When we see a bright star next to a dim star - what does that mean? Is
the bright star REALLY brighter? Or is it just closer? And when we say “bright,” do
we mean “How much light is reaching our eyes” or “how much light is that object giving off?
Just how DO we measure light in Astronomy?
You may have heard the term
“Apparent Magnitude.” {Display as m} This is a very old way to measure the
brightness of stars. In fact, it dates back to the earliest cataloguing of the stars,
started by the Greek astronomer Hipparchus around 130 BC and completed by Ptolemy around 150 AD.
This system classified 1,022 stars in 48 constellations into 6 magnitudes:
1 being the brightest, and 6 being the faintest, just visible to the naked eye.
Does this seem backwards to you? Here’s what Hipparchus was thinking: The first stars to
appear just after sunset are the brightest, so he said they were of the “First Magnitude,”
and assigned them magnitude 1. If you wait a little while, and it gets a little darker out,
more stars appear, so those are called magnitude 2. We continue like this all the way down to
stars of magnitude 6, which are so dim, you can only see them when the sky is completely dark.
When people started using TELESCOPES to look at the sky in the 1600s,
the apparent magnitude scale had to be extended to even dimmer stars. Also,
in this system, it’s possible for some (bright) heavenly bodies to have a NEGATIVE
apparent magnitude—think of the moon, for instance—it appears much brighter to us
than the brightest star. The Full Moon has an average apparent magnitude of about negative 12.
At its brightest, Venus is a negative 4. Our Sun is about negative 26!
Another detail was added to the concept of apparent magnitude in the 1800s,
when scientists discovered that human vision works on a logarithmic scale.
Astronomers agreed to a system where 5 steps down in apparent magnitude
means a star has 100 times greater apparent brightness. {show parallel scales or graph}
But...we’re still faced with this puzzle—is a star with a low apparent magnitude brighter
because it’s actually giving off more light? Or is it just closer to us?
To better visualize this problem, let’s bring it CLOSER to home. If you put a standard,
high pressure 250 watt sodium light bulb in a streetlight,
it casts a certain amount of light. But if that same size bulb is down at the end of the block,
it looks a lot dimmer. The farther away we get from the streetlight, the dimmer it looks.
Just because we move away from a streetlight, it doesn’t mean the LIGHTBULB actually dims.
It still puts out the same number of LUMENS (in the case of those streetlights, 27,000 lumens).
A lumen {lm} is the SI unit of LUMINOUS FLUX,
a measure of the total quantity of visible light emitted by a source per unit time. But wait,
earlier I said it was a 250 watt bulb. Why am I talking about lumens, now?
Even here on Earth, we’re changing how we talk about how bright a light is. For years,
WATTAGE was typically the measure of light bulbs’ brightness. (Watts are a unit of power,
equal to one joule per second). {on screen: 1 Watt = 1 Joule/sec = 1 kg m2/ s3} But our
perspective has changed since various forms of more efficient lighting, especially LED lights,
have become more practical. You can get the same lumens, or brightness, with much fewer watts.
For example, you get 450 lumens from a standard 40 Watt incandescent light bulb, or a 29 Watt halogen
bulb , a 9 Watt Compact fluorescent bulb, and a SIX Watt LED bulb. Let’s hear it for progress.
No matter what kind of light you’re using, there’s a dropoff in apparent brightness as you move
away. And this dropoff follows a predictable pattern: We call this the INVERSE SQUARE LAW.
As the distance we move away increases, the light has to spread over a larger surface area, and
the brightness decreases in a “one over distance squared” relationship. {illustration with larger
squares}. In other words, apparent brightness is proportional to 1 over the distance squared.
It’s easy for us to measure the distance between us and a streetlight.
But what about the distance between us and the stars?
How can we tell how “bright” something actually is, if we don’t know how far away it is?
Astronomers use a different term to describe the production of light:
LUMINOSITY. It’s a measure of a star’s INTRINSIC BRIGHTNESS, as opposed to APPARENT BRIGHTNESS.
Luminosity tells us the rate the star is radiating energy out in all directions.
Imagine a sphere of light coming off from the star. APPARENT brightness tells us how
much of that energy reaches us so we can detect it (with our eyes, or a telescope).
