TECHNICAL SHEETS | STAR SYSTEMS | ERTHA

THE ELUSIVE HAYDEE HOMESTAR

There are as many interesting places to visit within the former Chelok Empire as within the borderlands of the Dominion, let's take a look at some info about one of such places.

Once known as HD 117207, Lltlot is the parent star of the Haydee homeworld Ertha, the capital of their expanse, lying right here within 105 light-years from the Earth. Once visited by the Goll Unity somewhere around the 12.000~13.000s, the ancient Chelok judged the system not of any importance or threat to their existence, though just curious enough to be included in the records. One such early note paints Ertha as a place unworthy of further study.

"Ertha from above is a beautiful and violent world, storms covering the totality of its barren surface, allowing but the thinnest beams of sunlight to touch its tiny miserable islands. The oceans however teem with life as it has never been seen before, though within such a dark world, it seems unlikely anything of higher value can be extracted, or sprout from here."

STARS

spectral type ID'd through temperature, luminosity might differ from real-world stars with the same type

LLTLOT / ???

G7V yellow-white star
Temperature 5750 K
        (in solar units)
Mass 1.05
Luminosity 1.16
Radius 1.07
Metallicity Z* ~1.55 [Fe/H]
Abs. Magnitude +4.67

PLANETARY SYSTEM

Lltlot system possesses only four planets.

b) Unnamed rocky world

A scarred and cratered airless planet, this unremarkable rock has 0.02 Earth masses and orbits at 0.4 AU.

c) ERTHA, ???

An oceanic terran world, similar to Earth in mass and size, it has no moons, and the lack of any significant continents or mountains at all sums to the planet's fast rotational period of just about 20 hours accounts for a rather permanent storm system. Its oceans are comparable to that of Earth in terms of depth and overall composition but are at least an order of magnitude richer in biodiversity due to their advanced age. Though Chelok explorers never gave much attention to its very depths, Ertha is the current home planet of an aquatic spacefaring species, believe it or not.

d) A lesser gas giant

A typical light and ringed gas giant, with many icy moons, oblate and low density. Its moons served as fuel outposts within the ancient Chelok empire. Legend has it that derelict technologies left behind from these and countless other expeditions ended up uplifting what would have been an otherwise stay-at-home civilization.

e) A jovian gas giant

With twice the mass of Jupiter, this short-period gas giant orbits at around 3.79 AU from its star, when seen from Ertha it appears more than twice as bright as Jupiter on Earth's skies. There once were many derelict probes from Chelok, Arrene, and Unknown origin many thousands of years ago, those were long scrapped by the Haydee.

b) Unknown object

Arrene observations have sort of identified a point of interest between 37 and 40 astronomical units from Lltlot, radiation signatures point to what could be either an artificial gateway out of the system from where Haydee ships and their allies (if any) have to pass through to get in and out of the system, a literal landfill structure dedicated to discarded nuclear fuel and other technologies, another yet unidentified planet at a highly inclined orbit which is being used as all of the above. Getting better angular resolution and funding for finding out what it is has been the subject of raised eyebrows for the Dominion authorities.

TRIVIA & LOCATIONS

Ertha's upper layers of the atmosphere are made mainly of escaping hydrogen, helium, and ozone, all byproducts of photolysis. The middle and lower atmospheres are predominantly composed of nitrogen, oxygen, carbon dioxide, carbon monoxide, water, and ammonia vapors, the immense surface pressure makes it very thick to move through, and some of the aquatic fauna of this planet have taken this to their advantage, taking short flights out of the water and nesting on the islands.

Although the Haydees breathe the same gases as humans do, they need them in radically different proportions to one another, which makes each other's atmosphere strongly toxic to one another. The same is true for the typical operating pressure, whereas Haydees would just explode naked on the surface of the Earth, humans would be crushed into sausage filling at the bottom of Ertha's oceans.

If Ertha had clear weather like Earth does, it would be possible to see the huge cities across the shallow oceans during the day and see them glow at night.

Haydees, alike most lifeforms in Ertha, are completely colorblind to red and yellow tones. Their vision consists almost exclusively of medium and shortwave light. This is why all of their technology focuses on exhibiting vibrant green, blue, and violet colors wherever needed.

The reason Haydee starships look like airships is that they really are airships, but they work best in worlds with thick atmospheres such as their own.

The reason Haydees refuse to communicate with other spacefaring species is a mystery, some say that their scientists have literally no clue as to how to communicate with them. Haydee speech only works underwater and under immense pressure, working in what most would describe as a cacophony of clicks and whistles, yet the Haydee have a sort of written language, which can be seen as inscriptions in the lower decks of their ships, some believe that Haydee written language can shine a light on how to communicate with them, but intercepting those comms is risky and very hard. One frowned-upon theory suggests that the Haydee may have been much friendlier in the past, but some catastrophic encounters lead them to the aggressive posture they have today, conspiracy theorists across the Dominion speculate that these harassers were the Chelok, and a great war was the cause of the fall of the ancient chelok empire.

Due to obvious difficulties in accessing the past and present of Ertha, many speculate that the Haydees were either intentionally or accidentally uplifted by the Chelok researchers - it is indeed hard to believe that a whole civilization living underwater has managed to find ways to dominate metallurgy and rise to the skies and space in such a "short" amount of time between the height of the Ancient Chelok Empire and the rise of the Arrene, and it is still unclear how they do it.

MORE COMING SOMEDAY!

- M. O. Valent, 08/02/2023

- M. O. Valent, 21/07/2023

SCIENCE&ARTWORK | HOKU ARCHEOLOGIST ON CHELOK PEOPLE | PART 1

A PERSONAL ACCOUNT OF FIVE YEARS AMONGST THE CHELOK IN THEIR CAPITAL OF DHEGHО̄M

By Jaqehura Fadasa (Verdant Hilltop)

Archeologist for the now-extinct Voliloshoku Academy of Xenoarcheology

*mentions of time and space have been translated to common units

"If I knew when the world began, I've would have started my account from there..." - a common ancient saying amongst chelok historians

Despite my age, I am still enchanted by what the fields have to offer, I enjoy hard work and confident supervision of my digs, which is why I have a brood of students and assistants to handle all the paperwork, as I am talking to the chelok natives, many feet underground exploring ancient facilities long used for varying purposes over time. None of the decades of academia could prepare me for this experience despite my fascination with its cultures and ingenuity, so when I learned that ship scrappers were preparing an expedition into space from the defunct Hoku Expansion, I had to take a temporary fat to bring my team to board.

THE TRIP

Unfortunately for me and the misfortune of my countrymen, my generation is one of the last that still remembers the Expanse in its glory days, before the Relentless Force struck. My training is not so commercially useful for my people on the brink of extinction, but it is useful for these foreign 'pirates' who aim to get high-value parts - because our way of building is so foreign to them. We left Forzai straight to the heart of the Expanse, our arrene sponsors gave us the luxury of manning a mining ship, the Eye of Ririth (apparently named after the hero of the forge in ancient arrene), which they expected us to bring back full of riches. The path through the existing star routes would take us just over nine months to complete, but due to the incessant stops along the way, thanks to our secondary transport services, it took us about two years to reach the border of Hoku space.

Already inside the Expanse, there were some stops initiated en route, by some old mining systems long since abandoned, the reason would be rumors that the old militias used these dark border systems as bases of operation and repair, which meant that there could be dozens if not hundreds of pre-war hoku warships and weaponry in these regions, and my team being the only natives, were commanded to classify and identify any equipment we found, as well as unlocking the genetic barriers of our military bases. And as we expected, we found a dozen hangars containing hundreds of hoku starfighters, some under repairs that were never finished, some that were never paired with their pilots. Despite the great cultural importance that these fighters have for my people, the main crew did not allow us to take charge of any, but it didn't cost much to try...

