Lowest/Highest mass of a star, star system

[Stephanus]

Dear PF Forum,
My friend just tell me about Kelt - 4A.
Kelt - 4A orbits 3 stars.
I think such thing is not uncommon in the universe for binary/ternary systems. It's a matter of probability.
Probability means that for any system there can be many celestial objects. So how many percent do they have two celestial objects in a system where both are greater than the lowest possible mass of a star.

Now, what I want to ask is this.
1: What is the lowest mass of a star? 10 Jupiter mass? 100 Jupiter mass?
2: What is the higest mass of a star?
Last year, in PF a mentor/staff/advisor told me that a star can't be bigger than 200 (or 1000?) solar mass.
Even in this scenario he/she said.
If there's a nebula, say 1 million solar mass, then the star won't be 1 million solar mass. It is in 200 (or 1000?) solar mass. Because of the strong star wind the expell the material.
Okay.. I can picture this. So there's a star inside the nebulae and the rest 999,000 solar mass is not part of the star.
But what is the definition of a star anyway?
A celestial object that fuses hydrogen to helium (in main sequence), and helium and carbon up to iron?
So not all the material in that nebulae can be called a star because not all material undergo fusion?
And if so, why we call the sun is 1 solar mass star? Because if I'm not mistaken, only the core of the sun fuses hydrogen. And its mass is only 30% of the sun.
So what I want to ask in number question number 2 is this.
If, there's a nebulae 1 million solar mass, why can't there be a star 1 million solar mass? All the material will be expeled by the explosion of the 1000 solar mas "star" (whatever we call it) inside it right?
Isn't that the case of the sun. That the sun can't crunch to 12000 km because there's a fusion inside it that keeps the sun from collapsing. And STILL we call the sun is 1 solar mass star although it's the core that sustain it.

Thanks for any reply.

 

[Drakkith]

So how many percent do they have two celestial objects in a system where both are greater than the lowest possible mass of a star.

If you're asking what percent of star systems are binary systems, then the percent is fairly high. This link claims that the percentage of stars in some form of multiple-star system might be as high as 85%.

1: What is the lowest mass of a star? 10 Jupiter mass? 100 Jupiter mass?

The lowest mass for a star is around 80 Jupiter masses. Below that, the object cannot fuse hydrogen-1 in its core, though it may fuse lithium and deuterium, which are much easier to fuse than hydrogen-1.

2: What is the higest mass of a star?
Last year, in PF a mentor/staff/advisor told me that a star can't be bigger than 200 (or 1000?) solar mass.

There's no hard upper limit that I know of, but stars are constrained by the fact that as they form and heat up, their radiation pushes away the in-falling gas and dust. This probably puts a soft limit on the high mass for a star, as past a certain point, the gas simply can't collapse fast enough to become part of the star before being blown away.

But what is the definition of a star anyway?
A celestial object that fuses hydrogen to helium (in main sequence), and helium and carbon up to iron?

A luminous object composed of gas and plasma held together by its own gravity and able to fuse hydrogen-1 in its core, generating the energy required to shine for millions to billions of years. Objects which meet the first criteria but not the second are not stars, but are substellar objects. An obvious example is a brown dwarf, but I've seen some other odd examples.

And if so, why we call the sun is 1 solar mass star? Because if I'm not mistaken, only the core of the sun fuses hydrogen. And its mass is only 30% of the sun.

Because the Sun is not made up of only a core, but of many different layers. It is also practical, as it is relatively easy to measure the mass of a star as a whole, but nearly impossible to measure the mass of just the core.

If, there's a nebulae 1 million solar mass, why can't there be a star 1 million solar mass? All the material will be expeled by the explosion of the 1000 solar mas "star" (whatever we call it) inside it right?

The actual formation process involves a huge gas cloud. When this cloud collapses under its own gravity it does not do so in a uniform manner. Fragmentation of the cloud occurs, which separates different areas of the cloud, each of which continues to collapse under its own gravity.

Isn't that the case of the sun. That the sun can't crunch to 12000 km because there's a fusion inside it that keeps the sun from collapsing.