We can express this relationship mathematically as B = L/(4pi d2), where B is the intensity,
or apparent brightness in watts per meter squared, L is the luminosity of the star
in watts, and d is equal to the distance to the star in meters. In other words,
the brightness of a star equals its luminosity divided by the surface area of the sphere.
The traditional form of this equation was in Watts, but you’ll also often see the luminosity of
a star compared to our Sun—in other words, we can use our own Sun as a standard for brightness. A
solar luminosity unit is written like this: (L☉) . That circle with a dot is the symbol for our Sun.
So in these terms, what sort of luminosities do we see? There’s a wide range. You may know about
Proxima Centauri, our closest neighboring star outside of our own solar system. It’s
1.3 parsecs away, and its visual luminosity is 0.00005 solar luminosities. You’ll need
a good telescope to see that. On the other end of the scale, deep in the Carina nebula
is eta Carinae. It’s 2300 PARSECS away, yet we can see it with our naked eye. That’s
because it has an intrinsic brightness of almost 5 MILLION solar luminosities.
To standardize these comparisons in terms of distance, astronomers use
the term ABSOLUTE MAGNITUDE. {display as M} This is the apparent magnitude a
star WOULD have if it were a distance of 10 parsecs from Earth. So for example,
IF our Sun were moved to 10 parsecs away from us, its apparent magnitude would now be +4.8,
instead of -26. So the Absolute Magnitude of our Sun is: +4.8. Remember, with these magnitude
scales, less is more—negative magnitudes are brighter than positive magnitudes.
Drawing comparisons between a star’s Apparent Magnitude and its Absolute Magnitude allows
us to address that persistent puzzle—whether a star is especially bright because it’s close,
or because it’s actually giving off a lot of light.
If a star is exactly 10 parsecs away, its APPARENT Magnitude exactly equals its ABSOLUTE
Magnitude. There ARE some stars right around this distance. Pollux, in the Gemini constellation,
is pretty close, at 33.8 light years away, or 10.4 parsecs. That means its apparent
magnitude should be close to its absolute magnitude, and it is: 1.14 versus 1.09.
But if a star is farther away than 10 parsecs,
that means the star looks dimmer than it really is. The flipside is if a star is
closer than 10 parsecs, it appears brighter than its true luminosity.
Here’s how to resolve the situation. We can take the difference between the
apparent magnitude and the absolute magnitude—a calculation called the
DISTANCE MODULUS. {m-M}. We can convert the distance modulus into
an actual distance by putting together the information we’ve discussed so far.
Cutting to the chase, m-M = 5 log (d) -5, where m is the apparent
magnitude of the object, M is the absolute magnitude of the object,
and d is the distance to the object in parsecs. We can turn around and determine
the DISTANCE of an object by solving for d. {display formula d = 10(m-M+5)/5 parsecs}
We’ll save showing you all the math involved in that derivation for another video, along with
some practice problems. You’ll find THESE kinds of videos on our website, socratica.com. You should
sign up for our email list so we can keep in touch and tell you about our newest mathy videos.
We’re not finished, Socratica Friends. There’s yet one more phrase used by astronomers when
they want to talk about the ACTUAL amount of light an object radiates, as opposed to the
apparent brightness. This is the term STANDARD CANDLES. A standard candle is an astronomical
object that has a KNOWN absolute magnitude. This is also commonly measured in Solar Luminosities
So what’s a very bright thing we can use as a standard candle? There’s the Type 1A supernova,
which involves a white dwarf exploding at a certain mass, which means we know the exact
luminosity of the explosion. Unfortunately, these events don’t last for very long.
The most commonly used standard candles in astronomy are Cepheid Variable stars.
They’re known as “Variable Stars'' because their brightness varies. It turns out, their luminosity
varies PREDICTABLY, and the absolute magnitude of the star can be determined from its periodicity.
And then, when you know the luminosity, as well as how bright it appears to us here on Earth,
you can calculate its distance. There’s a whole interesting story about this
discovery by astronomer Henrietta Leavitt..which really deserves its own video, so stay tuned.
We’re adding more astronomy videos on our website,
socratica.com. Why don’t you take a little looksee? {make binoculars with hands}. Oooh!