1.2 The challenge of distances in Astrophysics
Astrophysics is the discipline within science that focuses on
the understanding of our Universe. To get a glimpse of the fabric of its
gigantic structure, it is important to determine the place of the objects
within it. Various types of coordinates were developed to locate objects
depending on their place in our sky, but the crucial and most difficult
parameter to estimate is their heliocentric distance.
Spectroscopy provides useful data to estimate those distances.
In fact, spectral analysis of stars can provide information on their absolute
magnitude. The apparent magnitude of an object is a measure of its luminosity
when observed from Earth, on an inverse logarithmic scale. These apparent
magnitudes are biased by extinction from dust located in the interstellar
medium. The absolute magnitude of an object is its apparent magnitude if it
were observed from a distance of 10 parsecs, and corrected for extinction, so
it is distance-independent. Thus, using those two magnitudes, it is possible to
extract distances. This technique is called spectroscopic parallax, in contrast
to true parallax which is a geometric measurement. Recently, the European Space
Agency's Gaia mission has published over a billion (true) parallaxes of stars
in the sky, providing a huge leap in our understanding of the structure of the
Milky Way.
However, the accuracy of Gaia's parallax measurements decrease
rapidly with distance, and it is useful to consider alternative methods of
distance estimation. To estimate absolute magnitude, a metallicity-based
technique was developed by Iveziéet al. [2].
In Astrophysics, every element heavier than hydrogen or helium
is referred to as a metal. This comes from the fact that those metals are
really rare compared to hydrogen and helium which constitute 98% of the mass of
our baryonic Universe. That is why astrophysicists use the shorthand of
metallicity to refer to chemical composition. It is often quantified by the
[Fe/H] ratio defined as in Equation 1.2.1, where
Nx are the abundances in element x and the e
index refers to the values of the Sun. The spectrum of an object varies
substantially as a function of its metallicity, since the elements composing it
produce absorption rays. Hence Iveziéet al.'s approach of specifically
taking into account the metallicity of an object when computing its magnitude
is a reasonable data analysis strategy.
[Fe/H] = log10
(NFe/NH)e
NFe
-- log10 (1.2.1)
(NFe)e
NFe/NH
2
One issue with spectrometric data is that it is very costly in
instruments and time to acquire it. In fact, spectroscopy requires the
observatory to target a specific object to measure its parameters and the
exposure times can be huge for faint objects.
An alternative to real spectroscopy is to build up a very
low-resolution spectrum based on multi-band photometric data. Those are much
quicker to obtain since imaging cameras can record numerous objects (up to many
millions) at the same time. Indeed, photometric data are obtain by using
cameras with various filters (hence the "multi-band" qualification) which
allows one to cover all the wavelengths tackled in spectroscopy. Nowadays, with
various surveys like Gaia, Pan-STARRS or SDSS and others, a huge amount of
photometric data is available. This takes astrophysics into the world of big
data, which
3
is of no surprise since the number of objects in the Universe
itself is tremendous. And with big data it is natural to consider using
techniques like machine learning.
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