CHEMICAL ABUNDANCE EFFECTS ON SPECTRAL ENERGY DISTRIBUTIONS
CHEMICAL NOMENCLATUREDefinition of "metallicity":
As mentioned above, we lump together all elements other than
hydrogen and helium under the moniker "metals".
An assumption (not always a good one) is that when
we change the abundance of one metal species (e.g., iron)
the relative abundance of other metals (e.g., carbon, nitrogen,
calcium) change in the same proportion.
Astronomers commonly use iron as tracer of the total metal
content under the assumption that all metals change abundance in proportion
to how Fe changes in abundance (not always true!!)
In this scheme, we describe the "metallicity" of a star
with the symbol [Fe/H], which describes how many iron atoms there
are to every hydrogen atom.
The square braces mean this is a logarithmic scale and also that
this is a comparison to the ratio of iron to hydrogen in the Sun:
The adoption of iron as the metal abundance indicator, despite the fact that iron is
not one of the most abundant elements in the universe, comes from the fact that
there are many iron lines visible in the spectra of many stars and generally they
are easier to measure.
But note, in common parlance [Fe/H] can mean either:
The actual measure of iron atoms to hydrogen.
A proxy for the general metal abundance of a star, with "Fe" meaning
"any metal" in the assumption of lockstep enrichment of all elements in
Perhaps even more confusing, in many cases people
will spectroscopically measure some other heavy
element, like Mg or Ca, which has stronger, easier to measure lines for some stars,
and then quote them as [Fe/H] under the implicit assumption of solar relative
Often, to be more clear about this, some authors will write "[m/H]", meaning
abundances in general.
We can write other ratios, like:
Note that taking ratios compared to H or Fe is the most common thing.
[X/Fe] variations typically cover a much smaller range than [Fe/H] itself --
that is, if a star is poor in iron, it is generally poor in other metals as well.
It is typically easier to get abundances relative to Fe more accurate than to H, and so
working in [ /Fe] format can be more reliable.
In some cases, when we are talking about the abundance of certain
elements that have a similar origin, this is summarized with corresponding
nomenclature to the process.
For example, elements formed by the progressive addition of helium nuclei
(e.g., 12C, 16O, 20Ne, 24Mg,
28Si, 32S, 40Ar, 40Ca and possibly
48Ti and 52Cr)
-- the alpha nuclides -- are sometimes summarized in proxy form as "[α / Fe]".
These elements are made in the course of normal nuclear fusion in low mass stars
(up to C and O) and high mass stars (up to even Ti and Cr in high mass stars,
in the "onion layer model" of nucleosynthesis).
Again, it may be that only one or several of these elements would actually be measured, and
the [α / Fe] is written under the assumption of lockstep enrichment of these
(In some cases, "[O / Fe]" is adopted as an alternative shorthand to [α / Fe], even
if some other α is actually measured.)
Other "processes" include neutron capture onto seed nuclei (like iron), and
include "r" and "s" atomic species, formed by dramatic events, like supernovae or
neutron star mergers (rapid
neutron capture or "r-process"), or in evolved (likely asymptotic giant branch)
stars (slow neutron capture or "s-process").
So we could, e.g., measure s-process elements like La and Y and use them to formulate
a summary as [ s / Fe ].
Note the varied use of the term light element, depending on the context.
In some cases when astronomers refer to the light elements, they are
referring to those elements created by primordial nucleosynthesis in the Big Bang:
H, Deuterium, He (both 3He and 4He), and 7Li.
In other contexts, astronomers use the term as a sweeping reference to all elements
less than the "iron peak" (see below).
For reference, the periodic
tables below summarizes the origin of the elements in a succinct way.
BUT NOTE: The understanding of nucleosynthesis for some elemebts is continually evolving,
as evidenced by the dramatic change in the Wikipedia Tables of the Elements from the years
2016 and 2018, shown below.
Obviously, both tables agree that the Big Bang makes most of the H and He in the universe.
And the primary source of Li, Be and B in the universe today is thought to come from
cosmic ray spallation, which is when a ray particle (e.g., a proton) causes nuclear
fission of a heavier atomic element (like C, N, O).
Li, Be, and B are not typically generated in the normal
course of stellar nucleosynthesis, but, instead, are destroyed by it.
Other elements up to the elements near Fe are made by supernovae Ia ("exploding white dwarfs")
and II ("exploding massive stars").
However, notice the dramatic shift even from 2016 to 2018 in our understanding of where
neutron capture species come from.
The 2016 table attributes the elements heavier than iron as arising from either large evolved stars via the s-process or as arising from supernovae via the r-process.
