Duration of H burning?
I.N. Galidakis
for the sun?
Wiki mentions an average lifespan of 10^10 years for sun-like stars, but this
includes the red-giant phase.
I am interested in knowing (roughly) when Hydrogen fuel gets exhausted as a
function of a sun-like star's lifespan, i.e. for stars with: Mass ~ M_{sol} and
Type ~ G2V.
Many thanks,
--
Ioannis
Sjouke Burry
Michael Toms
"I.N. Galidakis" <morp...@olympus.mons> wrote in message
news:1247795927.576946@athprx03...
Dave Typinski
There's more than one red giant phase. Hydrogen runs out at about 80%
total stellar lifespan, if you count a white dwarf as being "dead."
http://math.ucr.edu/home/baez/timeline.html#future
--
Dave
Yousuf Khan
"The Seven Ages of the Sun"
Hydrogen Burning Phase: 11 Gyr
First Red Giant Phase: 1.3 Gyr
Helium Burning Phase: 100 Myr
Second Red Giant Phase: 20 Myr
Unstable Pulsation Phase: 400,000 yr
Planetary Nebula Phase: 10,000 yr
White Dwarf Phase: forever...
http://www.astronomy.ohio-state.edu/~pogge/Lectures/vistas97.html
Yousuf Khan
sl...@ncsa.uiuc.edu
Very nice.
An interesting question is, how is the sun's energy output distributed
across these phases?
(What if, instead of physical time, you used fraction-of-total-
lifetime-luminosity as the
"clock" for timing these stages?)
The hydrogen-burning phase is much longer, but the luminosity goes
'way up at times
during the red giant phases.
A good way to look at this could be Bill Paxton's "EZ" stellar
evolution code:
http://www.kitp.ucsb.edu/~paxton/EZ-intro.html
Could be a fun project.
Andrew Usher
> An interesting question is, how is the sun's energy output distributed
> across these phases?
> (What if, instead of physical time, you used fraction-of-total-
> lifetime-luminosity as the
> "clock" for timing these stages?)
Consider that H to He produces much more energy per unit mass than any
other nuclear-burning stage. Therefore, the integrated luminosity in
each phase is roughly proportional to the mass of H burned.
Given this, it is easy to see that the integrated luminosity during
the main-sequence and later phases must be of the same order of
magnitude.
Andrew Usher
Steve Willner
Andrew Usher <k_over...@yahoo.com> writes:
>Consider that H to He produces much more energy per unit mass than any
>other nuclear-burning stage. Therefore, the integrated luminosity in
>each phase is roughly proportional to the mass of H burned.
Fair enough, though this neglects gravitational energy, which is
important in some types of supernovae.
>Given this, it is easy to see that the integrated luminosity during
>the main-sequence and later phases must be of the same order of
>magnitude.
But I don't see how this follows. For low-mass stars (approximately
solar mass and below), essentially all the hydrogen is burned in the
main sequence phase. The star doesn't evolve off the main sequence
until virtually all the hydrogen is gone. For high-mass stars, the
main sequence ends when the core mass reaches approximately a solar
mass, and obviously the fraction of hydrogen burned to that time
depends on the inital stellar mass. The amount of hydrogen burned
subsequently depends on how and when the star's life ends. Stars in
the few-solar-mass range expel a good deal of their hydrogen rather
than burn it. Massive stars (tens of solar masses and up) end by
going supernova and may have burned only a small fraction of their
hydrogen before they blow up.
The bottom line seems to be that low-mass stars emit most of their
luminosity during the main sequence phase, whereas high-mass stars
emit most of their luminosity in later phases. It wouldn't astonish
me, though, to find out I've overlooked something important.
--
Help keep our newsgroup healthy; please don't feed the trolls.
Steve Willner Phone 617-495-7123 swil...@cfa.harvard.edu
Cambridge, MA 02138 USA
Andrew Usher
> In article <ad65aadc-c3d0-4035...@e27g2000yqm.googlegroups.com>,
> >Given this, it is easy to see that the integrated luminosity during
> >the main-sequence and later phases must be of the same order of
> >magnitude.
