## A question about star's luminosity, temperature and mass.

My question is : if two stars have the same luminosity and temperature, do they have to be at the same mass and size?
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 Recognitions: Homework Help Science Advisor Typically yes - stars are pretty much blackbodies so their luminosity is a function of temperature and size. edit - Although that would only be absolutely true for luminosity in the same band - in theory it would be possible for a small hot star to put out the same total energy as a large cool star.
 Except for metallicity effects, which can cause stars of the same luminosity and temperature to have drastically different masses. Which was something I only realized, to my great consternation, about half-way through writing this one paper.

## A question about star's luminosity, temperature and mass.

If memory serves me correctly then. Luminosity = 4*pi*r^2*(boltzman constant)*T^4

(where t is temperature and r is the radius of the star).
 Whoa! I think it's far too rash to make these sweeping generalizations. The previous posters #2 #3 statements "absolutely true" or "true except for metallicity" are reckless. Stars with the same luminosity could have different sizes and masses for a lot of reasons. I think the age, composition, and the radiative or convective description of the star are paramount. I don't think luminosity is any simple function of a star's mass and size. I'll await an astrophysicist's verdicit on this one.

 Quote by Helios Whoa! I think it's far too rash to make these sweeping generalizations. The previous posters #2 #3 statements "absolutely true" or "true except for metallicity" are reckless. Stars with the same luminosity could have different sizes and masses for a lot of reasons. I think the age, composition, and the radiative or convective description of the star are paramount. I don't think luminosity is any simple function of a star's mass and size. I'll await an astrophysicist's verdicit on this one.
I have just consulted the Hertzsprung-Russell diagram . It can be an answer for this quest.
 Apologies for the late arrival, but now I am in a position of having to ask similar questions to this; I have the task of offering up 'plausible' (if not necessary hyper-accurate) stellar statistics based on only a few initial conditions: mass (and perhaps constituency of that mass in H, He, and metallicities) versus age (how long it has been around.) This nags me like knowing I know a word that is just beyond the tip of my tongue. I could use all these solar ratio based equations we have derived to 'guess' at a star's features, but it seems to me as though if you know initial mass you know everything. Initial gravity -> initial inward pressure -> required force to initiate fusion -> outward pressure from the energy released by said fusion -> hydrostatic equilibrium -> radius; meanwhile backtracking a bit, that released energy -> radius/surface area -> outward luminosity -> surface temperature. Oversimplistic perhaps, but is there anything missing here?

 Quote by ~jet Apologies for the late arrival, but now I am in a position of having to ask similar questions to this; I have the task of offering up 'plausible' (if not necessary hyper-accurate) stellar statistics based on only a few initial conditions: mass (and perhaps constituency of that mass in H, He, and metallicities) versus age (how long it has been around.) This nags me like knowing I know a word that is just beyond the tip of my tongue. I could use all these solar ratio based equations we have derived to 'guess' at a star's features, but it seems to me as though if you know initial mass you know everything. Initial gravity -> initial inward pressure -> required force to initiate fusion -> outward pressure from the energy released by said fusion -> hydrostatic equilibrium -> radius; meanwhile backtracking a bit, that released energy -> radius/surface area -> outward luminosity -> surface temperature. Oversimplistic perhaps, but is there anything missing here?
Opacity. Heavier elements in the core means it has to be hotter to fuse and thus fusion goes quicker. That's why stars get brighter as they age on the Main Sequence. Luminosity is usually a simple function of effective temperature and stellar photospheric area - but increased opacity in very cool stars changes that simple relation.
 Recognitions: Gold Member Science Advisor The fact stars can be binned in the H-R diagram suggests common denominators - such as mass and elemental composition. Low mass, high luminosity stars and high mass, low luminoisty stars are uncommon.

 Quote by qraal Opacity. Heavier elements in the core means it has to be hotter to fuse and thus fusion goes quicker. That's why stars get brighter as they age on the Main Sequence. Luminosity is usually a simple function of effective temperature and stellar photospheric area - but increased opacity in very cool stars changes that simple relation.
Makes sense; I shall investigate further. May have more questions after the fact =)

 Quote by Chronos The fact stars can be binned in the H-R diagram suggests common denominators - such as mass and elemental composition. Low mass, high luminosity stars and high mass, low luminoisty stars are uncommon.
Oh, I believe it; that's why I was surprised not to find a 'stellar' equation that could simply equate reasonably predictable stellar 'characteristics' based purely on initial mass and current age (the two details I will know at the outset of my programming.)
 Aside from opacity, would steadily decreasing mass (through dissemination of solar wind, energy, CMEs, etc) also technically increase a star's mass as it ages during its main sequence? Less gravity = less inward pressure = new hydrostatic equilibrium upwards = wider radius = more surface area to produce radiance = more luminosity. I realize that the difference might be slim, but can it be a factor? I've ready the sun is 20% brighter today than during its infancy.
 Mentor Whoa! If two stars have the same temperature and luminosity, they *must* have the same size. That's a consequence of stars being blackbodies, and has nothing to do with any energy generating mechanism. They do not have to have the exact same mass, although as a practical matter, it will be fairly close.
 Sure, but that's observing only the consequences of the mechanics going on rather than addressing them directly. If not for the energy inside producing resistance to a mass's overall gravity, you couldn't have a hydrostatic equilibrium determining said mass's radius at any given point in time.
 i think it's not always there, same luminosity and temperature does not make em of same size there are many stars in the universe which nearly as hot and as bright as the sun (the super red giants) but they are a way big than sun . and also there are starts who are as bright and luminous as proxima centauri but they are big in size . but if you mentioned the age factor also then it can be thought of
 Mentor Rishavutkarsh, I am sorry, but none of that is true. The luminosity of a star is determined by its radius and temperature.

 Quote by Vanadium 50 Rishavutkarsh, I am sorry, but none of that is true. The luminosity of a star is determined by its radius and temperature.
betelguese is brighter than sun ? sure it isn't it's just as luminous as proxima centauri but if the stages of life of two stars are also included then things can be said this way right?