Not understanding Hulse Taylor period shift calculation

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Discussion Overview

The discussion revolves around the calculation of the period shift in the Hulse-Taylor binary pulsar PSR 1913+16, which is considered indirect evidence for gravitational waves. Participants are exploring the nature of the cumulative period shift over time, questioning whether it exhibits linear or non-linear characteristics, and how this relates to the estimated time for the final inspiral event.

Discussion Character

  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • One participant expresses confusion about the cumulative period shift, noting that it appears to double every 10 years and questions how this aligns with the estimated 300 million years until final inspiral.
  • Another participant asserts that the period shift does not follow an exponential distribution but is instead a parabola, suggesting that the decrease in period is approximately linear over a few decades.
  • Some participants challenge the assertion of linearity, arguing that the cumulative increase is not linear and pointing out discrepancies in the expected values from the graph.
  • A later reply acknowledges that the cumulative period shift is not doubling as initially thought and provides specific values for different years, indicating a more linear trend from 1985 to 2005 but noting significant non-linearity in earlier years.
  • Another participant calculates specific integrated shifts and identifies consistent second differences, arguing that this supports the idea of a parabolic relationship, with the derivative being linear.

Areas of Agreement / Disagreement

Participants do not reach consensus on the nature of the cumulative period shift, with some arguing for linearity and others for a parabolic relationship. The discussion remains unresolved regarding the implications of these differing interpretations on the overall understanding of the period shift calculation.

Contextual Notes

There are unresolved questions about the assumptions underlying the calculations and the nature of the period shift, particularly regarding the expected linearity over the estimated time frame for the inspiral event.

Prometeus
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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.
 
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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.
 
mfb said:
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.
 
Prometeus said:
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.
 
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?
 
mfb said:
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.
 
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.

pulsar.png
 

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