I believe we had brought about 12 of those starfighters, half of which were of those brand new, while I had to personally supervise by order of the captain, the careful dismantling and scrapping of 24 such vessels for their compact jump-drives and weapons. Had something gone wrong in those tedious and tense weeks, the whole asteroid belt would have exploded like chained crackers in new year's eve. After three years in deep space, we were at last, half-way through our mission.

[missing image]

The other half of the cargo we're supposed to fetch within this deserted space were all sorts of Chelok artifacts. The Hoku Expanse was a prime place for such scavenging because of its proximity to the world of Dhegо̄m, thus, the sponsors thought we might be able to smuggle some old but still working tech of any sort. I myself knew of a few places in literature where the arrene pirates could get their treasure, one of those was back in my homeworld of Voliloshoku.

For unknown reasons, many of the capital outworlds of our expanse were merely glassed by the Unrelenting Force, which left shortly after. We would be historically safe in these regions but you can never be too wary out here, it is known for a fact that they still patrol the Muhori and Paza systems, the heart of the expanse, and there is nothing one can do about it.

Voliloshoku is the only known world if its kind, orbiting a red dwarf in the Lagrange point of its companion, which in turn orbits a brighter white star. Such is its strangeness, that here water freezes by nightfall and simmers before midday, and the temperatures rise and drop within weeks, as the planet moves around its parent star, at times closer and at times farther from the brighter ones, it is rarely fully dark because of its three stars. It is a swampy hellscape with no trees or grass or animals of any kind, but the ones that survived the glassing around our major colonies. The air is breathable but moist and heavy, one shall not wander in broad daylight unshielded.

Despite its nasty appearance and inhospitable conditions, we the Hoku were not the first here to wonder if Voliloshoku's intemperate weather could ever be tamed. Ancient ruins found in the south pole have been attributed to Chelok settlers some 7 thousand years ago, the reason why the massive colony was ultimately abandoned lies in the extreme radioactivity of the area, it is uncertain if the whole region suffered a disastrous nuclear waste leak, or if it was bombarded from space in times of war, nevertheless, there is no scarcity of chelok artifacts beneath the muddy surface, or across the other planets of Nigutal'za, the red dwarf. Although, everything was long dead due to radiation exposure and severe weathering, to these pirates there was nothing of value in these ruins, so after a few days of sifting through the oxidized remains, we departed nonchalantly. While I was upset at leaving the ruins, the crew was very happy to find a dormant communications satellite that could be used to upgrade our own ship with a stronger radar - one of my technicians gave them assistance with the components.

[missing image]

The icy poles of the nearest planet, Nigutaline, offered us a renewal of the water and helium supplies, while also hiding another dormant hangar. For the looks of it, other pirates have been here before, given some abandoned hacking and drilling equipment used to trespass the walls, whoever got there before, didn't go much deep into the base. Our native pass allowed us to verify the operational status of the purifying station which found itself mostly intact, I convinced the crew to tow one of the Volkalian cargo ships with us, and I guaranteed that what we could find with such greater range far surpassed what I owed them for towing the ship. I've got to highlight here that did not have any exosuits for our kind onboard, and that the ones we got for exploring the planet's surface for a little bit came with that ship. In their defense, I must admit I've grown quite a distaste for their kind as well as I grew within the Dominion, but they didn't help me conciliate either. I've met other more friendly members of the main crew over the course of these three years, but their group cohesion is infuriating, even if they know they are being unfair to you, it is particularly humiliating to live amongst such small, yet powerful beings...

At this point, we still had 3 months of starlanes ahead before getting anywhere close to Dheghо̄m, and now nothing else in our way, though the holes in our lightsail would get us late by a few days. In our trip towards the chelok world, we found a returning qire merchant ship, to whom we managed to sell two of the unmarked starships we'd brought onboard.

ARRIVAL AT DHEGHО̄M

The Eye of Ririth traced a free return route around Soh - Dhegо̄m's parent star - so it could not waste any more time with my endeavors, allowing me and my crew to detach with our Volkalian ship, we were towed and guided by chelok authorities in a two-week journey down to their world. During this time, we had full liberty to study the ship's architecture and documentation, many of which are pretty standard still according to Arrene law nowadays, though these M-AM drives might need some refurbishing in 5 years' time. Since hoku port licenses are no longer recognized by the Dominion nor Chelok spaces, we had to rebaptize the ship's documentation according to standard naval law, a process which delayed our touch down by about four days, mainly because we had to vote upon a new name for it - we've decided for Kotishera, goddess of Crafts and War of the ancient Hukat - giving our new registry MOV 201 KTXR.

[missing image]

Dhegо̄m is a small oceanic planet with two moderately-sized moons, to which we had a full spectacular view during the entire time - because Kotishera has no landing capabilities, we had to hire a small freighter ship to get us off lunnocentric orbit, as they call it, and down to the ground for a very salty price, passing through the stationary port station to get ourselves checked, scanned, and most importantly - have our suits and skin heavily bleached and suntanned by the sterilizing process, before FINALLY getting on a somewhat comfortable hour-long flight down to Urafar, their port capital, akin to Aa-Iritesh'akar back in Argost.

Urafar is a large city made of concentric ring-like districts at the bottom of a huge canyon, the canyon walls span hundreds of meters and the only way out is following the river downstream or up the dozens of gates across the canyon walls, the temperate forest around it appears to be seeping in like a waterfall - the vegetation and climate within the canyon is rather incompatible with the outside, since the higher atmospheric pressure creates a different humidity and temperature profile, having a patch of rainforest extending inside from the north. We were told that this canyon is the result of billions of years of continental movement, trying to break apart this dense continent, and that within half a billion years a new strait will be formed in this area.

The city's architecture differs very much from what you'd usually see anywhere on Argost, here, prevail ancient buildings, pyramids, roads, and monuments are carved out of stone, with a few trading centers made of your typical reinforced steel and glass classical style. The spaces between the city districts are filled with wildlife reserves and farms, with irrigation channels diverting part of the river upstream to different parts of the city, going through circular treatment pools before being returned to the delta.

[missing image]

Parts of the city are very new judging by the fresh stone cuts and the currently occurring masonry work we were able to see by ourselves, though these few projects seem more restorative, attempting to preserve the original look of whatever stairway or road had centuries ago. For that reason, heavy vehicles are only allowed at designated lanes and zones, forcing you to walk or pedal to whatever destination you have. Our guide took us to a supposedly 'millenia-old' hotel still in operation - we were of course skeptical of all the other trivia given to us about the hotel, though the city is pretty, it would not be a proper city without any snakes trying to get one extra out of foreigners like ourselves.

APPEARANCE

At this point, my colleagues and I are pretty familiar with their appearance and somewhat familiar with the local customs - which might not be the case for my peers - understandably because we've been secluding ourselves to preservation colonies after The Fall - so I will try my best attempt to describe them and their ways.

While other species in the Dominion tend to be rather short when compared to ourselves, very rarely reaching out taller than 1.6m - the chelok have their shortest people around that height, on average standing eye-to-eye with any hoku. That is also because they walk on their hindlegs unlike the arrene, which are strong but not as strong as ours and with very short ankles. They are very similar in body shape to ourselves, though possessing flat feet with small front-facing toes, five fingers, and a single strong thumb on each hand which points inward when at rest.

