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Two days ago I asked how we can detect a (really) small black hole. The best answer (to me) was "gamma rays". Since this black hole is relatively close to our planet (a few AUs), this could be a problem because in my story it should not be a threat. So I was wondering if gamma rays are always harmful (I know that this kind of radiation is used in cancer treatment) and in particular if I can make harmless the gamma rays of my mini-black hole for our biosphere.

Black hole properties (if it helps) :

  • Radius: 2.5 attometers;
  • Mass: 1.7 millions of tonnes;
  • Hawking temperature: 6.3 GeV;
  • Total power output: 20 PW;
  • Lifespan: ≈ 80 years;
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  • $\begingroup$ epa.gov/radiation/radiation-health-effects Please read and understand that there are several ways in which gamma rays are harmful, in the link they call it "acute" and "chronic". This is the same principal you might know from other harmful substances. You can overdose on cocaine or suffer long-term health problems for example. Even the smallest dose can cause cancer because statistics, but it cannot cause radiation sickness. Also please note that there is "natural" gamma radiation all around us $\endgroup$ – Raditz_35 Jul 26 '17 at 13:11
  • $\begingroup$ Gamma rays are used in cancer treatment because they are more harmful to cancer cells than normal healthy tissue. As a rule of thumb, gamma rays are always harmful. It's the dosage that's critical. The best way for safety is to keep your mini-black hole a suitable distance away from Earth. $\endgroup$ – a4android Jul 26 '17 at 13:13
  • $\begingroup$ @a4android Yup, but I can't make the math ^_^" $\endgroup$ – Lupetto Jul 26 '17 at 13:15
  • $\begingroup$ @Lupetto The math will depend on the exact distance between the black hole and the planet, so you'll need to make it a bit more specific than just "a few AU". Sadly, that's all the help I can give since I don't know how to calculate gamma ray emissions either. $\endgroup$ – F1Krazy Jul 26 '17 at 13:18
  • $\begingroup$ @F1Krazy Let's say that I wish that my mini-black hole was at a safe distance. 30 AUs is a safe distance? Let's put it there. $\endgroup$ – Lupetto Jul 26 '17 at 13:23
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Gamma radiation is NOT harmful in the amounts present in your system.
As other answer have mentioned, gamma rays are basically always harmful. Even robots or other non-organic lifeforms will be slowly deteriorated by the ionizing effects of gamma radiation.

However, that assumes you're getting hit by relatively high amounts on a consistent basis.

Realistically, I don't think your black hole puts out nearly enough radiation to be a threat to anything on Earth.

Radiation from the Black Hole
Your other question says the black hole is in one of the L4/L5 Lagrange points of Jupiter. Those points are on the same orbit as Jupiter, so the minimum distance between Earth and the black hole is the difference between Jupiter's orbital distance and Earth's orbital distance. Earth orbits about 1.5 million km from the Sun and Jupiter orbits about 778 million km. The difference is then around 776.5 million km.

According to the answer to your other question, the black hole emits 125.7 TW of energy. At 776.5 million km, that's $16.59 \frac{pW}{m^2}$. So a square meter receives 16.59 pW per second, or $0.523 mJ$ in a year.

Radiation from Elsewhere
I'm having a difficult time figuring out just how much ionizing radiation exists outside the Earth's atmosphere. However, we should be able to get a ballpark figure.

This 2002 study on ionizing radiation says astronauts at the ISS receive about 160 mSv per year with the sun at a maximum (when the cosmic radiation is lowest). This approximately equates to 160 mJ/kg (edit alert: I originally wrote 160 J/kg, which is a thousand times too high, though my overall opinion is still the same).

I'm not sure the average mass of an astronaut, but height requirements (at the time of the 2002 study) where roughly 5-6 feet tall. If we assume an average of around 5'6" (66") and mostly male astronauts, the ideal mass, given by the Devine formula is $50 kg + 2.3 kg \cdot \frac{(h-60 in)}{in}$ $=63.8 kg$.

All told then, each astronaut receives about $63.8 kg \cdot 160 \frac{mJ}{kg}$ $=10.2 J$ per year.

Relative Radiation
The end result of these calculations is that your black hole is only increasing radiation by a maximum of about 5 thousandths of a percent.

