# Work Process and Continuing Impact

Figure 9 (and the upper, 3-prism, spectrum in Fig. 5a) shows Spectrum Plate c493 of the star Procyon, shown with Payne-Gaposchkin's handwritten notes below, at approximately true size. Procyon is also called alpha Canis Minor (α-CMi) because it is the brightest star in the constellation Canis Minor. Procyon (F5 VI-V) is a late-stage F-type, on the border between being a main sequence-"dwarf" (IV) or “subgiant” (V) star, with seven times our Sun’s luminosity. It has a temperature of 6350K.

Early astronomers worked with glass plate photonegatives, or reverse images, of the spectra. To have it look the way it would to the eye, astronomers would have had to print a "positive" of each photo onto special paper coated with more chemicals. They usually just used the negative directly. Because this is the negative of what you would actually see - the white lines are really dark absorption lines, like the dark lines in Figs. 7 and 8. The handwritten notes and measurements are reversed here because the astronomers made notes on the back of the plates, thus avoiding damage to the photographic emulsion on the front. The plates could be cleaned and reused, so historians are lucky these notes are still there!

Figure 9

In figure 9a below, the spectrum from c493 has been enlarged and some notes have been added. Although Payne-Gaposchkin was working with this plate in the 1920s, it was taken in 1887, almost 40 years before. Even then, the Harvard College Observatory glass plates were being used as a historical database.

Balmer Hydrogen lines Beta through Epsilon are visible. Payne-Gaposchkin has also noted Calcium and Titanium lines (in Angstrom units; 1 A = 10 nm), probably because the definition of an F-Type star means it has strengthening spectral lines of Calcium H and K and has weaker lines of Hydrogen and ionized metals. (The "H" and "K" lines are named so because they were labeled this way by Joseph von Fraunhofer, who discovered absorption lines in the Sun's spectrum in 1814.)

Figure 9a

The green box in Figure 9b indicates the wavelength range covered by c493 on the "F" type spectrum from Figure 7, showing what a small portion of the total spectrum the plate includes.

Since the beginning of photography in astronomy, a relative scale, using reference plates and a system defined by Antonia Maury, had been used to compare the brightness and darkness of absorption/emission lines in photos of star spectra. With the advent of mechanical "microphotometer" machines, able to precisely measure what percentage of a beam of light could pass through any spot on a glass plate photograph, absolute measurements became possible, to the great excitement of astronomers.

In June 1924, Harvard College Observatory published a method to precisely measure line intensity using a Moll microphotometer (see Figure 10), instead of visually comparing a line to a standard star’s spectrum. (Harvard Bulletin 805 -- “Preliminary Report on the Brightness of Absorption Lines”, and “Broad Absorption Band in Class A Spectra”). In July 1926, a second paper was published describing the methods of measurement and calibration of photo plate traces and microphotometer readings. (Harvard Reprint 28 - Proceedings of the American Academy of Arts and Sciences, Vol 61., No. 10 -- July, 1926, "On the Distribution of Intensity in Stellar Absorption Lines.")

Figure 11 shows an example photometer trace of how much light passed through a plate photonegative for part of the Sun’s spectrum near Hγ. Unfortunately, although we know the traces were made on special Bromide paper and were 20" x 5" in size (from the machine documentation), we do not have a surviving example of an actual trace. Though we do not have originals, we do have examples of particularly important or representative scans from publications. The trace in Figure 11 is from a paper about this machine in 1934, but it is used here as if it is from plate c493 for illustration.

Because the negative of the star's spectrum is being scanned, the value $$m$$ of light passing through the bright Hγ line in the plate is not the actual value of interest! A deep notch in the trace here means a lot of light passing through the white line of the negative. Since the actual line is dark, the desired value is the amount of light NOT passing through the plate. This is equal to $$l$$, the amount of light passing through the dark spectral line in the positive spectrum. The value of $$l+m$$ is from the blackbody radiation, while $$n$$ is the amount of background noise.

At the beginning of each trace, a reading with an opaque strip placed over the plate was taken (top blue line in Fig. 12). This was to calibrate "no light passing through plate" = "darkness", or full plate exposure. Then a reading of the general background exposure of the plate near the spectrum was taken to represent "clear film" = no exposure (bottom blue line in Fig. 12). This allowed definition of the full dynamic range of the plate photograph.

