Pulsar mass calculation doesn't make sense

Alright, I read this article on a newly discovered pulsar which is
notable because it is the fastest spinning X-ray pulsar ever discovered.
Here's a link to the article:
http://www.universetoday.com/am/publ...ng_pulsar.html

I was trying to do a simple calculation with the facts presented in the
article and it wasn't making any sense. Here are the relevant facts:

"The orbital period of the system is also impressive; the two stars
orbit each other every 2.5 hours, but are separated by roughly the same
distance as the Moon and the Earth. On the pulsar in IGR J00291+5934 a
day lasts 0.0016 seconds and a year is 147 minutes!"

Okay, so we have the orbital period of 147 x 60 = 8820 seconds. The
mean distance between the Moon and Earth is 384,400 km = 3.84e8 meters,
which is comparable to the distance between the pulsar and the other
star. So, now that we have these two facts, we can use Newton's form of
Kepler's Second Law to determine the total mass in the system:

(Period)^2 = 4pi^2/(G(m1 + m2)) x (Radius)^3

Okay, just plug in the numbers I've given and solve for (m1 + m2) and
you get:

(m1 + m2) = 4.32e29 kg

This number doesn't make any sense. The mass of Sol is 2e30 kg, so the
total mass of this pulsar-and-other-star system is supposed to be only
0.2 Solar masses? This doesn't make any sense. From my research on
pulsars they are at LEAST one Solar mass. And don't forget the other
star in this system.

It just doesn't add up. Either something in the article is wrong, or
I'm failing to take something in account. Would relativistic effects be
so notable as to make Newton's Law totally irrelevant?

Thanks for the help, guys. This article has been bugging me.

--
~ Cyde Weys ~
So say we all.

Cyde Weys wrote:

[snip]

This number doesn't make any sense. The mass of Sol is 2e30 kg, so
the
total mass of this pulsar-and-other-star system is supposed to be
only
0.2 Solar masses? This doesn't make any sense. From my research on
pulsars they are at LEAST one Solar mass. And don't forget the other

star in this system.

0.2 solar masses huh. Where is the problem?

The only problem I would see is if the mass is either absurdly small
[planetary] or absurdly large [beyond the Chandreskahar limit, ~1.6
solar masses]. Why don't you explain why 0.2 solar masses is too small
for a pulsar?


It just doesn't add up. Either something in the article is wrong, or

I'm failing to take something in account. Would relativistic effects
be
so notable as to make Newton's Law totally irrelevant?

The mass is off most likely because you are using Newton instead of GR.
That is is definetly a time where you don't want to use weak-field
approximations.


Thanks for the help, guys. This article has been bugging me.

It works for me. It is on the right side of the maximal mass of a
neutron star.


--
~ Cyde Weys ~
So say we all.

"(m1 + m2) = 4.32e29 kg
This number doesn't make any sense.
....
This doesn't make any sense.
From my research on pulsars
They are at LEAST one Solar mass.
And don't forget the other star in this system.

It just doesn't add up. Either something
In the article is wrong, or
I'm failing to take something in account.
Would relativistic
Effects be so notable as to make Newton's Law
Totally irrelevant?

Thanks for the help, guys.
This article has been
Bugging me."

~ Cyde Weys ~
So say we all.

"Try this ~ Repeat your sequence
Several times,
Add a few rhymes.
Offer a gesture of resignation, repeat this ~
After an instant's pause, straighten
Up. Spread your hands. Twist your upper
Body, as if searching the air
For nothing ~ Linger on your stair!
Accelerate, hold your partner, cup her
Butt, until your arrive, your tempo waiten ~
Same as when your jumpin'
Began ~

Repeat, again ~
Motion antiphonal ~ An interrupted-spiral
Motif, folding inward, then exhale!

Your pulsar, or mass ejection, or
Change partner ~ !*"
~ Twittering

Eric Gisse wrote:
Cyde Weys wrote:

[snip]


This number doesn't make any sense. The mass of Sol is 2e30 kg, so
the
total mass of this pulsar-and-other-star system is supposed to be
only
0.2 Solar masses? This doesn't make any sense. From my research on
pulsars they are at LEAST one Solar mass. And don't forget the other
star in this system.


0.2 solar masses huh. Where is the problem?
The only problem I would see is if the mass is either absurdly small
[planetary] or absurdly large [beyond the Chandreskahar limit, ~1.6
solar masses]. Why don't you explain why 0.2 solar masses is too small
for a pulsar?

Pulsars are neutron stars. Neutron stars always have masses above
about 1.4 solar masses. If the mass were below that, it would be
a white dwarf, not a neutron star.

See e.g. he
http://pegasus.phast.umass.edu/a100/handouts/neutron/neutron.html

I think it's possible that a neutron star loses mass after its
formation, but I would think that as soon as its mass goes below
1.4 solar masses, the inner pressure would overcome the gravity of the
outer layers, the star would expand and become a white dwarf.


