Estimating Sun's Lifetime -- what's wrong ?

[Widdekind]

NGC 6287 is the oldest Globular Cluster in the Milky Way Galaxy. And, according to this article, the cluster's Main-Sequence Turnoff happens at a V-I Color Index of ~1.3.

 

 

Then, according to this site, that V-I Color Index corresponds, according to the formula:

 

[math]T_{eff} = \frac{9385}{0.95 + (V-I)} K[/math]

 

to an effective surface temperature of roughly T_eff = 4200 K.

 

 

Finally, according to the appendix of Carroll & Ostlie's Introduction to Modern Astrophysics (1st ed.), that effective surface temperature corresponds most closely with Spectral Class K5, which has [math]M \approx 0.67 M{\odot}, L \approx 0.15 L_{\odot}[/math]. Such a star should have a stellar lifetime longer than our Sun's by a factor of roughly (M / L) = 4.5.

 

 

CONCLUSION (?!?): Since our Universe is purportedly under 14 billion years old, and then even if NGC 6287 is nearly as old, our Sun should have a lifetime of at most 14 Gyr / 4.5 = 3.1 Gyr. And, conversely, if our Sun really has a lifetime of roughly 10 Gyr, then NGC 6287 (and the Universe) must be at least 45 Gyr old.

 

What went wrong ??

 

[swansont]

 

What went wrong ??

 

 

Lifetime ≠ age

[Widdekind]

Shouldn't a K5-class (orange) dwarf live for roughly 4-5 times as long as the Sun ? And, if the K5-class stars in NGC 6287 are already beginning to turn off from the Main Sequence ... ??

[D H]

What justifies your assumption of orange dwarfs, Widdekind? The age of those old globular clusters is determined by red giants that have turned off the main sequence, not orange dwarfs.

[Widdekind]

What am I missing ? Isn't the "Main Sequence Turnoff" that group of stars that are "still just barely" on the Main Sequence ?

 

According to the cited sources, the last stars still on the MS have a V-I CI of ~1.3, which theoretically corresponds to a T_eff ~ 4200 K...

 

which would be, as a MS star, a K-6 or K-5 class orange dwarf... yes??

 

So, stars smaller than K-6 are still on MS in NGC 6287, while stars bigger than K-5 have already begun (to varying degrees) to "peel off" the MS... yes ??

[swansont]

I misunderstood what you were claiming before.

——

 

Why are you using 1.3?

 

http://venus.mporzio.astro.it/~marco/gc/cluster_4.php?ggc=NGC%206287

 

V-I is given as 1.74.

[Widdekind]

I misunderstood what you were claiming before.

——

 

Why are you using 1.3?

 

http://venus.mporzio.astro.it/~marco/gc/cluster_4.php?ggc=NGC%206287

 

V-I is given as 1.74.

 

Thanks for the link. Is that V-I for the complete cluster, or for the Main Sequence Cutoff ? (Are they the same, or different ?)

[Widdekind]

I misunderstood what you were claiming before.

——

 

Why are you using 1.3?

 

http://venus.mporzio.astro.it/~marco/gc/cluster_4.php?ggc=NGC%206287

 

V-I is given as 1.74.

 

Wouldn't V-I = 1.74 > 1.3 "make the problem worse", since that would correspond to an effective temperature of 3500 K ? I'm still confused.