Gravity and its
effects.
The Lives of the Stars.
In the Cosmos of 1980, Carl
Sagan explains to us how gravity determines the formation and evolution of
stars. It is also responsible for motions of gaseous or rocky bodies around
them, so that orbiting objects receive starlight without interruption… a light
that could sustain life forms. The miracle of life on a planet is indeed
associated with the mysterious behaviour of the force that holds it close to
its companion star. The Sun’s gravity force decreases as we move away from the
star, and more specifically, the law of universal gravitation tell us that such
force is inversely proportional to the square of the distance. This spatial
behaviour plays a critical role. In the 19th century, mathematician Joseph
Bertrand demonstrated that the only attractive central force decreasing with
distance r and producing stable
closed orbits is that one varying as 1/r2
[1].
Carl Sagan also described a "magic gravity machine" that
allowed us to guess how buildings and living things could look on planets with
gravitational fields other than the Earth one, or how an undesirable change in
Earth's surface gravity would affect us. Together with the Cheshire cat1,
we discovered that gravity does not just affect people, our everyday objects,
planets, and stars. For example, a light ray does not propagate in a straight
line in the presence of a gravitational field. Light describes curved paths,
and a very strong field can even completely stop the particles (photons) that
form it. Could we use gravity to "freeze" light? Let's imagine that
the Cheshire cat has travelled to the Sun and tries to return to Wonderland. To
leave the solar surface, the cat needs to jump at a speed that allows it to
escape from the star's gravity. This escape velocity is (2GM๏/R๏)1/2, where G is the universal gravitational
constant, and M๏ and R๏ are the mass and radius of the Sun, respectively.
After some simple calculations, we find that the magic cat must travel more
than 600 kilometres per second to meet again Alice. Although it needs a great
boost and a special suit to be protected in such a hostile environment for
life, gravity does not prevent it from returning home. However, the situation
is getting complicated if the Sun collapses suddenly to a radius of about 3 km.
The escape velocity would then be about 300,000 kilometres per second and even
light would be frozen on its surface2. For a distant observer, the
star would go out, turning into a black hole.
Despite obtaining basically correct conclusions, we have discussed the
effect of gravity on radiation by “cheating”, considering photons with mass
subject to Newton's laws. However, we know that photons forming a light ray
have no mass, but a certain amount of energy that is proportional to the light
frequency. Additionally, in Newtonian
mechanics, a particle with zero mass (m
= 0) does not suffer the gravitational pull of another object with mass M, since the mutual force is
proportional to the product of both masses m x
M = 0. Albert Einstein developed a more
general perspective by assuming the equivalence between mass and energy, which
allows us to understand the deviation and slowing down of photons in the
presence of a massive object. For example, if a body emits blue light and is
progressively collapsing, a distant observer will initially see a blue dot in
the sky, which in a chameleon way turns red, then becomes invisible to the
human eye, although potentially detectable with a radio antenna, and eventually
joins the immense dark sky. That is, photons progressively lose energy (they
are slowed down), gradually decreasing the frequency of the observed light.
There is currently compelling evidence of the existence of black holes that are
fossils of massive stars that have suffered a huge collapse during their
evolution.
But Einstein went further by assuming that gravity is a distortion of
space and time caused by the matter/energy content. To verify the validity of
this theory of General Relativity (GR), many astronomical observations have
been made over the past 100 years. In 1919, Arthur Eddington and his
collaborators compared the apparent position of stars close to the Sun during a
total eclipse with their true position. The data were reasonably consistent
with the light deviation that predicts the GR: 4GM๏/R๏c2 = 1.75 arc-seconds. Recent
observations during the 2017 total eclipse have been used to measure a
deviation of 1.75 arc-seconds, with an error of only 3% (one hundredth of a
degree!) and in excellent agreement with the GR [2]. Moreover, astronomers at
the University of California-Los Angeles have observed in the infrared the
position of thousands of stars in the central region of the Milky Way for more
than 20 years, allowed them to study their motions. Some of these stars appear
to orbit the Galactic Centre as the planets around the Sun do (see the left
panel of Figure), and their orbits suggest the presence of a black hole of
about four million solar masses in the heart of the Milky Way. The S0-2 star is
particularly relevant, as when it passes through the pericenter3 it
is located only 17 light hours from the supermassive black hole (about four
times the distance separating Neptune from the Sun), so it must be affected by
relatively strong gravitational effects. The GR predicts a significant
reduction of photon energies (gravitational redshift), as well as an orbital
precession of about 12 arc-minutes. Such effects have finally been detected by
the GRAVITY collaboration [3].
