In the early decades of his work, Edward Pickering had compared the brightness, or magnitude, of all stars to Polaris, the pole/north star, by using mirrors and prisms to bring it into photos of the sky where it was not normally visible. Comparison of the magnitude of a star to a reference star is known as Photometry. The ancient Greek astronomers divided the stars visible to the naked eye into six magnitude groups. The first magnitude stars were the brightest, whilst the faintest stars visible to the naked eye were of 6th magnitude. When a quantitative photometric system was developed in the 19th century, it was made to agree closely with this existing system.
In practice the apparent magnitude of an object X is measured by reference to a standard star of known apparent magnitude:
magX = magSTD − 2.5 log10 ( fluxX / fluxSTD )
The magnitude of the standard star thus defines the magnitude of the star whose brightness we have measured; in other words, photometry is relative. (The previous explanation, as well as further discussion of photometry, can be found here, and here is a slideshow of the types of complex correction used in modern photometry.) Today, all stars are compared to the brightness of Vega, also known as alpha Lyrae. The advent of astronomical photography in the late 1800s made it possible for humans to study stars as faint as 16th magnitude, as well as document very bright stars with "negative" magnitudes which are brighter than Vega.
To avoid needing to have Polaris as a reference in every photo, Pickering gave Miss Leavitt the task of creating a consistent standard for magnitude by identifying new reference stars spread across the entire sky and comparing them to sixteen long-period variable stars in the polar region. Once the visual and photographic judgments were cross-checked and calibrated, many stars could then be used as known references; hopefully one would naturally appear in a photo taken of any part of the sky. Leavitt would choose one variable as a starting point and then proceed from star to star across a glass plate photonegative, judging each one’s magnitude and making a notation in her scientific notebooks. At that time, and with the instruments available, a star’s diameter in a photo was used as a reasonable approximation for brightness.
In her 1909 article in Popular Astronomy (ADS:1909PA.....17..530L), "Standard Photographic Magnitudes", Leavitt verified that the Harvard Photometric Scale agreed closely with three different methods of measuring a star's absolute magnitude. Figure 11a is an excerpt from the article, in which she states: "We apparently have a satisfactory working basis for determining the magnitudes of stars in all parts of the sky, on an approximately correct scale."
Astronomers quantified their instrument limitations and error sources as much as possible, trying to account for and quantify even tiny sources of error. The use of a "fly spanker" as discussed above (Figure 8) to calibrate the magnitude of a reference star on a photographic plate to take into account variations in exposure, weather, telescope settings, etc. is one example. Averages were often used to compensate for possible atmospheric effects which might have reduced starlight reaching the telescope for a non-variable star, e.g., a very fine haze not noticed by the observer, or a plate taken near the horizon. Multiple exposures of the same star would be measured, and the average of three measurements used as the official magnitude of record.
Instrumental effects caused by physical changes or defects in the setup could include:
- Mapping of the image of the curved sky to a flat glass plate, which distorted star shapes at the edges of the plate. Think of a globe versus a map of the Earth. If a star was too close to the edge of a plate, it was not used for measurement.
- Under- or over-exposure of a star – That star would not used for measurement, as when too close to the plate edge.
- If the plate angle relative to the telescope optics varied even by a fraction of a degree in the holding clamp, relative distance between stars on a plate would be shifted as in the example in Figures 7 and 9 above. This effect was usually not an issue when overlapping small areas of the plates for study. Note that the offset grows larger the farther away from the aligned section.
Other possible equipment variations (e.g., perhaps the glass plate itself might not be exactly flat, the chemicals on plates might vary from batch to batch, possible imperfections in the optics might exist, and especially temperature changes which could cause expansion/contraction of equipment materials) were also noted and compensated for whenever possible.
Another source of uncertainty in measurement is the instrument's response to starlight, including the human eye's response for each individual! In addition, the chemicals used in glass plate photography are sensitive to a different wavelength band than the human eye, shifted toward low ultraviolet with less response in the red.
Leavitt published a paper in 1915 to try to quantify these effects for a red star. (ADS:1915HarCi.188....1L) This paper included observations made by her collegue, Annie Jump Canon, who worked at HCO from 1896 until her death in 1941; Figure 12 shows the two of them together. Figure 13 provides a summary graph of the differences in magnitude between visual observation and photographic measurements for star S Cephi, a "carbon red" star, which was difficult to photograph.