Whereas in the 2018 table, the r-process is attributed to "merging neutron stars".
A 2016 Wikipedia version of the periodic table showing primary sites for formation of the different elements. Note that most of the most massive elements from r-process are shown to be made in supernovae.
The 2018 Wikipedia version of the peridic table, now attributing the r-process to
merging neutron stars!
Abundances by weight:
It is sometimes convenient to describe the chemical content of a star
by fractional weight in different elements.
This is usually done by:
X = weight of hydrogen
Y = weight of helium
Z = weight of everything else
For the Sun, ( X, Y, Z ) = (0.70, 0.28, 0.02), though there is some
uncertainty in the solar helium abundance since the sun is too cool to
express He lines.
Especially useful because the actual abundances of metals to H and He are so small, but
this weights their contributions by their heavier atomic masses.
If we assume that the distribution of the elements summarized in "Z " is
universal, then we can write:
[Fe/H] = log[ Z / X ]* - log[ Z / X ]Sun
Accounting for the last term with the actual solar values, an approximate conversion
between Z and [Fe/H] is (Bertelli et al. 1994, A&AS, 106, 275):
log(Z ) = 0.977 [Fe/H] - 1.699
[Fe/H] = 1.024 log(Z ) + 1.739
If one relaxes the assumption of a universally scaled solar heavy element
distribution, then the correspondence between [Fe/H] and Z depends obviously on
the relative distributions of elements.
In this case then it is more appropriate to write
[m/H] = log[ Z / X ]* - log[ Z / X ]Sun
But note that differential variations in the n(X) values of
the individual elements that make up Z, and therefore how they distribute
by weight within Z, means that there is not a rigidly strict, universal
correspondence of Z to [m/H], but one that is different depending on specific
As we shall learn, a very important modulation on the abundance patterns derived
from the relative proportions of the enrichment of the interstellar medium by supernovae
of Type II versus Type Ia.
A prominent difference is that Type II supernova inject back into the
ISM matter that is enriched with α-elements, with minor amounts of iron.
On the other hand, Type Ia SNe inject mainly Fe, with minor α-element
Type II SNe come from massive main sequence stars that have short lives
and thus happen early in the life of a stellar population,
whereas Type Ia SNe come from mass exchange binaries, and take longer (> 1 Gyr)
to show up and start pumping out iron.
Thus, the earliest stars formed in a stellar system are dominated by the
nucleosynthetic yields of Type II stars and tend to be rich in
For example, the stars in the Milky Way halo show a significant enhancement
of α elements compared to the Sun, with [α/Fe] ~ 0.3-0.4, while
more recently formed stars look more like the Sun, with [α/Fe] ~ 0.0.
So, an interesting way to account for these variances in α/Fe mixtures is to
use an equation that accounts for them (Salaris & Cassisi, Evolution of Stars
and Stellar Populations):
[m/H] ~ [Fe/H] + log(0.694fα + 0.306)
where fα = 10[α/Fe].
So, for example, for [α/Fe] = 0.3, this gives:
[m/H] ~ [Fe/H] + 0.2
(which shows that the Fe is off as a proxy of the total metallicity content by a few
0.1 dex in this case, because of the α-enhancement relative to the Sun).
The following table and associated figure
gives the abundances of the elements in the Sun, given
in proportion to H. Note that it is common to give values in a system
log(A) + 12 (i.e., number of atoms per 1012 H atoms)
in order to work with positive values:
From The Observation and Analysis of Stellar Photospheres by David F.
A few things to notice:
The general decline in abundances with atomic number is obvious.
Carbon and oxygen are the most abundant metals in the Sun (and universe generally).
Superposed on the general declining trend is an overall "odd-even effect",
where elements that are even multiples of a He nucleus are enhanced
(for less heavy elements, probably as a result of synthesis by
alpha particle capture).
The huge drop in abundance for the light nuclei
Li, Be, and B arises primarily from the instability of nuclei of mass
5, making the early creation of these elements in the universe rare, as
well as the easy destruction of these elements
in stars, particularly when convection
drops the atmospheric nuclei to the hotter interior.
Elements around iron (V, Cr, Mn, Fe, Co, Ni)
show enhanced abundance, forming an "iron peak". These elements have
the highest binding energy, which is the energy required to remove
a nucleon or the energy released when a nucleon is added.
From http://rst.gsfc.nasa.gov/Sect20/A7.html. Note that the A shown in
the abscissa here is Mass Number, NOT the abundance of the element, as shown above.
Indeed, elements lower than Fe release energy as fusion adds nucleons,
whereas elements past iron require energy to do this.
