Start with a bang.


This isn’t her first appearance in this blog either. Know her name: Dr. Jedidah Isler. I didn’t know this but we are from the same area. She was born in Virginia Beach, Virginia. I was born and raised in Hampton just across the bay. Dr. Isler earned her Bachelor’s degree in physics from Norfolk State University in Virginia, received her first Maser’s at
Fisk University in Tennessee, then her second Master’s at Yale, and later her PhD from Yale, just in 2014. She is well-known and renowned in the field for her research in blazars and quasars which are supermassive black holes powering an extremely strong jet of crazy energetic particles, radiating light that is detected here on Earth and then studied by experts like her. Dr. Isler had a fairly normal life growing up, in fact it seems she was somewhat similar to me! We both grew up adoring the stars but never really knew how to get into such a specific path. Though I’ll admit she sounds like she was a way better student than I was. She genuinely was always curious and pursued valuable interests and opportunities but not without ever noticing she was the only black woman there. Because of this, Dr. Isler fought more obstacles to get to this point today,

After earning her PhD from Yale in 2014, as the first African American woman to do so in physics, she went on to be a National Science Foundation Astrophysics Postdoctoral Fellow for 3 years at Vanderbilt University while she continued her research. Today – as in right now – she works at Dartmouth College as an assistant professor of astrophysics! She is not a trailblazer yet. She is currently trailblazing – at this very moment (*ALSO she is hiring!)! I’d like to honor her strength, courage, and hard work by including her as not only an amazing female astrophysicist you should know but also as the first amazing female astrophysicist you should know.


Dr. Fabiola Gianotti is currently the director-general of CERN – The European Organization for Nuclear Research – based in Switzerland. The CERN facility is mainly to study particle accelerations and mechanisms with particle accelerators like the Large Hadron Collider (LHC). The CERN facility is appropriately famous for several ground breaking discoveries since beginning operation including the famous 2012 discovery of the long-sought Higgs boson particle.
CERN is seriously a display of amazing capabilities. The LHC is the world’s most powerful particle accelerator and is made of MILES long construction of magnets. It’s a big deal. And Dr. Gianotti is a big deal because she’s in charge of it. Not only that, but she is the first female to do so. She is currently serving her second term of office as the director-general. Dr. Gianotti received her PhD in experimental particle physics from the University of Milan in Italy in 1989. She has authored and co-authored over 500 publications in peer-reviewed scientific journals and has been awarded several very prestigious awards including the Medal of Honor of the Niels Bohr Institute of Copenhagen in 2013. As a woman pursuing a career in a male-dominated field, it was no easy thing to push through barriers to get to where she is today. Today, Dr. Gianotti aims to provide ample support for her colleagues, both male and female, who have children. Many women in physics struggle to maintain a successful balance between a rewarding career in physics and having a family and sometimes feel forced to choose between the two. Dr. Gianotti speaks from some personal experience and women who work in this field can surely relate (I can). Hats off to Dr. Gianotti, helping the workplace become women-friendlier!


Dr. Jocelyn Bell Burnell is, like, a personal hero of mine. Well, all of these women are but I have a soft spot for Jocelyn because we both got wowza’d by the same thing – pulsars. Dr. Burnell, however, was the first one ever to be wowza’d by pulsars. She was even a part of naming the darn things!
In 1967, Dr. Burnell was a PhD student at University of Cambridge in the UK when she noticed a “bit of scruff” on her chart recorder while investigating the radio sky. She was taken aback by this detection and half heartedly pursued confirming the detection, thinking it was probably nothing. Suffering from imposter syndrome, she would surely believe she made a silly error before believing she just discovered a new astrophysical object. Her graduate supervisor would end up partially believing the blip, which turned out to be extremely regular in its repetition and behavior, to be extraterrestrial intelligence. So much so, he coined the object “LGM” for little green men. Later, it was understood to be an astrophysical object and today, known as a pulsar. A furiously rotating neutron star, spewing beams of light towards Earth, like a light house; A beacon of light that you can count on seeing in a predictable way.

Dr. Burnell today is very well known for this discovery and for some small controversies around the Nobel Prize in Physics in 1974 going to her graduate supervisor for the discovery of pulsars. Although, Dr. Burnell seems to hold no resentment about it. I’ve had the opportunity to speak with Dr. Burnell and she is quite a fascinating woman who now advocates loudly for women and women with children in our field. She is a big, outspoken victim of imposter syndrome (which, for other victims, like me, greatly appreciate her bravery and wisdom). She is not only the discoverer of the beacon of light from pulsars but also is a beacon of hope for all women in the physics field.


