Stefan-Boltzmann constant is faulty for massive stars?

[Kochav Israel]

I have a star that symbolizes America in my fictional universe, and it has an absolute magnitude of -17.76, which corresponds to luminosity of around 1 billion x Sun.

When I automatically put it into Celestia, using the temperature of 3500 K and the magnitude, it gives a radius of 220'000 times that of Sun. Don't ask me why I made such massive star.

But if I go through the same formula hand by hand, I get 6.5 billion x Sun.

220'000 * 695'700'000 m = 153'054'000'000'000 m
153'054'000'000'000^2 * 4 * pi = 294 373 853 063 102 262 121 925 836 142.09
294 373 853 063 102 262 121 925 836 142.09 x 350 ^4 = 4.4174476325281783209671495786073e+43
4.4174476325281783209671495786073e+43 * 5.6703e-8 = 2.5048253310724529533380028255577e+36
2.5048253310724529533380028255577e+36 / 3.846e+26 = 6 512 806 373.04329941065523355579

Here is what it looks like in Celestia, for the reference I used 2013 version 1.7.0

Something seems off...

[Gurren Lagann]

Congrats, you just broke the world record for largest star (shared publically) in Celestia. The previous record was 86,000 solar radii (by the Sextans A addon).

[Kochav Israel]

@GurrenLagann

I did this by total accident. Originally stars were meant to be within Sextans A's addon style, I expected a -17 magnitude to correspond to that star with 86'000 R_sun, but instead Celestia did this.

If the star is caltculated by ratio of T_star/T_sun to the 4, which is about 7, the radius works out to be 244'000.
Using ratios one can find out that a star with -17.76m would be about 32'000 R_sun if it had the same T as the sun, 5778 K. And indeed if I set it to that, it happens to be this way. Then, once the energy factor is 7 times smaller, area must be 7 times larger therefore for the star to produce the same amount of energy. This means a radius of around 89'000, or how star in my fictional world was intended to be.

But if I work it from the raw values, the luminosity is off by a factor of like 8. I used also 244'000 R_sun, more precise one using S-B law from -17.76m, worked backwards, and the ratio there is 8. I am probably missing some factor in this formula or two, but either this is something that Celestia is screwing with or me.

I ran this experiment with T = 57800 K, which is 10 times bigger than sun, and the given-out radius was 10x smaller. But if this is calculated from scratch (3300 x 1391400000)^2*57800^4*pi*5.6708e-8, the resulting factual luminosity is 100x larger. Raising the temperature 10 times leads to power gain of 10000 times, thus radius loss of 10000^(1/2) = 100 times, but here 10. what

The ratio seems to go well preserved only for 5780 K lol.

But I am going to keep the 240'000 radius star for USA. I just want to clear up what its actual luminosity is.

[Kochav Israel]

And speaking of the largest star... I got this one.

[onetwothree]

A star's radius is calculated in https://github.com/CelestiaProject/Celestia/blob/master/src/celengine/star.cpp#L958 :

Code: Select all

    // Calculate the luminosity of the star from the bolometric, not the
    // visual magnitude of the star.
    float solarBMag = SOLAR_BOLOMETRIC_MAG;
    float bmag = getBolometricMagnitude();
    auto boloLum = (float) exp((solarBMag - bmag) / LN_MAG);

    // Use the Stefan-Boltzmann law to estimate the radius of a
    // star from surface temperature and luminosity
    return SOLAR_RADIUS * (float) sqrt(boloLum) * square(SOLAR_TEMPERATURE / getTemperature());

We have:

Spoiler

#define SOLAR_BOLOMETRIC_MAG 4.75f
#define LN_MAG 1.085736

float
Star::getBolometricMagnitude() const
{
return absMag + details->getBolometricCorrection();
}

float
StarDetails::getBolometricCorrection() const
{
return bolometricCorrection;
}


case StellarClass::Spectral_M:
period = rotperiod_M[lumIndex][subclass];
bmagCorrection = bmag_correctionM[lumIndex][subclass];
break;

static float bmag_correctionM[3][10] =
{
// Lum class V (main sequence)
{
-1.38f, -1.62f, -1.89f, -2.15f, -2.38f,
-2.73f, -3.21f, -3.46f, -4.10f, -4.40f,
},
// Lum class III
{
-1.25f, -1.44f, -1.62f, -1.87f, -2.22f,
-2.48f, -2.73f, -2.73f, -2.73f, -2.73f,
},
// Lum class I
{
-1.29f, -1.38f, -1.62f, -2.13f, -2.75f,
-3.47f, -3.90f, -3.90f, -3.90f, -3.90f,
}
};