Technically the Sun can't collapse any further because all that radiation and heat inside the core is pushing outwards on the Sun's outer layers, preventing them from collapsing. Fusion simply replaces the energy lost from the Sun. Once the Sun runs out of fuel, there is nothing to replace the energy radiated away from the Sun (which ultimately comes from the core) and this outward pressure and radiation drops, allowing the Sun to collapse. The actual process is quite complicated and non-intuitive (the collapse actually heats up the Sun?!?), so if you want to think of it as, "fusion keeps the Sun from collapsing", then go right ahead.

 

[Stephanus]

If you're asking what percent of star systems are binary systems, then the percent is fairly high. This link claims that the percentage of stars in some form of multiple-star system might be as high as 85%.

Actually I'm not asking how many percents systems are binary. But thanks for your answer. 85%? Wow, that high. So our sun with its 9 8 is uncommon I guess.

The lowest mass for a star is around 80 Jupiter masses. Below that, the object cannot fuse hydrogen-1 in its core, though it may fuse lithium and deuterium, which are much easier to fuse than hydrogen-1.

80 Jupiter mass? Ok
You say

A luminous object composed of gas and plasma held together by its own gravity and able to fuse hydrogen-1 in its core

Not just "A luminous object composed of gas and plasma held together by its own gravity and able to fuse any material in its core?"
Now, if it's about language then you're saying that a 10 solar mass "star" which fuses carbon is not star? It has to be hydrogen?
No, don't debate it. I get your point.
Okay about this lithium and deuterium fusion.
How (on earth) do the star has lithium to fuse if it doesn't fuse hydrogen at the first place? Perhaps 2nd generation star?
And even if it fuses lithium to generate light, it doesn't belong to the star category?

There's no hard upper limit that I know of, but stars are constrained by the fact that as they form and heat up, their radiation pushes away the in-falling gas and dust. This probably puts a soft limit on the high mass for a star, as past a certain point, the gas simply can't collapse fast enough to become part of the star before being blown away.

Soft limit, eh? Okay, if some mentor in PF says "soft limit" I can accept it.
Part of the star?
Sun structure are:
The core
Photosphere
Chromosphere
and
Corona
So, the rest of the nebulae can't be part of this because they're blown away by star wind, so the mass of the star is not the mass of the nebulae.
The mass of the star inside the nebulae is the core + the photosphere + the Chromosphere + the corona. Do I get it right?

Technically the Sun can't collapse any further because all that radiation and heat inside the core is pushing outwards on the Sun's outer layers, preventing them from collapsing. Fusion simply replaces the energy lost from the Sun. Once the Sun runs out of fuel, there is nothing to replace the energy radiated away from the Sun (which ultimately comes from the core) and this outward pressure and radiation drops, allowing the Sun to collapse. The actual process is quite complicated and non-intuitive (the collapse actually heats up the Sun?!?), so if you want to think of it as, "fusion keeps the Sun from collapsing", then go right ahead.

Yes. I have understood this part before. Our sun fate is white dwarf?
And if I can ask 1 more thing that just crossed my mind.
In 5 billions years in the future, how many percent of helium will our sun have when it's in white dwarf state? Now, it's 20%, right.

Thanks

[Add: Sol can't fuse helium, right]

 

[Janus]

[Add: Sol can't fuse helium, right]

Sol will be fusing helium when it swells to its Red giant stage.

 

[Drakkith]

Actually I'm not asking how many percents systems are binary. But thanks for your answer. 85%? Wow, that high. So our sun with its 9 8 is uncommon I guess.

My mistake. I must have misunderstood your post. What were you asking about?

Not just "A luminous object composed of gas and plasma held together by its own gravity and able to fuse any material in its core?"
Now, if it's about language then you're saying that a 10 solar mass "star" which fuses carbon is not star? It has to be hydrogen?

A star that fuses carbon did not start out that way. It started out on the main sequence fusing hydrogen in its core. So the definition of a star could be modified to say, "that fused hydrogen-1 at some point in its life".

How (on earth) do the star has lithium to fuse if it doesn't fuse hydrogen at the first place? Perhaps 2nd generation star?
And even if it fuses lithium to generate light, it doesn't belong to the star category?