Figure 13 shows these calibration values from Figure 12 next to an explanatory diagram from Harvard Reprint 28. The spectrum's background signal $$n$$ was determined by eye, and its placement was one of the few sources of error dependent on the person doing the measurement. For each peak, the background $$n$$ (difficult to determine when peaks overlap), photometer reading $$m$$, and total dynamic range of the photo, $$l+m+n$$ , were carefully measured by hand with a glass rule etched every half millimeter (measurement locations on a peak are illustrated by vertical lines).

Payne-Gaposchkin's application of this process to Plate c493 is shown in Fig.14 below. This page from her notebook is an analysis of c493's photometer trace, referenced in her notes as μ-φ 2458, or the 2458th trace made with the photometer of a plate in the C series. (In her handwriting, the letter $$n$$ looks like a $$u$$, but it is definitely an $$n$$. To see the entire section of her notebook dedicated to analysis/calibration of this plate, click on Figure 14. Scroll down to the third page to see the beginning of the table shown here.)

She noted 180 peaks in her notebook for the trace of c493, with special notes in red to indicate the Balmer lines. The full dynamic range, $$l+m+n$$might vary slightly across the length of the spectrum, so one value was chosen to use for analysis. The columns $$n$$ and $$m+n$$ with bars above indicate when measured values have been normalized to the dynamic range chosen for the analysis. A value of 590 was chosen for analysis of this plate. Figure 14a shows a section of the page in Fig. 14 a little lower down, and you can see that the third column shows ranges of 595 and 600 instead of 590. Thus, the values in the fourth and fifth columns have been adjusted slightly downward to compensate.

Figure 14a

The columns $$[n]$$, $$[m+n]$$, $$dm$$, and $$dl$$ will be discussed in the Normalization section below.

## Calibration of Spectral Plate Intensities (Brightness)

The response of the photochemicals used on the glass plates varied non-linearly as they got closer to full exposure and slightly with the wavelength of the incident light. The coating could also potentially vary from batch to batch of plates. Taking at least two different-length exposures of a spectrum on each plate allowed astronomers to graph a "plate response" or "material" curve at each wavelength to take this into account. A shorter exposure has fewer photons hit the plate than a longer exposure, giving two chemical response points for a given wavelength peak.

Plate c493 is shown in Fig. 15 as an example of a plate with multiple exposures of different lengths (4 vertical stripes). The traces of the line at different exposures shown in Fig. 16 are not from this plate because we do not have any surviving traces, only a few from published papers. We are using this one from Harvard Bulletin 805 as a stand-in. Figure 16 shows microphotometer traces of the H-δ line in the spectrum of Vega at four different exposures. The shortest exposure was the upper curve, with exposure time increasing as the curves get deeper. The lowest curve was overexposed because the chemicals in the center of the line were saturated and couldn't respond to any more light.

As shown in Figure 17 below, Payne-Gaposchkin chose four peaks (each two-point line is from one peak) from the trace of c493 to create a calibration curve. The four lines include one that got close to full exposure in the longer exposure (pointed to by orange arrows, as if taken from Figure 16) and one that did not show in the shorter exposure (note in blue at bottom of Figure 17). These four lines covered the entire range of both axes, with a fair amount of overlap.

The Y-axis values for these "material reduction curves" are the manual measurements from the microphotometer trace as in Figure 12 and 13. The X-axis values are deflection of the galvanometer leaf within the microphotometer -- in other words, the displacement of a small, electric-charge sensor that would become excited with the touch of light. The deflection of the leaf was measured in half millimeter increments, with the minimum deflection calibrated to Darkness and maximum deflection (243 half-mm) calibrated to Clear Film.

In Harvard Circular 301, Payne-Gaposchkin showed that it wasn't necessary to create a calibration curve for each individual line in the spectrum to be analyzed. Any change in the plate response must be locally linear, i.e., smooth and gradual. (If it isn't, then something drastic happened, like a cloud passing or the chemicals being spread unevenly on the plate.) Thus, the overall plate response could be calibrated by choosing two exposures for each of enough spectral lines to span the full dynamic range, and then overlapping these lines to get the callibration, or "reduction", curve for the entire plate. See Figs 17 and 18 below.

## Normalization

Once the nonlinear response of the chemicals on the plate could be converted to the response of the microphotometer with the "reduction curve", Payne-Gaposchkin could finally calculate the measured line intensities (brightnesses), $$l$$. Figure 19 below shows how her raw measurements of $$n$$ and $$m+n$$ from the trace were converted using the reduction curve for Plate c493. Use of the curve was indicated in the column headings in her notes by the braket [ ] operator. The result, $$dm$$, is the change in the deflection of the leaf for the amount of light getting through the plate above the background.

