Over the last couple of weeks, we have mainly focused on wrapping up loose ends, with filling out data that we’d already got equations for, fixing some error parts, and some other little bits here and there. But the end is in sight! Report writing is now well underway, hoping to get it done with some days to spare, for reading over and checking everything. A slight spanner in the works has been thrown in that we are actually not expected to have a theory section and instead it should be integrated into other sections of the report. After having thought about it for a little while, Harry and I discussed it and came to the conclusion that just continuing what we were doing was best and then copy pasting bits and bobs from the theory and putting it in other sections instead once everything was finished was what would work best. This would allow us all to continue working on our separate sections without getting in each other’s way. This does mean that some parts may need rewording at the end, but this is again part of the reason we hope to finish with enough time before the deadline.
We also have created a presentation with some plots and results and a summary of our project to present to our peers at the end of week 18, which took up a lot of our time. It was a good opportunity to prepare for the PLACE mini-conference, which takes place later this year.
Monte Carlo method
Other than finishing off loose ends, another aspect that we have been focused on, but particularly Harry is using the Monte Carlo method to get our final number of planets that fit within these parameters and their error. This method fits Gaussian’s over all parameters within two standard deviations and after running it 100 times, an average is found and it gives a realistic estimate with errors for the amount of planets that fit into our parameter limitations, accounting for errors.
The results found for different limits of our parameters can be seen here:
We have spent the last few weeks writing the scientific report that explains the background and methodology of our investigation in more detail and further analyses and discusses the data above. If you are interested in reading it, it will be published in this Summer’s edition of NLUAstro, with the other PHYS 369 Group Projects from this year, so please keep an eye out for it.
This post is a short summary of the last few weeks’ work.
Habitable Zone Research
Owen did some research into calculating the habitable zone for exoplanets. He found a pair of very simple equations corresponding to the inner and outer edge of the habitable zone:
The inner Edge of the HZ (r_i) is the distance where runaway greenhouse conditions vaporize the whole water reservoir and, as a second effect, induce the photodissociation of water vapor and the loss of hydrogen to space. The outer edge of the HZ (r_o) is the distance from the star where a maximum greenhouse effect fails to keep the surface of the planet above the freezing point, or the distance from the star where CO2 starts condensing.
The article Owen found these equations on backs using the Stellar Flux over equilibrium temperature which cancels any dependence on albedo. This makes determining values for Stellar Flux’s easier as albedo differs only slightly in every spectral type of star. This article came to the conclusion of using 0.53W/m^2 and 1.1W/m^2 for the outer and inner stellar flux’s, respectively, by using the bolometric correction. These values were clarified in [Kasting et al., 1993, cited below; Whitmire et al., 1996].
We wanted to create our own formula, with different assumptions, to compare with equations Owen had found. Amaia did some research into this and found an equation that we could manipulate:
We rearranged this equation to make the orbital radius D the subject and then subbed in temperature limits to find the inner and outer limits of the habitable zone radius. For our temperature limits we used:
647K – critical temperature of water
273K – freezing point of water
When creating our own formula for the habitable zone, we made a few assumptions on the way. We started off by assuming the planets are black bodies, meaning the albedo a is 0 and emissivity ε is 1.We set the ratio of the area of the planet that absorbs power Aabs and the area of the planet that radiates power Arad to ½, which assumes a slow-rotating planet and makes sense as only about half of the planet will be facing the star at a time. We have assumed a circular orbit as we use a sphere radius of D. We have also assumed no greenhouse effect and an even temperature around the planet, which is not the case but is taken as an average.
Determining Parameters to Define our ‘Habitable Planet’
Amaia and Harry selected which parameters we would use as our definition of a habitable planet and have determined value ranges for each parameter.
Max Gravity: (3-4)g
Minimum mass: 0.3 Earth Masses
Stellar star classification: F, G, K
Temperatures associated with these spectral types: F(6000K-7600K), G(5000K-6000K), K(3500K-5000K)
Habitable Zone: We will use the equation Owen found and the one we create ourselves
Planet Density: >2000kg/m^3 (anything less is probably a gaseous planet)
Harry found that Kepler’s law does hold for our dataset (with very circular orbits of single-star systems). Nevertheless, we couldn’t just decide to dismiss all eccentric orbits as this would eliminate a huge amount of our data.