Because the solar cycle will die down, increasing cosmic radiation to your astronauts (to about double), and Earth won't always be quite as close to Jupiter (not really a factor, since the difference is only about 0.4%), your black hole will be even less of a relative danger much of the time. Also, an astronaut doesn't intersect a full square meter, and might therefore take up less than half the radiation calculated above.

Also, because gamma radiation is pretty much entirely blocked by the atmosphere, it won't be dangerous to anything on the planet's surface.

A Note on Specifications
I used the value 125.7 TW from the top answer on the other question, because it looks like they actually did the math for it. This question asserts the power output is 20 PW, or about 160 times more power output. The end result is still less than one percent difference in harmful radiation.

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  • $\begingroup$ I think you added a factor of 1000 by mistake: 160 mSv per year is 160 mJ/kg, not 160 J/kg. $\endgroup$ – BenRW Jul 31 '17 at 22:37
  • $\begingroup$ @BenRW: Good catch. Corrected. The 20 PW version is getting close now, but still isn't ridiculously significant, and the 125 TW version is still insignificant. $\endgroup$ – MichaelS Aug 1 '17 at 5:55
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This is a very touchy (in many circles) question. The emphatic YES responses reflect the the current mainstream thinking about radiation damage, referred to as the Linear No-threshold (LNT) model. See the Wikipedia article.

However, there are some indications that the model may not hold for low-intensity exposure. There even exists the possibility (strongly denied by many) that very low exposure may actually have beneficial results. This effect (if it exists) is called radiation hormesis.

The classic evidence for such an effect is the Chen Taiwan paper. This reports on the health history of about 8,000 Taiwanese who lived in apartment buildings constructed with rebar which had been contaminated with Cobalt-60. The nature of the Taiwanese health system allowed tracking down virtually all the affected inhabitants and determining their subsequent medical histories. Most notably, a truly astonishing reduction in cancer deaths was reported. (On a personal level, I find the apparent benefits so prompt and so overwhelming that, frankly, I don't trust them. But read the paper yourself. YMMV.)

The reaction to the concept of radiation hormesis has strong political/ideological correlations, so discussions of the effect tend to go downhill pretty quickly. Accepting the proposition that "some level" of radiation exposure is not only acceptable but beneficial opens the door to all sorts of obvious unpleasant exploitation, so even if it's factually correct, it may be better in the long run to stick with the NLT model.

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from OP: /if I can make harmless the gamma rays of my mini-black hole for our biosphere./

I propose 2 ways, both involving ozone.

But first, how do incoming gamma rays hurt life on earth?

I knew that gamma radiation itself, while definitely bad for life, was not very problematic as regards extraterrestrial sources. It turns out that incoming gamma radiation expends itself on nitrogen molecules in the upper atmosphere. It creates reactive nitrogen oxides. It is the next step that is bad for life: reduced upper atmosphere ozone allows more UV radiation through and that is bad for life.

from https://en.wikipedia.org/wiki/Gamma-ray_burst

The long-term effects from a nearby burst are more dangerous. Gamma rays cause chemical reactions in the atmosphere involving oxygen and nitrogen molecules, creating first nitrogen oxide then nitrogen dioxide gas. The nitrogen oxides cause dangerous effects on three levels. First, they deplete ozone, with models showing a possible global reduction of 25-35%, with as much as 75% in certain locations, an effect that would last for years. This reduction is enough to cause a dangerously elevated UV index at the surface.

On reading up I encountered the recently proposed theory that the Ordovician mass extinction was caused by a gamma ray burst.

So the problem is a 2 hit scenario: gamma rays deplete ozone, then UV gets thru. The ozone depletion (and the mechanism) is similar to what chlorofluorocarbons do. The "ozone hole" was much bruited about some years back but it seems that global bans on CFC are helping and the hole is healing. Could Lupetto take a page from the ozone hole playbook to fortify Mother Earth against the black hole?

There is bad ozone and good ozone. It is all ozone. Good ozone is good because it is far away. Sort of like good tigers. Bad ozone is bad because it is next to me and I breathe it.

http://ciese.org/curriculum/airproj/ozoneprimer/

What is Ground Level Ozone? (back to top) Ozone (O3) is a gas that occurs in two layers of the atmosphere, the stratosphere and the troposphere. The stratospheric or "good" ozone layer, which extends upward from about 10 to 30 miles above the earth's surface, protects life on earth from the sun's harmful ultraviolet rays (UV-b). However, ozone found in the troposphere, the layer of the atmosphere that extends from the earth's surface to about 10 miles up, is deemed ground level or "bad" ozone. At ground level, ozone is an air pollutant that damages human health, vegetation, many common materials, and is a key ingredient of smog.