Nancy was a pioneer right around the same time Katherine Johnson was pioneering for black women at NASA. In the mid-1900s, NASA was not a workplace for women. Women were discouraged from studying math and science, Nancy being no exception.
Nancy recalls her mother showing her constellations in the night sky, grabbing her attention. She decided very young that becoming an astronomer was the path for her. In 1949, Dr. Roman earned her PhD from the University of Chicago. In 1959, she began work at NASA, where she became the first chief of astronomy in the Office of Space Science. She was also the first woman to hold an executive position at the space agency. Dr. Roman was called the mother of Hubble, the optical space telescope that was launched in 1990 and is still operating today, 30 years later. She was a program scientist who was basically the person who would convince people the mission was worth doing, as she puts it. Dr. Roman had a lot to do with how the telescope was designed and built and kept up appeal and interest from investors.

​On May 20, 2020, NASA announced it will name the next-generation space telescope after Dr. Roman. The Wide Field Infrared Survey Telescope (WFIRST) is currently under development and is set to launch in the mid-2020s. The new name of the telescope is now The Nancy Grace Roman Space Telescope. It will investigate open questions in astrophysics and cosmology such as the force behind the universe’s expansion and to search for distant planets beyond our solar system. NASA rejoices Dr. Roman’s efforts, describing her as ‘tirelessly advocating for new tools that would allow scientists to study the broader universe from space’. This is also in memory of Dr. Roman, who passed away in 2018 at the age of 93.


Cecilia is one of the women known as the Harvard Computers, which consisted of a number of women working as skilled astronomers, collecting and processing optical data at the Harvard Observatory in the late-1800s onwards. Cecilia was among Williamina Fleming, Annie Jump Cannon, and Henrietta Leavitt and others, who tirelessly studied light from stars. Studying stellar spectra, the Harvard computers made several major contributions to astronomy, including the famous stellar
classification system – Oh, Be A Fine Girl, Kiss Me! or OBAFGKM, which types the varying stars based on their optical spectra. ​​Cecilia, in particular, made a pretty big discovery herself, which she and her PhD thesis advisor squabbled over for years. Henry Norris Russell was one of the astronomers who developed the Hertzsprung-Russell Diagram, a fundamental graph displaying stellar evolution still used widely today. Russell was sure Cecelia’s work must be wrong.

In 1925, Cecelia submitted her PhD thesis, which was comprised of extensive analysis of a huge dataset of stellar spectra, all showing enormous abundances of hydrogen and helium, a surprising result at the time. Today, it is understood that hydrogen and helium are the most abundant elements in the universe. In the Milky Way alone, it is estimated the baryonic mass is roughly 74% hydrogen, 24% helium, and all else being remaining heavier elements. In 1925, however, it was still thought that stars were made up of similar composition as the planets, like Earth. There was no reason to believe otherwise until, alas, abundant evidence shows us that indeed, the universe is made up of mostly the two lightest elements. Her discovery profoundly changed our outlook on the universe, stellar evolution, cosmology, and more. By 1956, Cecelia had accomplished becoming the first female professor at Harvard and the first woman to become department chair. She passed away in Cambridge, Massachusetts in 1979.


So technically, Jeanette was a mathematician but I’ve included her as an astrophysicist because she is well-known for her contributions to knowledge on the Sun’s sunspot cycle. Jeanette was the first African-American mathematician to be employed at the NASA’s Marshall Space Flight Center, based in Huntsville, Alabama in 1964. Jeanette grew up in Alabama when segregation and other racial discriminatory laws and behaviors were normalized.
She went to an all-black school and graduated from high school in 1956. She went on to receive her Bachelor’s and Master’s from Alabama A&M University. Her 1967 report, Survey of Solar Cycle Prediction Models, provided new methods for improving predictions of the solar sunspot cycle. She went back to school some time later to earn her PhD in computer science and went to work at the Goddard Space Flight Center in Maryland. She worked as a computer systems analyst responsible for analyzing and directing NASA systems. During her career, she remained passionate about inclusion and equity. She volunteered as an equal employment opportunity officer in her spare time. Jeanette retired in 2005 and in 2017, NASA honored Jeanette for her skill, perseverance, and positive attitude as part of the first Alabama Historically Black Colleges and Universities Roundtable Discussion.

