Psr b1913+16: Impact of Periastron Epoch Change on Orbital Period Rate

[TrickyDicky]

How does the change in the epoch of periastron of the Hulse-Taylor pulsar, which accumulates in the last 35 years about 40 seconds of delay, relate to the rate of decrease of orbital period (orbital period rate of change) that amounts to approx. 76.5 microseconds per year?

 

[Drakkith]

Hrmm. Interesting. I've been looking up info on this for the past 30 min, but I don't know enough unfortunently. For example, what does Epoch of periastron mean exactly? The reference point in time for the closest approach of the two pulsars? And how does the orbital period effect that?

 

[TrickyDicky]

Hrmm. Interesting. I've been looking up info on this for the past 30 min, but I don't know enough unfortunently. For example, what does Epoch of periastron mean exactly? The reference point in time for the closest approach of the two pulsars? And how does the orbital period effect that?

Epoch of periastron refers to the shift in the time of arrival of the pulsar to the periastron, it is arriving now (well actually as of 2005) around 40 seconds earlier than in 1974- I wrote delay in the previous post but it is in fact the opposite, a time gain.
I just don't know how to reach this shift of more of a second per year from the yearly decrease of the orbit period of 76 millionths of a second.

http://upload.wikimedia.org/wikiped...450px-PSR_B1913+16_period_shift_graph.svg.png

 

[George Jones]

How does the change in the epoch of periastron of the Hulse-Taylor pulsar, which accumulates in the last 35 years about 40 seconds of delay,

Most of this is due to periastron shift predicted for orbits (e.g., the orbit of Mercury) by general relativity without taking into account gravitational radiation.

relate to the rate of decrease of orbital period (orbital period rate of change) that amounts to approx. 76.5 microseconds per year?

This is due to gravitational radiation

 

[TrickyDicky]

Most of this is due to periastron shift predicted for orbits (e.g., the orbit of Mercury) by general relativity without taking into account gravitational radiation.

No, that would be the periastron advance and is measured to be about 4.2 degrees per year, it advances in a single day by the same amount as Mercury's perihelion advances in a century.
The shift in the periastron time of arrival is the cumulated time over the years that the pulsar is observed to reach the periastron erlier than expected if its obit didn't decay, so it is a measure of orbital decay. I was trying to figure out the formula to get this shift from the decrease of orbital period observed which is about 76.5 millionths of a second per year.

see
http://en.wikipedia.org/wiki/PSR_B1913+16

 

[George Jones]

No, that would be the periastron advance and is measured to be about 4.2 degrees per year, it advances in a single day by the same amount as Mercury's perihelion advances in a century.
The shift in the periastron time of arrival is the cumulated time over the years that the pulsar is observed to reach the periastron erlier than expected if its obit didn't decay, so it is a measure of orbital decay. I was trying to figure out the formula to get this shift from the decrease of orbital period observed which is about 76.5 millionths of a second per year.

see
http://en.wikipedia.org/wiki/PSR_B1913+16

No, this is not correct. The Wikipedia link states

Orbital decay of PSR B1913+16. The data points indicate the observed change in the epoch of periastron with date while the parabola illustrates the theoretically expected change in epoch according to general relativity.

Here, "according to general relativity" means including periastron shift, orbital decay due to gravitational radiation, and other relativistic effects.

 

[TrickyDicky]

No, this is not correct.

What is not correct? I was talking about your confusing preccesion with orbital decay.
You said that periastron shift as referred to in the graphic I posted was due to an "orbit of mercury"-like effect, not related to gravitational radiation and I'm saying that on the contrary, the shift is just a way of showing the effects of gravitational radiation on orbital decay (both observed and predicted by GR).

Here, "according to general relativity" means including periastron shift, orbital decay due to gravitational radiation, and other relativistic effects.

Periastron shift as depicted in that graphic is just a way of measuring orbital decay.

 

[Drakkith]

So how does a reduced orbital period of 76.5 microseconds per year cause a 40 second delay in the time for the pulsars to reach periastron? Shouldn't it be reduced by the same amount as the orbital period? Or does some sort of relativity thing cause this?

Edit: I don't understand that precession has to do with this. Will the facing of the 2 pulsars towards us effect when/how we receive signals from them?

