Stellar Charactersitics

[DPSteve]

A question for all you smarter-than-me folks out there

Is there simplified formula or algorithm for coming up with the characteristics of a star based on it's classification (O B A F G K M) and it's mass?

For example, given a class B4 star, with a solar mass of 1.44, can one determine it's solar radius and luminosity?

I'm aware of the concept that luminosity is proportional to mass (L ~ M^3.5) but that only applies to main sequence stars. Rather, the M^3.5 seems to only apply to main sequence stars (Class V).

 

[rust]

I do not know a formula for the luminosity of a star, only one for its
radius, taken from GURPS Space 4 e:

R = (155,500 x square root of L) / T squared

where R is the radius, L is the luminosity and T the effective temperature
in Kelvin.

 

[EDG]

Not easily. A star's luminosity actually depends on its age as well as its mass - you can get (for example) F4 V stars that are different in mass and have different luminosities as a result.

 

[DPSteve]

Not easily. A star's luminosity actually depends on its age as well as its mass - you can get (for example) F4 V stars that are different in mass and have different luminosities as a result.

I figured as much. But if the mass is known, is it possible to generate radius and luminosity from that figure? I thought the 4 in an F4 V indicated age (at least partly), or is it an over simplification to say that an F4 is 40% of the way to a G0?

 

[Silvereye]

I'm not too sure whether there will be any crunchy maths, but the stars are catalogued by Spectrum, Heat and size.

Spectrum: (the hotter stars are at the top of the list)
Type O - intensley hot blue stars
Type B - cooler blue-white stars (e.g. Rigel)
Type A - cooler white stars (e.g. Deneb)
Type F - yellow-white stars (e.g. Polaris)
Type G - yellow stars (e.g. Sol)
Type K - orange stars (e.g. Aldebaran)
Type M - cool red stars (e.g. Barnard's Star)

There are also Type D (white dwarf), N and R (Carbon stars), S (Heavy metals) and something called a wolf-rayet which is a star thats had its outer materials stolen by a companion.

The numbers divide the spectrum into ten bands (0-9) with the lower the number meaning the hotter the star. F4 is hotter then F8.

Size: (roman numerals, the smaller the numeral the bigger the star)
I - Supergiant [Ia is brighter then Ib) (e.g. Betelgeuse)
II - Bright giant (e.g. Antares)
III - Giant (e.g. Pollux)
IV - Subgiant
V - Dwarf star (e.g. Vega)
Yopu may also see VI and VII which are subdwarfs

So Alpha Centauri is catalogued as G2V, K1V. Its a binary star system made up of very hot (2) yellow (G) dwarf (V) and a very hot (1) orange (K) dwarf (V). However the orange star will be a lot cooler then the yellow star.

In DPSteve's example above the F4 would actually be closer in heat to an A9 then the G0.

There's a pretty good wiki article on Stellar Classifications, however I don't know of any formula that can give you the size and temperature of a star. If you are just wanting to populate a system with bodies in about the right place, then the Titus-Bode relation might be of use as a guideline.

 

[DPSteve]

I'm not too sure whether there will be any crunchy maths, but the stars are catalogued by Spectrum, Heat and size.

Spectrum: (the hotter stars are at the top of the list)
Type O - intensley hot blue stars
Type B - cooler blue-white stars (e.g. Rigel)
Type A - cooler white stars (e.g. Deneb)
Type F - yellow-white stars (e.g. Polaris)
Type G - yellow stars (e.g. Sol)
Type K - orange stars (e.g. Aldebaran)
Type M - cool red stars (e.g. Barnard's Star)

There are also Type D (white dwarf), N and R (Carbon stars), S (Heavy metals) and something called a wolf-rayet which is a star thats had its outer materials stolen by a companion.

The numbers divide the spectrum into ten bands (0-9) with the lower the number meaning the hotter the star. F4 is hotter then F8.

Size: (roman numerals, the smaller the numeral the bigger the star)
I - Supergiant [Ia is brighter then Ib) (e.g. Betelgeuse)
II - Bright giant (e.g. Antares)
III - Giant (e.g. Pollux)
IV - Subgiant
V - Dwarf star (e.g. Vega)
Yopu may also see VI and VII which are subdwarfs

So Alpha Centauri is catalogued as G2V, K1V. Its a binary star system made up of very hot (2) yellow (G) dwarf (V) and a very hot (1) orange (K) dwarf (V). However the orange star will be a lot cooler then the yellow star.