Amaia suggested to use the circular, single star orbits to prove that Kepler’s law fits the dataset, and then use the specific relationship for the whole dataset to fill in the values. We spoke to David about this issue, and he suggested that orbital periods longer than the time we’ve been observing exoplanets for can skew the data. This might be contributing to the issue too. The periods longer than we’ve been studying exoplanets will have large errors and therefore give large errors. David also pointed out that Kepler’s Law should use the average distance not just “a”. The distance measured as “a” for some planets may simply be the detected distance, not an actual calculation of “a”. This is more to do with the way the database is written. If there is an accurate period given, it should always give you the average distance “a”. So, we just used Kepler’s law to fill in the gaps and propagated the errors.
Applying Kepler’s law to our dataset proved to be difficult and so Davids feedback was to not bother checking specifics with weird periods and eccentricities. We Just assumed Kepler’s law works for all because they are all within the same order of magnitude, so this is a reasonable assumption for astrophysics. Plus, the number of stars in the system doesn’t have much of an effect. In the end we concluded that it’s hard to prove that Kepler’s law holds for the data set we have, but we can assume it does for every star because it’s a geometric law. Also applies to semi major axis of course.
Calculating errors for our data
Amaia has calculated all the errors with a lengthy code that contains a lot of separate functions. Amaia found the difference between actual radius and calculated radius (and for mass) for the ones we have both for. Using bins instead of plotting all of them, she found the average deviation for the values in that bin. Too many small bins lead to empty bins, so she widened them enough that it worked. She added a linear relationship on either end of the mass-radius ranges rather than extrapolating outside the range to fit higher and lower values, because extrapolating didn’t return sensible values. Extrapolating for the other values were however successful.
Multiple Star Systems
In our dataset, we realise that a portion of these exoplanets orbit star systems of more than one star. Owen did some research into multiple star systems to see whether this would affect our results.
When a planet orbits a multiple star system, it can orbit the stars in several ways. For example, in a binary star system, the planet can either orbit one star (S-type orbit) or orbit both stars (P-type orbit). This qualitive information is not available in our dataset. So before proceeding into further research, we knew that this research wouldn’t be changing our results but would be good to include in our discussion section for the report.
Multiple-star systems can perturb a planet’s orbit, precluding any chance for life as we know it to survive. But even for planets in stable orbits, these stars can produce habitable zones that change dramatically as the stars move around each other. Habitable planets can dip out of the HZ for a small amount of time, and the resilience of the planets habitability strongly depends on its climate inertia. Combining orbital dynamics with simple climate models we demonstrate that the size of circumstellar habitable zones depends on a planet’s climate inertia. The higher a climate’s resilience to variations in the incident light, the higher the chances for planets to remain in a habitable state. In systems like α Centauri, a low climate inertia shrinks the habitable zone by 50%
As an avid reader for SOX, you probably know all about our legendary focus and mental stability, hence this week’s Quote of the Week!!!! Apparently we’re making this a thing now. As a brief overview of the week, we scared off a possible friendly group to cite in our report, we made some incredible advancements in our simulation code, ditched VULCAN and slid into Dr Zita Martins’ DMs.
Quote of the Week:
“You know, I’ve always wanted to break a group” – Joe Head
This masterpiece of a quote came after the Great Meme Lord Dr Sobral suggested we collaborate with the group HELP. This research team has spent the past 6 weeks scouring through exoplanet data and so would be a useful source for when we start using similar data. Naturally this group is hard working, intelligent and mentally stable. So Joe wanted to break them. Sadly, I fear he scared them off when he asked them about their favourite flowers and the colour of their eyes. Now they won’t even read our love letter 😦
A sudden turn of events!!!! Mid writing this and crying, we received a reply! We shall meet with them Monday and come bearing a whole new love letter!!!! They won’t know what hit them. I think it was the poem Joe wrote:
Having sent off an email to Dr Zita martins requesting a meeting to go over the biochemistry in our theories of extraterrestrial silicon life, we received a prompt reply; we now have an internet rendezvous, if you will, with the lovely lady. This will prove to be a huge milestone in our project, hopefully marking the end of the theory era and the beginning of the data analysis era! Sounds like an occasion to pretend to drink with Sobral if ever there was one.