The top curve is composed of visual observations by Mr. W. M. Reed (observer at HCO 1890-1900 who originated the card catalogue / bibliography of variable stars now at AAVSO) and Miss Cannon, who "agree very closely in their sensitiveness to color". Both had made many visual observations in the period during which photographs were taken of that area of the sky. The lower curve contains magnitude observations made from specially stained photographs, which are much fainter. It was noted that the time of peak brightness was different for the visual and photographic measurements.
The type of variable star Leavitt is most known for working with is now well understood. A classical Cepheid is a type of star that pulsates radially, varying in both diameter and temperature and producing changes in brightness with a well-defined stable period and amplitude. They undergo pulsations with very regular periods on the order of days to months. Classical Cepheids are 4–20 times more massive than the Sun, and up to 100,000 times more luminous. These Cepheids are yellow bright giants and supergiants whose radii change by millions of kilometers during a pulsation cycle (~25% for the longer-period I Carinae!).
The accepted explanation for the pulsation of Cepheids is called the Eddington valve, or κ-mechanism, where the Greek letter κ (kappa) denotes gas opacity. Helium is the gas thought to be most active in the process.
Doubly ionized helium (helium whose atoms are missing both electrons) is more opaque than singly ionized helium. The more helium is heated, the more ionized it becomes. At the dimmest part of a Cepheid's cycle, the ionized gas in the outer layers of the star is opaque, and so is heated by the star's radiation, and due to the increased temperature, begins to expand. As it expands, it cools, and so becomes less ionized and therefore more transparent, allowing the radiation to escape. Then the expansion stops, and reverses due to the star's gravitational attraction. The process then repeats.
Figure 14 shows Hubble Images of a Cepheid variable star taken in 2010:
Figure 14a links to an interactive map of variable stars in the Small Magellanic Cloud identified in the OGLE-III On-line Catalog of Variable Stars. (Source papers here.) The Optical Gravitational Lensing Experiment (OGLE) project is a long term project with the main goal of searching for the dark matter with microlensing phenomena. Clicking on the image will take you to a site where you can dig down to find light curves for individual variable stars.
The American Association of Variable Star Observers (AAVSO), founded in 1911, includes amateur and professional astronomers from all over the world. Their initial work was expanded-upon through the efforts of Harvard College Observatory (HCO) Director Edward C. Pickering, who encouraged the increased participation of much needed variable star observers among amateur and professional astronomers.
Today, the AAVSO coordinates, evaluates, compiles, processes, publishes, and disseminates variable star observations to the astronomical community throughout the world. Observers send their data to Headquarters, where they are checked, processed, and added to the AAVSO International Database. The data are available through the AAVSO website. The AAVSO and its observers frequently provide the professional community with archival data, intensive monitoring of interesting variable stars, and target-of-opportunity event notification for coordinated observing campaigns and satellite observations.
Figure 15 shows the constellation The Pleiades, with the major stars labeled. Until recently, it had been impossible for astronomers to calculate the distances to these stars from Earth. Figure 16 shows a graph of newly calculated star positions of the Pleiades using data from the Gaia mission. (The view from Earth is from the bottom of cube.) Figure 17 shows a stereoscopic view if you have a pair of the 3D glasses with red over one eye and blue over the other.
12. (1913). Annie J. Cannon [and] Henrietta S. Leavitt [photograph]. HUP Cannon, Annie Jump, Harvard University Archives, Cambridge, MA.
13. Leavitt, H. S. & Pickering, E. C. (1915). The Color Index of S Cephei. Harvard College Observatory Circular, 188, 1-4.
14. NASA, ESA, the Hubble Heritage Team (STScI/AURA), & Gendler, R. (2011). Cepheid variable star V1 in M31 [Image]. Retrieved from http://hubblesite.org/image/2847/news_release/2011-15.
15. Abramson, G. (2018). Around the Pleiades. Retrieved from https://arxiv.org/pdf/1808.02968.pdf
16. NASA, ESA, & AURA/Caltech. (2004). Annotated image of the Pleiades and HST field of view [Image]. Retrieved from http://hubblesite.org/image/1563/news_release/2004-20.
17. Abramson, G. (n.d.). A 3D plot of the positions of 1,600 Pleiades stars [Image]. Retrieved from https://www.syfy.com/syfywire/how-far-away-are-the-pleiades.