switch (lumClass)
{
case StellarClass::Lum_Ia0:
case StellarClass::Lum_Ia:
case StellarClass::Lum_Ib:
case StellarClass::Lum_II:
lumIndex = 2;
break;
case StellarClass::Lum_III:
case StellarClass::Lum_IV:
lumIndex = 1;
break;
case StellarClass::Lum_V:
case StellarClass::Lum_VI:
case StellarClass::Lum_Unknown:
lumIndex = 0;
break;

[Kochav Israel]

Thank you.

[Kochav Israel]

I checked the luminosity correction, and it gave me a factor of 7.2 times (-2.15f in this case becasue type is just plain M4).

Code: Select all

static float bmag_correctionM[3][10] =
{
    // Lum class V (main sequence)
    {
        -1.38f, -1.62f, -1.89f, -2.15f, -2.38f,
        -2.73f, -3.21f, -3.46f, -4.10f, -4.40f,
...

};

About what it should give in this case.

But on the other hand, what physical process causes luminosity correction in real life?

I mostly write stars using raw Stefan-Boltzmann law, how I wrote Israel and I won't change that, but this is just odd. So really, USA's absolute magnitude is -19.91, then due to this "luminosity correction" it becomes -17.76?

[onetwothree]

// Lum class V (main sequence)

Your start is a super-giant so you shouldn't use the main sequence corrections.

what physical process causes luminosity correction in real life

Absolute magnitude is for visible spectre only. But stars radiate in invisible wave spectre too.

[Joey P.]

Okay, the last image on this thread is going-off topic and is just being silly. But it's still funny

Here is an STC I made on stars symbolizing Danny Phantom characters. Going back to topic, they do obey the Stefan-Boltzmann constant (one of them is a hypothetical star that does obey constant; two are stellar degenerates).

Code: Select all

"Daniel Danny Fenton:Danny Phantom:Daniel Fenton:Daniel:Danny:Danny Fenton:Danny Pulsar"
{
   RA 107.7430367
   Dec -77.7775654
   Distance 7.72
   SpectralType "Q"
   AppMag 20
   Radius 12
   Texture "bstar.*"
   InfoURL "https://dannyphantom.wikia.com/wiki/Danny_Phantom_(character)"
}

"Dan Phantom:Dark Danny:3C58:Quark Star"
{
   RA 360.0
   Dec 62.1
   Distance 10000
   SpectralType "Q"
   AppMag 8.17
   Radius 10
        Texture "Quark-night.png"
}

"Tucker Foley:V436 Cep"
{
   RA 327.8769212
   Dec 57.7807745
   Distance 120
   SpectralType "G5III"
   AppMag 2.1
   Radius 14968300
}

"Samantha Sam Manson:Sam Manson"
{
   RA 357.77771264
   Dec 63.7894944
   Distance 71.29
   SpectralType "O2V"
   AppMag 1.995   
   Radius 12531600
}

"Penelope Spectra"
{
   RA 316.7918875
   Dec 38.88521167
   Distance 1283
   AppMag 5.29
   SpectralType "WNh"
   Radius 31329000
}

"Vlad Masters:Thorne-Zytkow object:TZO"
{
   RA 128.7918875
   Dec -21.27388521167
   Distance 12950
   AppMag 6.92
   SpectralType "M1Ia"
   Radius 1336007800
}

"Vlad Plasmius:Thorne-Zytkow object core:Neutron Star core"
{
   RA 128.7918875
   Dec -21.27388521167
   Distance 12950
   AppMag 15
   SpectralType "Q"
   Radius 12.5
}

(Y Canum Venaticorum is Jazz, Antares is Maddie, and Betelgeuse is Jack.)

Added after 4 minutes 29 seconds:
@Kochav Israel can you also send me an STC file for the United States and your mom, including textures? Thanks.

[Kochav Israel]

Speaking of "your mom" it was just an internal edit within the Size Comparison addon, it wasn't really an addon of my own.

I never intended it to be publicly shown, but since talks went about the "biggest star" I decided it would make a fun addition.