6 ms·

How come: 14.2 + 7.5 == 21.7 != 20.8 ? Does the gravitational wave contain 0.9 solar masses of energy?

by BenoitP 10y ago

antognini 10y ago
Yes. Gravitational waves transmit both energy (i.e., mass) and angular momentum.
- markus2012 10y ago
  So... build more detectors and pinpoint the direction the gravity wave is coming from?
  - infogulch 10y ago
    Yes! There are 2 now, so they can give a very coarse estimate of the direction with a precision of 'somewhere in this swath of the sky' (using the relative location, the wave propagation speed [light speed], and the arrival times relative to each detector). As more detectors come online they will be able to triangulate more accurately. The next one is supposed to come online in 2018 iirc.
  - antognini 10y ago
    That's the idea! I seem to remember that there are plans to build another detector in India. I'm not sure what its status is. http://gw-indigo.org/tiki-index.php?page=LIGO-India http://gw-indigo.org/tiki-index.php?page=LIGO-India
    - ahnitz 10y ago
      Funding for its construction was approved by India. We are hoping that it might coming online in ~ 5 years. It takes a long time to build everything from the ground up.
    - ziotom78 10y ago
      Note that the VIRGO detector, located near Pisa (Italy), has already taken a set of measurements a few years ago, and it would have been sensitive enough to detect waves like the one from last September. Unfortunately, Virgo was down for upgrades when GW150914 came. I recall that they plan to restart Virgo by early 2017, so it should be operational well before Ligo India. (And I like to underline that Ligo and Virgo joined together in the Ligo/Virgo collaboration and thus work together: as a matter of fact, the first guy who saw GW150914 in the raw data was from Virgo, and the papers presenting the detection were signed by people in both collaborations.)
ISL 10y ago
Because the event is extremely violent. Just as a nuclear bomb converts a small amount of mass to radiant energy (grams?), a merger can convert mass into other forms of energy, too. Gravitational waves, of which there are probably many passing through us all the time from many sources, carry a lot of power. The only reason we don't see them every day is that spacetime itself is extremely stiff.
- stouset 10y ago
  Isn't it also that power decreases over the cube of the distance to the event? A truly gargantuan amount of power (1 solar mass equivalent) distributed across a 3-dimensional shell dozens or hundreds of light years across should be minuscule at any Earth-sized point along that shell.
  - tehmaco 10y ago
    They put the distance at 440−190+180 Mpc. 440 megaparsecs is is around 1.2 billion light years away(!).
  - elihu 10y ago
    Wouldn't it be inverse square, not inverse cubed? Or do gravity waves behave different than other things we're used to, like light?
    - dsqrt 10y ago
      Actually the nice thing about gravitational waves is that we are sensitive to their amplitude, which scales as 1/r, and not to their energy, which scales as 1/r^2.
- specialp 10y ago
  Stoset is right. The reason why we do not notice them is due to the inverse square law. This event was 1.3 billion light years away. 1 Solar mass of energy being turned into a gravitational wave nearly instantly creates a very strong gravitational wave. But by the time it comes here, it deforms things by distances that we normally reserve for subatomic particles. What this finding shows is that this happens somewhat regularly in our Universe, it was just that we were previously unable to achieve the precision to measure such small deformations.
rubidium 10y ago
Yes (and good question!). From the article: "The initial binary was composed of two stellar-mass black holes with a source-frame primary mass m1 14.2 M⊙, secondary mass m2 7.5 M⊙, and a total mass of 21.8 M⊙. The binary merged into a black hole of mass 20.8 M⊙, radiating 1.0M⊙ in gravitational waves."
- deleted 10y ago
  [deleted]
- semi-extrinsic 10y ago
  For reference, one solar mass of radiation is about the same as the output from a gamma ray burst, or about 2000 times the output from a supernova. Or in less sensical units, the energy from detonating 1% of our galaxy's mass worth of TNT.
  - dsqrt 10y ago
    Gamma-ray bursts emission is strongly beamed into a small solid angle. So, although their equivalent isotropic energies (that is the energy that would be needed to power gamma-ray bursts if the emission was isotropic) are huge, the actual energies released in gamma-ray bursts are more or less compatible with those of supernovae (~0.1% of a solar mass).
  - Scarblac 10y ago
    As usual, XKCD provides some help to understand how much energy a supernova is: "Which of the following would be brighter, in terms of the amount of energy delivered to your retina: 1. A supernova, seen from as far away as the Sun is from the Earth, or 2. The detonation of a hydrogen bomb pressed against your eyeball? Answer: the supernova, by nine orders of magnitude." https://what-if.xkcd.com/73/ https://what-if.xkcd.com/73/
InclinedPlane 10y ago
Hey, let's do some math! The formula for gravitational potential energy is just mgh (mass times gravitational acceleration times height), and g is just GM/r^2, so the potential energy of one black hole in the other's gravitational field would be GMm/r, which would be the same for the other, so the total gravitational potential energy would be twice that. Also, the schwarzschild radius of a black hole is about 3km per solar mass (2e30 kg). Which means that before their event horizons touch the two black holes should be separated by a distance of at least 65.1 km. So, 2 * G * 14.2 * 7.5 * (2e30kg)^2 / 65.1 km is... 8.73e47 joules divide by c^2: 9.7e30 kg or 4.86 solar mass So the system actually had nearly 5 solar masses of gravitational potential energy in it, some of which was radiated away as gravitational waves.
- cyphar 10y ago
  You're just calculating how much kinetic energy the black holes had when they collided. This energy goes into the spin of the final black hole. The energy for the gravitational waves comes from loss of mass of the final black hole.