My previous statement about ditching the 3rd party software VULCAN was a little bit of click-bait I won’t lie. We had planned on using a 3rd party simulation to ensure the accuracy of Ben & Ross’ code however many of these software required certain variables without descriptions of what they are. As you can imagine, this is very frustrating especially since we were looking for accuracy. The software VULCAN seemed promising however as we began to learn to use it, Ben and Ross had a breakthrough with their code, allowing them to determine variations to a reasonable degree of accuracy! This means that the need for a 3rd party simulator is not needed and we can spend more time perfecting the theory and the current simulation instead of playing around with weird simulators.
The simulation seems to accurately([f]ish) calculate the maximum and minimum temperature variations on an exoplanet. Unfortunately, QTiPlot has decided to make plotting logarithmic lines of best fit nice and impossible. Here we see Ben trying to utilise the last 20 minutes of his free trial by plotting as many random best fit lines as he can:
At least we have a mew resource for learning about semiconductor physics, an important quality of Silicon and useful for the 313 Solid State module, taught by the one and only, Britney Spear; http://britneyspears.ac/lasers.htm
While Big Ben was working hard with Ross on that crazy code, Joe and Lucy made a start on the report. It has been said that Joe finds it hard to take things seriously at times so writing a professional report may indeed prove a challenge for him. How will he cope?! He probably won’t. Lucy on the other hand is a PRO writing person, she just needs to remember to cite things and fact check with that genius guy Joe… As well as this, Xinyi made some remarkable progress on looking into silane based compounds for life, it seems as though it may well be a possibility! We’ll need to discuss a little more with Dr Zita Martins on Wednesday, wish the team good luck!!!!
Previously on SOX…(remember to read in that cool advert, deep voice, you know the one) Ben and Ross tackle a python to get it to run code Lucy spends 8+ hours trying to get python to work before realising python is incorrectly installed What is silicon life? How does it work? Does anybody know? We don’t! (or do we?…) Find out more with the Joe and Xinyi show! Ned sits on many keyboards
As of this week (week 5, the sad week in which my french buddy drowned. I scratched Joe’s foot for a week after I heard that un-deux-trois cat sank), we reached a stage where in terms of theory for life, we have 3 habitable zones to look for and in terms of the program, it produces data that can almost accurately depict night/day cycles of an exoplanet based on measurable and predictable data.
In terms of Benedek & Ross’ code, it is at a stage where it produces a temperature against time graph of a certain location (or locations) on the planet. The script determines the energy loss and energy gain of the location and calculates the temperature curve based on that. The program determines the temperature curve based on: obliquity of the planet, radius of the orbit, radius of the planet, the star’s luminosity and the albedo of the planet. The program neglects the atmosphere/greenhouse effect, therefore it produces temperatures slightly lower than the actual data. The simulation is more reliable when not asked to simulate extreme conditions (for example north pole), as the simulation does not include heat redistribution of the surface of the planet. Now they’re working on determining how the composition and the thickness of the atmosphere creates the greenhouse effect and how it changes the temperature of the planet. The next steps for the code is to take into account greenhouse effects as they would raise the overall temperature of the planets.
For the 3 possible zones, we’re looking into one hot with a protic solvent (a solvent that breaks into H^+ and negative ions) such that tectosilicates or biogenic silica might become more reactive, one cold with a aprotic, non-polar solvent (N_2 or CH_4) for the long chained silanes and polysilicon halides which under other conditions is too explosive. The other zone we would like to look at is more comparable to earth conditions, hosting organic silicon crossover compounds that can host the same functional groups as organic compounds. In the coming weeks, we will look into these three zones in more detail to determine more specific requirements.
In terms of tangents, the group has been incredibly focused with no distractions. At all. Except when Joe and Lucy realised that using geothermal energy to ionise certain silicon based materials that might also hold Nitrogen or Helium allowing them to shoot lasers. Laser aliens could also feed their young with the energy from that if they were autotrophs. Here is a scientific diagram I made with my own two paws to describe this effect:
So no tangents at all. Oh yeah we also spent a few hours talking about european folk metal but that doesn’t count, a cat gotta waste his time somehow and that e-mail to Zita was already written up!
