beta-Perseus

Hi,
I wonder if anyone can help to supply or indicate where I can obtain
specific data on beta-Perseus?
I am particularly interested in the phase of the luminosity curve compared
to spectral velocity. During mid eclipse we would expect to find zero
velocity, and 180 degrees later zero once again, with +ve and -ve velocities
at +90 and -90 degrees. As a consequence of ellipticity and Kepler's second
law, the peak velocities may be advanced or retarded from 0 degrees, and it
is this data I seek.
Thanks in advance,
Androcles.

"Androcles" wrote in message
...
Hi,
I wonder if anyone can help to supply or indicate where I can obtain
specific data on beta-Perseus?
I am particularly interested in the phase of the luminosity curve compared
to spectral velocity. During mid eclipse we would expect to find zero
velocity, and 180 degrees later zero once again, with +ve and -ve
velocities
at +90 and -90 degrees. As a consequence of ellipticity and Kepler's
second
law, the peak velocities may be advanced or retarded from 0 degrees, and
it
is this data I seek.
Thanks in advance,
Androcles.



Beta Persei (Algol) is actually a triple system, with the familiar bright
star being eclipsed by a close companion every 2.867 d, and a third star
with a period of 1.862 yr.

The eccentricity of the close pair is low, e = 0.015. The orbit of AB
around the centre of mass with C has e = 0.23.

Reference: Hill, Barnes, Hutchings, Pearce, Astrophysical Journal 168, 443,
1971.

Apparently the eccentricity of AB, while low, is definitely non-zero, and
apsidal motion has been detected (the longitude of the major axis is
changing direction).
The system velocity of AB varies during the 1.8 yr cycle.

Things are therefore somewhat complicated but to a good approximation the
eclipses occur when the radial velocity of A is near the system velocity.

According to the reference, the spectrum of B has not been observed. Or if
it has, its radial velocity cannot be measured through the entire cycle.

--
Mike Dworetsky

(Remove "pants" spamblock to send e-mail)

"Mike Dworetsky" wrote in message
...
|
|
| "Androcles" wrote in message
| ...
| Hi,
| I wonder if anyone can help to supply or indicate where I can obtain
| specific data on beta-Perseus?
| I am particularly interested in the phase of the luminosity curve
compared
| to spectral velocity. During mid eclipse we would expect to find zero
| velocity, and 180 degrees later zero once again, with +ve and -ve
| velocities
| at +90 and -90 degrees. As a consequence of ellipticity and Kepler's
| second
| law, the peak velocities may be advanced or retarded from 0 degrees, and
| it
| is this data I seek.
| Thanks in advance,
| Androcles.
|
|
|
| Beta Persei (Algol) is actually a triple system, with the familiar bright
| star being eclipsed by a close companion every 2.867 d, and a third star
| with a period of 1.862 yr.

Hmm...
Quite a difference, 2.867 days and 1.862 years. It is really only the
shorter period close pair I'm interested in.


|
| The eccentricity of the close pair is low, e = 0.015. The orbit of AB
| around the centre of mass with C has e = 0.23.
|
| Reference: Hill, Barnes, Hutchings, Pearce, Astrophysical Journal 168,
443,
| 1971.
|
| Apparently the eccentricity of AB, while low, is definitely non-zero, and
| apsidal motion has been detected (the longitude of the major axis is
| changing direction).
| The system velocity of AB varies during the 1.8 yr cycle.
|
| Things are therefore somewhat complicated but to a good approximation the
| eclipses occur when the radial velocity of A is near the system velocity.
|
| According to the reference, the spectrum of B has not been observed. Or
if
| it has, its radial velocity cannot be measured through the entire cycle.
|
| --
| Mike Dworetsky
|
| (Remove "pants" spamblock to send e-mail)


This where I see a problem I'm trying to resolve.
The eclipse seems to be throughout 52 degrees of an almost circular orbit,
based on the duration of the eclipse (circa 10 hours out of 70 as I
understand it). This puts limits on the distance the stars can be apart.
Taking the diameter of the larger of the pair as 1, the smaller can be no
further than 4.56 stellar radii away, at which distance it would become of
equal size and therefore at any greater distance, the larger.
Refer to http://www.androc1es.pwp.blueyonder....golEclipse.JPG

Now you may ask why that should be a problem?
I refer now to
http://www.manybody.org/cgi-bin/starlab/binary_demo.pl
and by entering 4.56, 0.015, 1,1, 100 I get a period of 0.8 days.
2.867 days is observed. I would need to move the stars further apart (cannot
do and still retain 52 degrees of eclipse) or reduce mass to increase the
period, still retaining the diameter, thereby reducing their density.
I can come down to 0.077 solar masses for each and obtain the necessary
period, but I can't imagine a star being that tenuous and still be luminous.
By using unbalanced masses, we find the system has a short lifespan.
So, does the author of the page have his math right, or is there something
strange about the system?
I can calculate Kepler's third law just like anyone else, and I don't think
he does have his math wrong and I'd like for someone else to check.

