A large number of standard candles have been used over the recent history of stellar and galactic studies to estimate distances for sources well beyond those calculated from visual trigonometric parallax.
This laboratory is an activity for you to evaluate a standard candle of your choosing.
While it is part of the astronomy course principles of radiation astronomy, it is also independent.
Some suggested entities to consider are brightness, diameter, tilt, emission lines, absorption lines, periodic variability, mass, time, Euclidean space, Non-Euclidean space, or spacetime.
More importantly, there are your entities.
You may choose to define your entities or use those already defined.
Usually, searching follows someone else's ideas of how to do something. But, in this laboratory you can create these too.
Yes, this laboratory is structured.
I will provide one example of standard candles or their use. The rest is up to you.
Questions, if any, are best placed on the discussion page.
You are free to create your own notation or use that already provided.
For creating a standard candle, what would make an acceptable control group? Think about a control group to compare your standard candle or your process of creating a standard candle to.
The star Betelgeuse may still be too far away for visual trigonometric parallax. Standard candles have probably been used to estimate its distance from the Sun. Estimates from visual trigonometric parallax may be available to evaluate the historical accuracy of standard stellar candles.
In 1977 the first direct angular-diameter observations of 119 Tauri were made.
As a spectral type M2.2 Iab information is inferred about Betelgeuse (a type M2.2 Iab) from the occultation measurements of 119 Tauri. The occultations were on January 31, and April 23, 1977.
The spectral type of 119 Tau has been constant since 1940.
In 1977, 119 Tauri (CE Tau) was a spectral type M2.2 Iab, with a spectral range of M2.0-M2.4 Iab-Ib.
In 1977, Betelgeuse was a spectral type M2.0 Iab-, with a range of M1.3-M2.8 Iab-Ib.
For α Sco in 1980 it was M1.1 Iab with a range of M0.7-M1.5 Iab-Ib
As of 2014, 119 Tauri is an M2Iab according to SIMBAD.
As of 2014, Betelgeuse (alf Ori) is an M2Iab according to SIMBAD.
"The spectral type of α Ori varies roughly with the 5.8 yr period and epoch [...] for brightness, radial velocity, and possible angular-diameter variations. Recently, α Ori has shown the latest spectral type between 1973 and 1975 and again in 1980 January-February with a spectral type of M2.8 Iab-. Its spectral type was about M1.5 around 1969-1971 and again around 1977-1978. By 1982 or 1983, α Ori should again have a spectral type of about M1.5."
In 1977, apparently α Scorpii (Antares) was an M2.2 Iab, but in 2014 it is an M1.5Iab-b.
The standard candle being used in 1977 for spectral region K5-M4 is the CN (cyanide) index from the CN absorption in selected bands.
The apparent magnitude needed for calculating an object's distance in pc is obtained using a photospheric magnitude received for the 1.04 µm flux peak, I(104) in early-M stars.
Near-infrared "photometry on the narrow-band eight-color system [...] has been obtained for these stars. The mean [CN] indices and spectral types derived from photometry of the three supergiants are"
- 119 Tau, CN index = 18 ± 2, I(104) mag = +0.84 ± 0.03, MV = -5.2 (-4.8 to -5.6), distance = 417 pc,
- α Ori, CN index = 18 ± 3, I(104) mag = -2.68 ± 0.03, MV = -5.2, (-4.5 to -5.8), distance = 96 pc, and
- α Sco, CN index = 19 ± 3, I(104) mag = -2.28 ± 0.02, MV = -5.5, (-4.5 to -5.9), distance = 107 pc.
"The distance to α Ori is about half the value, 200 pc, that is almost universally used in the literature."
"The direct evidence for a distance of 200 pc [to Betelgeuse] is a trigonometric parallax of 0.005, which is 10 times smaller than the expected error of measurement [0.005 ± 0.05 mas]."
In 1977 using the absorption spectrum of cyanide believed to be applicable for the spectral region K5-M4 to produce a CN index and the relationship between apparent magnitude and absolute magnitude, a distance of 96 pc was estimated for Betelgeuse. Parallax measurements at that time estimated a distance of 200 pc, but the error was 10 times greater than the value derived.
A parallax measurement by the satellite Hipparcos indicated a distance of 197 ± 45 pc published in 2008.
While post 1980 adjustments were made to increase the estimated distance of Betelgeuse, the initial discrepancy is quite large, at least a factor of 2 using a standard candle.
Estimates made using standard candles rather than some type of direct measurement are expected to be inaccurate.
In 1977, the distance to Betelgeuse estimated by various standard candles suggested 200 pc, "almost universally used in the literature."
Adjustments after 1980 to the standard candle used to estimate the absolute magnitude of Betelgeuse and the 96 pc distance tended toward the universally accepted value.
The ESA's Gaia spacecraft is expected to start collecting data in May 2014 on approximately 109 Milky Way objects. This data will be used to determine their parallax and relative motions. Betelgeuse is a likely target.
Standard candles are hoped to achieve distances within an order of magnitude of reality. It may take another 50 years to produce a device beyond the technology of Gaia to determine distances directly to galaxies beyond the Milky Way.
The analysis of an attempt at a more precise distance to Betelgeuse which in 1977 was beyond direct measurement by trigonometric parallax demonstrates both the strengths and weaknesses of indirect measurements or estimates. Astronomical objects may be sufficiently novel, one to another, to make standard candles at best only good to an order of magnitude.
A standard candle distance to Betelgeuse
The standard candle of the absorption by cyanide (CN) to produce a CN index applicable to the spectral region K5-M4 was analyzed for the star Betelgeuse. The underestimate of the distance to Betelgeuse demonstrates both the value and limitations of standard candles.
In 1977 the direct measurement of the distance to Betelgeuse was lacking. To fill this gap, an accepted standard candle was used to estimate the absolute magnitude of Betelgeuse. Once estimated, an apparent magnitude obtained in the infrared provided an estimate of the distance.
The experimental effort was to locate and analyze the test of a standard candle for the distance to Betelgeuse.
In 1977 using the absorption spectrum of cyanide believed to be applicable for the spectral region K5-M4 to produce a CN index and the relationship between apparent magnitude and absolute magnitude, a distance of 96 pc was estimated for Betelgeuse.
The estimate did not conform to a universally accepted distance to Betelgeuse. The standard candle with some adjustments seems to be well founded in a qualitative approach to distance estimates currently beyond direct measurement.
Any effort to make a standard candle more accurate than an order of magnitude as a replacement for direct measurement is likely to be inaccurate.
Standard candles fill in a necessary gap between techniques of direct distance measurement and back of the envelope guesses.
To assess your standard candle, including your justification, analysis and discussion, I will provide such an assessment of my example for comparison.
Using only one standard candle is anecdotal. At least five separate standard candles, especially four others that were much closer to the universally accepted distance for Betelgeuse should have been included. This would have presented a more statistically sound treatment of standard candles.
- There is a minimum diameter to a blue star that yields a minimum distance for nearby galaxies.
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