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Motivation

The question is inspired by the astronomy journal preprint released publicly today, entitled: From impact refugees to deterritorialized states: foresighting extreme legal-policy cases in asteroid impact scenarios?. The abstract of that article begins:

Throughout recorded history, humans have crossed national borders to seek safety in nearby countries. The reasons for displacement have been generated by phenomena of terrestrial origin, but exposure to unexpected extra-terrestrial threats poses a different scenario. An asteroid impact warning implies a change of paradigm which would represent a historic precedent.

The scenario it considers is one when an asteroid or other extraterrestrial object impact on Earth that we are not able to use planetary defense methods to prevent from hitting populated land on Earth that has hundreds of thousands or many millions of people.

But, in the scenario it considers, we can determine where it will hit, there will be at least enough time to allow many people to evacuate the impact zone, and it won't be so bad that it won't be survivable for other large regions of the planet.

Thus, an impact creating a need for a mass evacuation and a mass refugee event, but causing only a bump in the road in the long term fate of our species or global civilization as a whole.

Event Scale

Much Smaller Than

I am considering an impact much smaller than the one associated with the Chicxulub impact with an estimated diameter of 11–81 kilometers that caused the Cretaceous–Tertiary (K–T) extinction event ca. 66 million years ago ending the dinosaurs, and also smaller than the event assumed in the Younger Dryas Impact hypothesis which "posits that fragments of a large (more than 4 kilometers in diameter), disintegrating asteroid or comet struck North America, South America, Europe, and western Asia around 12,800 years ago" creating a massive resurgence of the conditions associated with the Last Glacial Maximum ca. 20,000 just as it was ending.

Similarly, I am looking for an impact that has a smaller geographic range and climate effect than than the Toba volcanic eruption ca. 75,000 years ago that caused a thousand years of global cooling and left debris from South India to Indonesia and across much of Southeast Asia which "made a sizable contribution to the 100 × 35 km caldera complex" with a dense-rock equivalent (DRE) estimate of 2,800 km3 (about 7×1015 kg) of erupted magma, of which 800 km3 was deposited as ash fall. In terms of scale:

The erupted mass was, at the very least, 12 times greater than that of the largest volcanic eruption in recent history, the 1815 eruption of Mount Tambora in Indonesia, which caused the 1816 "Year Without a Summer" in the Northern Hemisphere. Toba's erupted mass deposited an ash layer of about 15 centimetres (5.9 in) thick over the whole of South Asia. A blanket of volcanic ash was also deposited over the Indian Ocean, the Arabian Sea, and the South China Sea. Deep-sea cores retrieved from the South China Sea have extended the known reach of the eruption, suggesting that the 2,800 km3 calculation of the erupted mass is a minimum value or even an underestimate. Based on new methods (computational ash dispersal model using a 3D time-dependent tephra dispersion model, a set of wind fields, and several tens of thickness measurements of the YTT tephra deposit), the Toba Caldera Complex possibly erupted as much as 13,200 km3 in total bulk volume.

This question is similar to the existing Worldbuilding.SE question: What size object could wreak havoc on a world but not destroy it?. But, unlike that question, I am interested in an actual extraterrestrial impact, rather than a near miss, and with an event of a much less extreme scale.

Bigger Than

But, I am considering an event significantly bigger than the Tungsuka event of June 30, 1908, which is generally attributed to the atmospheric explosion of a stony meteoroid about 50–60 meters in size that is the largest impact event on Earth in recorded history, or with the hypothetical a cosmic airburst meteor in around 1650BCE hypothesized to be associated with the Hebrew Bible story of Sodom and Gomorrah.

I am looking for an impact that would be at least somewhat worse than the 1815 eruption of Mount Tambora, the most powerful volcanic eruption in recorded human history, in terms of its geographic scope and overall magnitude of damage caused.

About This Big

For example, I am thinking about an impact that would kill the vast majority of people who didn't relocate in the immediate impact and the first few days that followed, in a geographic area comparable in scale to Cyprus or Singapore, or Belgium, or Northern Ireland, or the more densely populated parts of Liberia.

(My scenario would exclude impacts in countries geographically large enough to respond entirely with internal migrations like Australia or the United States or Russia or Indonesia, which is why I don't use larger countries in my examples above, but that detail isn't actually relevant to the answer to this question.)

Maybe A Swarm Of Smaller Impactors

But, I don't intend to exclude the possibility of a swarm of many Tungsuka event sized meteors in a fairly compact geographic area, perhaps from an imperfect planetary defense effort along the lines of those being considered by NASA, that breaks up an otherwise worse impact (and possibly diverts some, but not all, of the mass that would otherwise impact Earth).

Bottom Line Question

In particular, I am asking:

What would be (1) the scale (i.e. how big an object in meters, and/or how big in meters, and how many objects, for a swarm of objects in close geographic proximity to each other) and (2) likelihood (i.e. once every how many years on average), of an event that could produce this much less extreme outcome (ideally with a range of values or confidence interval)?

Naively, I would expect such an event to involve an impactor of a hundred to fifteen hundred meters in size, and a likelihood of less frequently than every couple thousand years, but more frequently than every couple hundred thousand years, but I don't really have anything solid to back that up.

I also expect, but don't know, that impact object size has a distribution similar to that of earthquake absolute magnitude or absolute flood size with frequency and size related in a similar way.

