Correlation between a Star's Luminosity and Distance?

In summary, the conversation discusses the correlation between a star's luminosity and its distance from Earth. The speaker created several charts using R-squared as a measurement and found values ranging from moderate to very strong. They also mention the possibility of a correlation between the distance of stars from the solar neighborhood and their luminosity. However, the correlation may be due to selection bias as only the brightest stars, which are visible from a greater distance, were plotted. The conversation also brings up the different types of stars and their lifespan, and suggests further research on the local population of stars.
  • #1
fizixfan
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33
I made three charts from several different sources plotting the luminosity and distance from Earth of 26 to 300 Stars. In each chart, there appears to be a correlation between a star's luminosity (in solar units) and its distance from Earth (or solar system, whichever you prefer) in light years. I used R-squared (Coefficient of Determination) as a measurement of the relationship between luminosity and distance. I got values of 0.43, 0.67, and 0.88 depending on the source and sample size. These appear to range between moderate to very strong. I'm no expert in statistics, but if you look at the charts there is a visible relation between the two variables (in my opinion).

I don't think these correlations are artifacts, but then again I'm only an amateur astronomer. However I have read in the literature that there are clusters of OB stars in the solar neighborhood which may include Rigel and the possible birthplace of Betelgeuse (an M-class star with started out as an O star) https://www.aanda.org/articles/aa/abs/2015/12/aa27058-15/aa27058-15.html. There is an interactive diagram which shows these star clusters in 3D: http://sci.esa.int/hipparcos/ob-stars-interactive/ This research may lend support to the idea that the solar system is in a kind of "gap" between large stellar structures and areas of star formation.

Within about 300 parsecs from the sun, it appears that the more distant the star, the greater its intrinsic brightness. Is it reasonable to hypothesize that there is a correlation between the distance of stars from the solar neighborhood and their luminosity?
300 Brightest Stars w-in 3,000 ly Lum & D (ly).jpg
26 Brightest Stars w-in 2,600 ly Lum & D (ly).jpg
172 Brightest Stars w-in 3,200 ly - Distance vs. Luminosity (02Nov2018) rsq.jpg
 

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  • #2
If you are talking about visible stars then yes. Stars with low luminosity that are far away are not visible.

Stars with names tend to be the visible stars.
 
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  • #3
You have plotted the brightest stars, as measured by apparent brightness as seen from the Earth. So of course, as stefan r said, a more distant star must be intrinsically brighter in order to appear in the list you started with. A faint distant star would be too dim to be in your list. If you were to plot all of the stars within some distance from the sun, regardless of apparent brightness, you would see no such correlation. Try it. This is a perfect example of what is called "selection bias"
 
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  • #4
stefan r said:
If you are talking about visible stars then yes. Stars with low luminosity that are far away are not visible.

Stars with names tend to be the visible stars.

That’s not what I’m taliking about. I mean the correlation between the intrinsic brightness of a star and its distance from the solar neighbourhood. It appears that the more luminous the star (in solar units) the more distant it is from us. Here’s an analogy: if you live in a sparsely populated rural area and you’re surrounded by several large metropolitan areas, then the farther you travel from the rural area, the denser the population will be. I tried to make that clear in my OP.

I understand that apparent magnitude decreases with the square of the distance it is removed from the observer.

“”Stars with names tend to be the visible stars.” I understand that too. But a bright star like Sirius is 25 times as luminous (intrinsically bright) as the sun but only 8.6 light years away, whereas a star like Rigel, which doesn’t appear quite as bright as Sirius, is about 800 light years away and 66,000 times as bright as the sun.

Perhaps you could try going back and reading my post again. Your answer doesn’t really address my question.
 
  • #5
phyzguy said:
You have plotted the brightest stars, as measured by apparent brightness as seen from the Earth. So of course, as stefan r said, a more distant star must be intrinsically brighter in order to appear in the list you started with. A faint distant star would be too dim to be in your list. If you were to plot all of the stars within some distance from the sun, regardless of apparent brightness, you would see no such correlation. Try it. This is a perfect example of what is called "selection bias"

No, I have NOT plotted the brightest stars by apparent magnitude, I have plotted them by luminosity in solar units, which is equivalent to absolute magnitude.