Idea 1 to protect the earth from gamma rays: More bad ozone. It is hard to increase ozone production high in the air. It is easy to increase it low in the air: smog is loaded with ozone. Although no-one writes this, ozone should stop UV wherever, high or low. I do not care if the bullet stops a kilometer from me or a centimeter from me, as long as it stops. So: a healthy ground blanket of ozone containing smog should be a failsafe against UV penetrating down thru a gamma-ray depleted ozone layer.

http://www.ibtimes.com/china-pollution-outdoor-activities-suspended-beijing-schools-new-smog-alert-2213153 enter image description here

Idea 2 to fortify the ozone layer: Make more good ozone. This is harder. I was interested to read that the agents which are produced by the gamma rays are reactive oxides of nitrogen. These react with ozone and destroy it. It is these same reactive oxides at nitrogen, now reacting with volatile organic chemicals, that produce ozone at ground level! So injecting volatile organic chemicals into the upper atmosphere would serve double duty: protect ozone by giving reactive nitrogen species other playmates, and generate more ozone with the same reaction that occurs at ground level.

http://ciese.org/curriculum/airproj/ozoneprimer/

How Does Ground Level Ozone Form? (back to top) Ozone has the same chemical structure (O3) whether it occurs miles above the earth or at ground level. At ground level, "bad" ozone is formed when certain compounds react in the presence of direct sunlight.

         VOCs + NOx + Sunlight = Ozone

VOCs, (volatile organic compounds) are widely used as ingredients in household products including; paints, varnishes, wax, fuels, cleaning, disinfecting, cosmetic, degreasing, and hobby products. Some VOCs are safe to handle and have little known health effects, while other VOCs are highly toxic. In addition to all of the man made sources of VOCs, natural sources of VOCs exist. For example, trees naturally release small amounts of VOCs.

NOx, (nitrogen oxide gases) is the generic term for a group of highly reactive gases, all of which contain nitrogen and oxygen in varying amounts. Many of the nitrogen oxides are colorless and odorless. The primary sources of NOx are motor vehicles, electric utilities, and other industrial, commercial, and residential sources that burn fuels.

When high levels of VOCs and NOx are present in the air, they can react. When they react in the presence of sunlight and hot weather, ground level ozone forms.

Of these two I like the prospects for the first better. A smoggy world is not hard to achieve.

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For all known life, high levels of gamma radiation is lethal.

The issue is that gamma radiation is very powerful ionizing radiation, which gives it the power to break molecular bonds with ease. All known life so far is very dependent on some bonds being rather permanent -- specifically those in DNA. We have some amazing healing mechanisms to repair DNA broken by things like gamma rays, but it's not a foolproof mechanism.

Of course, we don't full understand life itself. It may be that some amount of change is required to keep life moving forward. One might create a species which is more resilient with regard to molecular damage.

Without such a leap forward, the only thing we have to make gamma rays harmless is to put a bunch of lead in front of it. It makes it likely that the rays will strike molecules we don't care about (the ones in the lead object) rather than our own. However, this is only a probabilistic solution. Some gamma rays always get through, no matter how thick of lead you put in front of you.

The real trick to such radiation is not to render it harmeless, but rather to render it less harmful than the other things around you... like the corrosive oxidizers we breath in every day to set fire to glucose in well organized ways. That oxygen stuff will kill you!

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If we use gamma rays to cure cancer, it's because gamma rays are harmful to life, and cancer cells are regular cells that went crazy. That's what makes cancer such a pain in the ass - pun unintended - in that whatever kills cancer cells also kill regular ones.

I'm not sure if your black hole is legit considering its properties, particularly its size that's one thousand times smaller than an atom's nucleus and a million times smaller than an atom itself.

Regarding its mass and the distance from your world, it's possible that the amount of gamma ray it produces isn't to penetrate the Van Halen belt of your planet. More calculations will give you a final answer to these questions.

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