Spaghettification

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Astronaut falling into a black hole (schematic illustration of the spaghettification effect) Spaghettification (from NASA's Imagine the Universe!).png
Astronaut falling into a black hole (schematic illustration of the spaghettification effect)
Tidal forces acting on a spherical body in a non-homogeneous gravitational field. In this diagram, the gravitational force originates from a source to the right. It shows both the tidal field (thick red arrows) and the gravity field (thin blue arrows) exerted on the body's surface and center (label O) by a source (label S). Tidal field and gravity field.svg
Tidal forces acting on a spherical body in a non-homogeneous gravitational field. In this diagram, the gravitational force originates from a source to the right. It shows both the tidal field (thick red arrows) and the gravity field (thin blue arrows) exerted on the body's surface and center (label O) by a source (label S).

In astrophysics, spaghettification (sometimes referred to as the noodle effect) [1] is the vertical stretching and horizontal compression of objects into long thin shapes (rather like spaghetti) in a very strong, non-homogeneous gravitational field. It is caused by extreme tidal forces. In the most extreme cases, near a black hole, the stretching and compression are so powerful that no object can resist it. Within a small region, the horizontal compression balances the vertical stretching so that a small object being spaghettified experiences no net change in volume.

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Stephen Hawking described the flight of a fictional astronaut who, passing within a black hole's event horizon, is "stretched like spaghetti" by the gravitational gradient (difference in gravitational force) from head to toe. [2] The reason this happens would be that the gravitational force exerted by the singularity would be much stronger at one end of the body than the other. If one were to fall into a black hole feet first, the gravity at their feet would be much stronger than at their head, causing the person to be vertically stretched. Along with that, the right side of the body will be pulled to the left, and the left side of the body will be pulled to the right, horizontally compressing the person. [3] However, the term spaghettification was established well before this. [4] Spaghettification of a star was imaged for the first time in 2018 by researchers observing a pair of colliding galaxies approximately 150 million light-years from Earth. [5]

A simple example

The spaghettification of four objects falling towards a planet Spaghettification.gif
The spaghettification of four objects falling towards a planet

In this example, four separate objects are in the space above a planet, positioned in a diamond formation. The four objects follow the lines of the gravitoelectric field, [6] directed towards the celestial body's centre. In accordance with the inverse-square law, the lowest of the four objects experiences the biggest gravitational acceleration, so that the whole formation becomes stretched into a line.

These four objects are connected parts of a larger object. A rigid body will resist distortion, and internal elastic forces develop as the body distorts to balance the tidal forces, so attaining mechanical equilibrium. If the tidal forces are too large, the body may yield and flow plastically before the tidal forces can be balanced, or fracture, producing either a filament or a vertical line of broken pieces.

Examples of weak and strong tidal forces

In the gravity field due to a point mass or spherical mass, for a uniform rod oriented in the direction of gravity, the tensile force at the center is found by integration of the tidal force from the center to one of the ends. This gives F = μ l m/4r3, where μ is the standard gravitational parameter of the massive body, l is the length of the rod, m is rod's mass, and r is the distance to the massive body. For non-uniform objects the tensile force is smaller if more mass is near the center, and up to twice as large if more mass is at the ends. In addition, there is a horizontal compression force toward the center.

For massive bodies with a surface, the tensile force is largest near the surface, and this maximum value is only dependent on the object and the average density of the massive body (as long as the object is small relative to the massive body). For example, for a rod with a mass of 1 kg and a length of 1 m, and a massive body with the average density of the Earth, this maximum tensile force due to the tidal force is only 0.4 μN.

Due to the high density, the tidal force near the surface of a white dwarf is much stronger, causing in the example a maximum tensile force of up to 0.24 N. Near a neutron star, the tidal forces are again much stronger: if the rod has a tensile strength of 10,000 N and falls vertically to a neutron star of 2.1 solar masses, setting aside that it would melt, it would break at a distance of 190 km from the center, well above the surface (a neutron star typically has a radius of only about 12 km). [note 1]

In the previous case, objects would actually be destroyed and people killed by the heat, not the tidal forces - but near a black hole (assuming that there is no nearby matter), objects would actually be destroyed and people killed by the tidal forces because there is no radiation. Moreover, a black hole has no surface to stop a fall. Thus, the infalling object is stretched into a thin strip of matter.

Inside or outside the event horizon

Close-up of star near a supermassive black hole (artist's impression) Close-up of star near a supermassive black hole (artist's impression).jpg
Close-up of star near a supermassive black hole (artist's impression)

The point at which tidal forces destroy an object or kill a person will depend on the black hole's size. For a supermassive black hole, such as those found at a galaxy's center, this point lies within the event horizon, so an astronaut may cross the event horizon without noticing any squashing and pulling, although it remains only a matter of time, as once inside an event horizon, falling towards the center is inevitable. [8] For small black holes whose Schwarzschild radius is much closer to the singularity, the tidal forces would kill even before the astronaut reaches the event horizon. [9] [10] For example, for a black hole of 10 Sun masses [note 2] the above-mentioned rod breaks at a distance of 320 km, well outside the Schwarzschild radius of 30 km. For a supermassive black hole of 10,000 Sun masses, it will break at a distance of 3,200 km, well inside the Schwarzschild radius of 30,000 km.

