The photosphere of our Sun and most other stars exhibit a phenomenon called limb darkening where the disk is brighter at the center than at the edges at optical wavelengths. This effect is more pronounced towards the violet end of the visible spectrum than it is towards the red end.
Limb darkening occurs because there is a strong temperature gradient within the photosphere (deeper is hotter) and we see deeper into the Sun at the center of the disk then we do toward the edges. The deeper, hotter regions of the photosphere produce more visible light than do the shallower, cooler regions.
Does this non-uniformity of light emitted from the disk of a star mean we are “missing” some light in measuring a star’s brightness that would then affect our ability to accurately calculate the star’s total luminosity? Not at all. Here’s why.
Stars are almost always isotropic emitters of light. That means they emit light uniformly in all directions. At a given distance from the star, an observer would measure the same brightness of the star no matter what their direction from it. Even though the edges of the stellar disk are darker, the center is brighter, and the total integrated brightness is the same as it would be if all parts of the disk were emitting uniformly.
We calculate the luminosity of the star by measuring the amount of light we receive across our collecting area (whether that be the human eye or the telescope aperture), and then dividing this collecting area into the total surface area of a sphere centered on the star and having a radius that is our distance from the star. We then take that quotient times the amount of light we detect in our small collecting area to get the total amount of light emitted by the star in all directions.
The elements that make up the stars also exist here on Earth. In fact, our Earth, and indeed all the planets, were created from the dust and gas produced by previous generations of stars that existed before our Sun and solar system formed. We truly are made of stardust!
Stars are made up almost entirely of hydrogen and helium. Here is a table of the most abundant elements in our Sun.
% by atoms
Most abundant elements in the Sun
It is not a trivial matter to determine the abundance of elements in the Sun. For most elements, astronomers have to look at the strength of spectral absorption lines in the photosphere. Some elements, like fluorine, chlorine, and thallium, require looking for their spectral lines inside of sunspots, which are cooler-than-average regions of the photosphere. Other elements require that we look at spectral lines in the solar corona, or capture and analyze the solar wind. And some elements we are simply unable to detect.
The region of the photosphere that is amenable to spectral study represents only about 2% of the mass of the Sun. Since the Sun’s formation 4.6 Gyr ago, some gravitational settling of heavier elements and diffusion of hydrogen towards the surface means the Sun is not uniform in composition. Fortunately, the relative abundances of the elements heavier than helium are probably similar throughout the Sun.
Lithium, the third element in the periodic table after hydrogen and helium, is the odd element out. It has a relative abundance in the solar photosphere that is only 1/170th that found in meteorites. The Sun’s original supply of lithium has largely been destroyed by the high temperatures inside the pre-main-sequence Sun, and today at the hot bottom of the Sun’s convection zone.
Light pollution is a problem here on Earth, but on the Sun we have a problem with “line pollution”. There are so many spectral lines that the weak signatures from some elements become difficult or impossible to isolate and measure. There is much blending of overlapping lines, and some elements—most notably iron which is the ninth most abundant element in the Sun—are “superpolluters” with hundreds to thousands of spectral lines from both excited and ionized states.
Sometimes, the spectral lines of interest are in a region of the electromagnetic spectrum (ultraviolet, for example) that can only be observed from space, and that creates additional challenges.
Notably, the noble gases helium, neon, argon, krypton, and xenon have no photospheric absorption lines that can be observed, and we must look to coronal sources such as the solar wind, solar flares, or solar energetic particles for information about their abundances.
Helium—the second most abundant element in the Sun—requires an indirect approach combining a theoretical solar model and observational helioseismology data to tease out its abundance.
The following elements are undetectable in the Sun: arsenic, selenium, bromine, technetium, tellurium, iodine, cesium, promethium, tantalum, rhenium, mercury, bismuth, polonium, astatine, radon, francium, radium, actinium, protactinium, and all the synthetic elements above uranium on the period table.