Thus, we produce an abundance of iron peak elements through normal
Beyond this peak, elements cannot be made efficiently through charged
particle interactions due to the large Coulomb repulsion between
It was known early on (Burbidge et al. 1957) that most of these heavier elements
are synthesized via successive neutron captures onto iron-peak nuclei,
followed by β decays.
s-process: The neutron captures can occur on a
timescale long enough for all β decays to occur (slow
r-process: Neutron captures are on a time scale
short compared to β decay (rapid neutron capture).
The s-process as acting in producing elements and isotopes in the range of elements from Ag to Sb.
Two effects follow:
Even-numbered nuclei have smaller neutron capture cross sections than
odd-numbered nuclei, and this increases the abundances of the
even-numbered nuclei, leading to the odd-even effect (particularly
for s-process nuclei).
Closed neutron shells with 50, 82 and 126 neutrons have
smaller neutron capture cross-sections, leading to abundance peaks
near these nuclei.
The distribution of isptopes in the atomic number (Z = protons)) - neutron number (N) plane, summarizing some of the nucleosynthetic processes/pathways creating them (Big Bang Nucleosynthesis, pp-chain burning, CNO-cycle burning, the r-process, and s-process. The locations of the proton and neutron "magic numbers" of 2, 8, 20, 28, 50, 82, and 126 are indicated (for protons, these correspond to the elements helium, oxygen, calcium, nickel, tin, and lead (no element with Z = 126 has yet been created, though this magic number is reached for neutrons). Figure from Takigawa & Washiyama, Fundamentals of Nuclear Physics, c.2017, Springer Nature.
The following plots compare the abundances in the Sun (actually, the
solar system) to those in the Earth.
The Earth abundance plot is actually in terms of mass fraction, and shows that oxygen and
iron are the most abundant elements by mass for Earth (including the atmosphere).
We will return to the topic of nucleosynthesis and chemical evolution later.
Effects of Line Strengths on Broadband Colors: UBV Example
Metallicity effects play an important role on how the stars in a stellar population
are distributed in a color-magnitude diagram (CMD).
For example, the following plot shows the variation in the MS, SGB, and lower RGB
for thoretical isochrones (isochrone = sequence of stars of one age-chemistry combination) of stellar populations of the same age but different metallicities:
(Left) Isochrones for a set of stellar populations all of age 16 Gyr, but
with different [Fe/H] = -2.03, -1.78, -1.48, -1.26. From Bolte (1993, in
Galaxy Evolution: The Milky Way Perspective, PASP. Conf. Ser. 49,
ed. S. Majewski).
(Right) A more up to date version of the same from the MIST isocrhones (unfortunately, age of this set unknown -- sorry). From http://waps.cfa.harvard.edu/MIST/#.
Here is the same thing for actually observed stars in globular clusters of different
metallicities, but presumably similar ages.
Combined color-absolute magnitude diagrams for 14 globular clusters of similar age from Gaia DR2 data, with stars color-coded by metallicity.
From https://www.gaia.ac.uk/multimedia/gaia-dr2-hr-diagram-globular-clusters .
Obviously, if we want to use CMDs to interpret the age/metallicity characteristics
of a population, we need to understand how these metallicity effects change the
colors and magnitudes of stars.
I will focus initially on one particular example, metallicity effects in the UBV
system, not only to give flavor of how the CMD changes,
but because this particular example has played an important
role in Galactic astronomy/stellar populations studies.
A nice, lucid discussion of the UBV case
is given in Mihalas & Binney, Section 3.6; by extrapolation, the same
basic phenomena apply to other filter systems covering similar wavelengths (see below).
Another version of this is given in the original paper on UV-excess by
Wildey, Burbidge, Sandage & Burbidge (1962, ApJ, 135, 94).
In the following figure is shown the variation of the line-blocking
coefficient (LBC) with wavelength for various types of stars.
You can think of the LBC as something like (1-emissivity),
with the emissivity of a source defined as the ratio of true flux to that
from a BB of same temperature.
Line blocking as a function of stellar type in top three panels.
Bottom two panels shows change in the LBC for two stars of same
spectral type but different metallicity. From Mihalas & Binney (1980).
Here is another, more modern example of a comparison of two stars of the same nominal spectral type but vastly different metallicities:
Two early K giants differing by almost two orders of magnitude in metallicity, showing the spectral differences that result. The strongest variation comes in the ultraviolet. Figure from Gregg et al. (2005, "The HST/STIS Next Generation Spectral Library", The 2005 HST Calibration Workshop, Space Telescope Science Institute, 2005, A. M. Koekemoer, P. Goudfrooij, and L. L. Dressel, eds.).