So I conclude that something isn't right.

Again with a circular orbit, we would expect the maximum and minimum radial
velocities to be at +90 and -90 degrees. It is this information I seek,
because according to my model, the maximum and minimum radial velocities
will occur at +/- 26 degrees. If this is so, then we have a new model of
Algol.
Your comments please?
Androcles.

"Androcles" wrote in message
...

"Mike Dworetsky" wrote in message
...
|
|
| "Androcles" wrote in message
| ...
| Hi,
| I wonder if anyone can help to supply or indicate where I can obtain
| specific data on beta-Perseus?
| I am particularly interested in the phase of the luminosity curve
compared
| to spectral velocity. During mid eclipse we would expect to find zero
| velocity, and 180 degrees later zero once again, with +ve and -ve
| velocities
| at +90 and -90 degrees. As a consequence of ellipticity and Kepler's
| second
| law, the peak velocities may be advanced or retarded from 0 degrees,
and
| it
| is this data I seek.
| Thanks in advance,
| Androcles.
|
|
|
| Beta Persei (Algol) is actually a triple system, with the familiar
bright
| star being eclipsed by a close companion every 2.867 d, and a third star
| with a period of 1.862 yr.

Hmm...
Quite a difference, 2.867 days and 1.862 years. It is really only the
shorter period close pair I'm interested in.


|
| The eccentricity of the close pair is low, e = 0.015. The orbit of AB
| around the centre of mass with C has e = 0.23.
|
| Reference: Hill, Barnes, Hutchings, Pearce, Astrophysical Journal 168,
443,
| 1971.
|
| Apparently the eccentricity of AB, while low, is definitely non-zero,
and
| apsidal motion has been detected (the longitude of the major axis is
| changing direction).
| The system velocity of AB varies during the 1.8 yr cycle.
|
| Things are therefore somewhat complicated but to a good approximation
the
| eclipses occur when the radial velocity of A is near the system
velocity.
|
| According to the reference, the spectrum of B has not been observed. Or
if
| it has, its radial velocity cannot be measured through the entire cycle.
|
| --
| Mike Dworetsky
|
| (Remove "pants" spamblock to send e-mail)


This where I see a problem I'm trying to resolve.
The eclipse seems to be throughout 52 degrees of an almost circular orbit,
based on the duration of the eclipse (circa 10 hours out of 70 as I
understand it). This puts limits on the distance the stars can be apart.
Taking the diameter of the larger of the pair as 1, the smaller can be no
further than 4.56 stellar radii away, at which distance it would become of
equal size and therefore at any greater distance, the larger.
Refer to http://www.androc1es.pwp.blueyonder....golEclipse.JPG

Now you may ask why that should be a problem?
I refer now to
http://www.manybody.org/cgi-bin/starlab/binary_demo.pl
and by entering 4.56, 0.015, 1,1, 100 I get a period of 0.8 days.
2.867 days is observed. I would need to move the stars further apart
(cannot
do and still retain 52 degrees of eclipse) or reduce mass to increase the
period, still retaining the diameter, thereby reducing their density.
I can come down to 0.077 solar masses for each and obtain the necessary
period, but I can't imagine a star being that tenuous and still be
luminous.
By using unbalanced masses, we find the system has a short lifespan.
So, does the author of the page have his math right, or is there something
strange about the system?
I can calculate Kepler's third law just like anyone else, and I don't
think
he does have his math wrong and I'd like for someone else to check.

So I conclude that something isn't right.

Again with a circular orbit, we would expect the maximum and minimum
radial
velocities to be at +90 and -90 degrees. It is this information I seek,
because according to my model, the maximum and minimum radial velocities
will occur at +/- 26 degrees. If this is so, then we have a new model of
Algol.
Your comments please?
Androcles.



Here is what is wrong.

The masses of the A and B components are definitely not equal and are not
both 1 solar mass. There are some assumptions that need to be made about
the mass ratio to derive these figures, but B is large in diameter, cool,
faint, and much lower mass than A.

M(A) = 3.7, M(B) = 0.8, M(C) = 1.7. Yet, the eclipse model requires that
R(A) = 3, R(B) = 3.4.

I suspect the evolutionary software assumes both stars start on the main
sequence. But in Algol initially star B was more massive, evolved, and
transferred much of its mass to A, which grew. I do not think the program
allows for evolution at the starting point.

Eclipses are partial, not total, in Algol.

