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There was an answer mentioning that "the formation of many elements in earth was due to supernova nucleosynthesis" as told by someone. Hence, a question crosses my mind...

If the elements were formed due to the explosion of a supernova, then there should be a remnant like a black-hole or a neutron star nearby. Were there any nearby?

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The materials that made up the solar system can be studied through the analysis of pre-solar grains and the abundances of various isotopes in primitive meteoritic material.

Pre-solar grains were formed in the photospheres of stars pre-dating the Sun. These grains were then expelled into the interstellar medium (ISM) in stellar winds and also in supernova explosions. The grains are found inside meteoritic material and typically consist of minerals like silicon carbide. The analysis of isotopic ratios of a wide variety of elements betrays the origins of the material.

It is generally found that the material that makes up the solar system (and Sun) comes from many stars and via many routes, not just supernovae. In fact many of the elements n the solar system, contrary to a common misconception, are not produced in massive stars and disseminated into the ISM via supernovae. Elements like C, N, F, a variety of heavier elements like, Ba, Rb, Sr, Pb and many others are dominantly made in intermediate mass asymptotic giant branch stars and enter the ISM through convective mixing followed by mass loss in stellar winds. Other sources of elements include type Ia supernovae, novae, cosmic ray spallation, neutron star mergers...

So, the solar system is not really the product of one or even a few events., but many such events that have all become mixed in the ISM over billions of years.

Now having said that, some think that there is evidence that the Sun formed in a large cluster of stars and the protosolar nebula was contaminated by the debris from a nearby (within a light year) supernova event (see the excellent review on the birth environment of the Sun by Adams 2010). The evidence for this comes in the form of short-lived extinct radionuclides such as 60Fe found in meteorites. This has a half-life of about 2 million years and decays to 60Co and then 60Ni. By checking the abundances of 60Ni vs other iron isotopes it has been claimed that the solar system was polluted with 60Fe by a blast from a supernova more-or-less at the time of formation. The interpretation is still keenly disputed.

Even if it were the case that a single supernova remnant has left its "fingerprints" on the solar system composition, it is hard to see how we would find the remnant (black hole or neutron star) it left behind. Firstly, over 4.5 billion years, the Sun has travelled many times around the Galaxy, so it is (probably) nowhere near where it was born; so it is no good looking nearby for anything. Secondly, supernova remnants (i.e. the nebulae) are comparatively shortlived (a million years or so) and the compact black hole or neutron stars that are produced often have very sizeable velocities imparted by the supernova and swiftly depart the centre of their nebular remnants. Thus we wouldn't know where to look and there is every chance that the neutron star or black hole could even have escaped the Galaxy or could be on a highly elliptical Galactic orbit and be nowhere near the Sun. Finally, looking for old neutron stars and black holes is difficult. They are not pulsars and will not emit much in the way of electromagnetic radiation unless they are still in a close binary system and accreting from a normal star.

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