Why are the 'Fixed Stars' so FIXED?

"Henri Wilson" HW@.... wrote in message
...
On Sat, 17 Feb 2007 14:22:20 -0000, "George Dishman"

wrote:
"Henri Wilson" HW@.... wrote in message
. ..
....
For the purposes of predicting brightness curves, I only have to
consider edge
on orbits. My 'yaw angle' is that for an edge on orbit. It is not the
conventional definition....but it works and it makes the programming
much
easier.

For elliptical orbits in general you have to consider
the angle between the major axis and the line of sight
which I guess is your yaw, but for J1909-3744 we can
ignore it.

If the orbit is near circular we can.

Eccentricity is 3*10^-7 so negligible.

Yes, what your program really tells you is v*sin(i)
(using the standard convention for inclination)
rather than v itself.

It doesn't tell me anything about v.

I FEED IN the measured value of maximum observed velocity (If I can get
it).

I don't think you quite understand the principle involved George.

Trial and error Henry, you feed what you think is the
true value of v*sin(i) and see whether the curves match
the observations. If not you alter the value until you
get a match and then you have found the value of v*sin(i).
At that point the predicted velocity curve should match
the published curve and you have found the true velocity
which takes into account the effect of ballistic theory
on the Doppler. Isn't that how you use it?

Not exactly.
Unless I have access to a reliable figure for the maximum radial velocity
I
cannot really come to a firm conclusion about distance or unification
rate.

But you cannot ever get that because the variable
speed messes up the Doppler equation. As with any
modelling technique, you put in your initial guess
of the actual parameters, the program caclulates
the observed signals and then you iterate until
the predicted observables match that actuals.

I really need three quantities, Vmax, distance and magnitude change. I can
determine yaw angle and orbit eccentricity when matching the basic SHAPE
of a
brightness curve ....if I have such a curve.

All that can ever be observed are the spectral shift
and brightness for normal stars or the PRF for pulsars.
none of your results are valid unless you are working
back from those.

Anyway, put the numbers into your program and tell
me what you get and then we can discuss their
interpretation. Check the results for zero distance
first and make sure you get the right speed and
phase.

Naturally for zero distance I get no brightness variation. The observed
velocity is in phase with the true velocity.

You should still get a very small variation due to
the conventional bunching you reminded me of at the
top.

Not if the observer is at the orbit centre.

George, I think you are refering to the pulses emitted by the pulsar
itself.
These will be observed to have a cyclic doppler shift.

The 'bunching of pulses' I refer to is not the same.

I will explain for the case of an orbiting star.

The program assumes the star emits identical pulses of light towards the
observer at regular intervals as it moves around its orbit...I can use
20000,
33000 or 60000 points per orbit. 30000 is usually enough to produce a
smooth
curve.

The pulses are assumed to move at (c+v)cos(a) towards a distant observer,
where
a is the angle between the orbit tangent and the LOS.

Rats! I assumed you would ignore the cos(a) term because
the orbit radius is much smaller than the distance to
the system so cos(a) ~ 1. Setting the distance to zero is
then equivalent to finding the rate that the pulses hit
a flat plane perpendicular to the line of sight say just
beyond the orbital radius and before any bunching can take
place, or having the right orbital speed but zero radius.

The program then
calculates the arrival times of all the pulses emitted over a number of
orbits
at the observer distance.
At any instant the pulse positions form a regular spatial pattern. As this
pattern moves past the observer, it gives the impression of brightness
variation. (dn/dt = dn/dx.dx/dt)

Thus, a bunching of pulses shows up as a brightness increase.

That's what I expected. At the distance where the
pulses first overlap (the fast ones catch the slow
ones) you get zero time between pulse arrivals hence
the inverse is an infinite number per second or
infinite brightness. It isn't really infinite as
there are only a finite number of pulses in the
stream but the calculation will go to very high
levels.

Brightness variations are converted to the conventional log output before
being
displayed on the screen.