From the above figures notice that:
Line-blanketing is weighted heavily towards shorter wavelengths
for all spectral types (note the source of the blanketing
for the A0V star...).
So strong in UV that it is difficult to find places where there is
any blackbody continuum.
The later the spectral type, the larger is the overall
line-blanketing, greater the departure from a true blackbody.
From the variation of the LBC with wavelength, it is clear that
if you start with a pure BB -- a star with zero metals and no lines --
and gradually increase the abundance, all wavelengths are affected, but
bluer wavelengths more so.
Since most "metallic" lines are in the UV, a
star with more lines (because it is a later spectral type
or because of a higher metal abundance) will have more absorption lines
in UV and, consequently, will give off less UV flux.
U band designed to measure the
line strength of metals in stars, concentrated to
a large extent in the ultraviolet.
Therefore, the U-B color is sensitive to:
the temperature of the star, and
the metallicity of a star.
Since U-B color measures both simultaneously,
to separate metallicity and temperature effects one can make a
"two-color diagram" where B-V sorts stars by
temperature, and variations in U-B show metallicity effects.
Two-color diagram from Wildey, Burbidge, Sandage, and
Burbidge (1962, ApJ, 135, 94) showing the line-blanketing
effects of increasing metal line absorption (stars get redder
in U-B when they have more metals). The locus of stars of different
temperatures from 5500 to 10000 K
and with metal abundances like the Sun is shown as the bottom curve.
The other curvy lines show the locus of stars of different temperatures
but with 0.1 and 0.01 the metals as the Sun. These more metal poor stars are bluer
(i.e., more UV flux) than metal rich stars of the same B-V color (i.e.,
What is happening in above diagram?
If we start with stars of no metallicity and therefore no metal lines, and
then gradually increase abundances to solar type, the star
should become redder in B-V, but even redder in U-B, simply
on the basis of the line blanketing effect.
But this is not the entire story. We also have several competing effects.
One of these compensating effects that comes into play to interpret the relative color
changes is backwarming:
All other things being equal,
the same amount of energy still has to leave the star.
Can only do so between lines in spectrum.
Thus, the continuum emission levels become elevated,
and make the star (in continuum) appear as if it is a star of hotter
Backwarming effect mitigates and competes with the line blanketing effect.
U band: (line blanketing) >> (backwarming)
B band: (line blanketing) >~ (backwarming)
V band: (line blanketing) <~ (backwarming)
These effects are obvious in the K giant spectra shown above.
Thus, in the (B-V,U-B) two-color diagram, the
line blanketing vectors are nearly vertical --
showing that Δ(U-B) is more strongly changed than
Δ(B-V) for given change in metals.
Blanketing vectors for stars of different temperatures
from line-free colors (shown by crosses) to solar metallicity
locus (shown by the curve). From Wildey et al. (1962).
We say that metal-poor stars show an "Ultraviolet
Excess" or "UVX'' (comparatively more UV flux) than metal-rich
stars - which have a lot more UV absorption lines
Now here is a more modern version of the same plot, shown in the Sloan filter system (two versions of the same plot are shown, with one inverted for comparison to the UBV versions of the plot shown elsewhere on this webpage).
Theoretical models and observed stellar spectra from SDSS/SEGUE DR8. Colors indicate metalllcity for both the models and the actually observed stars. The panels from left to right in each version of the figure show stars that are approximately giants, subgiants, and dwarfs, respectively.
From Casagrane & VandenBerg (2014, MNRAS, 444, 392).
Quantifying "Ultraviolet Excess":
Traditionally adopt the locus of stars in the Hyades
open star cluster to represent "solar metallicity" .
Note, however, actual Hyades [Fe/H] ~ +0.25
(i.e., a bit more metal rich than the Sun...)!
The UVX, written as:
is the difference of a star's (U-B) color from that
of a Hyades star of the same (B-V) color.
Modified from Wildey et al. (1962) and
Mihalas & Binney (1980).
Wildey et al. (1962; Table 4)
tabulate blanketing vectors
and corresponding δ(U-B) for
Connection between δ(U-B) and [Fe/H]...
... unfortunately, the connection of
the size of δ(U-B) to the size
of [Fe/H] is a function of B-V!!
Isometallicity lines from Sandage (1969). Note
that the "guillotine'' represents the limit of UVX
for stars with no metals.
To bring some uniformity to the translation of
δ(U-B) to [Fe/H],
Sandage (1969, ApJ, 158, 1115 ) invented a normalization of
δ(U-B) for different B-V.