Indeed. The lithium is already present in the nebula prior to the formation of the star. But just because these objects burn lithium doesn't mean they are stars. We have purposely defined a star as an object which fuses hydrogen-1 in its core. This is because objects which do not fuse hydrogen-1 are, in general, significantly different than those which do. Note that deuterium fusion actually has no hard cutoff. From wikipedia's article on brown dwarfs: https://en.wikipedia.org/wiki/Brown_dwarf

Currently, the International Astronomical Union considers an object with a mass above the limiting mass for thermonuclear fusion of deuterium (currently calculated to be 13 MJ for objects of solar metallicity) to be a brown dwarf, whereas an object under that mass (and orbiting a star or stellar remnant) is considered a planet.[27]

The 13 Jupiter-mass cutoff is a rule of thumb rather than something of precise physical significance. Larger objects will burn most of their deuterium and smaller ones will burn only a little, and the 13 Jupiter mass value is somewhere in between.

So even objects lower than 13 Jupiter masses may burn deuterium at some point in their lives, but will quickly fall below the temperature necessary to continue burning it.

So, the rest of the nebulae can't be part of this because they're blown away by star wind, so the mass of the star is not the mass of the nebulae.
The mass of the star inside the nebulae is the core + the photosphere + the Chromosphere + the corona. Do I get it right?

Pretty much.

Yes. I have understood this part before. Our sun fate is white dwarf?
And if I can ask 1 more thing that just crossed my mind.
In 5 billions years in the future, how many percent of helium will our sun have when it's in white dwarf state? Now, it's 20%, right.

Not sure. A 1 solar mass white dwarf should be composed primarily of carbon and oxygen, but may have a shell or atmosphere of helium and/or hydrogen. I don't know what the percentage of each of these elements would be.

 

[Stephanus]

Actually I'm not asking how many percents systems are binary. But thanks for your answer. 85%? Wow, that high. So our sun with its 9 8 is uncommon I guess.

I should have said. Our sun with 8 planets is uncommon

 

[Ratman]

Actually the fraction of binary stars is much lower. The more massive and luminous stars, such as most of the visible ones, tend to have stellar companions. But fun fact is that they are in the minority. The red dwarfs, which vastly outnumber sun-like and brighter stars, are mostly solitary.

And there is a cutoff for the most massive stars, thought at the moment it is not precisely known. Stellar behemoths known as Wolf-Rayet stars strip away their own outer layers due to immense radiation. Too massive star => too furious thermonuclear fusion => star disintegrates. I used to learn about the limit of 150–200 solar masses, but there is a monster in Large Magellanic Cloud (R136a1) with approx. 315 solar masses. It experiences immense mass loss, it is thought to have shed ~50 suns worth of mass until now, but it still does exist.

 

[rootone]

I should have said. Our sun with 8 planets is uncommon

So far our abilities to see small planets directly is very limited, almost all of those which have been positively confirmed are gas giants.
Smaller planets have been inferred by indirect methods such as a noticeable 'wobble' of the parent star, but that kind of thing is very easy to miss unless conditions are exactly right.
I would think that a hypothetical observer at 100ly from the solar system using our present level of technology, should see Jupiter and Saturn OK, but everything else I am doubtful.

 

[snorkack]

Counting the 8 nearest star systems to Sun:

1. Sun 1050
2. Alpha Centauri AB 1,2 triple (Proxima red dwarf)
3. Barnard´s Star - red dwarf
4. CN Leonis - red dwarf
5. Lalande 21185 - red dwarf
6. Sirius AB 2,06
7. Luyten 726-8 1,02 both red dwarfs
8. Ross 154 - red dwarf

And now counting the 8 nearest planetary systems to Sun:

1. Mercury -
2. Venus -
3. Earth 81
4. Mars 60 000 000
5. Jupiter 13 000
6. Saturn 4200
7. Uranus 25 000
8. Neptune 4800

What is not odd is the scarcity of planets small in mass compared to their star outside Solar Systems - small planets are hard to see.
What IS odd is scarcity of planetary systems close in mass in Solar System. 3 out of 8 nearest star systems contain a secondary with mass ratio of 2 or less. None of the 8 planetary systems in Solar System has a mass ratio under 81.