[missing image]

Another key obvious difference between us and them is that chelok have very short skulls, nearly round or oval skulls, most of it which is occupied by their brain, their faces are pretty flat, with only two front-facing eyes in the middle of the face, one on either side, with their sclera in white and iris in a different color for each individual. Their nose sticks out from the middle of the face, it is generally tetrahedral with different degrees of roundness. The mouth rests just below the nose, at rest the characteristic lips go not wider than the space between the eyes, when it opens, no fangs or menacing teeth pop out of the jaw, instead revealing flat blade teeth for cutting the food in the front of the mouth, and flat crushing molars in the back of the mouth for extended chewing, inside the mouth rests a short muscular tongue, like ours, and like us, their vocalizations are their primary manner of language.

With one rounded ear on either side of the head - their ears were adapted to simply funnel sounds into the inner ear, thus they lack the ability to express emotions through them like we do - on the other hand, their faces can shift in ways unthinkable to our kind, it was amusing and fascinating to me and my crew seeing the amount of facial expressions they can make. The chelok are also devoid of any protective feathers, or scales, or thick hide, instead being barely covered by thin hairs over smooth skin, it which can vary in tans just like ours - the hairs are more prominently grown in the head, face, chest, and privates.

THE CHELOK FROM URAFAR

The great majority of the population residing at Urafar has dark skin similar to ours, though we've been a few individuals with both lighter and even darker skin than that - the males generally opt for shaving their heads bald, while those in higher positions of power cultivate long and decorated braids. The females are quite a curious case, it seems that the traditions of a third of their people prohibit their females from exhibiting their faces and bodies, while the other portion is not required at all by their beliefs - which is from where we noted one of the primary differences between male and female - the chelok, like some burrowing animals from Auot'zae, are mammals, so their females feed their brood during a short period of their initial lives using either of the two mammary glands they sport on their chests - and, unlike males all females seem have liberty on how to trim their head hairs, though those are higher positions choose to tie them short or have none at all for some reason we don't yet understand.

[missing image]

Apart from being strange to their customs of this era, we were also stunned upon hearing the amount of languages spoken all over the place, signs are standardized to four writing systems, but we saw store banners displayed in at least ten. Merchants will attempt to sell you anything by changing through every language they know and get frustrated at us, we quickly learned that the side-to-side head swing also seems to indicate "no" for them as it does for us.

Because their skin is so fragile, and they possess no physical offense but the blunt force of their muscles, it is a consensus amongst chelok that clothing is an important accessory not only for rituals, or status, but also for daily activities, shielding them from the sun's rays in fashion - and must I say, their clothes and accessories are all in for metals, glasses, and jewels adorning their fabrics. It is hard to say whether most of it is tradition or what's in vogue right now. Stopping at the markets looking to blend in their apparel we found both what seemed to be both natural and synthetic textiles. Some of those clothes see very straight, hard cuts and designs with neutral or 3 color palettes, while some go out of their way to be floral or full of natural-looking colorful patterns. Got to admit we've ended up looking even more foreign by picking up articles of clothing by ourselves than what we were using before, I myself choose to keep my current robes for a little more.

I should add that a day in Dhegо̄m are only three-quarters as long as our common day, so we had to get back inside pretty soon, prompting us to also get some very sketchy quality wristwatches. The first few days were full of discoveries, but our mission was far from starting as our translator attempted to contact the local archeological society. For now, we tried to enjoy the vistas around the expansive Urafar. 

One thing we noticed after a few hours touring by the city - or better yet, did not notice - was the presence of synths of any kind, at best, some chelok which sported all sorts of extensions - jaws, arms, spinal, and retinal extensions, none of which they were ashamed to hide, instead even wearing ripped apparel to show up their extensions, such as arms or legs.  Another absent thing across the city is the color blue (or green, or both, unable to translate), blue(?) pigments used in the painting seem very muted or too dark whenever they are present, with a richness of ochres, reds and oranges everywhere, apart from the black and white which is very prominent - which is an interesting indicator of what ancient lineage these chelok descend from, as they are biologically less sensitive to any blues - as a result of that, dark blues and black are used interchangeably all over the place.

[missing image]

During our introduction to the city we've also experimented with their local foods and common specialties from the Dominion - because of the way this canyon varies temperature and pressure, different plants and animals are farmed at different places across the formation - granting great variety, some of which I believe are impossible to find anywhere else. We've seen characteristic animals that are only bred by them, animals which we all have seen in historical and archeological records but never in vivo before, I'm particularly impressed by the color variety of said 'chickens', as one would usually say it indicates different kinds, but chickens were purposedly bred for millenia to have this coloration variety. They have mounts that some cultures consider very reasonable and preferable to eat, in that matter I'd say horses are very similar to our antillos, except with no horns or large digging claws, and considerably smaller and hairier. We've chosen to stay a little bit closer to home in our first meal, ordering a few insects and crustaceans, the cook gave us all quite a show, throwing and stirring our food at ridiculous speed and height between pans before serving us with a boiling-hot meal and large glass of cold white sweet juice of a green fruit he opened on site, once the food was cool enough to savor we could attest chelok cuisine is just as fantastic as described by the trader texts, perhaps, even more, depending on the dish.

After a local week had passed, we finally got a return from the Urafar Archeological Society to visit a place they called Northern Site D-24. We were greeted by a stub and pale elderly chelok, practically dressed like one of us, which we found pretty amusing because the whole crew was dressed like chelok hikers, he was also the only one who actually spoke perfect Hukat with us. It SEEMS that the UAS sent us a Hoku xenoarcheologist and I'm not exactly sure whether to feel offended or grateful, the latter seems professionally more reasonable - since they are well aware that a chunk of our records were lost during The Fall. After a very pleasant lunch within the premises of the very spacious minimalist building of the UAS, we got onto rovers to visit the site, which was located some 50 kilometers upstream.

- M.O. Valent, 14/03/2023

Happy π-day

SCIENCE&ARTWORK | BINARY STAR SUNDIAL | PART 2

WHAT ABOUT DIFFERENT STARS?

So excited Nyrath from Atomic Rockets shared my last post! LETSGOOO

A few reddit users pointed out if the bisolar clock I designed assumes that both stars are the same mass, thus orbiting a common center of mass equally spaced between them, here is why I made this initial assumption while working on the model:

So as you can see, we've got a bit of a problem here, not only with getting the instant time of the day when the two stars are not of similar mass, but also getting the time at any point in their orbital period, since this geometric center would wobble back and forth.

However, the greater the mass difference, the greater the difference in luminous output from the stars, so in a way - the greater mass difference would make the secondary component less relevant for the clock building.

1.0 Msol ~ 1.00 Lsol

0.8 Msol ~ 0.50 Lsol

0.5 Msol ~ 0.10 Lsol

0.2 Msol ~ 0.01 Lsol

and so on...

So with greater mass difference, unless we're dealing with massive stars like F or A-types, the less relevant the secondary component becomes, but luminosity follows roughly the cube root of the stellar mass, which means that although the luminosity from the secondary isn't as influential, its mass still is. That dim star would still make the brighter component wobble.

From the given examples above, the 1:2 system has an orbital period of 41.17 days, and the 3:1 of 43.66 days - the 1:1 system is the same as the previous post. The secondary in each of the two examples has luminosity as 0.06 and 0.02 Lsol, quite insignificant for any clock building purposes, as the primary is about 10x as luminous.