On a more serious note, we did hypothesise that silicon based organisms could be autotrophic, feeding off thermal energy, chemicals or light from their surroundings similar to deep ocean fish and plants. This is a little more complex than we need to go for determining conditions but it is interesting & could be helpful in future work.
On an optimistic note, Xinyi made lots of progress in researching possible solvents, in terms of more protic solvents, it could be possible to use Sulfuric, Silicic or Hydrochloric acid meanwhile the cooler planets may be able to use liquid nitrogen, methane or even ethane. In terms of a more earth-like zone, possible solvents could even be water or maybe ammonia! After we look at the reactivity of certain materials with these, we can determine possible solvents then use their melting and boiling points as a range of habitable temperatures.
As the most important member of the group, it’ll be me, Ned Head, who shares the progress and inner functions of the project SOX (Silicon-based Organisms on eXoplanets). In this project, the bald looking thumb cats in the photo below are gonna try to find the conditions at which a silicon based life could form and whack that into the Drake equation.
Fig.1 – Project SOX after whooping the Yankees at football and volleyball and sports. Left to right: Joe Head, Communications lead and Ned Supervisor; Lucy Cryer, Administrator and Report lead; Xinyi Zhou, Data and Theory lead; Ned the Cat, Distraction and Cuteness lead; Benedek Kovacs, Co-ordinator and Programming lead; Ross Booker, Error Analysis lead and Coding Aid; Dr David Sobral, Lecturer/lead for PHYS369.
Silicon compared to carbon is like a scraggy ginger tom compared to a gorgeous Tabby (like myself). In that, I mean they have almost identical outer electronic structure so can form analogous compounds to what we see in biochemistry. However these are often either explosively reactive or sit there like a block of quartz. In our research, we will be analysing the properties of possible silicon biochemistry and using that to compare how silicon life may change certain cosmological values, such as the Habitable zone, and values in the Drake Equation.
Overall, there are a few catflaps to pass before we can get our result. Firstly, we need a theory on what kind of chemicals & compounds might make up silicon based life. Lucy, Xinyi and Joe are chewing on that one and waiting for a meeting with Dr Zita Martins (Astrobiologist that can hopefully correct their awful chemistry understanding). Meanwhile, Benedek and Ross aren’t just napping and beating up the neighbor’s dog, they’re working on an atmospheric simulation of an exoplanet which produces a surface temperature profile based on various different parameters. This simulation will also take into account day and night cycles, as well as seasonal change. By comparing these new temperature simulations to the requirements for a silicon based life, we can determine a new habitable zone and search the NASA exoplanet archive and determine how common possible host planets are.
Having thoroughly researched what defines a “habitable planet,” we came to a decision on what exactly our research question would be. The end goal of our project will be to find an estimation of f_sp from the CETI equation. This equation aims to calculate the number of intelligent alien civilisations currently in the galaxy, with whom we could communicate. According to the equation, the number of CETI (Communicating Extra-Terrestrial Intelligent civilisations) depends on a number of factors, including f_sp, the fraction of stars in the galaxy which host at least one suitable planet, in a habitable zone, which could support life, out of all the stars in the Galaxy which are older than 5Gy.
To find an estimate for this, we need to analyse as much data about exoplanets in our galaxy as we can, and filter it according to our definitions of “suitable planet, in a habitable zone” and we will achieve this using data from the NASA Exoplanet Archive. The archive includes a catalogue of data for exoplanets which have been discovered and about which there is published research, among a number of other resources. This particular database contains a wealth of information both about exoplanets and the stars they orbit, including but definitely not limited to masses, radii and orbit periods of planets and temperatures and spectral types for their host stars. This database has specifically been designed to be easy for researchers to work with, with so many characteristics all in one place.
You might think, therefore, that it would be relatively easy to then add some simple filters based on the constraints we researched in the previous week, count how many planets fit all of our criteria for “habitable” and then calculate a value for f_sp (this being our ultimate project aim).
