Vol. Science · Astronomy · Stellar life

Stellar lifetime
mass and light

A star’s mass sets how brightly it shines on the main sequence, and how long the core hydrogen lasts. Eker et al. 2018 fit log₁₀(L/L☉) = a log₁₀(M/M☉) + b in six pieces, from just above 0.179 solar masses to 31. The lifetime scaling is t ≈ 10 Gyr × (M/M☉) / (L/L☉). Slide the mass, or tap a cited star. The rough end — white dwarf, neutron star, or black hole — is a label, and the boundaries are approximate. Where that luminosity sits against temperature is the HR diagram. The curve behind a temperature and a radius is the blackbody desk. Spectral type and the life-path cartoons are the stars desk. The same luminosity, spread over an orbit, is the habitable zone.

Classroom scaling. Not a stellar-evolution model, not a remnant prediction, and not a catalog. The luminosity line is Eker et al. 2018, Table 4, and only inside 0.179 < M/M☉ ≤ 31. The pieces are separate least-squares fits. They are not joined, and this page does not extend them. The 10 Gyr zero is the round classroom number beside NASA’s 4.6-billion-year-old Sun and about 5 billion years still on the main sequence. That sum is 9.6 billion years. It is not a published stellar-model age. End-state labels follow NASA’s classroom split. The edges are approximate and move with metallicity, rotation, and mass loss.

Interactive · Mass, luminosity, lifetime

Low mass left · long life up · the line is the fit · dots are cited M/L

Fit
Cited M/L
Planck age
White dwarf
Neutron star
Black hole

Formula outputs are approximate scaling estimates. They are not the cited luminosities, ages, or remnant masses.

Cited stars · the mass and the luminosity are the paper’s

Mass M☉

Nominal luminosity · mass is 1 by definition

Sun

1 M☉ · nominal 1 L☉

Cited L1 L☉ · nominal
Scaling L0.984 L☉ · approximate
Life, cited L10 Gyr · approximate
Life, scaling L10.16 Gyr · approximate
Planck age13.797 ± 0.023 Gyr
Against that ageShorter than 13.797 Gyr
End stateWhite dwarf
Fit pieceLow mass
Cited age4.6 Gyr

The nominal luminosity is 1 L☉. The fit at 1 M☉ is not exactly 1, because the low-mass line was not forced through the Sun. The lifetime scaling with L = 1 is exactly 10 Gyr.

IAU 2015 Resolution B3 sets the nominal solar luminosity at 3.828 × 10²⁶ W. NASA Science calls the Sun a 4.6-billion-year-old main-sequence star and expects about another 5 billion years of core hydrogen fusion.

The scaling rows are approximate. They are not the cited values on this card.

The slider needs JavaScript. The cited anchors are still below. The nominal Sun is 1 M☉ and 1 L☉, so t = 10 Gyr × 1/1 is 10 Gyr. The low-mass fit at 1 M☉ is log₁₀(L/L☉) = −0.007, about 0.984 L☉, and 10 / 0.984 is about 10.16 Gyr. Proxima Centauri is 0.120 ± 0.003 M☉ and 0.00151 ± 0.00008 L☉ (Ribas et al. 2017). That mass is below 0.179, so the fit is not applied. 10 × 0.120 / 0.00151 is about 795 Gyr, longer than the Planck age 13.797 Gyr. Sirius A is 2.063 ± 0.023 M☉ and 24.74 ± 0.70 L☉ (Bond et al. 2017); 10 × 2.063 / 24.74 is about 834 Myr. Vega is 2.15 M☉ and 44 L☉; 10 × 2.15 / 44 is about 489 Myr. Rigel is a blue supergiant at 23 M☉ with log(L/L☉) = 5.08 (Moravveji et al. 2012). Putting that luminosity into M/L is about 1.91 Myr, and it is not a main-sequence lifetime. Eker et al. 2018, Table 4, is the luminosity fit. The Planck age 13.797 ± 0.023 Gyr is the TT,TE,EE+lowE+lensing column.

Not a clock

M/L is a scaling. It is not how long this star has left.

The lifetime row divides a mass by a luminosity and multiplies by 10 billion years. It does not integrate a stellar model. It does not know the hydrogen fraction already burned, the mixing, or the wind. Two stars with the same mass and the same luminosity get the same number here. A real age needs the spectrum and a model grid.

