# How Far are the Stars? (part 2)

A few months ago, I shared with you how astronomers measure distances to the nearest stars using simple geometry. I also pointed out, however, that we can measure only our small neighborhood using the geometric method we call parallax.

How then, can we possibly know the distances of stars even farther out?

Well, we all know that a light gets dimmer the farther away it is.  Therefore, we can estimate a star’s distance if we can measure how bright it appears to us and then compare that to how bright it’s ‘supposed to be.’

 Hipparchus

Astronomers describe the brightness of any celestial object as its magnitude.  The term goes back to antiquity when the Greek astronomer Hipparchus put stars into six classes of brightness.  The brightest stars he could see were called first magnitude, and the dimmest stars he could barely make out were sixth magnitude.  For one thing, this means that lower magnitudes describe brighter objects, while higher magnitudes describe dimmer objects–the reverse of what most people would expect.  Also, this means that the scale is logarithmic rather than linear, as the human eye does not detect brightness linearly.

A star’s brightness as it appears to us is its apparent magnitude.  Astronomers also define a star’s absolute magnitude as the brightness it would have if it were 10 parsecs (about 32.6 light years) away.  The difference between a star’s apparent and absolute magnitudes is the distance modulus, a direct measure of the star’s distance.  A star’s absolute magnitude is related to its luminosity (the amount of light it emits).  Objects of known luminosity, enabling us to measure their distance, are called ‘standard candles.’

Standard Candles

Among the more important standard candles for determining distances are stars called ‘Cepheid variables.’  These are stars that vary in brightness over a period of several days as they pulsate (expand and shrink again).  The period over which Cepheids vary in brightness indicates their luminosity.

Cepheids are one of several types of variable stars in the instability strip of the Hertzsprung-Russell diagram.  These stars pulsate because in these stars, a layer of helium is subjected to enough heat and pressure that helium atoms lose their electrons and become ionized.  Doubly-ionized helium or He III (with both electrons gone) readily absorbs light that a normal helium atom transmits.  Therefore, He III makes stars slightly dimmer.  However, all heated gases expand and then cool as a result of the expansion.  Thus, the Cepheid pulses outward, and in the cooler environment of the expanded star, electrons recombine with helium ions.  No longer ionized, the helium no longer absorbs light, and the star brightens again.  When the star has expanded too far, its gravity causes all the stellar material to fall back towards the center of the star.  In the heated environment of the compressed star, helium atoms lose their electrons again, the star dims, and the process repeats itself.  In 1917, Arthur Stanley Eddington suggested that Cepheids were types of heat engines; Sergei A. Zhevakin in 1953 correctly identified helium as the particular gas involved.

From Pulsation to Mass, Mass to Luminosity

Since a star’s mass determines how fast and how far it will expand before collapsing under its own gravity, the period of a Cepheid’s pulsation is related to its mass.  A star’s mass, in turn, is related to its luminosity.  As a result, we when we measure how much time it takes for a Cepheid variable to brighten, get dimmer, and brighten again, we have information about its luminosity.  Comparing this to the star’s observed apparent magnitude tells us its distance.  Once enough Cepheids have been observed, it becomes possible to establish a relation that lets us measure distances to any Cepheids, even those in nearby galaxies.

In 1784, English amateur astronomer John Goodricke discovered that the star Delta Cephei varied in brightness over a period of about six days.  Since most stars known at the time to change their brightness were novae or supernovae, Delta Cephei became the prototype of a new type of variable star.  (It turns out that a few months earlier, Goodricke’s friend Edward Pigott had discovered that the star Eta Aquila varies in the same way as Delta Cephei.  Nevertheless, the name ‘Cepheid’ remains).

 Lesser Magellanic Cloud Photo courtesy of NASA

In 1908, Henrietta Swan Leavitt was studying photographic plates that Edward Charles Pickering had taken of the Magellanic Clouds when she noticed a strong relationship between Cepheids’ brightness and the log of their pulsation period.  Leavitt assumed (correctly) that the Magellanic Clouds were much, much smaller than their distance from us; all the stars she was measuring on her photographic plates were thus at about the same distance away.  Thus Leavitt’s period-luminosity relation was a way to determine the luminosity of a Cepheid independently of its distance.

Edwin Hubble & the Andromeda Galaxy

In 1924, Edwin Hubble used Leavitt’s relation to show that the Andromeda Galaxy was indeed a different galaxy and not a nebula in our own Milky Way as many believed at the time.  In 1929, Hubble and Milton Humason used distances to galaxies calculated using Cepheids to establish that more distant galaxies recede from us faster than nearby ones, thus formulating Hubble’s law.