The normalization is such that we correct all
δ(U-B) to the
δ(U-B) of a star with the
same metallicity but (B-V)=0.6.
This table from Sandage (1969)
gives the corrections
for interpolation to the "standard"
See also Box 5.4 in Binney & Merrifield for a description of
Armed with normalized δ(U-B)0.6,
we may now estimate the [Fe/H] for any star.
Several schemes have been given:
Mihalas & Binney (1980, eqn. 3-42) give the simple relation
"for modest values of
Laird et al. (1988, AJ, 95, 1843) gives
(see Binney & Merrifield Box 5.4):
δ(U-B)0.6 ~ -0.0776
Why Are There "Subdwarfs"?
It was noticed in the 1950s (perhaps earlier?), that stars with an
ultraviolet excess also appeared to be subluminous with respect
to normal Population I type stars.
For example: figures from Eggen & Sandage (1962, ApJ, 136, 735) showing
the color-absolute magnitude diagram for stars of measured parallax sorted
by their ultraviolet excess.
These panels show a correlation of
δ(U-B) with subluminosity compared to, say, the Hyades.
Figures from Eggen & Sandage (1962).
Note that the above figures are very hard to make (properly)
because it requires having trigonometric parallaxes
for these subdwarfs.
Because subdwarfs are associated with Population II
there are very few of them near the Sun, where reliable parallaxes
can be obtained!
This is a continuing problem in astronomy, and the situation
is only marginally better after HIPPARCOS, which contributed only
a few more parallaxes for subdwarfs.
Figure from Reid (1999, ARAA, p.203) showing the current state of the
art after HIPPARCOS obtained parallaxes for a few more subdwarfs.
A concerted effort by the US Naval Observatory to do CCD parallaxes
of subdwarfs has also contributed to this endeavor.
Traditionally this problem has been greatly affected by a statistical bias (called the Lutz-Kelker
bias) inherent to creating a figure like the above out of the
few subdwarfs we had managed to be able to get parallaxes for
(a problem that also affects Gaia, but not to the same degree --- we will return to in the distance scale section of
Now that Gaia is out, we can finally get large numbers of metal-poor stars that
can be used to calibrate our subdwarf sequences "once and for all". We show here
again one version of this, the globular cluster sequences we already showed above.
Combined color-absolute magnitude diagrams for 14 globular clusters of similar age from Gaia DR2 data, with stars color-coded by metallicity.
From https://www.gaia.ac.uk/multimedia/gaia-dr2-hr-diagram-globular-clusters .
(Note that wwe already saw on the previous web lecture
that Gaia shows a sorting of high velocity stars to "subdwarf" areas
of the absolute magnitude CMD for nearby stars).
Figures like those above are critical components to the distance
scale problem, because they are used to get distances to globular
clusters from main sequence fitting.
What is the origin of the subdwarf effect?
Recall that in the V band, backwarming dominates
line blanketing as we add metallicity to a star.
Thus, as we make a star more metal-poor
(i.e., as we deblanket it), by the backwarming effect one would think
that not only does the star become bluer
in (B-V) [and (U-B)], but it also should get fainter
Color-magnitude vector for subdwarfness by Wildey et al. (1962).
So, from the combination of stellar atmospheric blanketing/backwarming effects one would think that the
main sequence locus, for increasingly metal poor
populations moves left (blueward) and slightly down (fainter) in the
CMD, something like this:
But there is also a competing stellar interiors effect that as one decreases
the metallicity of a star, the opacity is reduced. This makes the overall energy
output at the surface greater and the luminosity of the star increases.
Thus, ironically, "subdwarfs" are actually more luminous than their higher metallicity
counterparts of same mass, and so "subdwarfs" is therefore a misnomer!
The truth of the matter is that while the subdwarf "sequence" lies below
the high metallicity main sequence, subdwarf and solar metallicity stars at the
same color have different mass, and subdwarfs of the same mass are bluer and brighter
than their more metal rich counterparts.
Similar atmosphere/interior effects manifest themselves along other stellar loci in
the CMD, for example, the reason why red giant branches
vary for clusters of different abundance (see the Gaia globular cluster plot above, and
the MIST isochrones, repeated here:
A more up to date version of the same from the MIST isocrhones (unfortunately, age of this set unknown -- sorry). From http://waps.cfa.harvard.edu/MIST/#.
Connection between δ(U-B)0.6
One can use the Wildey et al. (or other) calibrations of
blanketing effects and
make the direct connection between ultraviolet excess
One calibration of the relation by Laird et al.
(1988, AJ, 95, 1843) gives (see Binney & Merrifield, P. 277):