Interestingly, helium was discovered in the Sun before it was discovered on Earth! That’s why this element is name after Helios, the Greek god of the Sun.
The energy source that allows stars to shine steadily, often for billions of years, is fusion. Fusion in a star can only occur where both the temperature and pressure are very high. Usually (but not always!), this occurs in the core of the star. When the element hydrogen fuses into helium, a huge amount of energy is released in the process. Lucky for us, fusing hydrogen into helium is difficult to do in a one-solar-mass star. On average, any particular hydrogen atom in our Sun has to “wait” about five billion years before having the “opportunity” to participate in a fusion reaction!
In order for sustained fusion to occur in the core of a star, the star must have sufficient mass so that the core temperature and pressure is high enough. Present thinking is that the lowest mass stars where sustained fusion can occur have about 75 times the mass of Jupiter, or about 7% the mass of the Sun.
No, it’s not the name of a rock band. Astronomers (unlike everybody else) consider all elements besides hydrogen and helium to be metals. For example, our Sun has a metallicity of at least 2% by mass (Vagnozzi 2016). That means as much as 98% of the mass of the Sun is hydrogen (~73%) and helium (~25%), with 2% being everything else.
Traditionally, elemental abundances in the Sun have been measured using spectroscopy of the Sun’s photosphere. In principle, stronger spectral lines (usually absorption) of an element indicate a greater abundance of that element, but deriving the correct proportions from the cacophony of spectral lines is challenging.
A more direct approach to measuring the Sun’s elemental abundances is analyzing the composition of the solar wind, though the material blown away from the surface of the Sun that we measure near Earth’s orbit may be somewhat different from the actual photospheric composition. The solar wind appears to best reflect the composition of the Sun’s photosphere in the solar polar regions near solar minimum. The Ulyssesspacecraft made solar wind measurements above both the Sun’s north and south polar regions during the 1994-1995 solar minimum. Analysis of these Ulysses data indicate the most abundant elements are (after hydrogen and helium, in order of abundance): oxygen, carbon, nitrogen, magnesium, silicon, neon, iron, and sulfur—though one analysis of the data shows that neon is the third most abundant element (after carbon).
The elephant in the room is, of course, are the photospheric abundances we measure using spectroscopy or the collection of solar wind particles indicative of the Sun’s composition as a whole? As it turns out, we do have ways to probe the interior of the Sun. Both helioseismology and the flux of neutrinos emanating from the Sun are sensitive to metal abundances within the Sun. Helioseismology is the study of the propagation of acoustic pressure waves (p-waves) within the Sun. Neutrino flux is devilishly hard to measure since neutrinos so seldom interact with the matter in our instruments. Our studies of the interior of the Sun (except for sophisticated computer models) are still in their infancy.
You might imagine that if measuring the metallicity of the Sun in our own front yard is this difficult, then measuring it for other stars presents an even more formidable challenge.
In practice, metallicity is usually expressed as the abundance of iron relative to hydrogen. Even though iron is only the seventh most abundant metal (in the Sun, at least), it has 26 electrons, leading to the formation of many spectral lines corresponding to the various ionization states within a wide range of temperature and pressure regimes. Of the metals having a higher abundance than iron, silicon has the largest number of electrons, only 14, and it does not form nearly as many spectral lines in the visible part of the spectrum as does iron. Thus defined, the metallicity of the Sun [Fe/H] = 0.00 by definition. It is a logarithmic scale: [Fe/H] = -1.0 indicates an abundance of iron relative to hydrogen just 1/10 that of the Sun. [Fe/H] = +1.0 indicates an abundance of iron relative to hydrogen 10 times that of the Sun.
The relationship between stellar metallicity and the existence and nature of exoplanets is an active topic of research. It is complicated by the fact that we can never say for certain that a star does not have planets, since our observational techniques are strongly biased towards detecting planets with an orbital plane near our line of sight to the star.
Vagnozzi, S. 2016, 51st Recontres de Moriond, Cosmology, At La Thuile