How come: 14.2 + 7.5 == 21.7 != 20.8 ? Does the gravitational wave contain 0.9 solar masses of energy?

by BenoitP 10y ago

How come: 14.2 + 7.5 == 21.7 != 20.8 ? Does the gravitational wave contain 0.9 solar masses of energy?

antognini 10y ago

Yes. Gravitational waves transmit both energy (i.e., mass) and angular momentum.

markus2012 10y ago
So... build more detectors and pinpoint the direction the gravity wave is coming from?
- infogulch 10y ago
  Yes! There are 2 now, so they can give a very coarse estimate of the direction with a precision of 'somewhere in this swath of the sky' (using the relative location, the wave propagation speed [light speed], and the arrival times relative to each detector). As more detectors come online they will be able to triangulate more accurately. The next one is supposed to come online in 2018 iirc.
- antognini 10y ago
  That's the idea! I seem to remember that there are plans to build another detector in India. I'm not sure what its status is. http://gw-indigo.org/tiki-index.php?page=LIGO-India http://gw-indigo.org/tiki-index.php?page=LIGO-India
  - ahnitz 10y ago
    Funding for its construction was approved by India. We are hoping that it might coming online in ~ 5 years. It takes a long time to build everything from the ground up.
  - ziotom78 10y ago
    Note that the VIRGO detector, located near Pisa (Italy), has already taken a set of measurements a few years ago, and it would have been sensitive enough to detect waves like the one from last September. Unfortunately, Virgo was down for upgrades when GW150914 came. I recall that they plan to restart Virgo by early 2017, so it should be operational well before Ligo India. (And I like to underline that Ligo and Virgo joined together in the Ligo/Virgo collaboration and thus work together: as a matter of fact, the first guy who saw GW150914 in the raw data was from Virgo, and the papers presenting the detection were signed by people in both collaborations.)

ISL 10y ago

Because the event is extremely violent. Just as a nuclear bomb converts a small amount of mass to radiant energy (grams?), a merger can convert mass into other forms of energy, too. Gravitational waves, of which there are probably many passing through us all the time from many sources, carry a lot of power. The only reason we don't see them every day is that spacetime itself is extremely stiff.

stouset 10y ago
Isn't it also that power decreases over the cube of the distance to the event? A truly gargantuan amount of power (1 solar mass equivalent) distributed across a 3-dimensional shell dozens or hundreds of light years across should be minuscule at any Earth-sized point along that shell.
- tehmaco 10y ago
  They put the distance at 440−190+180 Mpc. 440 megaparsecs is is around 1.2 billion light years away(!).
- elihu 10y ago
  Wouldn't it be inverse square, not inverse cubed? Or do gravity waves behave different than other things we're used to, like light?
  - dsqrt 10y ago
    Actually the nice thing about gravitational waves is that we are sensitive to their amplitude, which scales as 1/r, and not to their energy, which scales as 1/r^2.
specialp 10y ago
Stoset is right. The reason why we do not notice them is due to the inverse square law. This event was 1.3 billion light years away. 1 Solar mass of energy being turned into a gravitational wave nearly instantly creates a very strong gravitational wave. But by the time it comes here, it deforms things by distances that we normally reserve for subatomic particles. What this finding shows is that this happens somewhat regularly in our Universe, it was just that we were previously unable to achieve the precision to measure such small deformations.

rubidium 10y ago

Yes (and good question!). From the article: "The initial binary was composed of two stellar-mass black holes with a source-frame primary mass m1 14.2 M⊙, secondary mass m2 7.5 M⊙, and a total mass of 21.8 M⊙. The binary merged into a black hole of mass 20.8 M⊙, radiating 1.0M⊙ in gravitational waves."

deleted 10y ago
[deleted]
semi-extrinsic 10y ago
For reference, one solar mass of radiation is about the same as the output from a gamma ray burst, or about 2000 times the output from a supernova. Or in less sensical units, the energy from detonating 1% of our galaxy's mass worth of TNT.
- dsqrt 10y ago
  Gamma-ray bursts emission is strongly beamed into a small solid angle. So, although their equivalent isotropic energies (that is the energy that would be needed to power gamma-ray bursts if the emission was isotropic) are huge, the actual energies released in gamma-ray bursts are more or less compatible with those of supernovae (~0.1% of a solar mass).
- Scarblac 10y ago
  As usual, XKCD provides some help to understand how much energy a supernova is: "Which of the following would be brighter, in terms of the amount of energy delivered to your retina: 1. A supernova, seen from as far away as the Sun is from the Earth, or 2. The detonation of a hydrogen bomb pressed against your eyeball? Answer: the supernova, by nine orders of magnitude." https://what-if.xkcd.com/73/ https://what-if.xkcd.com/73/

InclinedPlane 10y ago

Hey, let's do some math! The formula for gravitational potential energy is just mgh (mass times gravitational acceleration times height), and g is just GM/r^2, so the potential energy of one black hole in the other's gravitational field would be GMm/r, which would be the same for the other, so the total gravitational potential energy would be twice that. Also, the schwarzschild radius of a black hole is about 3km per solar mass (2e30 kg). Which means that before their event horizons touch the two black holes should be separated by a distance of at least 65.1 km. So, 2 * G * 14.2 * 7.5 * (2e30kg)^2 / 65.1 km is... 8.73e47 joules divide by c^2: 9.7e30 kg or 4.86 solar mass So the system actually had nearly 5 solar masses of gravitational potential energy in it, some of which was radiated away as gravitational waves.

cyphar 10y ago
You're just calculating how much kinetic energy the black holes had when they collided. This energy goes into the spin of the final black hole. The energy for the gravitational waves comes from loss of mass of the final black hole.