If only it were that simple…
Due to the use of a variety of methods to detect the planets, not every planet has an entry for every variable, leading to “holes” in the data. This is where the bulk of our scientific work has been targeted so far, and it is likely to be that way for most of the length of the project. Some variables have established relationships to each other, based on well-understood physical characteristics. For example, Kepler’s 3rd Law directly relates the semi-major axis of an elliptical orbit with the orbital period and knowing one of these variables should allow the other to be found with relative ease. Others are a little more complex.
One of the criteria we identified as necessary for humans to survive is to have a surface gravity strength within the correct range. The surface gravity of a planet depends on its mass and radius according to Newton’s Law of Universal Gravitation, butnot every exoplanet in the table has entries for both mass and radius. Since the density of an exoplanet (i.e. the relationship between mass and radius) is dependent on its material composition, which is as yet unknown for many of these, it is not possible to directly infer one from the other. Our solution was to derive a relationship between mass and radius for all those that had entries for both, and then apply this relationship to the rest of the planets to fill in the gaps, making it then possible to estimate the surface gravity for every planet.
Harry and Amaia have been spending weeks 3 and 4 doing exactly that. Harry found a linear log-log relationship between the planets’ masses and radii, and used it to find the missing values for the other exoplanets. He then used these values to estimate the surface gravity of these planets. The plot for the known masses and radii (from which the relationship was derived) can be seen below. Although the actual distribution of points looks a bit more like a kingfisher than a straight line, the simple linear relationship is a good enough approximation to first order.
When it came to calculating the errors in these new values though, they had some initial difficulty. Originally, the errors were calculated in such a way that they were not independent from one another, and changed depending on whether the missing radii or masses were filled in first. This was clearly not ideal. Then, the plan had been to calculate the errors individually for each exoplanet, but this idea led to complications with the code, and was overly detailed. After some consultation with David, Amaia is now working on code that will assign mass and radius errors based on the range in which the values lie. The hope is that once the code that is being developed has been used successfully on one pair of variables, it could be repurposed relatively easily for other combinations. This has been an excellent example of how projects like this are not always smooth sailing, but still always contain opportunities to learn.
Our plan for thenext week is to fix the errors in the newly calculated mass and radius values, which allows us to accurately calculate the errors in the gravitational field strength estimates. We also hope to use Kepler’s 3rd Law to begin filling in missing values for orbital radius, which can be used to determine whether or not a planet orbits in its host star’s habitable zone.
During the past couple of weeks, we have been working as a group, researching parameters that might be appropriate to determine a planet as habitable, and their boundaries according to past research.
Our data lead Harry did some research into boundaries of what gravity humans could withstand. Harry found an article claiming that humans could withstand a gravity of up to 3-4 times the strength of Earth’s. It is conclusive that these humans would have to have had considerable training to increase their muscle mass and cardiovascular fitness to endure this new strength of gravity. A test was carried out with participant Hafthor Bjornsson(aka The Mountain), former world’s strongest man) where he was put under the simulated conditions of 5 times the Earth’s gravity. He had passed the test but not everyone has the freak genetics of this elite athlete. For most humans, 5g causes near impossible locomotive motion due to the stress on the bones. We concluded that habitable exo-planets have an upper bound value of 4g.
Searching for the lower bound proved to be more difficult as most articles only discuss 0g. However, this could be an interesting discussion point as our journey to exoplanets may have to be on spaceships, where we would be under 0g. The effects of prolonged periods on a spaceship with 0g would weaken our bones and muscles, which would be bad news if we were migrating to an exo-planet with gravity stronger than Earths. Further studies shows that bones lose about 1% density per month (elderly Earth-bound humans lose about 1.5% per year) when in 0g environments. Without any exercise, muscle mass could fall by 20% after 6-11 days.
With further research, an article was found stating they found a critical mass of 0.3 Earth Masses as the lower bound for planetary masses life can exist. This is as a result of deteriorating tectonic activity needed for life to survive.
Amaia, our group coordinator, did the research for atmospheres of habitable exo-planets. One important property of atmospheres that was explored was pressure. Pressure is significant as it affects the boiling point of water, which is essential for life. Amaia came across a significant term called the Armstrong Limit. This is the pressure at which atmosphere pressure is sufficient for water to boil at the temperature of the human body. This leads to no life. This led to the conclusion that the lower limit of habitable pressure would be around 75kPa.