[snip]

Bye,
Bjoern

Cyde Weys wrote:
Alright, I read this article on a newly discovered pulsar which is
notable because it is the fastest spinning X-ray pulsar ever discovered.
Here's a link to the article:
http://www.universetoday.com/am/publ...ng_pulsar.html

I was trying to do a simple calculation with the facts presented in the
article and it wasn't making any sense. Here are the relevant facts:

"The orbital period of the system is also impressive; the two stars
orbit each other every 2.5 hours, but are separated by roughly the same
distance as the Moon and the Earth. On the pulsar in IGR J00291+5934 a
day lasts 0.0016 seconds and a year is 147 minutes!"

Okay, so we have the orbital period of 147 x 60 = 8820 seconds. The
mean distance between the Moon and Earth is 384,400 km = 3.84e8 meters,
which is comparable to the distance between the pulsar and the other
star. So, now that we have these two facts, we can use Newton's form of
Kepler's Second Law to determine the total mass in the system:

(Period)^2 = 4pi^2/(G(m1 + m2)) x (Radius)^3

Okay, just plug in the numbers I've given and solve for (m1 + m2) and
you get:

(m1 + m2) = 4.32e29 kg

This number doesn't make any sense. The mass of Sol is 2e30 kg, so the
total mass of this pulsar-and-other-star system is supposed to be only
0.2 Solar masses? This doesn't make any sense. From my research on
pulsars they are at LEAST one Solar mass. And don't forget the other
star in this system.

It just doesn't add up. Either something in the article is wrong, or
I'm failing to take something in account. Would relativistic effects be
so notable as to make Newton's Law totally irrelevant?

Thanks for the help, guys. This article has been bugging me.

Looking up the preprint linked to at the bottom of the article,
astro-ph/0501507, I don't find any mention of the distance between
the two stars. So I wonder where the author of this article got
it from. I suspect that when he wrote the story, he asked one of
the scientists about that and got an answer like "well, something
like the distance between the Moon and the Earth" (as a quick dirty
estimate), and misunderstood or misrepresented that to "roughly the
same distance as the Moon and the Earth". Such misreporting is quite
typical in popular science.

Actually, the distance is probably greater. Consider also that
the mass depends on the third power of the orbital radius - so
small changes in r give comparably large changes in m. You need
about 10 times the mass (2 solar masses would be a sensible result
instead of 0.2 solar masses), so a radius which is 10^(1/3) = 2.15
times larger would already suffice.

If you want to clear this up, I recommend to you first scanning the
preprint mentioned above more thoroughly than I did and see if you
can find anything about the distance there, and if you don't, mailing
the reporter and asking him where he got his numbers from, and what
these exactly were.


Bye,
Bjoern

Cyde Weys wrote:
Alright, I read this article on a newly discovered pulsar which is
notable because it is the fastest spinning X-ray pulsar ever discovered.
Here's a link to the article:
http://www.universetoday.com/am/publ...ng_pulsar.html

I was trying to do a simple calculation with the facts presented in the
article and it wasn't making any sense. Here are the relevant facts:

"The orbital period of the system is also impressive; the two stars
orbit each other every 2.5 hours, but are separated by roughly the same
distance as the Moon and the Earth. On the pulsar in IGR J00291+5934 a
day lasts 0.0016 seconds and a year is 147 minutes!"

Okay, so we have the orbital period of 147 x 60 = 8820 seconds. The
mean distance between the Moon and Earth is 384,400 km = 3.84e8 meters,
which is comparable to the distance between the pulsar and the other
star. So, now that we have these two facts, we can use Newton's form of
Kepler's Second Law to determine the total mass in the system:

(Period)^2 = 4pi^2/(G(m1 + m2)) x (Radius)^3

Okay, just plug in the numbers I've given and solve for (m1 + m2) and
you get:

(m1 + m2) = 4.32e29 kg

This number doesn't make any sense. The mass of Sol is 2e30 kg, so the
total mass of this pulsar-and-other-star system is supposed to be only
0.2 Solar masses? This doesn't make any sense. From my research on
pulsars they are at LEAST one Solar mass. And don't forget the other
star in this system.

It just doesn't add up. Either something in the article is wrong, or
I'm failing to take something in account. Would relativistic effects be
so notable as to make Newton's Law totally irrelevant?

Thanks for the help, guys. This article has been bugging me.


((4 * (pi^2) * ((384 000 000^3) (m^3))) / G) / ((8 820^2) (s^2)) = 4.3062091 × 10^29 kilograms

Either your period or the radius is in error for masses that include a
neutron star as the minimum neutron star mass is greater than
solar mass * 1.44 = 2.8640448 × 10^30 kilograms

Increasing the distance a bit, say 950,000 km works for two neutron stars
orbiting each other with a total mass of 3.14852462 solar masses or
6.26216359 × 10^30 kilograms

"Bjoern Feuerbacher" wrote in message
...
Eric Gisse wrote:
Cyde Weys wrote:

[snip]


This number doesn't make any sense. The mass of Sol is 2e30 kg, so
the
total mass of this pulsar-and-other-star system is supposed to be
only
0.2 Solar masses? This doesn't make any sense. From my research on
pulsars they are at LEAST one Solar mass. And don't forget the other
star in this system.