>
> But I don't see how this follows. For low-mass stars (approximately
> solar mass and below), essentially all the hydrogen is burned in the
> main sequence phase. The star doesn't evolve off the main sequence
> until virtually all the hydrogen is gone.
This is not true. Virtually all the H _in the core_ is burned, but the
core (except in fully convective stars <0.4 Msun) is but a fraction of
the whole star. This core mass fraction, as I recall, reaches a
_minimum_ at the boundary between low- and intermediate-mass stars.
I regret I can't find any grid of stellar models including
composition; I know that I did see such once.
> For high-mass stars, the
> main sequence ends when the core mass reaches approximately a solar
> mass,
This isn't true either. In the case of stars that will become a
neutron star or black hole, the (helium) core exceeds considerably the
Chandrasekhar limit.
> The bottom line seems to be that low-mass stars emit most of their
> luminosity during the main sequence phase, whereas high-mass stars
> emit most of their luminosity in later phases. It wouldn't astonish
> me, though, to find out I've overlooked something important.
This can't be right. The most massive stars have a luminosity that
actually falls through their lifespan (Eddington limit and the star's
mass is shrinking), while they still spend at least 3/4 of their lives
on the MS. The trend (excluding the fully convective dwarfs) has to go
the opposite way.
Andrew Usher
Steve Willner
Andrew Usher <k_over...@yahoo.com> writes:
> Virtually all the H _in the core_ is burned, but the
>core (except in fully convective stars <0.4 Msun) is but a fraction of
>the whole star.
A quick estimate (solar luminosity * 10^10 yr / 0.01*M*c^2) suggests
the Sun will burn about half its hydrogen before leaving the main
sequence.
>> For high-mass stars, the
>> main sequence ends when the core mass reaches approximately a solar
>> mass,
>
>This isn't true either. In the case of stars that will become a
>neutron star or black hole, the (helium) core exceeds considerably the
>Chandrasekhar limit.
That's after the star has left the main sequence. Formation of the
helium core is what starts the post-main sequence phase.
>> The bottom line seems to be that low-mass stars emit most of their
>> luminosity during the main sequence phase, whereas high-mass stars
>> emit most of their luminosity in later phases. It wouldn't astonish
>> me, though, to find out I've overlooked something important.
>
>This can't be right. The most massive stars have a luminosity that
>actually falls through their lifespan (Eddington limit and the star's
>mass is shrinking), while they still spend at least 3/4 of their lives
>on the MS.
Only the _very_ most massive stars are Eddington-limited, and they
essentially don't have a main sequence phase at all. (They leave the
main sequence before or just after they've finished forming.)
Ordinary high-mass stars (30-100 solar masses) evolve at more or less
constant luminosity, and my memory is that the main sequence time is
not more than half the lifetime of the star (but I could easily be
mistaken here). However, most of the energy emitted by these stars
comes out in the supernova phase, powered largely by gravitational
collapse.
Andrew Usher
> In article <f302d63e-5305-4439...@b15g2000yqd.googlegroups.com>,
> Andrew Usher <k_over...@yahoo.com> writes:
> > Virtually all the H _in the core_ is burned, but the
> >core (except in fully convective stars <0.4 Msun) is but a fraction of
> >the whole star.
>
> A quick estimate (solar luminosity * 10^10 yr / 0.01*M*c^2) suggests
> the Sun will burn about half its hydrogen before leaving the main
> sequence.
Must be a bad estimate, because the correct numbers gives 9.5% in
10^10 yr.
(3.86e26 W)(1e10 yr)(3.16e7 s/yr)/(0.0071)(2.0e30 kg)(3.00e8 m/s)^2 =
0.095
This is on the order of what I expected for radiative-core stars.
> >This isn't true either. In the case of stars that will become a
> >neutron star or black hole, the (helium) core exceeds considerably the
> >Chandrasekhar limit.
>
> That's after the star has left the main sequence. Formation of the
> helium core is what starts the post-main sequence phase.
For convective-core stars the entire core exhausts its H at the same
time.
> >This can't be right. The most massive stars have a luminosity that
> >actually falls through their lifespan (Eddington limit and the star's
> >mass is shrinking), while they still spend at least 3/4 of their lives
> >on the MS.