Since both systems have similar luminosity, I will set up our observer planet at 0.75 AU for both. The maximum elongation of the primary is then 6.35° for the 1:2 case, and 4.74° for the 1:3 case.

If we keep the 36 hour day, that means our clocks may be up to 38 and 28 minutes ahead/behind barycenter time. And since this difference develops slowly over the course of some...

1:2 case ~ 50.97 days, planet year is 213.8904 Earth-days,

1:3 case ~ 54.32 days, planet year is 226.8933 Earth-days,

We can just add those variations to the equation of time, by adding a sine wave with the equivalent time difference amplitude and synodic period of the stars. I'll use 20° axial tilt and 0.01675 eccentricity for the EoT generation.

1:2 case

1:3 case

Given this solution, any ordinary Earth sundial works in such world, for as long you consider this modified equation of time for your planet, just look for the darker shadow whenever checking the time.

KEEPING TIME AROUND AN 8-SHAPED ORBIT???

Another user spoke about a project they have involving a planet with a 8-shaped orbit around its two parent stars, with a pretty usual set of circumbinary planets after it.

Now, since it is not the goal of the project to be 100% Interstelar-level physics plus some magic dust sprinkled on top, I'm not getting into how to plan those orbits, or how no planets could form under such conditions, let's just exercise and have fun, because some realities are just sad.

You might also want to look into Arenstorf Orbits - those can be pretty dope and are used for planned satellite missions. About the 1 year period, I'm rather unsure if that's possible at all without having the stars several AU apart (and the planet freezing midway to the other pair), the proximity to the stars and orbital speed necessary for orbital transfer inside the gravity well of whole stars would mean that the planet likely going to complete the circuit in a few days or even hours, in what it is called a Free Return trajectory.

In this situation, no conventional methods for time keeping work, because sundials work on the regular passage of the sun, and it gets even worse if one actually opts of an Arenstorf-like orbit, where you've got many loops of different sizes. Given that, it seems more efficient to track the time at night, when the stars are visible - if the planet rotation happens within reasonable fraction of the planet orbital period, say like, within 7 local days, or if the planet somehow rotates at such speed that a single hemisphere always faces forward in the orbit, and the other trails behind.

At different points of the orbit, the night/dark sections of the planet would point towards different constellations of the local zodiac, ex; some constellations appear on the east only if you're approaching the smaller stars, while the same constellation appears on the west as you leave that star - because the planet is now facing the other direction.

As the stars orbit each other over a period of less than 100 days, those constellations would change as well (given sun-like stars at < 1.0 AU), returning as they were after some 3 months. Plus, given the planet rotation being similar or even longer than its orbital period, we get some trippy sun movements, I suppose even more confusing around two stars.

For timekeeping during the day, there is one simple scheme I propose, a pinhole projection clock!

As the planet races from one star to another, the apparent size of the stars in the sky changes, and a safe way to measure this is through a pinhole projection, since the projection size is always proportional to the object's true size in relation to its distance from the observer.

R/D = r/d

Where R is the real diameter and D the real distance, and the r is the projected diameter and d the distance between pinhole and screen.

By tracing concentric circles of different sizes inside the box, one can know the precise time in terms of the planet's trajectory around the suns - like quarter, half-way, and maximum diameter for one or both stars, and all you have to do is to point the box and look inside through a lateral aperture. People have used a very similar setup to watch solar eclipses here on Earth.

With the invention of glass and lenswork, a more compact and sophisticated method can be used, using a small telescope or lens to project onto a small screen (I imagine such an instrument would be size of a toothpaste box), and the same concentric circles inscribed in the screen would serve to tell the time down to the day.

UNTIL ANOTHER DAY!

- M.O. Valent, 09/03/2023

SCIENCE&ARTWORK | BINARY STAR SUNDIAL | PART 1

IS IT POSSIBLE TO CONSTRUCT A BINARY STAR's SUNDIAL?

WHY?

So this last week I've been trying to work on my own sundial to settle up an argument (with a flatearther, ugh), It works pretty nicely and got bit damaged by rain since it is made of paper, but my brief study of Gnomonics got me pretty interested in the craft as a whole, there are 'easy' and 'hard' ways to make sundials and solar calendars. You can scroll right to the end if you're not interested in the whole thought process behind its end design.

My first print of my gnomonic sundial, the lines are created by projecting a spherical grid onto a plane which is the dial plate. 

Anyone can use a base and a stick to simply mark the hours by the gnomon's shadow, but the instrument will only be able to tell hours. But to be able to tell the day and months/seasons, the designs and matemathics get a little bit more complex.

Fellas over the northern hemisphere might already be familiarized by the sundial design above, formed by a disk or dial plate, with a triangular gnomon on top of it. None of the shapes here are of arbitrary dimensions, the inclination angle of the gnonmon has to match your Latitude (North/South coordinate), and the size of the gnomon in relation to the plate will determine wether the instrument can only tell hours or include the seasons/month markings. For the northern hemisphere inhabitants, one can eyeball the inclination of the gnomon by pointing to Polaris, the North Star, whereas southern people have to use known landmarks and constellations to get a sense of where to point it.

If you look at my design, you will notice a straight line, and two opposing hyperbolae, the straight line is called the Line of Equinoxes, it is where the shadow of the gnonomon falls during the Autumn and Vernal equinox days (Equinox or Equinoctis meaning "equal nights") - the two opposing hyperbolae are the Solstice lines, where the shadow falls during the summer and winter soltices respectively, by marking intermediary hyperbolae one can mark the passsages of months and weeks through the solar cycle.

Because of the Earth's tilt, one can draft a simple grid like the one I did by constructing a spherical grid marked 23.5° north and south of the equator, then putting a light source at its center, then tilting said spherical grid to the user's latitude - the resulting projection onto a sheet of paper will be your markings, and the distance from the paper to the center of the sphere is the same from the plate to your gnomon's tip, which is what you can see I rendered in the 3D software, then printed.

Without a 3D grid (physical or virtual), it takes a lot of math to traditionally work out the specific lines you'll need for you sundial, that's why the ancients often cut the middle-man and just projected their sundials onto convex hemispheres and rings!

There is a whole bunch of other types of sundials each specific to what their projectionists wanted to be told by the sun as well, but do any of those work for a world with two suns?

THE SETTING

The system's stats I will be using thoughout this post

First of all, a quick googling of "Binary Star Sundial" retrieves not a lot of material, if someone has ever worked on anything like that, they didn't publish it on the internet, there are a couple posts on stackexchange and reddit dating back to 2016 but no solutions, most of them assume you can get away with a normal sundial since the shadows created onto a circumbinary planet would mostly be off by about 10° maximum - but this would only work as an approximation, depending on the specifics of the system, this would mean the clock could be offset by about 1h of the actual time (assuming the planet has 24h day/night cycle).

So before tackling the problem as a whole, let's see what changes from the traditional Terran sundial, so we can better know what challenges lie ahead:

DIFFERENCES BETWEEN SOLAR AND BISOLAR CLOCKS

1. MOVING SUNS

In the traditional solar clock, one can assume an inertial reference point, that could be either the static Earth with the Sun moving around it, or the static Sun-Earth system, with the Earth rotating around its axis.

On a bisolar clock, we have to consider not only either of those scenarios, but also that the suns are not static in the sky, they revolve around a common center of mass. Which means that for either scenario, the suns would always move significantly on a day to day basis - what would in itself, create a solar subcycle our natives to work with.

