Not understanding Hulse Taylor period shift calculation

[Prometeus]

I have been studying Hulse Taylor PSR 1913+16 calculation of period shift which is regarded as indirect proof for gravitational waves, but I don't understand one thing.
If you look on the graph of Cumulative period shift, around every 10 years the shift doubles.
https://en.wikipedia.org/wiki/File:PSR_B1913+16_period_shift_graph.svg

It is in seconds, so it seems no big deal, but the final inspiral is calculated to happen in 300 millions years, which a lot of time. But when the cumulative period continues to double like every 10 years, the final inspiral would happen much sooner, estimating it certainly at less than 100 000 years.
So what is wrong with my understanding of it? Is the period shift something which has some periodic nature, so the period shift is not always decreasing, but also increasing?

I couldn't find any published detailed description of the calculation and how this would fit both geometrically increasing period shift and 300 millions year to inspiral. It would be helpful, if somebody could link detailed and complete calculation.

 

[mfb]

It does not follow an exponential distribution, it is a parabola.

The decrease in period is approximately linear (at least within a few decades), so its integral is a parabola.

 

[Prometeus]

It does not follow an exponential distribution, it is a parabola.

The decrease in period is approximately linear (at least within a few decades), so its integral is a parabola.

Im not a math wizard, but it is obviously not linear. Cumulative of linear increase would be a straight line on graph. In reality it is obviously doubling every 10 years so it is not linear.

 

[Vanadium 50]

Im not a math wizard, but it is obviously not linear. Cumulative of linear increase would be a straight line on graph. In reality it is obviously doubling every 10 years so it is not linear.

None of those three things are true. You might want to look at the graph and mfb's message again.

 

[mfb]

If it is "obviously doubling every 10 years", which values do you get from the graph for 1984 and 2004? There are 20 years in between, so it should be a factor of 4. Is it?

 

[Prometeus]

If it is "obviously doubling every 10 years", which values do you get from the graph for 1984 and 2004? There are 20 years in between, so it should be a factor of 4. Is it?

OK, looked on it again and you are right, it is not doubling. From 1975 to 1985 was the cumulative period shift around 5 seconds, from 1985 to 1995 it was 15 seconds and from 1995 to 2005 it was 20 seconds. So we can say, that from 1985 to 2005 it was quite linear, but there is significant non linearity in 1975 to 1995. Why is it there? How can it be? It should be perfectly linear, when it should last for 300 millions years.

 

[mfb]

I get 0 seconds, 4.5 seconds, 17.5 seconds, and 39 seconds for the integrated shift, respectively. The differences are 4.5 seconds, 13 seconds and 21.5 seconds, and the second differences are 8.5 seconds and 8.5 seconds - they are the same. That is exactly what you expect for a parabola. And the derivative of a parabola is a linear function.