Since the X-axis covers the full range of motion of the microphotometer galvanometer leaf, 243 half-mm, $$dm$$ must somehow be converted to $$dl$$, the amount of light absorbed by the dark line. The conversion method is not clear, but the resulting value of light that was absorbed by the line was referred to as "percentage light lost" for the line. Since the conversion is not a simple proportion of the full range, perhaps there was a conversion table for half-mm to %-of-range we are missing that took into account behavior of the microphotometer.

Finally, the "percentage light lost" for each peak was normalized relative to a standard measurement for a reference star of that type. At the beginning of her work with this plate, Payne-Gaposchkin listed the standard measurements of $$dm$$ and $$dl$$ for the Balmer lines of this type of star with the note, "Standard is taken from H. C. 306", referring to Harvard Circular 306. (See lower left in Figure 20 below.) As mentioned earlier, the Hydrogen Balmer lines are indicated in red in her list of trace line measurements, with the reference values of $$dm$$ written in the column next to the value derived from the calibration curve as in Figure 19. The exact normalization process for this last step was not described and so is not currently known. As with the conversion from leaf deflection to % light loss above, it may be as simple as a reference table so standard noone thought to cite it.

Before microphotometer measurements were available, the assumption had been that the Balmer absorption lines were so dark that almost no light was getting through. Much to astronomers' surprise, as much as 25% of the light was getting through, indicating an enormous amount of radiation being emitted at those wavelengths. By integrating the area under the curve for emitted light, it is possible to calculate the power emitted by the star at that wavelength. As explained in the quote in Figure 22 below from Harvard Bulletin 805, a huge percentage of this star's intensity was being emitted through only one of the Balmer lines.

Today we know this makes sense because stars are composed mostly of hydrogen. Though this was published in 1924, before Payne-Gaposchkin's thesis was published, the idea that the composition of stars mirrored that of Earth was so strongly entrenched that her advisor required her thesis to say her results for the proportion of hydrogen and helium must be incorrect. (See Figures 4 and 5 above.)

## Modern Astronomy

Astronomical instruments are now powerful enough that they can measure spectral signatures from absorption by exoplanet atmospheres! Figure 23 is a diagram showing how a star's spectrum might be affected from passing through an exoplanet's atmosphere.

The Transiting Exoplanet Survey Satellite (TESS) is an MIT-led NASA mission, an all-sky survey for transiting exoplanets. Transiting planets are those that go in front of the star as seen from the telescope and, to date, this is the most successful discovery technique for finding small exoplanets. TESS monitors more than 200,000 stars for temporary drops in brightness caused by planetary transits. The TESS Follow-up Program (TFOP) notifies other telescopes to scan more precisely. Figures 24 and 25 show a schematic of the procedures for TESS and TFOP, respectively.

In a paper released in late 2018, Megan Mansfield, et. al., confirm the independent detection of helium in exo-planet HAT-P-11b with both the Hubble Space Telescope and the CARMENES instrument, making it the first exoplanet with the detection of the same signature of photoevaporation from both ground- and space-based facilities.

## Image Sources

9. (1887). Plate c493. Center for Astrophysics | Harvard & Smithsonian, Photographic Glass Plate Collection, Cambridge, MA.

12. Payne-Gaposchkin, C., & Shapley, H. (1926). On the distribution of intensity in stellar absorption lines (Harvard reprint ; 28). Cambridge, Mass.: Astronomical Observatory of Harvard College.

13. Adapted from Figure 2 from On the distribution of intensity in stellar absorption lines by C. Payne & H. Shapley, 1926, p. 464. (Harvard reprint ; 28). Cambridge, Mass.: Astronomical Observatory of Harvard College.

15. (1887). Plate c493. Center for Astrophysics | Harvard & Smithsonian, Photographic Glass Plate Collection, Cambridge, MA.

19. Wargelin, M. (2019). [Diagram.] Cambridge, MA: John J. Wolbach Library.

21. Adapted from Figure 2 from On the distribution of intensity in stellar absorption lines by C. Payne & H. Shapley, 1926, p. 464. (Harvard reprint ; 28). Cambridge, Mass.: Astronomical Observatory of Harvard College.

23. NASA, ESA, & Levy, Z. (2018). Starlight yields clues to exoplanets’ atmospheres [Image]. Retrieved from https://www.spacetelescope.org/images/heic1802f/

24. Transiting Exoplanet Survey Satellite (TESS). MIT TESS [Logo Image]. Retrieved from https://tess.mit.edu/

25. Vanderspek, R. (n.d.).Imaging and spectroscopy diagram [Image]. TESS Science Operations Center, Cambridge, MA.