The 10 Gyr zero is the classroom round number. NASA Science’s star-types page calls the Sun a 4.6-billion-year-old main-sequence star and expects about another 5 billion years before the red-giant phase. The sum is 9.6. The same page also says the Sun becomes a white dwarf in about 10 billion years, after the giant phase. Those are NASA’s sentences. This desk’s 10 is the round zero in t ≈ 10 Gyr × M/L, not either of those clocks, and not a published model age.

Stars well below about 0.45 solar masses are fully convective. They can keep feeding the core fresh hydrogen, so a larger share of the star is fuel than the solar fraction assumed here. This page does not add that correction. NASA notes that some red dwarfs around a third of a solar mass can live far longer than the age of the universe, up to about 14 trillion years. Proxima’s 795 Gyr row is only 10 × 0.120 / 0.00151. It is not that trillion-year figure, and the mass is below the fit, so there is no scaling luminosity either.

At the other end, winds remove mass. A 23-solar-mass star does not arrive at core collapse still holding 23 solar masses. Rigel has already left the main sequence. The fit at 23 M☉, about 1.01×10⁵ L☉ and about 2.27 Myr, is the scaling for a main-sequence star of that mass. Rigel’s published log(L/L☉) = 5.08 is the supergiant. Putting 5.08 into M/L, about 1.91 Myr, is not a main-sequence lifetime.

The end-state word is NASA’s classroom split: under 8 solar masses a white dwarf, about 8 to 20 a neutron star, heavier a black hole. Heger et al. 2003 say the remnant depends on the helium core and the hydrogen envelope at death, and on metallicity through the winds. In one solar-metallicity sketch, neutron stars are typical up to about 20–25 solar masses, and fallback black holes sit higher. Rotation moves the core too. The label on this page is the NASA edge. It is not a prediction for the star in front of you. Sirius A’s white-dwarf label is the rough end for a single star of that mass. It is not a description of Sirius B.

Literacy · the numbers on the readout

Mass–luminosity fit: log₁₀(L/L☉) = a log₁₀(M/M☉) + b, Eker et al. 2018, Table 4. Six separate least-squares lines. The lower edge of each piece is exclusive and the upper edge is inclusive. Ultra low-mass, 0.179 < M ≤ 0.45: a = 2.028, b = −0.976. Very low-mass, 0.45 < M ≤ 0.72: a = 4.572, b = −0.102. Low mass, 0.72 < M ≤ 1.05: a = 5.743, b = −0.007. Intermediate, 1.05 < M ≤ 2.40: a = 4.329, b = +0.010. High mass, 2.4 < M ≤ 7: a = 3.967, b = +0.093. Very high mass, 7 < M ≤ 31: a = 2.865, b = +1.105. The lines are not forced to meet. At 1 M☉ the low-mass line gives log₁₀(L/L☉) = −0.007, about 0.984, not 1.
Outside the fit: The slider runs from 0.1 to 60 solar masses. The fit does not. Below or at 0.179, and above 31, the scaling luminosity and the scaling lifetime say “Not calibrated.” The end-state label still follows the mass. Proxima, at 0.120 M☉, is the preset that shows the refusal.
Lifetime scaling: t = 10 Gyr × (M/M☉) / (L/L☉). With the nominal solar luminosity, L = 1, the Sun’s row is exactly 10 Gyr. With the fit’s 0.984 L☉ it is about 10.16 Gyr. Both are approximate. Neither is a stellar-model age.
Cited L versus scaling L: A preset keeps the paper’s luminosity in one row and the fit’s luminosity in another. Sirius A’s published 24.74 L☉ is not the fit at 2.063 M☉. Vega’s 44 L☉, from a rapid rotator seen nearly pole-on, sits above the mean line. Rigel’s 10^5.08 is a supergiant luminosity. The fit at that mass is a main-sequence scaling.
The Planck line: Planck Collaboration 2020, A&A 641, A6, Table 2. The column TT,TE,EE+lowE+lensing gives an age of 13.797 ± 0.023 Gyr. The column that also uses baryon acoustic oscillations gives 13.787 ± 0.020 Gyr. The dashed line is 13.797. The label “~13.8 Gyr” is that central value rounded to one decimal. A marker lifetime longer than 13.797 Gyr has outlived that age on this scaling. Proxima’s cited-L row does. The Sun’s 10 Gyr does not.
End-state label: NASA Science, Star types: a main-sequence star less than eight times the Sun’s mass leaves a white dwarf; about 8 to 20 leaves a neutron star; heavier stars leave a stellar-mass black hole. Heger, Woosley, Fryer, and Langer carry typical neutron stars to about 20–25 solar masses at solar metallicity. The bands on the plot are the NASA edges. They are not sharp.
Cited age: Shown only when a paper prints one. The Sun’s 4.6 Gyr is NASA’s age, not M/L. Sirius A’s 237 ± 15 Myr is Bond et al.’s YREC age from the zero-age main sequence. Vega’s 700 Myr is Monnier et al.’s evolutionary age, with uncertainties −75 and +150 Myr. The M/L row for Vega, about 489 Myr, is shorter than that cited age. The two numbers are not the same quantity.

