The Cloud in God's Eye

Henrietta Leavitt published her finding that the intrinsic (the “real”) brightness of a Cepheid variable was strongly related to its period (the duration of its fluctuation cycle) in 1912.   It didn’t take long for astronomers to realize the important implications of this relation.  If they could just figure out the actual distance to even one Cepheid (obviously, that would have to be a cepheid closer to our neck of the woods than the collection Henrietta discovered in the Small Magellanic Cloud), they could calculate the distance to the SMC using the inverse square law!

How?  Remember a couple of blogs ago, when I explained the inverse square law using a pair of identical candles?  The two conditions needed to made the law work were, one, you had to know the actual distance to one member of the pair (in my example, it was the distance to the nearer candle), and two, both candles had to be identical, so they would shine equally brightly if placed at the same distance from you.  That way, after your friend put the second candle some unknown distance away, you could be confident that the only source of their (now) differing brightness was their unequal distance.

With those two factors in mind, consider our old friend Delta Cep.  Long before Henrietta Leavitt turned her attention to the Cepheids in the SMC, Delta Cep’s period had been determined to be 5.4 days, and its apparent magnitude (brightness) had been pegged at 4.3 at the dimmest point in its cycle (by the way, that’s about mid-way between the brightest and dimmest stars visible to the naked eye.  You can find Delta Cep yourself in the circumpolar constellation Cepheus if you consult a star chart and live in an area with reasonably dark skies).  Today, we know from parallax measurements with the Hubble Space Telescope that Delta Cep is about 891 light years away.  Courtesy of Leavitt’s discovery, any Cepheid whose period is equal to Delta Cep’s has the same intrinsic brightness; a pair of such stars would be like identical candles.  If an astronomer from 1912 had known Delta Cep’s distance, then using the Period-Luminosity functions from Leavitt’s SMC sample, he or she could have easily calculated how bright a Cepheid with Delta Cep’s period would be if it was located in the SMC (or, if you like, the brightness of Delta Cep itself if it were in the SMC). 

The figure below illustrates how this would have been done.   First, you would have located the point along the X-axis that corresponds to the log of Delta Cep’s 5.4 day period (about the 0.5 point). Then, you’d have drawn a straight line up from the 0.5 point to the lower of the two period-luminosity plots inside the figure (that’s the one that plots the Cepheids in the SMC at the dimmest point in their cycles).  Next, you’d have drawn a horizontal line from the plot across to the Y-axis (the horizontal red line in the figure), and simply read the magnitude where the line intersects that axis.  When I do that, just by eye I get an apparent magnitude of approximately 15.8.

Finally, all the conditions would be met to employ the inverse square law!  The difference between an object of magnitude 15.8 and an object of magnitude 4.3 corresponds to a difference in brightness of 11.5 units along the magnitude scale.  In turn, that difference translates into the fact that Delta Cep’s putative twin in the SMC would be roughly 33,750 times dimmer than the real Delta Cep (the magnitude scale astronomers use to measure brightness is another log-based scale, so it’s highly non-linear).  The inverse square law tells us that brightness falls off with the square of the distance, so Delta Cep’s twin would be about 184 times as far away as Delta Cep (squaring 184 yields approximately 33,750).   Finally, since Delta Cep is itself 891 light years away, its twin (and therefore the SMC itself) must be 184 multiplied by 891, or 164,000 light years distant - a figure within respectable shouting distance of the modern estimate, which is around 210,000 light years.

Of course, I cheated.   Astronomers in 1912 didn’t know the distance to Delta Cep, so they couldn’t compute that actual distance to the SMC.  They would have had to be content with the knowledge that, however far away Delta Cep was, the SMC was some 184 times further away than that.  A pretty strong clue, you’d have to admit, that some of the objects in the night sky were very, very far away, indeed.

But astronomers of the time wanted more: they wanted the actual distance to the SMC! Energized by the prospect, a contemporary of Henrietta Leavitt’s, Earnest Hertzsprung, set out to measure the distances to known Cepheids within our galaxy using several distance-measuring techniques that I won’t get into here.  Although none of these techniques was as accurate as the trigonometric parallax method, Hertzsprung still managed to derive crude distance measurements to not one, but 13 Cepheids. 

Those distances gave Hertzsprung the tools he needed to make a preliminary determination of the distance to the SMC using the method described above.  The value he obtained, 30,000 light years, was far short of the modern value of over 200,000 light years.   But even Hertzsprung’s gross underestimation was large enough to deal another devastating blow to the Biblical story of Creation.  According to literalist biblical scholars, the universe is only about 6000 years old.  Furthermore, according to Genesis, all the sources of light in the night sky were created in a single 24-hour period – the fourth day after God initiated the Creation process (and there are records of peoples in the Southern Hemisphere having seen the SMC as long as thousands of years ago, so it was definitely present in the sky during biblical times).  But if the SMC was created only 6000 years ago, the light from the cloud has not had time to cross more than a small fraction of the distance between it and the Earth, even with Hertzsprung’s gross underestimate. Given our current understanding of the true distance to the SMC, the cloud could not appear in our skies until after 200,000 AD!  That’s so far in the future I can’t even imagine it.

Is there an alternative way to save the biblical story?  In one of the earlier blogs in this series, I considered a rather unlikely account for how the literal account of Creation could be reconciled with the fact that even the nearest stars are so far away that their light takes years to reach the Earth.  On the fourth day of creation, God would have had to place those stars within the confines of our own solar system (so that their light had a chance to make it to the Earth before the fourth night descended), and then He would have had to whisk them out to their current positions.  While God would have had to hurry some of these stars along pretty fast – at 26 light years away, a star like Vega would take longer than 6000 years to reach its present position even if it was moving as fast as our fastest jetliners – our spacecraft travel much faster than that, so I don’t think God would have found it a problem. 

But even this rather far-fetched account would fail miserably for the Small Magellanic Cloud.  6000 years is not nearly enough time to transport the SMC even 30,000 light years away unless God was moving all the stars in the cloud far faster than the speed of light!  Not only would that violate all known laws of physics, but it would once again have rendered the Small Magellanic Cloud invisible; its light could not reach us if it was moving away at more than the speed that light travels!

Unfortunately for those who believe in the literal interpretation of Genesis, we’re not finished with the biblical devastation wrought by Cepheid variables.  In the next installment, we’ll tackle some Cepheid-fueled discoveries of an astronomer named Edwin Hubble.  You may have heard of him, or at least of the telescope named after him.