2. MISALIGNED ECLIPTIC

On Earth, the Ecliptic plane is the apparent path of the Sun across the sky throughout the year, it is pretty easy to follow through and it is what defines the constellations of the zodiac. On a circumbinary system however, one could either define the ecliptic as the planet's orbital plane, or the star's own orbital plane, in either case, both stars would constantly fall above and below the ecliptic as they orbit each other. Which means that the difference in orbital inclination between the stars and observer planet would change throughout the year as well. Anyone familiar with tracking the movements of Mercury and Venus in the sky will known how crazy the paths can look.

Because all of those movements are specific to the times and cycles at play, I will outline my process with an example so you can work out your own models of bisolar clocks. Since we cannot experience such a place, I will be using 3D software to simulate what it should look like based on the model stats given in my sketch.

UNDERSTANDING THE SKY

To keep things simple, I will work with geocentric coordinates, swapped the Sun in the solar system by a pair of twin stars with 80% of the mass, just so the brightness matches just the same on our planet, which had its tilt reduced to 20°. The star's also orbit each other at an angle of 5° from the planet's orbit.

Although for an external observer, the twin suns orbit each other every 36.1 days, the planet which is also orbiting the stars do not perceive this as being 36 Earth-days, we need to calculate the synodic period of the stars by using:

Which works out to be 41.25 Earth-days, or 990 hours, now we can use this information to set up the planet's rotation into some neat value that's easier to work with.

I will set the planet's rotational period to about 36 hours, this gives us a simple 10° per hour rotation, it approaches the solar subcycle to roughly 27.5 sidereal days (similar to a lunar month) - and makes the year about 192½ days. Meaning our stars move 13.1° over the course of a day, and half as much during daytime.

corrected suns declination at +0.624°

Usually, the planet's tropics would be located at latitudes 20° North and South of the Equator, but because the suns can gain about 0.62° of declination along their orbit, we can say that the tropics are found between 19° and 21° from the equator. This means that depending on the suns-planet alignment, the extra declination can come during solar opposition (suns seem aligned) or during maximum elongation (suns seem further apart).

The maximum elongation or separation between the suns in the sky would be about 14.5°, and this gives us another interesting alternative to measure the solar day, Mean Solar Time, which is measured from the barycenter, considered static while the suns orbit around it.

Further refinements put the sidereal day at 35h52m33s for a perfect 36 hour solar day

Let's also start our year in a point in the orbit when the suns seem further apart.

DESIGNING THE HOROLOGIUM BISOLARII

PRELIMINAR EXPERIMENT

An anallematic sundial consists of a vertical gnonom which marks the time throughout the day, but also tracks the months through the solar anallema by the length of the gnomon's shadow.

On Bisolaria, such an anallematic clock would produce two shadows which dance with twice the speed of the suns orbital period.

Each square is 10cm wide for scale, and the gnomon has 10cm from the base to the center of the sphere, the star light was tinted yellow and blue to differentiate, each time they switch sides corresponds to half a solar subcycle, and the whole animation takes place over two years (~385 sidereal days) on this planet, Bisolaria.

Each frame in the animation is taken at exact mean solar noon - if we picked a star to count solar days, then the frame of reference would wobble back&forth across all the four cardinal directions as that sun moves across the sky throughout the year, undesirable, which is why we count from the barycenter. Here we can also see the effects of the star's orbital inclination, at times a shadow appears longer than the other by a noticeable amount.

I bet we can use that tilt in the stellar orbital plane and the fact we are working with two shadows to come up with a creative horizontal anallematic clock and calendar. Why not double down with two gnomons then? My initial idea is to use two longer gnomons spaced in such a way that their shadows cross most of the time, the line at which they cross would determine the time of the year, while the point at which they cross would make up for the current hour of the day.

LOOKING AT THE SKY

So throughout the years, we would see the suns eclipse each other only during the planet's passage through the nodal line, where the sun plane crosses the ecliptic plane. We would also see the sun plane appear to tilt north or south as we cross the south and north pointing sides of the orbit, which by itself would be a good teller of seasons.

But we also have to consider the effects of the planet's orbital eccentricity, because the planet moves faster around the suns when it's closer than when it is farther - this causes the mean solar time to go faster and slower than the planet's true rotation period by a few minutes, which is what the Equation of Time is about.

I'm not mentally stable nor know math enough to digest the needed equations so I could explain them better, but I've found a couple tools online that will be useful in generating the data require to produce a clock for a fictional world:

• Analemma Calculator
• Sage Cell - Equation of Time

While the Analemma Calculator is pretty straightforward with single-sun systems, we'd need more work for the paths of the two or more suns we include. Below is a generalized version of the SageCell code, pointing where you need to input your data - if you're not familiar with Earth's parameters.

TECHNICAL SHEETS | STAR SYSTEMS | ARGOST

URR'UHRST̪θ' (Origin Point)

In hoku astronomy, Degazaakoza'pa (Dgazakzp) is the brightest system in the Sailboat constellation, during the summer in the southern hemisphere this constellation stands above the horizon pointing south, forming the base of the greater sail part of the boat. But across the Dominion it attends for its endonym Urr'uhrst̪θ', better known for its Human approximation Argost, and for Hoku travelers as Arihu'risitch (Arihurisit).

The name Argost actually refers to the homeworld of the Arrene, but this became a misnomer amongst their stellar neighbors, like mistaking the 'solar system' for 'Earth'. The star's actual name is noted down as Aa Rithel, or "The Sun" in common arrene.

Aa Rithel is an old single orange dwarf, and stars like it are found all throughout the Dominion.

STAR

parameters ID'd after HD 219134

AA RITHEL, The Sun

K3V orange dwarf star
Temperature 4700 K
        (in solar units)
Mass 0.80
Luminosity 0.26
Radius 0.77
Metallicity Z* ~1.28 [Fe/H]
Abs. Magnitude +6.30
Rotational period 8 days

PLANETARY SYSTEM

Aa Rithel's system possesses five planets, and one brown dwarf.

b) Unnamed rocky planet

A Mars-mass airless rocky world, its cratered and scarred surface is very similar to Mercury's.

c) Unnamed Venusian planet

A superterran wet Venusian, its high surface gravity didn't allow for the star's radiation to blow its atmosphere away, accumulating gas and vapors ever since its formation.

d) Ykaga, the Giant

A T-class brown dwarf at 0.54 AU, 27.44 Jupiter-masses and 12.12 Earth-radii, its upper atmosphere is full of alkali metals, carbon monoxide and methane at 830°C.

It has four satellites: Argost, and three unnamed Moon-like worlds.

The brown dwarf plays a dominant role across all ancient religions of Argost, it also dictates hot and cold days, as the planet slowly rotates away from it.

e) Argost, Origin Point

A terran tropical world orbiting at 12 million kilometers from the brown dwarf, at this distance the planet receives 0.15x solar constants from its parent, and 0.90x solar constants from its brighter parent, the mean surface temperature fluctuates between 30°C and -17°C along its orbital period. Being 2/3rds of the Earth's mass and 90% as large, Argost's gravity lies in the comfortable zone for every sentient race in the Dominion. Its day duration is about 80 hours.

The planet's surface possesses clean-cut preservation areas that can be observed from space, while the rest of the surface is speckled with a mix of beautifully planned urban environments and farming spaces.

The native population tops at about 6 billion while another estimated 15 billion other aliens live amongst them - despite that, it is quite rare to see an arrene at all, that is because the upper layers of their society live in luxurious space habitats or the city centers among themselves, the only the lowest ranking ones live in contact with other alien species, generally occupying roles such as police, army, private militias, town hall members, lawyers, weaponsmiths, ship pilots - with a few exceptions for those who focus their business towards exclusively alien clients.