It turns out that there are a variety of stars in the Cepheids’ instability strip.  Walter Baade in the 1940s discovered a second type of Cepheids now called W Virginis variables, after their prototype star in Virgo, the Virgin.  Less massive and dimmer on average than the classical Cepheids, these are older population II stars with fewer heavy elements.  Conflating the two types of Cepheids had introduced errors in distances to nearby galaxies.  For example, Baade’s corrections increased the known distance to the Andromeda Galaxy by a factor of four.  Still smaller and dimmer, with shorter periods of pulsation, are the RR Lyrae variables, named after their prototype star in Lyra, the Lyre.  Astronomers use RR Lyrae stars to measure distances in our own galaxy, but their dimness makes them hard to detect in other galaxies.

The use of Cepheids as standard candles continues into recent decades as well.  The Key Project of the Hubble Space Telescope was to determine the Hubble constant (the rate at which a galaxy at a given distance from us is receding from us)  by measuring the distances to 18 different galaxies using Cepheids.

With modern methods, we are able to detect Cepheid variables in galaxies up to 29 million parsecs (94.6 million light-years) away.  With Cepheids, then, we can measure much more of the universe than with parallax alone.  However, much of the observable universe is so far from us  that it still remains out of reach.  To measure even greater distances, we will need other standard candles, which we shall discuss at a later time.

# Everything you need to know about the Hubble Telescope

Next month marks the 20th anniversary of the Hubble Space Telescope’s launch into space.  On Apr. 24, 1990, at 8:33 a.m., the Space Shuttle Discovery (STS-31) took off, carrying Hubble as its primary payload.  Hubble is the result of a collaboration between NASA and the European Space Agency (ESA), the first of four space telescopes in NASA’s Great Observatories program.  The other three are the Compton Gamma Ray Observatory (de-orbited in 2000), the Chandra X-ray Observatory, and the Spitzer Space Telescope.  Hubble is the only Great Observatory that takes images in the visible light that we all see.  Hubble, therefore, has captured the public’s imagination like no other telescope.

In 1946, Lyman Spitzer wrote the paper “Astronomical advantages of an extraterrestrial observatory.”  In this paper, he discusses the two main reasons to put a telescope above the atmosphere. First of all, our atmosphere distorts images.  Have you ever looked up while standing underwater?  Did you notice how the water distorts images of thing above the surface?  Our air has precisely this effect on the stars.  Of course, the air’s effect is less pronounced than the water’s, but we see it when we observe point sources such as stars.  A star’s twinkling is in fact our attempt to rectify the position of a star, given that its precise position in the sky continues to change slightly due to the atmosphere.  Astronomers quantify this distortion as the atmospheric seeing.  The seeing limits the angular resolution of a telescope (the minimum distance between distinguishable objects in an image).  A telescope in space can therefore see better than even a much larger telescope on the ground.  Secondly, our atmosphere absorbs much of the infrared and ultraviolet light from space, including virtually all UV light less than 310 nm in wavelength. Above the air, Hubble can detect infrared, visible and ultraviolet light. We thus learn more about stars and galaxies by studying more of the light they emit.

Hubble orbits 347 miles above the Earth, a little over twice the distance from Houston to San Antonio.  That orbital height places Hubble in the exosphere, the thinnest, outermost layer of the Earth atmosphere which is in fact a transition between Earth’s atmosphere and interplanetary space.  It also leaves Hubble close enough to Earth that Earth’s disk blocks much of the potential field of view.  Low Earth orbit was required however, so that Space Shuttle crews could reach Hubble and service it.  This turned out to be critical as the primary mirror installed and launched in 1990 had an error.  Instead of being perfectly hyperbolic, the mirror was too flat at the edges by 2.2 microns (.0022 mm).  This was enough to introduce severe spherical aberration into all images.  The crew of STS-61, aboard the Space Shuttle Endeavor, installed corrective optics in 1993.

Here are some interesting facts about the Hubble Telescope:

• Hubble travels at 5 miles per second, completing one orbit every 97 minutes.  The diameter of the telescope (constrained by the size of the Space Shuttle in which it was launched), is 94.5 inches.
• The Space Telescope Science Institute (STScI) in Baltimore, Maryland, is the science operations center for the Hubble Space Telescope.  Astronomers at this institute allocate telescope time and schedule Hubble observations.  They also receive, archive, and distribute data taken with Hubble.
• Optically, Hubble is a reflecting telescope with a Cassegrain design.  In this design, light entering the telescope first encounters a primary mirror and is then focused onto a secondary mirror which in turn focuses the light through a small hole in the primary mirror to an array of instruments on board.