0.2 solar masses huh. Where is the problem?
The only problem I would see is if the mass is either absurdly small
[planetary] or absurdly large [beyond the Chandreskahar limit, ~1.6
solar masses]. Why don't you explain why 0.2 solar masses is too small
for a pulsar?

Pulsars are neutron stars. Neutron stars always have masses above
about 1.4 solar masses.

Is that the current mass or its original mass (before mass loss due to a
lifetime of radiation and collapse into a neutron star).

If the mass were below that, it would be a white dwarf, not a neutron
star.

....

--
---------------------------------------------------------------
Michael J. Strickland
Quality Services
703-560-7380
---------------------------------------------------------------

Michael J. Strickland wrote:
"Bjoern Feuerbacher" wrote in message
...

Eric Gisse wrote:

Cyde Weys wrote:

[snip]



This number doesn't make any sense. The mass of Sol is 2e30 kg, so
the
total mass of this pulsar-and-other-star system is supposed to be
only
0.2 Solar masses? This doesn't make any sense. From my research on
pulsars they are at LEAST one Solar mass. And don't forget the other
star in this system.


0.2 solar masses huh. Where is the problem?
The only problem I would see is if the mass is either absurdly small
[planetary] or absurdly large [beyond the Chandreskahar limit, ~1.6
solar masses]. Why don't you explain why 0.2 solar masses is too small
for a pulsar?

Pulsars are neutron stars. Neutron stars always have masses above
about 1.4 solar masses.


Is that the current mass or its original mass (before mass loss due to a
lifetime of radiation and collapse into a neutron star).

IIRC, the mass which the neutron star actually has.

[snip]


Bye,
Bjoern

Bjoern Feuerbacher wrote:
Eric Gisse wrote:
Cyde Weys wrote:

[snip]


This number doesn't make any sense. The mass of Sol is 2e30 kg, so
the
total mass of this pulsar-and-other-star system is supposed to be
only
0.2 Solar masses? This doesn't make any sense. From my research
on
pulsars they are at LEAST one Solar mass. And don't forget the
other
star in this system.


0.2 solar masses huh. Where is the problem?
The only problem I would see is if the mass is either absurdly
small
[planetary] or absurdly large [beyond the Chandreskahar limit, ~1.6
solar masses]. Why don't you explain why 0.2 solar masses is too
small
for a pulsar?

Pulsars are neutron stars. Neutron stars always have masses above
about 1.4 solar masses. If the mass were below that, it would be
a white dwarf, not a neutron star.

Wh-ooops.

Wrong mass range. Thanks!


See e.g. he
http://pegasus.phast.umass.edu/a100/handouts/neutron/neutron.html

I think it's possible that a neutron star loses mass after its
formation, but I would think that as soon as its mass goes below
1.4 solar masses, the inner pressure would overcome the gravity of
the
outer layers, the star would expand and become a white dwarf.


[snip]

Bye,
Bjoern

Sam Wormley wrote:

Cyde Weys wrote:
Alright, I read this article on a newly discovered pulsar which is
notable because it is the fastest spinning X-ray pulsar ever discovered.
Here's a link to the article:
http://www.universetoday.com/am/publ...ng_pulsar.html


snip

(m1 + m2) = 4.32e29 kg

This number doesn't make any sense. The mass of Sol is 2e30 kg, so the
total mass of this pulsar-and-other-star system is supposed to be only
0.2 Solar masses? This doesn't make any sense. From my research on
pulsars they are at LEAST one Solar mass. And don't forget the other
star in this system.

snip

((4 * (pi^2) * ((384 000 000^3) (m^3))) / G) / ((8 820^2) (s^2)) = 4.3062091 x 10^29 kilograms

Either your period or the radius is in error for masses that include a
neutron star as the minimum neutron star mass is greater than
solar mass * 1.44 = 2.8640448 x 10^30 kilograms

You might be going just a little overboard with those 'significant'
figures! Anyway, according to the _Astronomy & Astrophysics_ paper
cited in the article the orbital period is quite precisely known: the
figure given (citing in turn Markwardt _et al._, 2004, _The
Astronomer's Telegram_, 360) is 147.412 +/- .006 min. (Why do they
use minutes?) I couldn't find any mention of the radius in the paper,
so I'm inclined to go along with Bjeorn's hypothesis that "separated
by roughly the same distance as the Moon and the Earth" came from
somebody's off-the-cuff, order-of-magnitude 'guesstimate'.

Increasing the distance a bit, say 950,000 km works for two neutron stars
orbiting each other with a total mass of 3.14852462 solar masses or
6.26216359 x 10^30 kilograms

Give or take roughly the same mass as the Moon's, eh?

--
Odysseus