In DPSteve's example above the F4 would actually be closer in heat to an A9 then the G0.

There's a pretty good wiki article on Stellar Classifications, however I don't know of any formula that can give you the size and temperature of a star.

I was already aware of the relationship between O B A F G K M, as well as the sub-classifications. I actually pull a lot of data from that Wiki page you linked. Thank you though

If you are just wanting to populate a system with bodies in about the right place, then the Titus-Bode relation might be of use as a guideline.

This I will look into, although it is not of immediate use to my current situation.

Thank you, I appreciate the input

 

[EDG]

Titius-Bode is pretty bunk actually. There may be a relation between orbits due to resonances etc, but it's not really all that predictable.

This article I wrote may also be useful as a primer on how stars evolve: http://evildrganymede.net/rpg/world/stellar.htm

 

[Gaidheal]

I've just realized... I know you. :¬)

 

[BP]

Well, since the classifications are broad, the technical answer is no (for the given data)...

But some generalizations can be made (I believe this was done in CT Book 6 Scouts which has tables for Lum, Temp, Radius and mass based on spectral class and subclass).

Ok, my data (and neurons ) may be out of date... but:

Look at an H-R Diagram - that should give you ballpark Luminosity and Temp based on spectral class, then use these to determine radius...

From some old notes of mine (> 20yrs) I have:

Luminosity = [Surface Area] x C x Te^4

Where C is Stephan's constant (5.67x10^-8 - look that up) and Te is Effective Temperature (of stellar surface) - which gets raised to the fourth power (Te x Te x Te x Te)

[Surface Area] is 4 x Pi (3.14159...) x Radius x Radius

Thus you could get Radius from the Luminosity and Temperature (likewise the temp of the sun was estimated in this way...):

R = square root(L / (4 x Pi C x Te^4))

The metric units would be Kelvin, meters and watts, though conversions to Solar Radi/Lum. would be simpler.

The Luminosity here would be total (bolo) and this is simply a black body equation giving the 'power' output based on the Harvard classifications...

There is a lot of slop in these type of things - as there are in most astronomy measurements due to the scales we are dealing with and the limitations of our current measuring devices (the spectral classes and Magnitudes hark back to subjective naked eye measurements) - we don't even have anything but fuzzy pictures yet of Pluto's atmosphere - much less Stellar bodies other than our own sun (past a certain relatively tiny number of lightyears, our estimates of stellar distances are given as +/- 50%)...

The equations themselves are simple (and simplifications, truth be told) that basically work - but the measurements are another story - and as EDG I believe pointed out - Luminosity depends on a number of factors (and is not actually static). For instance, the above equation assumes a perfect sphere - and certainly would be off in the event of major flare activity and stars distorted by motion/gravity. For the swag of Stellar Classifications and RPG it should suffice...

 

[DPSteve]

Well, since the classifications are broad, the technical answer is no (for the given data)...

But some generalizations can be made (I believe this was done in CT Book 6 Scouts which has tables for Lum, Temp, Radius and mass based on spectral class and subclass).

Ok, my data (and neurons ) may be out of date... but:

Look at an H-R Diagram - that should give you ballpark Luminosity and Temp based on spectral class, then use these to determine radius...

From some old notes of mine (> 20yrs) I have:

Luminosity = [Surface Area] x C x Te^4

Where C is Stephan's constant (5.67x10^-8 - look that up) and Te is Effective Temperature (of stellar surface) - which gets raised to the fourth power (Te x Te x Te x Te)

[Surface Area] is 4 x Pi (3.14159...) x Radius x Radius

Thus you could get Radius from the Luminosity and Temperature (likewise the temp of the sun was estimated in this way...):

R = square root(L / (4 x Pi C x Te^4))

The metric units would be Kelvin, meters and watts, though conversions to Solar Radi/Lum. would be simpler.

The Luminosity here would be total (bolo) and this is simply a black body equation giving the 'power' output based on the Harvard classifications...

There is a lot of slop in these type of things - as there are in most astronomy measurements due to the scales we are dealing with and the limitations of our current measuring devices (the spectral classes and Magnitudes hark back to subjective naked eye measurements) - we don't even have anything but fuzzy pictures yet of Pluto's atmosphere - much less Stellar bodies other than our own sun (past a certain relatively tiny number of lightyears, our estimates of stellar distances are given as +/- 50%)...

