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It has been suggested here:

How long does it take a black hole to eat a star?

that it can take (at best) a rather short amount of time for a supermassive black hole to eat a star as viewed by a distant observer (that is - to fall through the event horizon). But we're also told that if an astronaut fell into a black hole, to the observer it would appear to take a very long time indeed for the astronaut to complete the fall due to relativistic effects and time would appear to the observer to have stopped for the poor astronaut (also being spaghettified).

In other words, how can a black hole find time to eat at all with such a case of indigestion, as it were?

How does one reconcile the two statements?

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    $\begingroup$ You can't. The first one is incorrect. An "external observer" can never see anything fall through the event horizon. $\endgroup$ – Rob Jeffries Mar 15 '16 at 21:06
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    $\begingroup$ Manty related questions that you should look at e.g. physics.stackexchange.com/q/102202 physics.stackexchange.com/q/21319 The latter is a possible duplicate. $\endgroup$ – Rob Jeffries Mar 15 '16 at 21:11
  • $\begingroup$ So why do we ever see emissions from black holes as in quasars? Are we watching effects from matter that fell a very, very long time ago? Thanks Rob! Will do. $\endgroup$ – Ted Jackson Mar 15 '16 at 21:12
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    $\begingroup$ The radiation comes from regions well outside the event horizon - at least 3 Schwarzschild radii. $\endgroup$ – Rob Jeffries Mar 15 '16 at 21:13
  • $\begingroup$ So if a star were traveling directly at a black hole at say 300,000 km/h and we were watching it from far away wouldn't there just be a flash and then nothing but a black hole after that? Or are you saying it will forever be bright because we never see it go completely in? $\endgroup$ – Bill Alsept Mar 16 '16 at 21:28
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The answer to this would be highly variable depending on the size & gravity of both the star and the black hole, their proximity, motion, spin, tidal forces and bonds in the star (i,e quark stars and neutron stars would decay at different rates than gas giants.)

That said, you could consider instead the time it takes for a star to become completely ripped apart and become part of the accretion disk.

For a more concrete scenario, this star is estimated to be ~10 solar masses and is not yet fully devoured over the course of a decade. illustration of devoured star based on xray readings The article suggests the sun would take roughly 2 years to be consumed.

source material figures

a, The long-term source rest-frame 0.34–11.5 keV unabsorbed luminosity curve. The Chandra, XMM-Newton and Swift observations are shown as blue squares, red triangles and green circles, respectively. Error bars show the 90% confidence intervals of the measurements. For the first Chandra observation (C1) in 2005, the 3σ upper limit is shown with an arrow. We have merged the seven Chandra observations in 2011 to create a single coadded spectrum, given the lack of significant spectral/flux change in these observations. Similarly we also created a coadded spectrum from the combination of S2–S5 and another one from S6–S8. For clarity, we have offset S2–S5 to be one month earlier, because they are too close to S6–S8 in time. The solid line is a model of disrupting a 2 M⊙ star by a black hole of mass 106 M⊙ with slow circularization and super-Eddington effects (see Supplementary Information). Such a model describes the data well. The dashed line plots t−5/3, assuming a peak X-ray luminosity of 1044 erg s−1 that is reached two months after disruption of the star; it represents the typical evolution trend for thermal TDEs24,30, which obviously last much shorter than our event. MJD, modified Julian date. b, The unfolded X-ray spectra. The X1 and C10 observations were fitted with a diskbb model (red dotted line) plus a powerlaw (green dot-dashed line), and the C2, X2, X3 and C3–C9 observations were fitted with a CompTT model (the X2 spectrum is not shown, but looks very similar to X3). Note that C10 can also be described with the CompTT fit to C3–C9 subject to a fast warm absorber. For clarity, we show only pn data for the XMM-Newton observations. Also for clarity, the spectra were rebinned to be above 2σ in each bin in the plot.

The source material for the same article has some further reading on other similar scenarios with actual stars.

Of course, as you mention, an outside observer will not see all the matter of the star fall beyond the event horizon according to general relativity. However, we can extrapolate velocities and measure fading light intensity. Just like relativistic speeds are more difficult to achieve the closer you get to the speed of light, the majority of the distance to the horizon is traversed sooner rather than later with the most time dilation closer in. Just act like an engineer at that point and couple the estimate with the note, 'time curves toward infinity after x point'

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The LIGO merger of two black holes can give a time frame for the merging

LIGO

Note that this is gravitational frequency on te Y axis.

From the data we see that the time for the event to happen is of order of seconds in our reference frame. It is worth looking at the link and the large number of data in both detectors that allowed too form the plot above.

A large star eaten by a black hole would give a similar pattern.

Now we do not see an event horizon, with its various definitions, we do see though a gradual build up and an end, so to all intents and purposes the disappearance of two into one has happened within five seconds from the time gravitational radiation became detectable.

This video discussing a second merger is interesting.

As the answer by Garet Claborn shows one can see with optical electromagnetic frequencies the process of a star being eaten by a black hole, which takes a lot of time. Detecting gravitational waves has not reached, and probably will never reach such details. So my explanation above should be taken as a limit for how fast the whole thing can end, within seconds, once the two gravitational bodies are close enough.

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  • $\begingroup$ sorry for the downvote but these are distinctly different events, as partly evidenced in my answer where a moderately large star takes over 11 years to be devoured. part of the issue is that black holes don't rip apart the same way into a bunch of gas etc. $\endgroup$ – Garet Claborn Mar 20 '17 at 6:53
  • $\begingroup$ @GaretClaborn Its OK. The above can be considered a limit on the lower side, i.e that it can happen in seconds from the beginning of detectability of gravitational waves. Optical frequencies are another story of course, as one can begin detection much earlier as detectors are more sensitive. $\endgroup$ – anna v Mar 20 '17 at 10:17
  • $\begingroup$ oh hmm that is true that it works as a lower limit to the time most of the action happens. good point, and LIGO is a nice way to look at this problem even though it's for black holes and neutron stars. your statement about providing a lower limit still makes sense, but LIGO incidents mainly need to be collisions rather than capture to be detected right now, correct? oh and it wont let me remove downvote unless answer gets edited tho $\endgroup$ – Garet Claborn Mar 20 '17 at 14:29
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    $\begingroup$ @GaretClaborn As I said it is OK, downvotes are good for rethinking, I had not thought of optical detection because I was so entranced by the LIGO data :). On second thought I will edit so it does not look like a completely wrong answer $\endgroup$ – anna v Mar 20 '17 at 14:37
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The linked question asks how long to cross the event horizon, but the answers state how long it takes for the meeting matter and the black hole to form a single object that is white dark. Which is technically different.

You never see anything cross an event horizon becasue event horizons are defined as surfaces that outside observers don't see past.

What happens is the two objects are merging and you always see the matter from before the horizon forms. Even the so called black hole, is actually just the older star from before the event horizon formed. You always see events from before the horizon formed.

But when something is close (in time) to the formation of horizon you see start seeing a nanosecond get stretched out to a year, and then you see a picosecond get stretched out to a billion years. And since most objects don't do much in such short times, things look red and slow and dark.

But the black hole never formed (as far as outside observers are concerned). The event horizon never formed. And there was anything to cross. And nothing ever does cross.

But it can look and act very similar to a black hole, so you could at some point model it with one and not be very off in your predictions.

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