How far did you say?

I bet from time to time you too get mesmerized with the night sky view, and the multitude of visible stars, particularly when far from big cities where night skies seem darker. One thing that’s notorious is how stars have different brightness and intensity, this is a direct effect of two factors, how hot that star is and how far away from us it is located. And maybe you wonder while contemplating the stars, if those that look brighter are nearer than the dimmer ones.

This isn’t a straightforward question, as stars come in a huge variety of sizes and luminosity, some of them being thousands of times bigger that our Sun, and of course all of them being scattered at different distances from us. But wait, isn’t it typical to listen from time to time, news where distance to certain stars or other celestial objects are mentioned; then, how astronomers can measure such distances? Well, the answer, as commented, isn’t as straightforward as it might seem.

First, is important to acknowledge that star distances are really, really big; so big that measurement in terrestrial dimensions is almost impractical. For example, considering our nearest star, aside of our Sun of course. This is Proxima Centauri, which is about 25 trillion miles (40 trillion km), away from Earth. So, which “more friendly”  distance units are used by astronomers then? This is also a staged answer, one method is to measure based on multiples of the distance from Earth to the Sun, this is denominated an Astronomical Unit (AU), which is the average distance from Earth to the Sun (approximately 149 million of kilometers or 93 million miles), using this scale, the distance to the mentioned Proxima Centauri star is 12,950 AU. Another method is to use the time that light takes to traverse certain distance; for example, the distance from Earth to the Sun is 8 light-minutes (this means that we see the sun as it was eight minutes in the past; all the time!). If we use this scale, the distance to Proxima Centauri is 4.22 light-years.

The Parallax method

The conception and study of how the universe is organized has evolved from Ancient Rome to modern times. Before the 19th century, Astronomy, the predecessor of astrophysics, was a kind of boring science, as it was mostly dedicated to the classification of planets and its moons, nearby stars and some asteroid or comet here and there. And certainly, there was no precise measure of the star’s distances. It was till the beginning of the 19th century when the parallax method started to be used, the effect was first noticed by Giuseppe Calandrelli, and used afterwards for precise measurements by Friedrich Bessel in 1838.

The so called Solar parallax, is a measurement done by checking the position of a target star against more distant stars in the background, this measurement is done twice, with 6 months of separation between measurements, this means that the first is done when earth is in one side of its orbit around the sun, and the second one is done exactly at the other end of it, being the distance between measurements equivalent to two Astronomical Units (AU). By using these readings, you can measure the angle of a hypothetical isosceles triangle formed between the Earth, the Sun and the target star. In this case, the key angle is registered due the apparent motion of the measured star compared to more distant objects located in the background. Since these measured angles are very small, they’re in the range of the “arc seconds”.

Parallax measurement (ircamera.as.arizona.edu)

If we consider that each one of the 360 arch degrees in a circle have 60 arch minutes, and each arch minute has in turn 60 arch seconds. With this method it was possible to measure distances to near stars, and this reference became the foundation for the “parsec”, the distance unit most used by astrophysicist nowadays, which is the distance at which one object is located to form a 1 arc-second angle, therefore the name parallax-second or “parsec”. One parsec is equivalent to 206,265AU, or roughly 3.26 light-years. Using our reference star, Proxima Centauri’s, its distance is equivalent to 1.3009 parsecs.

Standard candles.

The parallax method of course is limited as well by the precision on the measured angle, currently this precision is in the range of micro-seconds of arc (from  the Hubble telescope), this precision limits the distances that can be measured with this method to close to 3,066 parsecs (or 10,000 light-years), this being just around 10% of our Milky Way galaxy’s diameter.
This, of course, raised a problem, but with the astrophysicists’ wit, of course alternatives were found; what was used to solve this problem is based on the named Inverse square law, a physical law stating that the intensity or quantity from certain source is inversely proportional to the source’s distance. To explain this in more figurative terms, if you imagine a lamp in a dark room, the light intensity in a surface at one meter from this lamp will be four times as strong as the light intensity in a surface located at two meters from the lamp, and sixteen times stronger than the light intensity on a surface at 4 meters from the lamp; being more specific, the energy or intensity of the source decreases by 4 as the distance to the source doubles. So, by knowing how intense a light is, then you can determine how far it is. Simple, right?

Inverse square law (wikipedia.org)

The problem in astrophysics was how to find these standard candles, a source for which it’s luminosity was well known. Fortunately, the solution was provided by the American astronomer Henrietta Leavitt, who studied a particular type of stars called Cepheid variables in the Magellanic Clouds, these are stars that change its luminosity at regular intervals. In her studies she noticed how these star’s brightness changed in a well-defined and stable period and amplitude, allowing to know its true luminosity by observing its pulsation period, and in this way, have a special type of standard candle. Was Henrietta Leavitt’s work which allowed Edwin Hubble to discover that the know “Andromeda nebulae” was in fact a galaxy at great distance from our own Milky Way, and so noticing that the cosmos was a much bigger place, and our galaxy was just one of many out there in the cosmos. Hubble did this measurement by checking the distance of a Cepheid variable star in this nebula, back in 1924; and as a result, noticing that its distance was 2.5 million light-years (or 778 Kilo-parsecs), placing it outside our Milky Way, which is only one hundred thousand light years long.

Type 1A supernovae.

Cepheid variables were a valuable resource to measure distant objects, but this method has also its limitations, which is basically the telescope’s resolution to detect the pulsation on these stars. This limits this method to a maximum of around 50 Mega-parsecs. And again, there was another restriction to measure deep space objects. To solve this, additional methods were developed, but the golden standard to measure cosmic distances was the use of another occurring cosmic standard candle, the type 1A supernovae.

SN2014J_supernova (spacedaily.com)

A supernova is the way in which a massive star ends when it reaches its final evolutionary stages, this is characterized by a dramatic and catastrophic destruction, caused by a final epic explosion. A type 1A supernovae, is caused by the explosion of a white dwarf star in a binary system, this dwarf star have a companion star from which it steals and accumulates matter, until it reaches a point where it cannot longer hold the gravitational pressure and then explodes; these supernovas are less common, occurring on average once every 200 years in a galaxy like ours; these supernovae have a well-defined brightness at its peak, therefore making them excellent standard candles, with the added value of being extremely luminous, sometimes almost outshining its host galaxy. Considering that typically galaxies are composed of billions of stars, well, this is an extremely luminous object. Due these characteristics, these supernovae can be used to measure distances form deep space, covering practically all observable universe, which is about 14.26 giga-parsecs or 46.5 billion light years in any given direction.

Yet you might wonder, isn’t it true that supernovae explosions are a rare phenomenon in the cosmos? Then how can we be measuring distances continuously by using these elusive explosions? Well it is true, supernovae in general are a rare phenomenon, happening on average once every 50 years in a galaxy the size of our own Milky way, (containing 100 billion stars).

But, we must consider that the space is a very large place. The latest estimated figures on the number of galaxies are measured at 200 trillion in the observable universe, with this amount and a bit of dimensional analysis, it can be deduced that there are supernovae occurring every second; and if you look at any section of the sky it’s very likely that you can detect a supernova in hours or days, this means, that there’s a lot of reference material to perform these measurements.

So, the next time you look to the starry sky, you can rest assured that stars and galaxies’ distances are under control, and can be precisely determined, so, if you ask about this to your personal astrophysicists he surely will reply to you “we got this!”

Regards – Alex

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