 

[TrickyDicky]

I found the answer to my question clearly explained in this page, specifically is addressed just after formula (63) of section 5.1.

http://relativity.livingreviews.org/Articles/lrr-2001-4/

 

[George Jones]

Periastron shift as depicted in that graphic is just a way of measuring orbital decay.

From An Introduction to Modern Astrophysics by Carroll and Ostlie

For example, recall from section 17.1 that as Mercury passes through the curved spacetime near the Sun, the position of perihelion in its orbit is shifted by 43" per century. For PSR 1913+16, general relativity predicts a similar shift in the point of periastron, where the two neutron stars are nearest each other. The theoretical value is in excellent agreement with the measurement of 4.226595 +/- 0.000005 degrees/year. This effect on the orbit is cumulative; with every orbit, the pulsar arrives later and later at the point of periastron. Figure 18.29 shows the incredible agreement between theoretical and observed values of the accumulating time delay.

Figure 18.29 is the same as

http://upload.wikimedia.org/wikiped...450px-PSR_B1913+16_period_shift_graph.svg.png.

General Relativity with Applications to Astrophysics by Straumann gives a very detailed and complicated treatment of the Hulse-Taylor pulsar. Straumann derives a modified periastron aprecession equation that includes the effect of gravitational radiation damping. Straumann then writes an approximate equation for cummualtive time difference,

T_n - nP = \frac{\dot{P}}{2P} T_n^2 .

Here, T_n is the time of the nth periastron (with T_0 = 0 at the start of the data for the Hulse-Taylor pulsar) and P is the orbital period of the pulsar. Putting T_n = 30 years, P = 7.75 hours,and Pdot = -2.40 x 10^-12 into this approximate equation gives

T_n - nP = \frac{-2.40 \times 10^{-12}}{2 \times 7.75 \times 3600} \times \left(30 \times 3600 \times 24 \times 365.25 \right)^2 = - 39s .

 

[TrickyDicky]

So how does a reduced orbital period of 76.5 microseconds per year cause a 40 second delay in the time for the pulsars to reach periastron? Shouldn't it be reduced by the same amount as the orbital period? Or does some sort of relativity thing cause this?

I explained that it was not a delay but a time gain in my second post.

Edit: I don't understand that precession has to do with this. Will the facing of the 2 pulsars towards us effect when/how we receive signals from them?

To avoid confusions, we should differentiate two diferent types of precession, one of them, the rotation of the periastron similar to the perihelium advance of Mercury I already mentioned is not directly related to my OP.
The other,Geodetic precession however has to be accounted for, and actually is the reason we might lose sight of the pulsar beam around 2020.

 

[TrickyDicky]

From An Introduction to Modern Astrophysics by Carroll and Ostlie


Figure 18.29 is the same as

http://upload.wikimedia.org/wikiped...450px-PSR_B1913+16_period_shift_graph.svg.png.

General Relativity with Applications to Astrophysics by Straumann gives a very detailed and complicated treatment of the Hulse-Taylor pulsar. Straumann derives a modified periastron aprecession equation that includes the effect of gravitational radiation damping. Straumann then writes an approximate equation for cummualtive time difference,

T_n - nP = \frac{\dot{P}}{2P} T_n^2 .

Here, T_n is the time of the nth periastron (with T_0 = 0 at the start of the data for the Hulse-Taylor pulsar) and P is the orbital period of the pulsar. Putting T_n = 30 years, P = 7.75 hours,and Pdot = -2.40 x 10^-12 into this approximate equation gives

T_n - nP = \frac{-2.40 \times 10^{-12}}{2 \times 7.75 \times 3600} \times \left(30 \times 3600 \times 24 \times 365.25 \right)^2 = - 39s .

Thanks for the formula, I guess it is equivalent to the one I linked that instead of the periods uses the orbital frequencies that are just the inverse of the orbital periods.

Still as you can check for yourself the formula only uses orbital parameters that are unrelated to the 4.2 degrees of periastron precession which is rotation of the orbit, so I would say that what is cumulative is the orbital period rate of decrease: P derivative = -2.40 x 10^-12 s/s

 

[Drakkith]

To avoid confusions, we should differentiate two diferent types of precession, one of them, the rotation of the periastron similar to the perihelium advance of Mercury I already mentioned is not directly related to my OP.
The other,Geodetic precession however has to be accounted for, and actually is the reason we might lose sight of the pulsar beam around 2020.

I looked up Geodetic Precession, but I don't really understand it. I'll try to find some more info on this. Thanks!