How much energy is generally required to kill an elk with any given caliber? What is the cut off to stop shooting at an elk and expect it to die when hit in the heart and lungs?
Once more, Let's rephrase the question for simplicity.
1) Let's assume you have chosen the optimum bullet for your caliber, it will expand reliably to 1.3 X the caliber, never fragment, and always travel in a straight line.
2) your shot placement is perfect, such that straight line penetration will transect the great vessels at the top of the heart.
Is there a lower energy level at which a rapid kill (ie penetration to the vessels) is still almost guaranteed?
The answer is "it depends on the sectional density of your perfectly placed, perfectly composed projectile" and on the angle and necessary penetration depth. With all else being equal(ie ignore arguments on differently constructed bullets, since that is not your question, and assume the hits being in exactly the same place), the penetration will be a function of primarily two variables.
A 500 grain 12 ga shotgun slug with a
KE of 1000FTLB at 125 yds with a diameter of 0.73 is not an adequate elk round, even for behind the shoulder shots. 950FPS and SD of 0.13. E*SD=134
A 160 gr .277 at 600 yds would have a similar KE, about
1000 Ft. Lbs. But would have a velocity of 1620fps and an SD of 0.3 The penetration for a behind the shoulder shot should be adequate.. E*SD=306
With comparable projectiles and shot placement, the penetration will be a function of two variables, E and SD. In simplest terms, penetration potential (PP)= Kf(E)* Kf(SD) where the Ks are different constants. The energy is obviously a function of the square of the velocity, and decreases rapidly downrange as velocity slows.
There are rounds (especially flat point solids)that will reliably penetrate from the hip thru the great vessels and out the front. You will find that these rounds have a high E*SD out further than you can likely shoot accurately in a hunting situation. Legal requirements may preclude the use of solids, but the general idea is still correct.
So, the answer to your question, is "it's a matter of opinion". I would not choose to attempt even a behind the shoulder shot on a big elk if the weapon in hand produced an E*SD less than 225 at that particular distance..
Know your limits.
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Steve