 

[Jenab2]

The text in the table below will appear properly collimated when shown in Lucida Console, Courier New, or some other fixed-width-character format. (Edit: Oops, no it won't. The forum software removed spaces between some of the columns.) Ignore the 99.999 entries. The numbers shown are output from my curvefits to other people's astrophysical data, with bits from multiple sources, one of them being

http://www.pas.rochester.edu/~emamajek/EEM_dwarf_UBVIJHK_colors_Teff.txt

Estimated Characteristics of Main Sequence Stars.
M/Ms R/Rs Mbol Teff MKK B-V BC tms(y)
0.08 0.10 13.3004 2582 M8 1.938 99.999 9.7377e+12
0.09 0.11 12.8509 2646 M8 1.909 99.999 7.8231e+12
0.10 0.13 12.4523 2704 M7 1.883 99.999 6.4318e+12
0.11 0.15 12.1007 2756 M7 1.859 99.999 5.3876e+12
0.12 0.16 11.7921 2803 M6 1.836 99.999 4.5831e+12
0.13 0.18 11.5228 2847 M6 1.815 99.999 3.9496e+12
0.14 0.20 11.2892 2887 M6 1.796 99.999 3.4413e+12
0.15 0.21 11.0878 2925 M5 1.778 99.999 3.0272e+12
0.16 0.22 10.9153 2960 M5 1.761 99.999 2.685e+12
0.17 0.23 10.7686 2993 M5 1.745 99.999 2.3988e+12
0.18 0.24 10.6447 3024 M5 1.730 99.999 2.1571e+12
0.19 0.25 10.5407 3054 M4 1.715 99.999 1.9508e+12
0.20 0.25 10.4539 3082 M4 1.702 99.999 1.7734e+12
0.21 0.26 10.3818 3108 M4 1.689 -2.597 1.6197e+12
0.22 0.26 10.3218 3134 M4 1.676 -2.531 1.4855e+12
0.23 0.26 10.2718 3158 M4 1.665 -2.469 1.3677e+12
0.24 0.26 10.2297 3181 M4 1.653 -2.412 1.2637e+12
M/Ms R/Rs Mbol Teff MKK B-V BC tms(y)
0.25 0.26 10.1935 3203 M3 1.642 -2.357 1.1714e+12
0.30 0.27 10.0420 3303 M3 1.594 -2.129 6.5528e+11
0.35 0.28 9.8280 3387 M3 1.554 -1.951 3.6662e+11
0.40 0.31 9.4728 3460 M3 1.519 -1.809 2.0557e+11
0.45 0.38 8.9907 3524 M2 1.489 -1.691 1.1787e+11
0.50 0.46 8.4887 3581 M2 1.462 -1.591 8.2335e+10
0.55 0.49 8.0638 3847 M0 1.341 -1.192 5.7719e+10
0.60 0.57 7.6390 3936 K9 1.302 -1.079 4.3009e+10
0.65 0.64 7.2141 4071 K7 1.243 -0.923 3.2855e+10
0.70 0.69 6.7892 4343 K5 1.131 -0.665 2.5729e+10
0.75 0.71 6.3644 4700 K4 0.994 -0.409 2.0656e+10
0.80 0.76 6.0120 4948 K2 0.907 -0.278 1.7e+10
0.85 0.81 5.6733 5168 K1 0.833 -0.186 1.4343e+10
0.90 0.87 5.3484 5378 G9 0.767 -0.116 1.2406e+10
0.95 0.93 5.0373 5583 G6 0.706 -0.062 1.1001e+10
1.00 1.00 4.7400 5770 G2 0.654 -0.024 1e+10
1.05 1.09 4.4934 5861 G1 0.629 -0.009 8.3664e+09
1.10 1.17 4.2619 5959 G0 0.603 0.005 7.0817e+09
1.15 1.25 4.0438 6063 F9 0.576 0.018 6.0567e+09
1.20 1.32 3.8378 6175 F7 0.549 0.029 5.2276e+09
1.25 1.39 3.6424 6292 F6 0.521 0.038 4.5484e+09
1.30 1.46 3.4563 6415 F5 0.492 0.045 3.9854e+09
1.35 1.52 3.2786 6544 F4 0.463 0.050 3.5137e+09
1.40 1.58 3.1081 6679 F3 0.434 0.052 3.1145e+09
1.45 1.64 2.9442 6818 F2 0.405 0.052 2.7737e+09
1.50 1.69 2.7861 6963 F1 0.376 0.050 2.4806e+09
1.55 1.74 2.6334 7112 F0 0.347 0.044 2.2268e+09
1.60 1.78 2.4855 7265 F0 0.319 0.037 2.006e+09
