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
Julian date:  2457683.16
            "Never stop."

*THE DAILY ASTRONOMER*
*Thursday, October 20, 2016*
*The Cepheid Keys*


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TONIGHT'S SCIENCE LECTURE:
"Learning from Nature"
USM neurobiologist Dr.  Douglas Currie discusses how scientists
can learn more about human biology by studying animals in their
natural environments.

Where: Southworth Planetarium
When:  7:00 p.m.  (Doors open at 6:30 p.m.)
How much; by donation

Call 207-780-4249 or consult the web-page
http://usm.maine.edu/planet/learning-nature
for more information.
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Astronomical "facts" are all very well, but the most compelling aspect of
astronomy in our mind is the means by which astronomers garnered these
facts that we take for granted today.    Throughout the centuries, most
notably the last two of them, humanity has accumulated such a store of
astronomical knowledge that we couldn't learn it all even if we had ten
full lifetimes to devote to its study.     Every piece of that knowledge
was made possible through a combination of countless hours of observations,
meticulous data analysis and the collaboration of myriad researchers, most
of whom receive scant credit for their contributions.      Whenever we cite
these facts, we often gloss over the efforts of those obscure scientists
who acquired them for us.

Today, we provide elaboration on a topic we introduced in yesterday's
article: on knowing the Andromeda Galaxy's distance .     We mentioned that
it was more than 2.2 million light years away.     How were astronomers
ever able to measure that distance?

A light year, incidentally, is the distance light travels in one year
through a vacuum.   As this speed slightly exceeds 186,000 miles a second,
a light beam propagating through space traverses 5.8 trillion miles during
one Earth year!   To give one an idea about how much space separates
objects, the closest star to our solar system, Proxima Centauri, is 4.2
light years away.  The most distant stars we observe with the unaided eye
are about 3000 light years away.   With that in mind, it seems all the more
extraordinary that we know that the Andromeda Galaxy,* the closest major
spiral galaxy to our own, is 2.2 million light years away: a measurement
made less than one hundred years ago.

We begin with a famous relation in astronomy; something called "The
Distance Modulus," which relates a star's apparent magnitude (apparent
brightness), absolute magnitude (actual brightness), and distance. (See
"From the Catacombs of Infinite Knowledge.")   If one knows two of these
values, one can determine the other.    This modulus is quite intuitive.
We measure a star's apparent magnitude directly just by observing it on
Earth.    This brightness value does not yield information about its actual
brightness, however.  For all we know, a given bright star could be
comparatively faint, but close; conversely, a faint star could be quite
intrinsically brilliant, but far away.    If we can figure out the star's
distance, we would know its true brightness.  Or, if we can somehow
ascertain a star's absolute magnitude, we can compare it to its apparent
magnitude and measure its distance.

The trick is knowing a star's intrinsic brightness.   And, with a certain
type of variable star, Cepheid variables, we can directly know its
brightness by observing its variability period.   Cepheid variables are
giant stars that pulsate, growing larger and then smaller and then larger
again over a period that can last many weeks.  Conveniently, the
variability period: the between successive minima (least brightness) or
maxima (greatest brightness) depends on its intrinsic brightness.  The
brighter the Cepheid variable, the longer the variability period.   As
brightness relates directly to a star's luminosity, or energy output, these
correlation between the variability period and brightness is called "The
Period-Luminosity Relation."

This relationship was first established by a survey of Cepheid variable in
the Small Magellanic Cloud,  a satellite galaxy to the Milky Way
approximately 160,000 light years away.  It was noticed that the brighter
Cepheid variables in the SMC had longer periods than the dimmer ones.
As astronomers assumed that the stars within the SMC were at equal
distances from Earth, they determined that the Cepheidvariable's luminosity
affected the star's variability period.**

Edwin Hubble, certainly not an obscure astronomer, measured the distances
to Cepheid variables within the Andromeda Galaxy and, by extension, to the
Andromeda Galaxy itself   He knew the absolute magnitude by the amount of
time they needed to cycle through one variability period.  He then compared
it with the star's apparent magnitude, discernible through his powerful
telescope. He determined that the Andromeda Galaxy was about 900,000 light
years from Earth.  Though this measurement was enough to place the
Andromeda Nebula, as it was then called, well outside the Milky Way
Galaxy's boundaries, it was less than half the currently accepted value.
Astronomers later learned that there are two classes of Cepheid variables,
each of which has its own period-luminosity relation.   Hubble used
'cluster variables,' which yielded an incorrect distance to the Andromeda
Galaxy.