>
> Only the _very_ most massive stars are Eddington-limited, and they
> essentially don't have a main sequence phase at all. (They leave the
> main sequence before or just after they've finished forming.)
I define the MS as lasting until a helium core forms. And I think it
is true (I remember reading) that WR stars are less luminous than they
were on the main sequence.
> Ordinary high-mass stars (30-100 solar masses) evolve at more or less
> constant luminosity, and my memory is that the main sequence time is
> not more than half the lifetime of the star (but I could easily be
> mistaken here).
This would prove my thesis even more than if it were 3/4.
> However, most of the energy emitted by these stars
> comes out in the supernova phase, powered largely by gravitational
> collapse.
Right.
Andrew Usher
Andrew Usher
> I define the MS as lasting until a helium core forms. And I think it
> is true (I remember reading) that WR stars are less luminous than they
> were on the main sequence.
Here: ftp://cdsarc.u-strasbg.fr/pub/cats/J/A+AS/96/269/table1
The second, third, and fourth columns are time, remaining mass, and
log L. Note that the star's MS lifetime is about 70% of the total.
Andrew Usher
Steve Willner
SW> the Sun will burn about half its hydrogen before leaving the main
SW> sequence.
In article <60283ca9-34d6-4030...@j21g2000yqe.googlegroups.com>,
Andrew Usher <k_over...@yahoo.com> writes:
>(3.86e26 W)(1e10 yr)(3.16e7 s/yr)/(0.0071)(2.0e30 kg)(3.00e8 m/s)^2 =
>0.095
OK, I stand corrected. I should have pulled out the calculator
instead of doing it in my head.
>> >This isn't true either. In the case of stars that will become a
>> >neutron star or black hole, the (helium) core exceeds considerably the
>> >Chandrasekhar limit.
>>
>> That's after the star has left the main sequence. Formation of the
>> helium core is what starts the post-main sequence phase.
>
>For convective-core stars the entire core exhausts its H at the same
>time.
The last is correct because the core is convective. I think you are
right that core mass is above the Chandrasekhar limit for stars that
will become black holes but not for ones that will become neutron
stars, but I'd have to check to be sure. The true answer may not be
known because mass loss is so poorly understood.
>> >This can't be right. The most massive stars have a luminosity that
>> >actually falls through their lifespan (Eddington limit and the star's
>> >mass is shrinking), while they still spend at least 3/4 of their lives
>> >on the MS.
>>
>> Only the _very_ most massive stars are Eddington-limited, and they
>> essentially don't have a main sequence phase at all. (They leave the
>> main sequence before or just after they've finished forming.)
>
>I define the MS as lasting until a helium core forms. And I think it
>is true (I remember reading) that WR stars are less luminous than they
>were on the main sequence.
The main sequence is usually defined observationally according to
surface gravity. That works fine for most stars -- there's a very
large change in surface gravity at some stage of evolution. This
change is very poorly defined for the most massive stars, though, and
it's a little arbitrary whether you say they spend all or none of
their lifetime on the main sequence. The reality is that both
internal and external properties change fairly continuously until
some spectacular things happen at the end.
But this is only a tiny fraction of all stars.
> Here: ftp://cdsarc.u-strasbg.fr/pub/cats/J/A+AS/96/269/table1
From Schaller et al. 1992 AApS 96, 269.
> The second, third, and fourth columns are time, remaining mass, and
> log L. Note that the star's MS lifetime is about 70% of the total.
It isn't clear how to define main sequence for a star this massive
(120 solar masses). At half its lifetime, the star has already lost
more than 10% of its mass (according to this model). Some would say
that means it has already evolved off the main sequence. Notice also
how fast the effective temperature (column 5) drops.
However, even looking at table5 for 25 solar masses, I agree with you
that main sequence lifetime is more than half the total, and
luminosity doesn't increase all that much as the star evolves. I
don't see an easy way to tell what fraction of hydrogen has been
burned at each stage (or what fraction of the star's eventual output
has been emitted), but the bottom line seems to be that you are
basically right that massive stars emit most of their _nuclear_
energy (i.e., not counting gravitational energy released by the
eventual supernova) during the main sequence phase.