It is believed that the centre of virtually every galaxy contains a
supermassive dark monster. In April 2019, combining signals from eight radio telescopes
spanning the whole planet, the Event Horizon Telescope (EHT) obtained the first
image of a black hole storing more than six billion solar masses in the centre
of the nearby galaxy M87. This image along with notions of quantum gravity and
gravitational waves are included in the chapter 9.6 of this book (Black Holes by Ernesto Lozano). The
photo taken by the EHT collaboration shows a bright asymmetric ring with a
diameter of about 40 micro arc-seconds and surrounding a dark region. This
image is consistent with synchrotron emission from hot plasma around the black
hole, which has suffered the gravitational effects predicted by the GR.
Einstein's ideas seem to have passed "demanding examinations"
performed for a century on stellar systems and galactic nuclei, and as we will
see below, also on galactic scales.
When Carl Sagan published Cosmos, there was a discovery that confirmed
the GR on galactic scales and was going to have profound repercussions. In the
Ursa Major constellation (also known as the Big Deeper), Anglo-American
astronomers found two very close and almost identical images of the same
distant object Q0957+561 (see the top right panel of Figure). It is a galactic
nucleus nine billion light-years from us suffering from the gravitational lens
effect of a massive galaxy and a galaxy cluster located between the distant
source and Earth. In this case, the gravity of the massive monster does not
weakly deflect light from the remote source (as the Sun does with nearby
stars). The galaxy and its companion cluster act as a convergent lens: two
divergent rays passing on both sides of the galaxy + cluster system are
diverted to Earth to form two images separated by six arc-seconds.
Stars in the centre of the Milky Way (left), Q0957+561 (top right) and
the Cheshire cat (bottom right). The magic cat has replaced its eyes with the
two images of a double quasar, just when the right side image is suffering a
micro-lens effect. Figure created by the author using online and own materials.
Many distant galactic nuclei are active, including Q0957+561. This means
that its central black hole is embedded within an envelope formed by several
structures with gas and dust, whose emission is variable. They are usually
called quasars, and sometimes, as a result of gravitational lens effects, we
find quasars with multiple images or multiple quasars. Multiple quasars are a
Rosetta Stone to decipher the mysteries of Cosmos [4]. For example, when a
variation in the brightness of an image of a multiple quasar is detected, you
have to wait a few days, months, or even years to observe the same variation in
another image. These time delays predicted by the GR have become a fundamental
piece for accurately determining the current expansion rate of the Universe In
addition, when the light of an image penetrates a galaxy acting as a
gravitational lens, it may suffer an additional lens effect due to the
population of stars in the corresponding galaxy region. A micro-lens effect of
stars appears superimposed on the macro-lens effect of the galaxy as a whole.
The study of this physical phenomenon is allowing us to know the stellar
populations of relatively distant galaxies, and the inner structure of quasars.
Micro-lenses (stars) produce a selective source magnification. The brightness
of the hottest and most compact regions in the vicinity of the black hole is
more amplified than that of relatively cold and extended regions, resulting in
spectral bluing (see the bottom right panel of Figure).
Notes:
1 Smiling cat that disappears
and reappears at will in Alice’s Adventures in Wonderland (Lewis Carroll,
1865).
2 The speed of light in
vacuum is c = 299.792 km/s.
3 In an elliptical orbit it is the closest point to
the focus.
References:
[1] H. Goldstein, C. Poole & J. Safko, 2001, Classical Mechanics, Addison-Wesley, p. 89 [ISBN 9780201657029]
[2] D. G. Bruns, 2018, Gravitational
starlight deflection measurements during the 21 August 2017 total solar eclipse,
Classical and Quantum Gravity, 35, ID 075009
[3] GRAVITY Collaboration, 2018, Detection
of the gravitational redshift in the orbit of the star S2 near the Galactic
centre massive black hole, Astronomy & Astrophysics, 615, L15;
2020, Detection of the Schwarzschild precession
in the orbit of the star S2 near the Galactic centre massive black hole,
Astronomy & Astrophysics, 636, L5
[4] T. Treu, 2010, Strong lensing
by galaxies, Annual Review of Astronomy and Astrophysics, 48, 87
Luis J. Goicoechea
Santamaría.
PhD in Physics.
Professor of Astronomy & Astrophysics, Universidad de Cantabria.
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