THE SOUTHWORTH PLANETARIUM
207-780-4249       www.usm.maine.edu/planet
70 Falmouth Street  Portland, Maine 04103
43.6667° N,                    70.2667° W
Founded January 1970
           "Someday, in deep time, all the possibilities will come to fruition."



THE DAILY ASTRONOMER
Wednesday, January 13, 2016
Of Vega and Sirius


TO HV


Yesterday, we took much from Pandora's Jar.    This jar contains the
myriad astronomy questions we receive throughout the year.       As
often happens, answers to questions prompt other questions.   For this
reason a wit, whose identity I've fortunately forgotten, branded
science an exercise in futility as it never solves any problem. It
merely precipitates new problems by attempting to solve old ones.
Well, bah humbug, you wet blanket.    Look at it this way, science can
still toast our crumpets without having to explain the nature of
reality.

The first question answered yesterday pertained to Sirius.  The
questioner asked if it was always going to be the night sky's
brightest star.  We explained that in about 200,000 years, Vega,
presently the fifth brightest star in the night sky, will surpass
Sirius in apparent brightness and therefore become the brightest night
sky star.   Even though it will still be farther away than Sirius,
Vega will appear brighter because it is intrinsically brighter.
After reading this answer, a subscriber asked

"Why is Vega brighter than Sirius?"

This question, which we should have addressed yesterday, we will
answer now, as the DA hasn't devoted much time to explaining why stars
differ in brightness so profoundly.

We begin with the notion of "luminosity," defined as the amount of
energy a star produces every second.   A star's mass determines its
luminosity.   The more massive the star, the more luminous it will
become.    This mass-lumminosity relation is one of the cornerstones
of astrophysics.

Sirius is about two times more massive than the Sun and, consequently,
about 25 times more luminous than the Sun.
Vega is approximately 2.14 times more massive than the Sun.     Though
the mass difference between Sirius and Vega might seem slight, the
luminosity is very mass sensitive.*   Vega is 40 times brighter than
the Sun.

At this point, we will anticipate another question related to this answer:

"How do we know that Vega is intrinsically brighter than Sirius?"

To determine a star's true brightness, we first have to measure its
distance.  Vega and Sirius are so close we can determine their
distances through the parallax method.

For more information about this method, please refer to:
http://usm.maine.edu/planet/could-you-please-explain-parallax-again-how-does-it-work-when-youre-measuring-distances-stars

If we know the star's distance, we can then observe how bright it
appears to us.  We refer to this apparent brightness as its "apparent
magnitude."     By knowing a star's distance and its apparent
magnitude, we can determine its absolute magnitude.     "Magnitude" is
the scale astronomers use to specify a celestial object's brightness.
It is an inverse scale: the lower the number the brighter the object.
 So, for instance, a star of magnitude 1 will be brighter than a star
of magnitude 2, which is brighter than a star of magnitude 3.
The actual factor is 2.5, so a star of magnitude 1 will be 2.5 times
brighter than a star of magnitude 2.

Apparent magnitude measures how bright a star appears.
Absolute magnitude measures how bright a star would appear at a
distance of 10 parsecs, or about 32.6 light years.        Absolute
magnitude directly relates to a star's actual brightness, or
luminosity.

If we can know the star's distance and its apparent brightness, we can
work out the star's intrinsic brightness.     As an analogy, imagine
you have two lights of varying brightness positioned at different
distances across a football field.      You can measure the distance
to the lights by counting the yard markers separating you from them.
You can clearly see how bright the lights appear.  From these two
pieces of information one can ascertain the relative brightnesses of
the lights, thereby determining which is the brighter of the two.

If you want more math, please refer to a math zone page pertaining to
the distance modulus.

http://usm.maine.edu/planet/mz-3-using-distance-modulus-calculate-suns-brightness-various-distances


We hope these answers were helpful.




*We know that to some people these mathematical footnotes seem as warm
and friendly as 130-year old school marms armed with a gallon of
stomach-dissolving Castor oil.  We'll therefore try to proceed gently.
   For stars which are at least twice as massive as the Sun, but less
than twenty times as massive, a star's luminosity is proportional to
the mass raised to the power of 3.5.    So, for instance, a star that
is four times as massive as the sun will be 11 times more luminous
than a star that is twice as massive.    Even though Vega is 2.14
times as massive as the Sun, whereas Sirius is 2.0 times more massive,
that difference will make Vega 1.6 times more luminous than Sirius.






-Written by Edward Gleason
Manager, Southworth Planetarium