Sources · the papers, NASA, and the IAU

Cited, not invented

Eker et al. 2018, MNRAS 479, 5491 (arXiv:1807.02568) — Table 4, classical MLR. log₁₀(L/L☉) = a log₁₀(M/M☉) + b. Lower edge exclusive, upper inclusive. Ultra low-mass, 0.179 < M ≤ 0.45, N = 22: a = 2.028 (0.135), b = −0.976 (0.070), σ = 0.076, R² = 0.919. Very low-mass, 0.45 < M ≤ 0.72, N = 35: a = 4.572 (0.319), b = −0.102 (0.076), σ = 0.109, R² = 0.857. Low mass, 0.72 < M ≤ 1.05, N = 53: a = 5.743 (0.413), b = −0.007 (0.026), σ = 0.129, R² = 0.787. Intermediate, 1.05 < M ≤ 2.40, N = 275: a = 4.329 (0.087), b = +0.010 (0.019), σ = 0.140, R² = 0.901. High mass, 2.4 < M ≤ 7, N = 80: a = 3.967 (0.143), b = +0.093 (0.083), σ = 0.165, R² = 0.907. Very high mass, 7 < M ≤ 31, N = 44: a = 2.865 (0.155), b = +1.105 (0.176), σ = 0.152, R² = 0.888. The pieces are separate lines. This page does not extrapolate.
NASA Science — Star types — the Sun as a 4.6-billion-year-old main-sequence star, expected to remain one for another 5 billion years; a white dwarf after the giant phase in about 10 billion years; red giants for main-sequence stars less than eight times the Sun’s mass; neutron stars for about 8 to 20; heavier stars produce stellar-mass black holes. Some red dwarfs around a third of a solar mass can live up to about 14 trillion years. The shapes of the bands are not taken from that page.
Planck Collaboration 2020, A&A 641, A6 (arXiv:1807.06209) — Table 2. Column TT,TE,EE+lowE+lensing: age 13.797 ± 0.023 Gyr. The +BAO column: 13.787 ± 0.020 Gyr. The line is 13.797. “~13.8 Gyr” rounds that central value to one decimal. The same paper’s H0 = 67.4 ± 0.5 km/s/Mpc is the number on the redshift desk.
IAU 2015 Resolution B3 (Prša et al. 2016, AJ 152, 41) — nominal solar luminosity 3.828 × 10²⁶ W. On this page that constant is 1 L☉. It is a conversion constant, not a measurement of the Sun. The resolution text is also at the IAU archive.
Ribas et al. 2017, A&A 603, A58 — Proxima Centauri: M = 0.120 ± 0.003 M☉, L = 0.00151 ± 0.00008 L☉. The mass is from their stellar analysis, not a dynamical orbit. 0.120 is below 0.179, so the fit is not applied.
Bond et al. 2017, ApJ 840, 70 — Sirius A: dynamical mass 2.063 ± 0.023 M☉; luminosity 24.74 ± 0.70 L☉ adopted from Davis et al. 2011 adjusted to their parallax; YREC age relative to the zero-age main sequence 237 ± 15 Myr. The age is a model age. The white-dwarf label here is the rough end for a single star of this mass, not Sirius B. Also arXiv:1703.10625.
Monnier et al. 2012, ApJL 761, L3 — Vega: mass 2.15 M☉ with uncertainties +0.10 and −0.15, age 700 Myr with uncertainties −75 and +150, from rotating Geneva tracks. The mass is an evolutionary estimate, not a dynamical mass. The luminosity on this preset is not from this paper.
Hill, Gulliver, and Adelman 2010, ApJ 712, 250 — Vega: luminosity 44 ± 2 L☉. Seen nearly pole-on. The mass on this preset is Monnier et al. 2012, not this paper. Two citations on purpose.
Moravveji et al. 2012, ApJ 747, 108 — Rigel: log(L/L☉) = 5.08 with uncertainties +0.07 and −0.10. They adopt a mass of 23 M☉ from Przybilla et al. 2010 Geneva tracks that include rotation, and they do not print an uncertainty on 23. The mass is a track mass, not a dynamical mass. Rigel is a blue supergiant. It is not on the main sequence. The fit at 23 M☉ is a main-sequence scaling, not this luminosity.
Heger, Fryer, Woosley, Langer, and Hartmann 2003, ApJ 591, 288 — how massive single stars end. The remnant depends on the helium-core mass and the hydrogen envelope, and on metallicity through mass loss. They discuss a Fryer 1999 estimate: fallback black holes near a helium core of about 8 M☉ (about a 25 M☉ main-sequence star if there is no mass loss), and direct black holes for helium cores above about 15 M☉ (about 40 M☉ on the main sequence, no mass loss). They call those numbers uncertain.
Heger, Woosley, Fryer, and Langer, arXiv:astro-ph/0211062 — below about 8 M☉, white dwarfs only. Up to about 20–25 M☉, neutron stars are the typical solar-metallicity outcome in their sketch. Higher masses can leave fallback black holes. Mass loss, metallicity, and rotation move the boundaries. This page still labels with NASA’s 8 and 20.

