The Problem with Stellar Distances

The Problem with Stellar Distances
Image Credit: ESA Science & Technology:

So you are reading a post or article about a celestial object, and you notice that the distance to the object stated in the post or article is different from the same value stated for the same object in a different post or article. What gives, since the distance values cannot be right, or wrong for that matter, in both articles? If you have ever noticed a discrepancy in distance or other values for stars, galaxies, or star clusters, here is what you need to know to understand how discrepancies happen, and why distance and other values can both be wrong and right at the same time.

Luminosity/Distance Relationship

It must be stated right at the outset that discrepancies in stated values do not often result from sloppy work or evil intent on the part of astronomers. Having said that though, it must also be stated that even though there are an awful lot of assumptions and inferences involved when it comes to calculating stellar luminosities and by extension, stellar distances, astronomers generally do the best they can with the tools at their disposal to constrain stellar distances to within acceptable limits.

So how do astronomers calculate stellar distances in order to arrive at a luminosity value, and why are the two values so closely related? Well, for one thing, stars are not equally bright, but to account for this, astronomers use an inverse square law to level the playing field, so to speak. Here is how it works:

Inverse Square Law

From this image it should be obvious that the closer a bright object is to the observer, the brighter the object will appear since the light from the object is concentrated in a small area. However, as the distance increases, the amount of light emitted by the object, which is finite, spreads out over an ever increasing area, which has the effect of dimming the light from the object. In this scenario, there are two important values, namely 1) the objects’ intrinsic brightness, commonly referred to as that object’s “absolute magnitude”, which is the level of brightness that an observer would see it that object were positioned at a distance of 10 parsecs (32.6 light years) from the Earth, and 2) the objects’ “apparent magnitude”, which is that object’s brightness as it appears by an observer here on Earth.

So, what does this have to do with the distance to the object? As stated elsewhere, celestial objects all have different absolute magnitudes, but this is compounded by the fact that interstellar dust, gas, and even the radiation from other intervening objects can scatter, or absorb some of the light from a distant object. The effects of light extinction can to some extent be accounted for if on the one hand, the exact distance to the object is known, and exactly how much dust, gas, or other factors are contributing to dimming the light from the object, on the other. However, while it is often possible to account for the dimming effect of light scatter or absorption fairly accurately, calculating the distance to an object is not always so easy, except for objects that are within about 320 light years (100 parsecs) or less from us. To calculate distances that fall within this range, astronomers use a technique called Parallax.

Parallax

In these cases, calculating the distance to the object is easy since the parallax calculations are based on simple trigonometry, although the triangles found in parallax measurements have no relation to those found in “normal” trigonometry. In the picture at the top of the page, the distance that the star appears to have moved when viewed from different perspectives represents its distance. However, even at a relatively close distance, such as that of Proxima Centauri, which is only 4.2 light years away, this angle is extremely small. In fact, Proxima Centauri has a parallax angle of only 0.7687 ± 0.0003 seconds of arc, which roughly equates to an angle that subtends an object 2 cm across, but seen from a distance of 5.3 km away. As distances to objects increase, parallax angles get progressively smaller, until they become so small that they are impossible to measure, even with the most sophisticated equipment available today, and it is at this point that discrepancies in the distance/luminosity stats for objects arise.

Discrepancies Explained

Now that we have covered the basics of how distance and luminosity values are calculated, it is important to explain why different sources list different values for the same object.

At this point, it must be borne in mind that if the parallax angle for an object cannot be measured, astronomers are forced to use other methods to calculate the distance to that object. Many such methods exist, but the most commonly used ones involve extremely high-tech spectroscopic analysis of the object’s spectrum, comparison with objects that are known to be similar but whose distances may or may not be known, and “placing” all objects at a distance of 10 parsecs (32.6 light years) from Earth. The last method is a sort of “equalizer” that ensures that all objects are “viewed” as if from the same distance, regardless of its actual distance from Earth.

Nonetheless, several severe problems remain, which is why the Hipparcos satellite was used to constrain stellar distances more accurately. However, while the satellite was mostly successful, it only recalculated distances to about 100,000 or so objects, which leaves the data for nearly 3 million objects in a major database/catalogue such as SIMBAD (Set of Identifications, Measurements, and Bibliography for Astronomical Data), unchanged, and mostly uncorrected. While there are dozens of databases and catalogues available to professional and amateur astronomers alike, SIMBAD is the most accessible, and arguably the most comprehensive. However, this database is merely a collection of data from a great many sources (including other databases), but it only lists information for stars collected since 1950, and information for galaxies and other objects collected since 1983.

In practice, this means that distance/luminosity calculations made before 1950 or 1983 (and before the advent of modern technology) are for the most part unchanged, and may or may not be correct. However, when these calculations were made, they were based on knowledge and technology that was available at the time they were made. So, where does that leave you, the average reader of astronomy posts and articles?

Are all Astronomy Stats Wrong?

Well, no, but some are. In this context we must remember that calculating the distance to a celestial object, and then to infer its luminosity is one of the biggest challenges that astronomers have to deal with. On this basis, it can be said that while many stats are clearly wrong, they are only wrong because the astronomers of 50 or more years ago simply did not have the tools that astronomers have at their disposal today. Thus, while some stats have been shown by modern technology to be inaccurate, those same stats were “accurate” when they were calculated several decades ago.

Then again, there is the problem that in some cases, such as the Mintaka system in Orion’s Belt, there are as-yet-unexplained factors at work that make it impossible to calculate distances accurately. In fact, some of these factors are extremely resistant to rational explanation, so the next time you encounter irreconcilable, or unexplained discrepancies between astronomical sources, bear in mind that stars are very far away, and that even if a distance value in a database is off by as much as 10% or more in the case of very distant objects, astronomers still consider that value to be accurate to an acceptable degree, simply because of the severe problems that go with arriving at a plausible value at all.

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