TRIVIA & LOCATIONS

The political and economic capital of the Dominion is pretty well defended by hundreds of orbital defense platforms, inhabited by the wealthiest individuals of the Dominion apart from the arrenes themselves - but in such a wild and competitive place, there is no comfort without foul play. The descendants of bankrupt visitors and travelers overflow slums all over the place, its criminal and police brutality are unrivaled by anywhere else in the Dominion.

On Argost, as well as many capital worlds across the Dominion, the major cities form huge interconnected environments, with 30 to 100 million inhabitants, plus a few percent of travelers from across known space. The chaotic and stratified nature of the local society is a key piece of what keeps Argost and many other worlds under arrene control, keeping the rebels at bay with hunger and fire and petting the grateful so they don't rebel.

The largest and most populous city on the planet is Aa Iritesh'akar or 'The Enlightened City', it was initially built as a spaceport city to welcome visitors from the stars, being expanded over many millennia to accommodate more immigrants and their brood, some say that it hasn't completely lost its shine, you just need to stare at it longer to see it. 

Getting things, products, and weapons out of any arrene spaceport is not difficult, a myriad of licenses is often needed for that though, the hardest of which is to pilot or transport any pieces of arrene tech newer than some 1000 years - as long as those weapons are not engaged in prohibited space, armed travelers will be spared of a really bad time. Contrary to the rest of the Dominion, clone-presence is minimal to non-existent in the capital, AI presence is unrestricted however, with many platforms working manual and tiring jobs for their owners as a form of extra income.

Although isolationist as a whole, many arrene groups and individuals show great interest in the affairs of aliens, both in their homeworld and across the Dominion, those more interested individuals work hard to be sent to outworld prefectures, science expeditions, or just opt to straight-out live and trade amongst commoners - living in rather high standards, of course.

There are 50 annular black peninsulas and lakes observable from space scattered across one hemisphere, a relic from the height of the Qiro-Arrene wars - the rock in the region is completely blackened from the first and last act of aggression between the two civilizations, created by a relativistic projectile launched from the only Qire warship that ever managed to pass the outer planets. The bombardment of Argost by the Qire fleet was the last episode of a war that ended up bringing the Arrene on the edge of extinction, had it not been for outworld colonies re-settling their homeland, Argost would likely be a dusty wasteland like the northern hemisphere of Hokushoku. The flattened cities offered space for ambitious and planned architectural projects, which are nowadays, the trademark of places such as Aa Iritesh'akar.

MORE COMING SOMEDAY!

- M. O. Valent, 15/02/2023

- M. O. Valent, last updated 21/09/2023

OTHER | SEEKING CREMATORIA-LIKE WORLDS | PART 2

PREVIOUSLY, ON HARD SCI-FI...

We want a planet that:

Is somewhat habitable, but only if lighting conditions are just right, that is - it has an overilluminated side and a dark side. In which case, life would need to move or cover itself when the surface passes through the overilluminated side, and do its thing when it is dark until day comes again. Like Crematoria from Chronicles of Riddick.

EXPLORING WAYS TO MAKE CREMATORIA REAL:

From the previous post...

• Trojan planets around single stars
• Trojan planets around binaries

 Now exploring...

• S-type planets in close binaries
• Dying binaries
• Luminous black holes

LIFE BETWEEN TWO SUNS

Since we've already discussed how binary systems work in the previous  post, let's jump straight into a sketch of my plan for this setting:

Now, although in my sketch the stars are set in a 1:1 mass ratio, that will definetly not be the case, both for being a lone binary, and because we will need a generous safe zone around our planet's orbit in order to have minimum gravitational disturbing from the other star.

Since our planet needs to be sufficiently illuminated by the other component, we can already infer it lives within a close binary, which means we will have other P-type planets in the system as well, and this world would be actually a captured planet by one of the pairs.

If we make the parent star sun-like and put the planet in the habitable zone, then we would have to put the other component at +3 AU away, which is observationally bad for us since the illumination of the secondary pair would drop down to <10% of the solar constant.

But if the parent star is small, such as a red dwarf or orange dwarf, we can put the other brighter star much closer, it also helps that we get a significantly larger planetary disk around stars with mass disparity like that. In that case we will explore two sub-scenarios, in which this mass ratio is 3:1 and 2:1, the most common mass ratios for binaries.

3:1 case, system must be smaller than 0.26x the orbital separation

A ~ 1.00 Msol, 1.00 Lsol, 1.00 Rsol, 5778 K - G2V yellow dwarf

    Mean HZ for A: 1.00 AU

B ~ 0.32 Msol, 0.03 Lsol, 0.40 Rsol, 3800 K - M0V red dwarf

    Mean HZ for B: 0.21 AU

Orbital separation set to be at least 4x that of component B's habitable zone, or about +0.80 AU.

With minimum requirements, the solid airless surface of the planet would be at 310 K or 37°C, but we can cool it down to about 20°C if the parent star orbits the brighter star at a distance of 0.93 AU. Slap it a moderately thick atmosphere at 0.5 bar for an Earth-sized planet, and we got ourselves a simmering 50°C of surface temperature, with some 70°C at the equator, for a 24 hour rotational period.

That average temperature will ocillate between 32°C and 79°C as the planet orbits and points towards or away from the brighter star, changing irradiance between 1.47x and 2.63x the solar constant. These changes occur very quickly over the course of 66 days, but the planet is tidally locked to its parent star, making it a seasonal eyeball planet.

If we want to make it so it is not tidally locked, then the we can place it a bit further away at some 0.30 AU, decreasing the average temperature from 50°C down to 33°C, with an average irradiation of 1.50x the solar constant. Ocillating instead between 4°C and 87°C.

Because our red dwarf parent is quite large, we don't have to worry about sudden violent X-ray and UV flares even though we have a thinner atmosphere than Earth does. Plus, given we know the Earth's atmosphere cools at roughly 0.5~1.0°C per hour (depends on place, at my region it is roughly 0.8°C/h), we can tune the planet's rotation period to cool down to an acceptable level before heating up during the day, so if we want the temperature to drop from some 60°C during the day, down to 20°C at night, we'd have to set night-time duration to some 50 hours, which means our planet should have a rotational period of at least 100 hours to have decent cooling.

The rotational period of 100 hours bring the equator temperature to some 50°C as well, which means that during the night we have it dropping to 10°C. But that's only on the side of the planet which faces the two stars at once, we might not even have enough exposure time to hit some 70°C for most of the year. When the planet finds itself between the two stars the brighter side heats may cool down to some 14°C on average, and the dimmer side to a freezing -60°C. Because of the planet does not stop in this position for long, these potential extremes might not be reached, instead staying between well 70°C and -60°C in the equator across the whole orbit.

But temperatures might actually be stable and comfortable towards the planets poles given the softer ever setting suns or just by being in a temperate zone, though in general the whole planet's temperature changes drastically over the year.

We should also give it vast oceans, so we have ices and decent temperature buffers, so we don't end up with a venusian planet. Now, depending of the latitude, one will still get hot deserts during the day and freezing cold nights, and one half of the planet will always be considerably colder than the half facing the brighter star. So far, it seems we've accomplished our goal with moderate success.

After days in the dark, the brighter sun finally rises, thawing glaciers and lakes to form rivers which will flow fresh for the next two days until it sets again. Clibanus' thin atmosphere allows for stars and the system's outer planets to be observed even during the day, despite the radical changes in irradiation, flooded plains allow consistent liquid water for life

Compared to the original Crematoria, unless the atmosphere can dissipate the heat twice as efficiently as the Earth does, the planet of the movie cannot have 52 hour days, not can have the extreme temperature differences we see in the movie from 370°C to -180°C.