My goal is to have a fairly specific scientific astronomy based launching point for the kind of scenario that the new scientific journal article is considering from a geopolitical and legal perspective, which I could develop myself in other directions.

Optional related bonus question

The next two questions might be better as follow up questions to this one, put I note them in case an answer to the primary questions makes an answer to these questions trivial or at least much easier to answer, for example, because they rely on the same sources.

What would be the likely duration and magnitude of the global climate impact of an extraterrestrial impact of this scale?

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  • $\begingroup$ It has to be a highly catastrophic event to eliminate human species (more than Chicxulub, imho). There was a number of questions and discussions around that on this site. Do you want to set a more narrow criteria for the effects of the impact? $\endgroup$
    – Alexander
    Nov 29 '21 at 19:08
  • $\begingroup$ @Alexander Is "an impact that would kill the vast majority of people who didn't relocate in the immediate impact and the first few days that followed, in a geographic area comparable in scale to Cyprus or Singapore, or Belgium, or Northern Ireland, or the more densely populated parts of Liberia" not specific enough? $\endgroup$
    – ohwilleke
    Nov 29 '21 at 19:10
  • $\begingroup$ @ohwilleke Tunguska impact might kill majority of people in Singapore. Chicxulub impact will fit your criteria for other places, and we can probably go bigger. But I feel you want a more specific answer, right? $\endgroup$
    – Alexander
    Nov 29 '21 at 19:16
  • $\begingroup$ @Alexander "Tunguska impact might kill majority of people in Singapore" if so, that might be a partial answer. "Chicxulub impact will fit your criteria for other places and we can probably go bigger" definitely much, much smaller than that. Not looking for something mass extinction class. Worse damage that a major floor or hurricane, Probably with less of an impact than the Toba eruption . en.wikipedia.org/wiki/Toba_catastrophe_theory $\endgroup$
    – ohwilleke
    Nov 29 '21 at 19:20
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    $\begingroup$ A note to consider. The location / typography of the impact has a huge part to play in the results of the event. For instance. Many articles have spoken to the K/T impactor not having nearly the same effect it did had it not hit where it did. In a shallow but large body of water with a high sulfur content of limestone bedrock. $\endgroup$
    – Gillgamesh
    Nov 29 '21 at 19:48
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There are many variables concurring to a definitive answer here, therefore I will just outline the workflow for determining an answer for a given set of parameters, then play with it by changing them.

First of all, you said that you want your event to be bigger than the Tunguska event and smaller than the Tambora eruption. The Tunguska event is estimated at around 15 Megaton, while the Tambora eruption is estimated at 33 Gigaton.

Let's use this calculator to estimate some numbers, and let's assume the parameters for the impact as follows:

  • Distance from Impact: 500.00 km ( = 311.00 miles )
  • Projectile diameter: 500.00 meters ( = 1640.00 feet )
  • Projectile Density: 8000 kg/m3
  • Impact Velocity: 18.00 km per second ( = 11.20 miles per second )
  • Impact Angle: 90 degrees
  • Target Density: 2750 kg/m3
  • Target Type: Crystalline Rock

The calculation leads to

  • Energy before atmospheric entry: $8.48 \times 10^{19}$ Joules = $2.03 \times 10^4$ MegaTons TNT
  • The average interval between impacts of this size somewhere on Earth during the last 4 billion years is $2.3 \times 10^5$years

For the crater

  • Crater shape is normal in spite of atmospheric crushing; fragments are not significantly dispersed.

  • Transient Crater Diameter: 9.51 km ( = 5.91 miles )

  • Transient Crater Depth: 3.36 km ( = 2.09 miles )

  • Final Crater Diameter: 12.8 km ( = 7.97 miles )

  • Final Crater Depth: 638 meters ( = 2090 feet )

  • The crater formed is a complex crater.

  • The volume of the target melted or vaporized is 0.75 $km^3$ = 0.18 $miles^3$ Roughly half the melt remains in the crater, where its average thickness is 10.6 meters ( = 34.6 feet )

For the seismic effect

  • The major seismic shaking will arrive approximately 1.67 minutes after impact.

  • Richter Scale Magnitude: 7.5

  • Mercalli Scale Intensity at a distance of 500 km:

    • III. Felt quite noticeably by persons indoors, especially on upper floors of buildings. Many people do not recognize it as an earthquake. Standing motor cars may rock slightly. Vibrations similar to the passing of a truck.

    • IV. Felt indoors by many, outdoors by few during the day. At night, some awakened. Dishes, windows, doors disturbed; walls make cracking sound. Sensation like heavy truck striking building. Standing motor cars rocked noticeably.

For the ejecta

  • The ejecta will arrive approximately 5.57 minutes after the impact.
  • At your position there is a fine dusting of ejecta with occasional larger fragments
  • Average Ejecta Thickness: 585 microns ( = 23.1 thousandths of an inch )
  • Mean Fragment Diameter: 1.15 mm ( = 0.452 tenths of an inch )

As you can see, with this first attempt we are close to the upper limit of your energy range, with 20 Gigaton. Since there are several parameters to be tuned (size, density and velocity of the impactor, geometry and location of the impact), play with it by yourself and see how the estimated effects change.

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  • $\begingroup$ "and smaller than the Tambora eruption" Actually I was looking for bigger than both of those. My phasing must have been unclear which is why I added headings to clarify. $\endgroup$
    – ohwilleke
    Nov 30 '21 at 20:42

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