Here is a plot of the absolute magnitude vs. distance of the 900 closest stars. You can see that there is no correlation. But there does appear to be a correlation between M and D of the more distant stars.
900 Closest Stars - Distance & Magnitude01.jpg

Please read my post more carefully.
 

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  • #6
I'm sorry, I think you have cause and effect backwards...

Bright stars are visible from a greater distance because they are bright.
Happens that such are rare, as those massive stars 'burn' through their fuel disproportionately fast ( In cosmic terms !) but, meanwhile, they are visible from afar.

Mid-range stars such as main sequence GKF will last a lot longer, but their clocks are ticking...
( Our G8 is no exception...)

Conversely, the much more common, but very dim stars such as tiny red dwarfs, brown dwarfs, old white dwarfs etc will last a long, long time, but are hard to spot even in our own neighbourhood. IIRC, several new neighbours have turned up recently, via WISE etc infrared surveys, with some more expected.

IMHO, you need to study the 'local population' listed at...
http://www.recons.org/
https://en.wikipedia.org/wiki/List_of_nearest_stars_and_brown_dwarfs
and
http://www.johnstonsarchive.net/astro/nearstar.html
 
  • #7
Nik_2213 said:
I'm sorry, I think you have cause and effect backwards...

Bright stars are visible from a greater distance because they are bright.
Happens that such are rare, as those massive stars 'burn' through their fuel disproportionately fast ( In cosmic terms !) but, meanwhile, they are visible from afar.

Mid-range stars such as main sequence GKF will last a lot longer, but their clocks are ticking...
( Our G8 is no exception...)

Conversely, the much more common, but very dim stars such as tiny red dwarfs, brown dwarfs, old white dwarfs etc will last a long, long time, but are hard to spot even in our own neighbourhood. IIRC, several new neighbours have turned up recently, via WISE etc infrared surveys, with some more expected.

IMHO, you need to study the 'local population' listed at...
http://www.recons.org/
https://en.wikipedia.org/wiki/List_of_nearest_stars_and_brown_dwarfs
and
http://www.johnstonsarchive.net/astro/nearstar.html

No I do not have cause and effect backwards. You are simply not reading my post carefully enough. This looks like a case of "piling on."

Here again is a plot of the 900 closest stars (distance vs abs. mag.) within 50 light years. You can see there is no correlation. But there IS a correlation between distance and abs. mag. (luminosity in solar units) for stars within 3,000 light years, as I have noted in my OP. This is because there are large structures and clusters of very luminous stars (e.g., Betelgeuse and Rigel) within about 300 pc of the solar system (see second diagram), which makes the distribution of stellar matter discontinuous. The sun is in a gap between these structures.

900 Closest Stars - Distance & Magnitude01.jpg
.

star structures within 200 pc.png


These are my sources:
http://calgary.rasc.ca/nearbystars.htm
http://www.atlasoftheuniverse.com/stars.html
http://stars.astro.illinois.edu/sow/bright.html
https://en.wikipedia.org/wiki/List_of_stars_more_luminous_than_any_closer_star
https://en.wikipedia.org/wiki/List_of_most_luminous_stars
https://www.space.com/21640-star-luminosity-and-magnitude.html

You can look up the data at these sites and do the chars of Distance (ly) vs. Luminosity (solar units, sun = 1)
You can convert absolute magnitude or apparent magnitude to luminosity (sun = 1) using the following forumulas:
Luminosity = 100^0.2^(4.83-(m-5*LOG(D/32.6156))) where m = apparent magnitude, D = distance (ly)
or
Luminosity = 100^0.2*(4.83-M) where M = absolute magnitude.

TRY IT.
 