*​Cepheid Variable Curve.   A simplified light curve of a Cepheid variable
star.*
*As its outer layers contract and expand, the star dims and then brightens.
  Astronomers*
*know that the variability period is directly related to the star's
luminosity, or *
*intrinsic brightness. (A variability period is the time separating
successive minima)  The longer the period, the brighter the Cepheid.
Therefore, an astronomer can determine a Cepheid variable's true brightness
by observing its variability period.  *

When the two classes were defined, and the measurement to the Andromeda
Galaxy refined accordingly, astronomers realized that that splotch of light
in the sky we had called the Andromeda Nebula was 2.2 million light years
away!   The most distant object one can observe with the unaided eye.

Today, we know that the Andromeda Galaxy is just one of billions of
galaxies.  And, by cosmological standards, Andromeda is so close it is
almost the Milky Way Galaxy's Siamese twin.    However, calculating
Andromeda's distance served as a stepping stone toward the vast cosmic
reaches well beyond: reaches that even today we haven't fully fathomed.


*The Andromeda Galaxy, located in the constellation Andromeda, is well
positioned for viewing this time of year.    Find it high in the  evening
sky, just north of the Andromeda constellation; or to the northeast of the
Great Square of Pegasus.   Though approximately four degrees across, the
Andromeda Galaxy is somewhat diffuse and therefore observable only in
darker regions.   Note that the gibbous moon will often obscure it, even
when it is in a different part of the sky.   So, one might want to wait
until the weekend to start trying to find the Andromeda Galaxy.

**We know the stars in the Small Magellanic Cloud are not equidistant from
Earth.  However, we can assume they are for the purposes of this
observation.   People in Los Angeles are not all precisely the same
distance from us, but Los Angeles is far enough away that we can make a
safe assumption that they are.

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FROM  THE CATACOMBS OF INFINITE KNOWLEDGE
*"The Distance Modulus"*


*​*
The equation shown above is one of astronomy's most famous mathematical
formulae.  It relates three variables: M, a star's absolute magnitude; m, a
star's apparent magnitude, and d, a star's distance in parsecs.    (Yes, of
course we'll explain what we just wrote.)

"Magnitude" measures a celestial object's brightness. The small "m" refers
to the object's apparent magnitude, or how bright it appears.   The large
"M" refers to the object's absolute magnitude, or its intrinsic
brightness.  Technically,  the absolute magnitude equals the celestial
object's apparent magnitude from a distance of ten parsecs.   (A "parsec"
is equal to about 3.26 light years.)

The magnitude system is a logarithmic scale that assigns lower numbers to
brighter objects.  For instance, a star of magnitude 1 is approximately 2.5
times brighter than a star of magnitude 2, but 2.5 times dimmer than a star
of magnitude 0.    (See "Etched on a dimly lit wall in the catacombs of
infinite knowledge")

If we know two of these variables, we can determine the third.      As is
the case with the Andromeda Galaxy, an astronomer will know the Cepheid
variable's apparent magnitude (m) through direct observation.
 Observation of its variability period yields its luminosity or absolute
magnitude (M). Then, the astronomer can utilize her prodigious mathematical
skills to calculate the distance.
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ETCHED ON A DIMLY LIT WALL IN THE CATACOMBS OF INFINITE KNOWLEDGE
The 2.5 brightest factor in the magnitude system is actually 2.512.      It
was so designated because 2.512 is the fifth root of 100.    Therefore,a
star of magnitude 1.0 is precisely 100 times brighter than a star of
magnitude 6.0.   6.0 is generally the naked eye limit for celestial
objects.  However, some lynx-eyed sky watchers are able to observe slightly
dimmer stars than those of the sixth magnitude.
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