By default, this arrangement is pretty common and actually pretty likely to occur in nature, HOWEVER one thing I've stated at the start is that given  this planet is very close to the secondary star, it is possible that it is a captured planet, thus it might also sport other quirks such as high orbital inclination, high eccentricity, retrograde motion as well. The high eccentricity in particular seems like an interesting way to vary the temperature extremes even more, as well as varying the amount of water present in the planet's climate system.

For planets in more circular orbits, ie, that formed around the red dwarf, we are limited in how massive we can make that planet the same way we are limited with gas giant moons, in this case topping between 2 to 10 Earth-masses, which we could actually distribute in a planetary system of Terran and Subterran worlds which suffer from the same condition, but varying climates according to their specific atmospheres, water content, and distance from the red dwarf.

2:1 case, system must be smaller than 0.22x the orbital separation

A ~ 1.00 Msol, 1.00 Lsol, 1.00 Rsol, 5778 K - G2V yellow dwarf

    Mean HZ for A: 1.00 AU

B ~ 0.50 Msol, 0.10 Lsol, 0.57 Rsol, 4334 K - K6V orange dwarf

    Mean HZ for B: 0.39 AU

Now because our habitable zone around the secondary component expanded to double the previous orbital radius, we have to change the distance between the stars just a bit to accommodate those changes. So the system's minimum size, given the planet has to orbit within 22% of the orbital distance, is about 1.82 AU, orbiting every 2 years. This way, the star's hill sphere is about 0.8 AU in radius, snuggly fitting our habitable zone at 0.4 AU, and given our parent body is larger than the previous one, our planets can be up to 6 Earth-masses in size, even giving space for superterran worlds in orbit.

At such distances from the stars, the planet gets 0.63x and 0.30x the solar constant from its parent and the brighter star, respectively, being close enough to barely rotate instead of being tidally locked. Its equilibrium temperature is around -24°C, and it warms up to 10°C under 1 Earth-atmosphere. By setting the planet's rotation to 500 hours the equator is able to heat up to some 23°C.

When the planet is between the stars, the orange side drops down to -17°C and -4°C on the equator, while the yellow side to some -50°C.

We can already stop right here, as it was concluded from the last example and from the last post that trying larger stars help, but not a lot because of the greater distances involved.

DYING BINARIES

It is not (observationally) uncommon for a bright star to have a dead or almost dead companion in a binary pair, see the Sirius system, an A-type white star and its white dwarf companion Sirius B. However, since the Nova which forms a white dwarf most likely destroy the planets around it (if any survived the red giant phase) is too dim to provide any significant illumination, we will be looking at red giant pairs.

If we want planets in those systems to be habitable for a long time, then such systems would have to be either very old and originating from sun-like stars, or very young containing a sun-like star and a heavier pair. Whatever the case we choose, it will be composed of a star still in its main sequence, and a bright red giant. For the distances we can be somewhat liberal, alerting only for the absence or presence of planetary disks. Let's say that by the time our primitive planet starts developing complex life, our heavier star finishes its MS phase and starts diving into the red giant phase. A sun-like star spends two billion years in the red giant phase, with variable luminosity as time passes, very variable in the last few hundred million years, which means such worlds are pretty ephemerous. Let's use that as a basis, with a star that enters the sub-giant phase at the age of 4 billion years, setting the system's age half-way through the process. The chosen mass ratio is 5:2, still close to your typical common binary system.

A ~ 1.28 Msol, 2.47 Lsol, 1.22 Rsol, 6566 K - F5V yellow-white star (nominal stats)

Mean HZ for A: 1.58 AU

SUB-GIANT STATS:

Current Age: 4.48 Gyr, 400 million years until the Helium Flash.

Current temperature: 4000 K, it will continue to drop to 3000 K until the Helium Flash. 

Current luminosity: 5 Lsol, it will continue to steadly rise up to 25 Lsol, before taking off to 2500 Lsol for the Flash in a short period of 100 million years.

Current radius: 2 Rsol, it will steadly rise to 10 Rsol, until inflating to 200 Rsol (1.9 AU) when the Flash happens. 

Mean HZ for L ~ 5.0 and L ~ 25.0: 2.2 AU and 5.0 AU

B ~ 0.50 Msol, 0.10 Lsol, 0.57 Rsol, 4334 K - K6V orange dwarf

    Mean HZ for B: 0.39 AU

Just so we keep the secondary pair, and thus the planet, under a significant illumination from the dying star, the orbital distance will be about 3 AU. So as the ages pass, the planet will go from receiving 0.5 to 2.8 solar constants from the dying star, while getting a consistent 0.6x solar constants from its parent, so the total illumination will rise from 1.1 to 3.4 over the course of 400 million years. Under 1 Earth-atmosphere, the mean temperature rises from 22°C to 105°C over this period, staying about 20 degrees hotter than those in the equator. The coldest tropical nights in such a world simmer at 65°C, while the planet is more temperate towards the tropics, however, with such high temperatures, we need to make this a waterworld to buffer it all, or a dry rock so the clouds don't start a runaway greenhouse effect. We could also balance the temperature by smaking the planet smaller, which decreases air pressure and volcanism so we don't turn this world into a venusian right away. A half as thin atmosphere puts the planet on pair with the previous world even on the hottest phase of its life.

By varying the amount of water in the atmosphere and a little bit of the secondary star's eccentricity around the main component, we can better control the surface conditions, still obeying the same principles as before, though we now know such worlds will be flash burned when the subgiant becomes a red giant, elevating the mean temperature to about 850°C.

Given what we know from how atmospheres react to the incoming light of different stellar spectra, it is safe to say that once the insolation coming from the red giant exceeds 0.7~0.8 solar constants, the planet will be no longer habitable, for the amount of infrared the atmosphere receives can no longer be irradiated away to space efficiently, thus, the surface temperature rises several dozen kelvin for even the tiniest increase in luminosity.

Reproduced from Habitable Zones around Main Sequence Stars, JF Kasting et al, 1993

We can say for sure that our planet around a red giant won't be habitable for much longer than half of its life between main sequence and the helium flash.

Hence why whenever I set up a planet around red dwarfs I try to keep their insolation below 1.0 and above 0.5, one can go even lower if they wish to add brighter stars to the system, if those stars are considerably hotter, even a few percent more incidence will the job at illuminating and heating the planet up without tipping it over the edge of a runaway greenhouse event.

Though I admit a future me or one of my readers will eventually find something I overlooked or winged for sake of argument for this post series, after all, this is supposed to be an expositional guide, an exercise for you to explore other particular variations more invested than I was with those quick examples.

DO NOT GO GENTLE INTO THAT GOOD NIGHT

Ah yes, luminous black holes and their blanets (yes with a B, that's a thing). For the ones not familiar with the concept, it's the kind of scenario as presented in the movie Interstellar (2014), but for the ones not familiar with the inner workings of such systems, I must warn such systems in nature would be so rare and ephemerous that one might as well regard them as legendary oasis, from what I could find and understand.

WHAT KIND OF BLACK HOLES ARE SUITABLE?