1.65 1.82 2.3423 7421 A9 0.292 0.027 1.813e+09
1.70 1.86 2.2036 7582 A8 0.265 0.015 1.6439e+09
1.75 1.90 2.0694 7746 A7 0.238 0.001 1.4955e+09
1.80 1.93 1.9399 7913 A6 0.213 -0.016 1.3653e+09
1.85 1.96 1.8153 8083 A6 0.188 -0.034 1.2512e+09
1.90 1.98 1.6962 8255 A5 0.164 -0.054 1.1515e+09
1.95 2.01 1.5831 8429 A4 0.141 -0.075 1.0648e+09
M/Ms R/Rs Mbol Teff MKK B-V BC tms(y)
2.00 2.02 1.4766 8606 A3 0.119 -0.098 9.901e+08
2.50 2.17 0.6086 10133 A0 -0.031 -0.330 5.5638e+08
3.00 2.31 -0.1007 11562 B9 -0.121 -0.569 3.4742e+08
3.50 2.45 -0.7003 12900 B7 -0.140 -0.793 2.3331e+08
4.00 2.59 -1.2198 14152 B7 -0.156 -0.996 1.6525e+08
4.50 2.72 -1.6780 15324 B6 -0.169 -1.178 1.2191e+08
5.00 2.86 -2.0878 16423 B5 -0.181 -1.342 9.2863e+07
5.50 3.01 -2.4586 17453 B3 -0.192 -1.488 7.2599e+07
6.00 3.16 -2.7971 18421 B3 -0.201 -1.621 5.7986e+07
6.50 3.31 -3.1084 19330 B2 -0.210 -1.741 4.7156e+07
7.00 3.46 -3.3967 20186 B2 -0.217 -1.851 3.8941e+07
7.50 3.62 -3.6651 20994 B2 -0.224 -1.951 3.2585e+07
8.00 3.79 -3.9162 21756 B2 -0.230 -2.044 2.7582e+07
8.50 3.96 -4.1520 22477 B2 -0.236 -2.129 2.3584e+07
9.00 4.13 -4.3744 23162 B2 -0.241 -2.208 2.0347e+07
9.50 4.30 -4.5847 23812 B2 -0.246 -2.282 1.7695e+07
10.00 4.48 -4.7842 24431 B1 -0.250 -2.352 1.5499e+07
M/Ms R/Rs Mbol Teff MKK B-V BC tms(y)
11.00 4.84 -5.1550 25589 B1 -0.258 -2.478 1.2117e+07
12.00 5.22 -5.4935 26654 B1 -0.265 -2.592 9.6782e+06
13.00 5.60 -5.8048 27642 B1 -0.272 -2.695 7.8706e+06
14.00 5.99 -6.0931 28564 B1 -0.277 -2.790 6.4995e+06
15.00 6.38 -6.3615 29427 B1 -0.283 -2.877 5.4386e+06
16.00 6.79 -6.6126 30233 B0 -0.287 -2.958 4.6035e+06
17.00 7.21 -6.8484 30982 B0 -0.291 -3.032 3.9363e+06
18.00 7.64 -7.0708 31666 B0 -0.295 -3.099 3.396e+06
19.00 8.11 -7.2811 32277 O9 -0.299 -3.159 2.9534e+06
20.00 8.60 -7.4806 32800 O9 -0.301 -3.209 2.5869e+06

 

[Stephanus]

Thanks for your table. I'll study it

 

[Stephanus]

The text in the table below will appear properly collimated when shown in Lucida Console, Courier New, or some other fixed-width-character format. (Edit: Oops, no it won't. The forum software removed spaces between some of the columns.) Ignore the 99.999 entries. The numbers shown are output from my curvefits to other people's astrophysical data, with bits from multiple sources, one of them being
http://www.pas.rochester.edu/~emamajek/EEM_dwarf_UBVIJHK_colors_Teff.txt
Estimated Characteristics of Main Sequence Stars.
M/Ms R/Rs Mbol Teff MKK B-V BC tms(y)
0.08 0.10 13.3004 2582 M8 1.938 99.999 9.7377e+12
0.09 0.11 12.8509 2646 M8 1.909 99.999 7.8231e+12...

Perhaps I can rearrange it more clearly.
M/Ms: 0.08
R/Rs: 0.10
Mbol: 13.3004
Teff: 2582
MKK: M8
B-V: 1.938
BC: 99.999
tms(y): 9.7377e+12
I'd like to know
What is M/Ms? Mass per solar mass?
R/Rs? Radius per solar radius?
And the other number?