--
Mike Dworetsky

(Remove "pants" spamblock to send e-mail)

"Mike Dworetsky" wrote in message
...
| "Androcles" wrote in message
| ...
|
| "Mike Dworetsky" wrote in message
| ...
| |
| |
| | "Androcles" wrote in message
| | ...
| | Hi,
| | I wonder if anyone can help to supply or indicate where I can obtain
| | specific data on beta-Perseus?
| | I am particularly interested in the phase of the luminosity curve
| compared
| | to spectral velocity. During mid eclipse we would expect to find
zero
| | velocity, and 180 degrees later zero once again, with +ve and -ve
| | velocities
| | at +90 and -90 degrees. As a consequence of ellipticity and Kepler's
| | second
| | law, the peak velocities may be advanced or retarded from 0 degrees,
| and
| | it
| | is this data I seek.
| | Thanks in advance,
| | Androcles.
| |
| |
| |
| | Beta Persei (Algol) is actually a triple system, with the familiar
| bright
| | star being eclipsed by a close companion every 2.867 d, and a third
star
| | with a period of 1.862 yr.
|
| Hmm...
| Quite a difference, 2.867 days and 1.862 years. It is really only the
| shorter period close pair I'm interested in.
|
|
| |
| | The eccentricity of the close pair is low, e = 0.015. The orbit of AB
| | around the centre of mass with C has e = 0.23.
| |
| | Reference: Hill, Barnes, Hutchings, Pearce, Astrophysical Journal 168,
| 443,
| | 1971.
| |
| | Apparently the eccentricity of AB, while low, is definitely non-zero,
| and
| | apsidal motion has been detected (the longitude of the major axis is
| | changing direction).
| | The system velocity of AB varies during the 1.8 yr cycle.
| |
| | Things are therefore somewhat complicated but to a good approximation
| the
| | eclipses occur when the radial velocity of A is near the system
| velocity.
| |
| | According to the reference, the spectrum of B has not been observed.
Or
| if
| | it has, its radial velocity cannot be measured through the entire
cycle.
| |
| | --
| | Mike Dworetsky
| |
| | (Remove "pants" spamblock to send e-mail)
|
|
| This where I see a problem I'm trying to resolve.
| The eclipse seems to be throughout 52 degrees of an almost circular
orbit,
| based on the duration of the eclipse (circa 10 hours out of 70 as I
| understand it). This puts limits on the distance the stars can be apart.
| Taking the diameter of the larger of the pair as 1, the smaller can be
no
| further than 4.56 stellar radii away, at which distance it would become
of
| equal size and therefore at any greater distance, the larger.
| Refer to http://www.androc1es.pwp.blueyonder....golEclipse.JPG
|
| Now you may ask why that should be a problem?
| I refer now to
| http://www.manybody.org/cgi-bin/starlab/binary_demo.pl
| and by entering 4.56, 0.015, 1,1, 100 I get a period of 0.8 days.
| 2.867 days is observed. I would need to move the stars further apart
| (cannot
| do and still retain 52 degrees of eclipse) or reduce mass to increase
the
| period, still retaining the diameter, thereby reducing their density.
| I can come down to 0.077 solar masses for each and obtain the necessary
| period, but I can't imagine a star being that tenuous and still be
| luminous.
| By using unbalanced masses, we find the system has a short lifespan.
| So, does the author of the page have his math right, or is there
something
| strange about the system?
| I can calculate Kepler's third law just like anyone else, and I don't
| think
| he does have his math wrong and I'd like for someone else to check.
|
| So I conclude that something isn't right.
|
| Again with a circular orbit, we would expect the maximum and minimum
| radial
| velocities to be at +90 and -90 degrees. It is this information I seek,
| because according to my model, the maximum and minimum radial velocities
| will occur at +/- 26 degrees. If this is so, then we have a new model of
| Algol.
| Your comments please?
| Androcles.
|
|
|
| Here is what is wrong.
|
| The masses of the A and B components are definitely not equal and are not
| both 1 solar mass. There are some assumptions that need to be made about
| the mass ratio to derive these figures, but B is large in diameter, cool,
| faint, and much lower mass than A.
|
| M(A) = 3.7, M(B) = 0.8, M(C) = 1.7. Yet, the eclipse model requires that
| R(A) = 3, R(B) = 3.4.
|
| I suspect the evolutionary software assumes both stars start on the main
| sequence. But in Algol initially star B was more massive, evolved, and
| transferred much of its mass to A, which grew. I do not think the program
| allows for evolution at the starting point.
|
| Eclipses are partial, not total, in Algol.
|
| --
| Mike Dworetsky
|
| (Remove "pants" spamblock to send e-mail)

Ok, well, thanks for your effort. As I said above, the data I'm really
seeking is the velocity curve/luminosity curve and where/when max-min
velocity occurs in relation to the eclipse.
Androcles