Notes

  1. An 8-meter rod of the same strength, with a mass of 8 kg, breaks at a distance 4 times as high.[ citation needed ]
  2. The smallest black hole that can be formed by natural processes at the current stage of the universe has over twice the mass of the Sun.[ citation needed ]

Related Research Articles

<span class="mw-page-title-main">Black hole</span> Object that has a no-return boundary

A black hole is a region of spacetime where gravity is so strong that nothing, including light and other electromagnetic waves, has enough energy to escape it. Einstein's theory of general relativity predicts that a sufficiently compact mass can deform spacetime to form a black hole. The boundary of no escape is called the event horizon. A black hole has a great effect on the fate and circumstances of an object crossing it, but it has no locally detectable features according to general relativity. In many ways, a black hole acts like an ideal black body, as it reflects no light. Moreover, quantum field theory in curved spacetime predicts that event horizons emit Hawking radiation, with the same spectrum as a black body of a temperature inversely proportional to its mass. This temperature is of the order of billionths of a kelvin for stellar black holes, making it essentially impossible to observe directly.

<span class="mw-page-title-main">Tidal force</span> A gravitational effect also known as the differential force and the perturbing force

The tidal force or tide-generating force is a gravitational effect that stretches a body along the line towards and away from the center of mass of another body due to spatial variations in strength in gravitational field from the other body. It is responsible for the tides and related phenomena, including solid-earth tides, tidal locking, breaking apart of celestial bodies and formation of ring systems within the Roche limit, and in extreme cases, spaghettification of objects. It arises because the gravitational field exerted on one body by another is not constant across its parts: the nearer side is attracted more strongly than the farther side. The difference is positive in the near side and negative in the far side, which causes a body to get stretched. Thus, the tidal force is also known as the differential force, residual force, or secondary effect of the gravitational field.

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<span class="mw-page-title-main">Roche limit</span> Orbital radius that will break up a satellite

In celestial mechanics, the Roche limit, also called Roche radius, is the distance from a celestial body within which a second celestial body, held together only by its own force of gravity, will disintegrate because the first body's tidal forces exceed the second body's self-gravitation. Inside the Roche limit, orbiting material disperses and forms rings, whereas outside the limit, material tends to coalesce. The Roche radius depends on the radius of the first body and on the ratio of the bodies' densities.

The Schwarzschild radius or the gravitational radius is a physical parameter in the Schwarzschild solution to Einstein's field equations that corresponds to the radius defining the event horizon of a Schwarzschild black hole. It is a characteristic radius associated with any quantity of mass. The Schwarzschild radius was named after the German astronomer Karl Schwarzschild, who calculated this exact solution for the theory of general relativity in 1916.

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<span class="mw-page-title-main">Supermassive black hole</span> Largest type of black hole

A supermassive black hole is the largest type of black hole, with its mass being on the order of hundreds of thousands, or millions to billions, of times the mass of the Sun (M). Black holes are a class of astronomical objects that have undergone gravitational collapse, leaving behind spheroidal regions of space from which nothing can escape, not even light. Observational evidence indicates that almost every large galaxy has a supermassive black hole at its center. For example, the Milky Way galaxy has a supermassive black hole at its center, corresponding to the radio source Sagittarius A*. Accretion of interstellar gas onto supermassive black holes is the process responsible for powering active galactic nuclei (AGNs) and quasars.

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References

Inline citations
  1. Wheeler, J. Craig (2007), Cosmic catastrophes: exploding stars, black holes, and mapping the universe (2nd ed.), Cambridge University Press, p. 182, ISBN   978-0-521-85714-7
  2. Hawking, Stephen (1988). A Brief History of Time . Bantam Dell Publishing Group. p. 256. ISBN   978-0-553-10953-5.
  3. Astronomy. OpenStax. 2016. p. 862. ISBN   978-1938168284.
  4. Calder, Nigel (1977). The Key to the Universe: A Report on the New Physics . Viking Press. p. 143. ISBN   978-0-67041270-9 . Retrieved July 10, 2022. Published as a companion to the BBC TV documentary The Key to the Universe.
  5. "Astronomers See Distant Eruption as Black Hole Destroys Star" (Press release). National Radio Astronomy Observatory. Phys.org. June 14, 2018. Retrieved June 15, 2018.
  6. Thorne, Kip S. (1988). "Gravitomagnetism, Jets in Quasars, and the Stanford Gyroscope Experiment" (PDF). In Fairbank, J. D.; Deaver, Jr., B. S.; Everitt, C. F.; Micelson, P. F. (eds.). Near Zero: New Frontiers of Physics. New York: W. H. Freeman and Company. pp. 3, 4 (575, 576). From our electrodynamical experience we can infer immediately that any rotating spherical body (e.g., the sun or the earth) will be surrounded by a radial gravitoelectric (Newtonian) field g and a dipolar gravitomagnetic field H. The gravitoelectric monopole moment is the body's mass M; the gravitomagnetic dipole moment is its spin angular momentum S.
  7. "Spinning Black Hole Swallowing Star Explains Superluminous Event - ESO telescopes help reinterpret brilliant explosion". www.eso.org. Retrieved December 15, 2016.
  8. Hawley, John F.; Holcomb, Katherine A. (2005). Foundations of Modern Cosmology (illustrated ed.). Oxford University Press. p. 253. ISBN   978-0-19-853096-1. Extract of page 253
  9. Hobson, Michael Paul; Efstathiou, George; Lasenby, Anthony N. (2006). "11. Schwarzschild black holes". General relativity: an introduction for physicists. Cambridge University Press. p. 265. ISBN   0-521-82951-8.
  10. Kutner, Marc Leslie (2003). "8. General relativity". Astronomy: a physical perspective (2nd ed.). Cambridge University Press. p. 150. ISBN   0-521-52927-1.
General references