally difficult due to variation in line strength.[40][41] Some of the most common forbidden lines used to determine metal abundances in HII regions are from oxygen (e.g. [O II] λ = (3727, 7318, 7324) Å, and [O III] λ = (4363, 4959, 5007) Å), nitrogen (e.g. [NII] λ = (5755, 6548, 6584) Å), and sulfur (e.g. [SII] λ = (6717,6731) Å and [SIII] λ = (6312, 9069, 9531) Å) in the optical spectrum, and the [OIII] λ = (52, 88) μm and [NIII] λ = 57 μm lines in the infrared spectrum. Oxygen has some of the stronger, more abundant lines in HII regions, making it a main target for metallicity estimates within these objects. To calculate metal abundances in HII regions using oxygen flux measurements, astronomers often use the R₂₃ method, in which

${\displaystyle R_{23}={\frac {[{\text{O II}}]_{3727~\mathrm {\AA} }+[{\text{O III}}]_{4959~\mathrm {\AA} +5007~\mathrm {\AA} }}{{\text{H}}_{\beta }}},}$

where ${\displaystyle [{\text{O II}}]_{3727~\mathrm {\AA} }+[{\text{O III}}]_{4959~\mathrm {\AA} +5007~\mathrm {\AA} }}$ is the sum of the fluxes from oxygen emission lines measured at the rest frame λ = (3727, 4959 and 5007) Å wavelengths, divided by the flux from the H_β emission line at the rest frame λ = 4861 Å wavelength.[42] This ratio is well defined through models and observational studies,[43][44][45] but caution should be taken, as the ratio is often degenerate, providing both a low and high metallicity solution, which can be broken with additional line measurements.[46] Similarly, other strong forbidden line ratios can be used, e.g. for sulfur, where[47]

${\displaystyle S_{23}={\frac {[{\text{S II}}]_{6716~\mathrm {\AA} +6731~\mathrm {\AA} }+[{\text{S III}}]_{9069~\mathrm {\AA} +9532~\mathrm {\AA} }}{{\text{H}}_{\beta }}}.}$

Metal abundances within HII regions are typically less than 1%, with the percentage decreasing on average with distance from the Galactic Center.[40][48][49][50][51]