Classroom picture of mass, luminosity, and a main-sequence lifetime. The fit is Eker et al. 2018, Table 4, inside its printed window. t ≈ 10 Gyr × M/L uses the round 10, next to NASA’s 4.6 plus about 5. End states are NASA’s rough split, with Heger et al. 2003 on why the edges move. Preset masses and luminosities are the cited central values. Formula outputs are approximate scaling estimates. Not a stellar-evolution model and not a catalog. Earthrise preview: NASA / Bill Anders (public domain).

Keep going

Diagram

Across	Mass, logarithmic, from 0.1 to 60 solar masses. Low mass is left.
Up	Lifetime, logarithmic, from 100,000 years to 3,000 Gyr. Long life is up.
Curve	Six separate pieces. They are not joined. Nothing is drawn outside the fit.
Dots	Cited mass and the lifetime from the cited luminosity. The Sun’s dot uses L = 1, so it sits at 10 Gyr. A custom mass sits on the curve when the fit applies.
Dashed line	Planck 2018 age, 13.797 Gyr, labeled ~13.8 Gyr. The BAO column, 13.787 ± 0.020, is in the sources.
Bands	NASA’s rough end states: white dwarf below 8, neutron star from 8 to 20, black hole above 20. Approximate.

Presets	Sun, Proxima Centauri, Sirius A, Vega, Rigel. Each button places the cited mass. Sirius A and Vega sit close together on the plot. Use the buttons to tell them apart.
Plot	Tap or drag to set a custom mass from the horizontal position. That leaves the preset. It does not snap to a star.
Slider	Mass, logarithmic, from 0.1 to 60. The number field accepts the same range. Typing or sliding leaves the preset. Outside 0.179 to 31 the scaling rows say “Not calibrated.”

Plot	The canvas takes focus. Left and Right nudge the mass. Shift is a coarser step.
Buttons	Enter or Space selects. The pressed button is aria-pressed. Targets are at least 44 pixels on a side.
This dialog	The question mark, or ?, opens it. Escape closes it. Tab stays inside until you close it. Click the dim page behind the card to close it.

Stellar lifetime
mass and light

M/L is a scaling. It is not how long this star has left.

Cited, not invented

HR diagram

Blackbody

Stars

Habitable zone

Nearest stars

Solar map