Probably less.
What is 13,8 milliards? The age of whole universe?
First stars formed some hundreds of millions years later. Not sure how many hundreds. Deep fields tend to diminish that number.
From first stars in a cluster to first white dwarf and last supernova takes how long? Less than 100 million years, but is it 70 millions? 30 millions?
The 6 nearest white dwarfs, in order of temperature, are:
- Sirius B. 25 000 K, +11,18. 1,02 solar mass, 0,0084 solar radii. Has been a white dwarf about 120 million years, star for 100 million years before that. Guestimated as 5 solar masses on main sequence.
- Keid B. 16 500 K, +11,02. 0,57 solar mass, 0,014 solar radii. Colder than Sirius B but brighter because lighter and therefore bigger.
- Gliese 440. 8500 K, +13,2. Mass 0,56 solar, radius 0,01 solar
- Procyon B. 7700 K, +13,0. 0,60 solar mass, 0,012 solar radii. Has been a white dwarf about 1,2 milliard years, a star about 700 million years before that.
- Gliese 169 B. 7100 K, +13,72. 0,67 solar mass, 0,011 solar radii
- van Maanen´s star. 6100 K, +14,21. 0,67 solar mass, 0,011 solar radii. Estimated to have been a white dwarf for 3,5 milliards of years, a star 900 millions of years before that.
Note how most nearby white dwarfs cluster in 0,56...0,67 solar masses an 0,01...0,014 solar radii. Sirius B is unusually heavy and small.
What precisely does the white dwarf branch of a globular cluster Hertzsprung-Russell diagram look like?
Most white dwarfs are black bodies of nearly the same radius and different temperatures, so they should form a narrow band whose kinks are dictated by eye sensitivity and spectral class spacing. In the early end, it of course goes into O (the planetary nebula nuclei). But how does the late end act? van Maanen´s star, at 6100 K and late F is just 3,5 milliards of years and globular clusters are 13 milliards. Even stars which were 1 milliard years in main sequence will have been 12 milliards years white dwarfs.
When you approach heavy and small white dwarfs, they will be dimmer for the same temperature than lighter white dwarfs. But will they also be hotter for the same age? Does the late-class end of globular cluster white dwarf series actually turn to hotter and dimmer ones?