The upper limit of pressure was interestingly found through deep sea diving. It is confirmed that with a pressure below 4 bar, the body can function relatively normally but for no change in functioning, the limit is 2 bar.
Amaia also investigated the chemical composition of exo-planets with signs of life and explored deeply into their biosignatures. These compounds consisted of methane, oxygen, nitrous oxide and ammonia (caused by bacteria). We concluded that signs of some of these biosignatures were more signs for already existing life and that discovering a planet with these signatures would be groundbreaking, and therefore an unrealistic expectation. However, properties that are still essential to look for ozone-to protect us from solar flares and harmful UV rays, and water, in order to sustain life.
Spectral Types of Stars
Owen, the communications lead, researched which spectral types of stars would be the best candidates for habitable exo-planets to be orbiting. The types of stars were narrowed down to F, G, and K type stars. This because star types higher up on the spectrum have short life spans on the main sequence. This forbids the evolution of life and prohibits the sufficient time to develop complex life on land like trees and ither types of vegetation.
On the opposite extreme, stars with less than half of the Sun’s mass are more likely to tidally lock planets that are orbiting close enough to have liquid water on their surface too quickly, before life can develop. Tidally locking (or synchronous rotation of the star and planet) may eventually cause the destruction of a life-sustaining atmosphere through condensation on the cold, perpetually dark side of the planet. Moreover, most M-type red dwarf stars would tend to sterilize life on a close-orbiting Earth-type planet regularly with large stellar flares.
Therefore, NASA’s proposed Kepler Mission will search for habitable planets at nearby main sequence stars that are less massive than spectral type A but more massive than type M –dwarf stars of types F, G, and K. However, since low-mass M-and K-type stars so numerous, some astronomers and planetary scientists are continuing to model low-mass stars and possible planetary environments that may be potentially suitable for Earth-type plant and animal life, as well as for microbes.
Matt Fahey (pictured in front of the iconic Williamson Park Ashton Memorial in Lancaster), a fourth year MPhys Astrophysics student from near Oxford, is the newest member of the XGAL team, joining for a Masters studying Lyman-Alpha haloes around Active Galactic Nuclei (AGN) after having really enjoyed working with David for his third-year group project on AGN. His work is hoping to see if the Lyman-Alpha haloes around AGN look any different to those around star-forming galaxies and using them to understand the way the galaxy containing it evolves.
AGNs are Matt’s current interest and research focus, but he’s also always been interested in neutron stars, due to the insanely high energy that these stars harbour and the opportunities for collaboration between astrophysicists and particle physicists (who often have a bit of a rivalry). For Matt, there are certain things he wished he’d heard as a fresher or early on in his degree which he wanted to share, these two being key lessons he has learnt:
Don’t be afraid to ask questions, the only silly question is the one that doesn’t get asked.
Don’t be afraid of coding, it can be a bit daunting at first, but it will make sense in the end!
Welcome to ATMs Astrophysics Group. We’re not the money type, and surely not the richest, but instead we consider ‘Are They Metal-poor Stars?’
During this 10 week project we are going to study Population III stars, a hypothetical population of incredibly massive, luminous and hot stars with no metal content. We will bring you along with us during the process and each week we will post our most relevant discoveries.
Emily Wickens is a first year student at Lancaster University who applied to do an internship with the XGAL team, not expecting to be chosen, however, she ended up on the team due to a fantastic application.
Emily’s journey through astrophysics started when she was a child and a massive Doctor Who fan. During sixth form, she completed an astrophysics research project at the University of Hertfordshire, her local university, which was a fantastic achievement, and it made her decision to study astrophysics a no-brainer.
Her favorite topic that isn’t studied in the XGAL team is the early universe and how it formed. If she couldn’t do physics, she’d have indulged in her interest in the history of languages and studied linguistics.
This summer, Emily is working with Louis and Amaia on the GOODS-S catalogue of Lyman-alpha emitting galaxies (check out their project here), something that she’s excited about. One of the reasons that astronomy inspires her is that throughout history so many cultures and peoples have studied the stars and we’re still doing it today.