Black holes are a very interesting class of objects for their extreme variety of sizes and surrounding structures. The smallest black holes are created by stars above 23 solar masses, when their core collapses at the end of their lifes, compressing a good chunk of its matter into an infinetly dense point, at least some 2.9 to 3.0 solar masses, the infalling material and subsequent radiation burst ends up bouncing back up and eventually spewing all of the star's upper layers away into space, hence why the resulting black hole is rather small compared to the star's mass. Such small black holes are called Stellar-mass black holes, for they have the mass of typical high-mass stars, and typically, those black holes are the most dangerous for civilizations, for they are very small to the size of a few dozen kilometers, zipping through space at stellar speeds, gravitationally interfering with other systems as they fly by, and worst of all, they are often very dark - because the are rather small, it is very easy for matter to orbit and catapult around it without getting even a tiny bit close enough to be shredded or absorbed into it, thus they rarely emit or posess detectable signatures but the light-bending their gravity produces.

Stellar black holes are also much more aggressive than heavier ones for their small size, with a virtual density much higher than massive black holes, that is, the density you would expect if it was a solid object the size of its event horizon - a person standing 100 event horizon radii from a 5 Msol black hole would experience a gravitational gradient between their head and feet of ~750m/s, leading to instant material failure of the astronaut and resulting spaghettification. Whereas this same configuration with a 1000 solar mass black hole causes a difference of only 0.02m/s, far more tolerable.

Massive black holes are gentle giants.

Larger stars produce large black holes nearly twice the mass of these, but since stars rarely exceed masses above some 50~100 solar masses, stellar black holes cannot get any bigger than some 10 solar masses. From this point onward things get strange, black holes can only get bigger by absorbing lots of matter and other black holes, which means that the larger black holes are often much ancient than most stars, planets, or even the galaxy it currently inhabits.

When we look at massive black holes and supermassive blackholes, those which range from thousands to millions of times the mass of the Sun, we often find those which are surrounded by large disks of infalling matter, accretion disks. As matter accelerates towards the black hole, it rubs against other infalling molecules, heating up to thousands of degrees, generating all sorts of radiation, including light - those are the Luminous black holes. Non-luminous black holes include the ones such as Sagittarius A* at the center of the Milky Way, with 4 million solar masses, it has barely any accretion disk, existing in the dark, puppetteering nearby stars around a seemingly empty region of space. The feeding rate of a black hole, or accretion rate, is limited by its Eddington accretion limit, which is how much mass can fall into the black hole, before the resulting radiation pressure of the accretion disk counteracts the gravitational force of the infalling matter, the brightest luminous black holes such as quasars, blazars, and young radio galaxies find themselves near this limit or at super-Eddington limits, when the black hole also absorbs the extra radiation it would emit despite greater accretion rate. For obvious reasons, blanets and stars cannot reside near such monsters, because they would quickly be disintegrated into the accretion disk.

However, one detail we have to pay attention to while looking to settle black holes with habitable conditions, is that for most of their life, black holes will exist in their dark form, while luminous black holes are rather ephemerous. A single black hole might go through several luminous phases along its life, feeding on unlucky stars for a few million years, then waiting in the dark for the next prey, hence why radio galaxies are always young, as their central black holes did not have enough time to clear their surroundings, so not yet in their dark phase.

The amount of radiation released from a luminous black hole is directly proportional to the infall of matter, sometimes a black hole will traverse a region of space with little more gas than usual and shine very dimmly with a ghostly echo, or sometimes a whole rogue planet falls in, quickly spaghettified into a bright accretion disk which, like the rings of Saturn, will last a few million years.

Because we want blanets, moons, maybe even other stars around our luminous black hole, the gas around it which is the precursos to all of these bodies will be likely of solar-composition, with some sprikle of metals and not only hydrogen gas like the interstellar medium. The black hole would have to be near the end of its feeding / luminous stage, as we still want an accretion disk as energy source, but not so large of an accretion disk it just disintegrates any rocks with dense x-rays. So if the Eddington limit says the max accretion rate is a few billionths of a solar mass per year, then we will lean towards trillionths of a solar mass per year.

Because the surface area for an accretion disk around such black holes is immense, many times that of whole stars, the surface temperature of the disk should be star-like, between some 6000 to 2500 K, this works out to quite a headache of math when you're not familiar with the principles or equations behind it...

THE GENTLE GIANT

For an Interstellar-like scenario, we'll use a supermassive black hole about 100 million solar masses, spinning at 99.995% the speed of light, an ancient monster which hasn't fed upon anything for many millions of years, just now licking the breadcrumbs of its plate, that is, with a very thin ghostly accretion disk.

We're talking a 1.0 AU radii event horizon, with a disk that extends from 1.3 to 2.5 AU.

Our Eddington luminosity is around 4~6 trillion solar luminosities (depending on the gas makeup), with an accretion rate of 2 solar masses a year. So if we want the disk's Earth-like insolation zone to be at around 3 AU from the monster, we need an effective luminosity of 9 solar luminosities. So now we divide 9 by 4 trillion, we then get 2.25 trillionths of 2 solar masses, or 0.00012 Moon-masses a year. With a temperature between 288 thousand K near the ISCO down to 83 thousand K near the edge.

Even though the temperature is not enough for hard X-rays to be emmited through the ionization of metals within the disk, most of its emissions are still in the far UV spectrum. This can be avoided by increasing the opacity of the gas, making it partially ionized in a wider disk or toroidal cloud around the black hole. This makes the inner rim of the disk extremely hot while keeping the outer parts of the disk less hot, which means we need to lower the metal content of our gas cloud, or else the breaking radiation of relativistic electrons will increase the x-ray output of our accretion disk.

As for planetary formation around such objects, it would boil down to general rules of planetary formation, except the progenitor gas cloud would be the spewed guts of one or more stars devoured by the black hole, which for our purposes would have to be the black hole's last meal in a long time, or else the extreme x-rays would just photo-evaporate our blanets.

Those conditions will be very rare or even impossible to accomplish in real life, like, even a small rogue asteroid coming from interstellar space and falling in would increase the disk's luminosity by orders of magnitude - frying whatever life existed in the blanet surface. In the whole universe with its countless blackholes there might exist very few of those legendary oasis where conditions are just right, where life is possible hanging from a silk thread.

Because photon-matter interactions are rather too complex to bother going through, I'd admit handwaving most of them away would be the best course of action - for the sake of story telling, the habitable zone distances and time dilation regarding proximity to the black hole would have way more weight to it.

But realistically, given the many unknowns regarding radiation tolerances, a habitable blanet would look like the following:

Assuming the event horizon is some 10° wide in this image, the planet would find itself at 6 AU, receiving 1/4th of the Earth's insolation.

Would that be enough? I don't know, my IR correction equations are calibrated for stars, not massive accretion disks, the output for this case is right at the face of the event horizon inside the disk's inner radius, at 1.2 AU

An icy/oceanic superearth far far away from the black hole, some 10 Earth-masses and between 2.0 and 2.5 Earth-radii, the illumination is pretty dim compared to Earth's, but the incidence of x-rays and electron wind against the thick hydrogen/helium rich atmosphere reacts to produce scattered radiation, which warms it up to a tolerable temperature between 200 and 400 K. The atmosphere however would be rather anoxic, as the rays cannot penetrate very deep to react with the water or ammonia which pools on the surface as oceans, and any bacteria that develops here would be anaerobic, feeding on high energy or infrared light rays and minerals dissolved in the oceans, in a way, similar to Miller's planet - except much dimmer, much redder, and warmer.

For flavor we could add our habitable planet as a moon of a gas giant, or the more unlikely case - as the tidally locked planet of a red dwarf, working pretty much the same way as the first example from the start of the post, which seems to be the only viable way to obtain the desirable Crematoria-like effect

- M. O. Valent, 13/02/2023