This question is kind of a companion question to this question on the creation of heavier elements via head on stellar collision. Both arise from me thinking about Przybylski's Star. This star has short-lived elements, the shortest of which of is einsteinium, with the longest lived isotope of that element having a half-life of only 472 days. So, the question is, how is it still there? And, I read one explanation somewhere was that even heavier elements were decaying into einsteinium. So, my question is, would we be able to tell if heavier undiscovered elements were in a star's spectral lines?
We have previously discovered unknown elements spectroscopically. Helium (named for helios, “sun”) was identified in solar spectra decades before being isolated on Earth.
As for “how it is still there”: if you have short-lived isotopes whose populations are not decreasing over time, the decays must be in secular equilibrium with some production process. On Earth, we produce heavy actinides in chemically-significant quantities by repeated neutron capture on heavy elements.
There is speculation in nuclear physics that there may be an “island of stability” for very heavy nuclei. Or rather, speculation about a second “island of stability,” because there is already a gap between lead and uranium where all nuclides are short-lived. If such superheavy, relatively stable nuclei exist, and they are chemically important in this weird star, their decays could produce a population of nuclei which are too short-lived to occur in ores on Earth. There is precedent for this, too. The decay of trace amounts of uranium in concrete and bedrock can cause radon gas to accumulate in poorly-ventilated rooms.
I think that would be very difficult indeed. Unfortunately there are many elements, many isotopes and different ionisation states. Literally millions of transitions. Missing data and incorrectly estimated oscillator strengths mean there are often "unexplained" weak absorption lines in high resolution stellar spectra.
To make a convincing case for finding new elements there would have to be multiple lines identified and a reasonable calculation of where in the spectra those lines would be, based on some knowledge of the atomic physics for those elements. The lines themselves would have to be unblended from other nearby spectral lines and strong enough to be detected. This is not impossible, just very difficult.
I am not convinced by Gopka et al.'s identification of a single absorption line of Einsteinium. If it could be confirmed, then its short half-life means it was produced in the star. A leading explanation would be decay from heavier, long-lived elements in a hypothesised island of stability. Such elements themselves could be produced during neutron star mergers and the resultant kilonova explosions.