The problem is following. In the usual scenario for the star formation the stars would have formed almost instantaneously and star formation would not continue anymore significantly. Stars with the age of our sun however exist and star formation is still taking place: more than one half of galaxies is forming stars. So called starburst galaxies do this very actively. The standard story is that since stars explode as supernovae, the debris from supernovae condenses to stars of later generations. Something like this certainly occurs but this does not seem to be the whole story.
Remark: It seems incredible that astrophysics would still have unsolved problems at this level. During years I have learned that standard reductionistic paradigm is full of holes.
The notion of star formation quenching has been introduced: it would slow down the formation of stars. It is known that quenched galaxies mostly have a super-massive blackhole in their center and that quenching starts at the centers of galaxies. Quenching would preserve star forming material for future generations of stars.
To study this process a team of astronomers led by Tabatabaei turned their attention to NCG 1079 located at distance of 45 million light years. It is still forming stars in central regions but shows signs of quenching and has a super-massive blackhole in its center. What was found that large magnetic fields, probably enhanced by the central black hole, affect the gas clouds that would normally collapse into stars, thereby inhibiting their collapse. These forces can even break big clouds into smaller ones, she says, ultimately leading to the formation of smaller stars.
This is highly interesting from TGD point of view. I have already considered a TGD based model for star formation (see this). In the simplest TGD based model galaxies are formed as knots of long cosmic strings. Stars in turn would be formed as sub-knots of these galactic knots. There is also alternative vision in which knots are just closed flux tubes bound to long strings containing galaxies as closed flux tubes like pearls in necklace. These closed flux tubes could emerge from long string by reconnection and form elliptic galaxies. The signature would be non-flatness for the velocity spectrum of distant stars. Also in the case of stars similar reconnection process splitting star as sub-knot of galactic string can be imagined.
If stars are sub-knots in knots of galactic string representing the galaxies, the formation of star would correspond to a formation of knot. This would involve reconnection process in which some portions of knot go "through each other". This is the manner how knots are reduced to trivial knot in knot cobordism used to construct knot invariants in knot theory (see this). Now it would work in opposite direction: to build a knots.
This process is rather violent and would initiate star formation with dark matter from the cosmic string forming the star. This process would continue forever and would allow avoid the instantaneous transformation of matter into stars as in the standard model. At deeper level star formation would be induced by a process taking place at the level of dark matter for magnetic flux tubes: similar vision applies in TGD inspired biology. One could perhaps see these knots as seeds of a phase transition like process leading to a formation of star. This reconnection process could take place also in the formation of spiral galaxies. In Milky Way there are indeed indications for the reconnection process, which could be related to the formation of Milky as knot.
The role of strong magnetic fields supposed to be amplified by the galactic blackhole is believed to be essential in quenching. They would be associated with dark flux tubes, possibly as return fluxes at ordinary space-time sheets carrying visible matter (flux lines must be closed). These magnetic fields would somehow prevent the collapse of gas clouds to stars. They could also induce a splitting of the gas cloud to smaller clouds. The ratio of mass to magnetic flux ratio for clouds is studied and the clouds are found to be magnetically critical or stable against collapse to a core regions needed for the formation of star. The star formation efficiency of clouds drops with increasing magnetic field strength.
Star formation would begin as the magnetic field has strength below a critical value. If the reconnection plays a role in the process, this would suggest that reconnection is probable for magnetic field strengths below critical value. Since the thickness of the magnetic flux tube associated with its M4projection increases when magnetic field strength decreases, one can argue that the reconnection probability increases so that star formation becomes more probable. The development of galactic blackhole would amplify the magnetic fields. During cosmic evolution the flux tubes would thicken so that also the field strength would be reduced and eventually the star formation would begin if the needed gas clouds are present. At distant regions the thickness of flux tube loops can be argued to be larger since the p-adic length scale in question is longer since magnetic field strength is expected to scale like inverse of p-adic length scale squared (also larger value for heff/h=n would imply this). This would explain star formation in distant regions. This is just what observations tell.
A natural model for the galactic blackhole is as a highly wounded portion of cosmic string. The blackhole Schwartschild radius would be R=2GM and the mass due to dark energy of string (there would be also dark matter contribution) to mass would be M≈ TL, where T is roughly T≈ 2-11. This would give the estimate L≈ 210R.