The equations themselves are simple (and simplifications, truth be told) that basically work - but the measurements are another story - and as EDG I believe pointed out - Luminosity depends on a number of factors (and is not actually static). For instance, the above equation assumes a perfect sphere - and certainly would be off in the event of major flare activity and stars distorted by motion/gravity. For the swag of Stellar Classifications and RPG it should suffice...

Thank you, that's extremely helpful. I'm not looking for complete accuracy, just enough to make it semi-believable and realistic, so as you say:

For the swag of Stellar Classifications and RPG it should suffice...

 

[BP]

Sure No Problem! - just to note that rust's comment provided the same basic equation for radius (just the units were different and it was simplified)...

My only real contribution being getting the temp and Lum. from H-R diagram (Spectral class gives temp - Lum is dependent on size).


BTW: Don't know if you caught the main caveat:

Your topic post refers to Mass not Lum, which you pointed out can roughly approximate Lum for Main Sequence stars. For the other sizes though, there is a lot more variance (this from chemical composition/fusion methods).

As a common example - a young Main Sequence star will have a much different Lum when it becomes older (and moves off the Main Sequence) as its nuclear fusion changes due to the lighter/more common elements being transformed (i.e. running low on simple hydrogen fuel). Its mass will not have changed much relatively speaking (just the organization at the atomic level). Its temp changes as the reaction chains (fusing of heavier elements) vary. And its pressure changes along with it - thus the radius changes to accommodate gravity and thus the surface area and temperature changes - effecting the total energy output per unit area (Bolo Luminosity).

So basically, you have to make up the Luminosity or Size (Ia, ..V, Dwarf). CT had you generate Stellar Class and Size with roles - so the rest can be fitted to tables (curves on H-R diagram) and equations.

 

[DPSteve]

Sure No Problem! - just to note that rust's comment provided the same basic equation for radius (just the units were different and it was simplified)...

My only real contribution being getting the temp and Lum. from H-R diagram (Spectral class gives temp - Lum is dependent on size).

Oh no, I give rust full credit for that If I forgot to mention that at some point I apologize.

As I mention below, I have both size and class, and from these I am (messily) generating mass (using the ranges given in Wikipedia) by using even increments based on sub-class (which is probably dead wrong; I can go to a pure random mass using the high and low values given).

BTW: Don't know if you caught the main caveat:

Your topic post refers to Mass not Lum, which you pointed out can roughly approximate Lum for Main Sequence stars. For the other sizes though, there is a lot more variance (this from chemical composition/fusion methods).

As a common example - a young Main Sequence star will have a much different Lum when it becomes older (and moves off the Main Sequence) as its nuclear fusion changes due to the lighter/more common elements being transformed (i.e. running low on simple hydrogen fuel). Its mass will not have changed much relatively speaking (just the organization at the atomic level). Its temp changes as the reaction chains (fusing of heavier elements) vary. And its pressure changes along with it - thus the radius changes to accommodate gravity and thus the surface area and temperature changes - effecting the total energy output per unit area (Bolo Luminosity).

So basically, you have to make up the Luminosity or Size (Ia, ..V, Dwarf). CT had you generate Stellar Class and Size with roles - so the rest can be fitted to tables (curves on H-R diagram) and equations.

Currently the size and stellar class are random gens (size first, then stellar class). So I know the star is, for example, a G5 V or a B9 II.

Basically, I can generate three characteristics (one being a fudge of sorts): Size, spectral class (and subclass), and mass. I need to determine radius, luminosity, and temperature.

Although, I can probably fudge the temp same as the mass.

 

[BP]

OK since you have the Size - you got enough -

Use the size on the H-R diagram .. and you will have the luminosity (well, if you use the curves for given Size classifications on a chart like this and some pixel counting for a rough estimate)!

The temp comes from the Spectral Class .. then use the formula to determine the Radius!


For even more fun - generate Stellar Spectrum (they are colorful, techie looking props - I like to invert the absorption lines).
Have Fun...

 

[EDG]

If you really want to go the whole hog, you need to track down the latest Stellar Evolution grids (start at http://cdsarc.u-strasbg.fr/viz-bin/qcat?isindex=stellar+evolution+grid ). Find the grids for the mass and metallicity you need, interpolate within them as necessary to find the exact (modelled) luminosity for a star of a given mass and a given age, as well as where it is in its life cycle (main sequence, subgiant, giant, etc) and (more importantly) what its previous characteristics were so you can determine the effects of its increasing luminosity of the planets around it.

But that requires a lot of processing.