​Six extraordinary women of science and their stories

We acknowledge these women fought various obstacles in the workplace from historical and systematic oppression of their gender and for some, they were discriminated against for their race as well. We applaud these women for their courage, knowledge, and wit that it took for them to accomplish their goals in spite of added difficulty.


Writing these posts always brings me back… Senior year, my last year at Radford University. I was knee deep in physics coursework, running with Ruca by the New River, shenanigans on Downey Street on Darkside, and also in a blindingly toxic relationship.


Fall of my senior year I took an astronomy course, some general chemistry, Spanish, and … Goodness it’s been four years almost! I can’ t remember! I want to say it was electromagnetic theory I. I know in the Spring of my senior year I took quantum mechanics, Spanish, and the Arctic Geophysics course again. Honestly, it was a year where I was not very academically inclined, at least compared to years past. I don’t regret that though. I was fully aware it was my last year in college and I intended to enjoy a little more of the “college experience” before leaving. I was also a little distracted by my then-boyfriend (things did NOT end well, lol). But hey, it was a ton of fun. I made lots of good memories and friends. When I moved out of Radford, I was a sad girl for a long time. I was really excited for the next chapter of my life but, looking back, that was the first time baby Jordan really made a home for herself in a new place and now she was leaving it. 

And sure, when I moved home for the summer I was freshly (and not happy about it) single and things seemed really uncertain, even though at this point I had accepted Clemson University’s offer for their PhD program. It wasn’t until I actually moved to Clemson that I began to feel excited about my new life (though it still took a long time to adjust and to feel like Clemson was a new home, ya know).
Me decorating my graduation cap, the morning of my college graduation. May 2016.
The fall of my senior year is also when I “prepared” and took the graduate record examinations (GREs). For some subjects, you have to take both the general and the subject, where for me, the subject was physics. The GRE is basically the SAT of graduate school. It’s the usual standardized test that unnecessarily takes up your time and money. I did not do great (at all, not even a little bit) on the physics GRE. 


Like, I did really bad. I barely studied. Mainly because I didn’t want to in my free time. I mean, I’m in the middle of a full time semester. Why would I want to study for a test I just signed up for? Other than that it cost $500.00 to do so? Lol. That and I found out later that I had a small exposure to physics, even with a Bachelor’s degree from a small school. When I started at Clemson, I had to take some classes I was missing before entering the PhD program. I was really intimidated by that realization but I’ve since come a long way.

I am fourth from the left. May 2016 college graduation with some of my physics peers.


People always use this analogy on how to be successful life: Imagine you live your life day by day, with little planning. It’s like trying to balance a ruler on your fingertip but only focusing on the base of the ruler. The ruler falls every time. If you look at the entire ruler, however, you find that you can easily balance it. I always felt like I lived life by just focusing on the base of the ruler. Honestly, I still do. And it seems to work out pretty okay for me. I stumbled into graduate school much how I stumbled into college. Though I really stumbled into it this time.

Jordan, are you applying for graduate school? Are you taking the GRE? I just got into blank blank!! I just got an amazing job offer after I graduate!

​I sat down and asked myself what I wanted to do. Apply for career positions or apply for graduate school? After pondering it for about thirty minutes, I decided I like the dynamic of a school schedule. That was all it took for me to commit to applying to graduate school. Cue the GRE “preparation” and performance. I devised a list of graduate schools and kept track of statistics I found important. For instance, I wrote down how many applicants they received versus how many they enrolled, how many female students they had, what was the faculty to student ratio (i.e. would your thesis advisor be stretched thin with students? What if you’re like me and need your advisor to sometimes hold your hand through tasks?), and what their stipends were for teaching and/or research. I applied to 8 or 9 schools. Let’s see if I can remember them all.

I applied to University of Maryland in Baltimore, Clemson University, College of William and Mary, University of Virginia, University of North Carolina, Chapel Hill, Wake Forest University, University of South Carolina, North Carolina State University in Rayleigh, and Colorado University in Boulder (Woo! I got all 9). I spent – ahem, my parents​ spent – around ~$2,000 just applying to graduate schools. That includes the cost of taking both GREs (the general and the subject), fees to send the GRE results to select schools, and graduate school application fees. Guess how many I got into?


​Just guess.



I got one acceptance.

To Clemson University. And it wasn’t even formal. It was a hey, we have one or two more spots left for teaching assistants. Whoever responds first gets dibs! And you best believe I had that acceptance letter signed and sent that very same moment. At that point in time, I had just barely made it into graduate school. I just weaseled my way right in. Clemson simply needed more staff for their high demand in physics labs and I hopped right on that PhD train (and that is part of the reason why imposter syndrome has developed so strongly with me XD). 