There are several instruments and sensors on Hubble that allow it to take different images and readings. These include:

• The Wide Field Camera, which takes images in visible light and thus produces most of the beautiful photos associated with Hubble.  Earlier versions of this instrument were called ‘Wide Field and Planetary Camera” (WFPC).  WFPC 2 snapped a photo of the famous Hubble Deep Field (1994), imaging some of the most distant galaxies known.
• The Space Telescope Imaging Spectrograph, a spectrometer sensitive to ultraviolet, visible, and near-infrared light.
• The Near Infrared Camera and Multi-Object Spectrometer (NICMOS), a spectrometer sensitive to infrared light.
• The Advanced Camera for Surveys (ACS), which became the primary imaging instrument on board HST upon its installation in 2002, replaced the Faint Object Camera (FOC).  ACS imaged the Hubble Ultra Deep Field in 2003 and 2004.
• The Cosmic Origins Spectrograph (COS), installed this past May, replaced Hubble’s original corrective optics (the Corrective Optics Space Telescope Axial Replacement, or COSTAR).  COS takes spectra in the ultraviolet range.
 Jupiter in Ultraviolet (about 2.5 hours after R’s impact). The black dot near the top is a Galilean moon transiting Jupiter.

In 1993, as Hubble’s optics were restored to their full power, it was discovered that Comet Shoemaker-Levy 9 was on a collision course with Jupiter.  That collision occurred in July 1994.  With Hubble, astronomers could get much clearer and more detailed images of a space collision.  Hubble has provided us with unprecedented telescopic views of all the planets except Mercury, which is too close to the sun in our sky.

Hubble has contributed to the discovery of exoplanets (planets around stars other than our Sun).  In 2008, NASA released a composite of two photographs taken by the ACS in 2004 and 2006.  These photos showed that the bright star Fomalhaut has a companion planet, designated Fomalhaut b.

Astronomers have used Hubble to measure the distances to Cepheid variables (stars whose variation in brightness depends on their luminosity) more accurately.  By comparing this luminosity to the apparent brightness of the star, astronomers could determine the distance to the star and thus to distant galaxies containing them.  This helps astronomers constrain the value of the Hubble constant, the rate at which the universe is expanding.

Perhaps the most striking results from Hubble are the Hubble Deep Field and Hubble Ultra Deep Field.  In these images, Hubble’s sensitive optics produced images of galaxies billions of light years away.  HUDF includes galaxies up to 13 billion light years away (the accepted age of the universe is 13.7 billion years.

The foregoing is just a sample of the science done with Hubble.  Over 8,000 scientific papers based on Hubble data have been published in peer-reviewed journals.

Unfortunately, Hubble cannot last forever.  Even in the exosphere, there is a slight drag on Hubble than causes it to lose energy and slowly fall towards Earth. Further, Hubble’s instruments, like any machines, degrade and become inoperable if not serviced.

After the Space Shuttle Columbia exploded on re-entry on February 1, 2003, the NASA Administrator at the time, Sean O’Keefe, decided that all future Space Shuttle flights must have the option of docking at the International Space Station in the event of an emergency.  Since no shuttle flight can reach both the Hubble Space Telescope and the ISS on the same orbit, this rule canceled a servicing mission to Hubble planned for 2005.  An outcry from astronomers, the public, and elected officials prompted O’Keefe’s successor, Michael Griffin, to reconsider and reverse that decision.  Space Shuttle Atlantis launched on May 11, 2009, marking the fifth and final mission to service Hubble.  Atlantis astronauts installed a new Cosmic Origins Spectrograph and a third Wide Field Camera to replace the second.  They also replaced two batteries, a Fine Guidance Sensor and six gyroscopes which help orient the telescope.  With the refurbishments, Hubble should function at least until 2014.

One of Hubble successors, slated for launch in June 2014, is the James Webb Space Telescope.  This telescope will orbit the Sun (not the Earth) at the second Lagrangian point of the Earth-sun system.  An object at this point remains in line with the Earth and Sun, on the far side of the Earth.  This telescope will look for light from the earliest stars and galaxies in the universe, at infrared wavelengths. Because it images light only in the infrared, James Webb will not be a full successor to Hubble, however.

A fuller successor, should it be approved, built, and launched, would be the Advanced Technology Large Aperture Space Telescope (ATLAST).  This telescope, like Hubble, would form images in infrared, visible, and ultraviolet light.  However, its mirror would be much larger, between 320 and 660 inches in size. Such a telescope is far in the future, however.  If Hubble is gone after 2014, there will be some years without anything quite like it.

Hubble may be in its final years, but we can still experience its fantastic discoveries.  An IMAX film crew and camera accompanied Space Shuttle Atlantis astronauts of STS-125 on their May 2009 mission to service Hubble.  We are thus proud and excited to present to you Hubble 3D, a new IMAX film opening today in IMAX.  Blast off with Hubble 3D and travel across space and time on this amazing adventure.

Check out the preview below.