Then increase the distance to 3 light years
but keep everything else the same and tell me how
the amplitude and phase change. Those two checks
should just confirm your software is working, after
that we can try the more interesting questions of
mass etc. and see if we can put some limits on the
extinction distance.

My software works.

We'll see.

It has been checked thoroughly. Many of the values have been watched
through
the program to see if they are correct.

It predicts brightness curves. Orbit inclination does not affect curve
shape.

I can predict the brightness curve of the dwarf companion. Where can I
find the
observed one?

There is no observed brightness variation reported
but that can probably only be taken to say any
variation is less than 1 mag, the existing single
measurements are no more accurate than that.

Most variations are around 1.5 mag or less.
...and yes, I don't have much faith in the accuracies of many published
figures.

It's not a question of faith, numbers are accurate
but in this case there have only been two measurements
made AFAICS by different groups at different times.
It doesn't really matter, your brightness increase
would just be the number of pulses per second because
each pulse essentially carries the same energy other
than a random variation from pulse to pulse due to
the nature of the source.

I'm not sure what it is you are asking me to do.

OK, let's do it in small steps so that I can
give you clear questions.

Common to all: set the eccentricity to zero, yaw
becomes irrelevant. Set the orbital period to
1.5334494503 days.

Step 1. Set the distance to zero (your sim should
reproduce the conventional theory) and set the
actual velocity to 27983 m/s.

Check that the observed velocity curve you get
matches that and that the maximum velocity is
90 degrees after conjunction.

That wont work.
'Zero distance' means 'at the orbit centre'. Radial velocity is zero...so
is
brightness variation.

....So I'm not with you at all, here.

Understandable, I made an assumption about your
software that wasn't correct. The orbital radius
is 1.9 light seconds so if you set the distance
to one light hour, there should be minimal
bunching as the critical distance (below) is
8 light years and cos(a) = 0.999999861. You
should get the conventional curves to 1 part
in 10^7.

Step 2. Increase the distance until you just get
the velocity curves going to infinity and tell me
what distance you get.

I assume you mean the 'brightness curves'.

Effectively yes. I should have said the speed goes
to c, not to infinity.

Consider the pulsar at four points in the orbit
round the barycentre '+':

D

A + C Earth

B

The diagram assumes the motion is anti-clockwise.

The highest acceleration towards Earth occurs at
point A. Look closer at two consecutive pulses
assuming they occur equally either side of A:

v - * ~ -- slow, c-v
A-(
* - v ~ -- fast, c+v

At the critical distance, the fast pulse just
catches the slow pulse after 8 light years so
they arrive simultaneously for an observer at
that distance.

Compare that with the conventional view. It says
the maximum Doppler would be at point B. For the
pulses to arrive simultanseously, the pulsar would
have to be moving at c to keep up with the first
pulse and emit the second alongside.

I am guessing that the critical distance should be
around 4 light years but let's see what your program
says before we get on to the more interesting stuff.

Period = 0.0042 years
Velocity = 0.0000933c

Critical distance = ~ 8 LYs.

See: http://www.users.bigpond.com/hewn/J1909-3744.jpg

Note that the observed velocity curve (red) is very different from the
real
curve (blue) at that distance.

I asked and you answered:

2) Have you corrected your program to show the velocity curve
that would be derived from the ballistic Doppler shift?[*]

Yes.

At the point where the brightness goes to infinity,
the time between pulses goes to zero and the velocity
curve (red I think) should peak at c. That should be
coincident with point A which should be where your
blue line crosses the white axis and is rising.

(I'm having some trouble producing the right colours with Vbasic on
windowsXP).

The colours are distinguishable on the jpeg so I that's
fine. The real concern is with the phase shift between
the blue and others. I'll have to give a little more
thought to the effect of propagation speed on arrival
time but have a think about what I'm saying and see if
you think your program is producing what I expect.

George