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  • #8
fizixfan said:
No, I have NOT plotted the brightest stars by apparent magnitude, I have plotted them by luminosity in solar units, which is equivalent to absolute magnitude.
Please read my post more carefully.

Please read my post more carefully. I am not talking about your plot axes, I am talking about how you chose which stars to plot in the first place. Your criterion for choosing the stars which you plotted was that their brightness in apparent magnitude exceeded some value. This introduces a bias where distant stars need to be intrinsically more luminous in order to be included in your list.

Note the title of your first plot, "Luminosity and Distance of the 300 Brightest Stars". Brightest in this case refers to apparent magnitude.

Do you see now, or are you still missing the point?
 
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  • #9
phyzguy said:
Please read my post more carefully. I am not talking about your plot axes, I am talking about how you chose which stars to plot in the first place. Your criterion for choosing the stars which you plotted was that their brightness in apparent magnitude exceeded some value. This introduces a bias where distant stars need to be intrinsically more luminous in order to be included in your list.

Note the title of your first plot, "Luminosity and Distance of the 300 Brightest Stars". Brightest in this case refers to apparent magnitude.

Do you see now, or are you still missing the point?

Yep, I have seen the error of my ways. So I plotted Distance and Luminosity of the most luminous stars within 38,700 light years ( https://en.wikipedia.org/wiki/List_of_most_luminous_stars ) and found that the RSQ was only 0.03 and correlation was 0.2. I didn't use the remaining 40 stars because they were either in one of the Magellanic Clouds or in another galaxy altogether. So now I understand that there is no relation between the distance of stars in the solar neighborhood and their luminosity. It was an interesting and persistent delusion while it lasted, but now I can let it go. Thank you for you patience.

80 Most Luminous Stars - Distance vs. Luminosity (03Nov2018) rsq.jpg
.
 

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  • #10
fizixfan said:
Yep, I have seen the error of my ways. So I plotted Distance and Luminosity of the most luminous stars within 38,700 light years ( https://en.wikipedia.org/wiki/List_of_most_luminous_stars ) and found that the RSQ was only 0.03 and correlation was 0.2. I didn't use the remaining 40 stars because they were either in one of the Magellanic Clouds or in another galaxy altogether. So now I understand that there is no relation between the distance of stars in the solar neighborhood and their luminosity. It was an interesting and persistent delusion while it lasted, but now I can let it go. Thank you for you patience.

I'm glad you got it, and glad I could help. Keep asking those questions!
 
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  • #11
It's always a feel good moment when someone graciously accepts an error and learns from it. If only the history of Science had more examples like this and fewer 'fights to the death' between opposing ideas.
 
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Related to Correlation between a Star's Luminosity and Distance?

1. What is the relationship between a star's luminosity and distance?

The relationship between a star's luminosity and distance is known as the inverse square law. This means that as the distance between a star and an observer increases, the apparent brightness or luminosity of the star decreases. This is due to the spreading out of the light as it travels through space.

2. How is the distance to a star measured?

The distance to a star is typically measured using the parallax method. This involves observing the star from two different points on Earth's orbit around the Sun, and measuring the change in its apparent position. The distance can then be calculated using trigonometry.

3. Is there a direct correlation between a star's luminosity and its distance?

No, there is not a direct correlation between a star's luminosity and its distance. The luminosity of a star depends on its size, temperature, and age, in addition to its distance from Earth. Two stars at the same distance from Earth may have very different luminosities.

4. How does the distance to a star affect our perception of its luminosity?

The farther away a star is, the dimmer it appears to us. This is because light from the star is spread out over a larger area as it travels through space. So, even if a star has a high luminosity, it may appear dim if it is located at a great distance from Earth.

5. Can the correlation between a star's luminosity and distance be used to determine the distance to other celestial objects?

Yes, the inverse square law can be applied to other celestial objects, such as galaxies and quasars, to determine their distances from Earth. This is an important tool in astronomy for understanding the vastness of the universe and the relationships between different objects within it.

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