No hard feelings though. I took what I could get and I feel like Clemson is really glad to have me (and vice versa). But, when I got the offer from Clemson, I was like who? 

​Where even is Clemson? I asked myself. Quick Google search showed it was still in the Appalachia, where Radford is, just farther south in South Carolina. I thought, okay cool so similar surroundings; rural and mountainous. Sign me up! And that was that. I barely registered what Clemson University was all about. Didn’t register during applying – only mattered when I realized that that is where I was going to live for the next however-many-years-it-takes-to-get-my-PhD. 

The heart of Clemson University.
In short, I basically live my life as a sequence of on-a-whim, off-the-cusp decisions and opportunities. So far it has been a decent method for me.

Clemson did indeed turn out to be the perfect mixture of rural and development that I needed. Clemson is a huge University (from where I was coming from) and a way bigger town than Radford but still small and rural just outside of campus. It is a beautiful town and area, as is much of the Appalachia in my opinion. 

And even though I didn’t feel very lucky at the time, the break up I had before graduating ended up being a really good thing for me because that first year into the PhD program at Clemson was hard!  I am thankful and grateful, looking back, that I had Ruca and little distractions. I was able to focus on physics and get where I needed to be to pass exams and pursue my PhD. Ruca kept me sane. I didn’t do much socializing or integrating into the community my first year there. I felt a little alone. It was a new place with new faces plus I was really busy with school work. That first year, I spent a lot of time exploring the area with Ruca. 

Ruca and I discovered South Carolina Botanical Gardens on Clemson’s campus. It is one of my favorite places to be! This was taken in March 2017, the spring semester of my first year at Clemson.
Let’s recap briefly.


I was a mediocre student my last year of college. I got a C in quantum (but I definitely deserved a D). I was distracted by a boy I really liked but our relationship was really toxic and ultimately distracted me and made me be less academically successful than my previous college years. But, I still had a great time, enjoying all the non-academic activities that college often brings and it was hard to say goodbye to Radford when it was time. I stumbled into graduate school on a whim with little thought though lots of time and money were spent into applying. I only got one offer which I accepted. I later graduated college in May of 2016 with my Bachelor’s in physics and was anticipating beginning the PhD program at Clemson University. In August of 2016 I moved to Clemson, South Carolina – not knowing a soul down there. It was just me and Ruca for that first year and I wouldn’t trade that for the world.

So far, the cliche “Nobody ever said it would be easy, they just said it would be worth it” is, like, totally true for me.



Welcome to my first DIY blog post!

It’s going to be really short because I am not one to start my own DIY projects. So, I don’t have my own DIY to share but rather the tips and tricks to a pre-existing one that I’ve found extremely useful. It began a few years back when I really needed my hair trimmed but I couldn’t afford a hair cut. 


As a disclaimer, I love my hair. I LOVE it. I love having long hair and am very, very picky about who touches my hair. I don’t even like hair dressers that try to tell me how to cut it – the last time I took a hair dresser up on a suggestion to “cut all my dead hair off” I looked like Dora the Explorer going into my freshman year of college (never again). This led to a big hiatus from going to the hair salon.

A few years back, I was in Clemson, SC with hair that hadn’t been cut in over a year and I was needing a trim badly but I didn’t want to go to a new salon and I certainly didn’t want to pay for it. I googled DIY haircut hacks and found a good sample of DIY hair hacks for long hair. This is the one I use exclusively because it’s super easy, quick, and pretty hard to mess up!

There are some really nice perks to doing your own hair, specifically using this technique:


  • Buy TWO utensils but virtually pay nothing for any future hair trims! 
  • You pick the amount you want to cut
  • Get a great, layered hairstyle in less than ten minutes
  • A perfect V shape style in the back
  • You get to pick when you cut your hair and how often without breaking the bank 🙂

Whenever I see those dead ends growing out of control, that’s when I start considering doing this trim again. But, as this great influencer in the video mentions, for other hair styles, it’ll probably be best to leave it up to the experts ;-). For now though, this has kept my hair in tip-top shape as a ~baller on a budget~! 

Here are the utensils I use!

The cut-razor comb – $5.99 at Sally’s Beauty! This thins and fluffs the hair edges. I use this after trimming the dead ends off.
Procare styling shears (5.5in) – currently on clearance for $10.19 at Sally’s Beauty! This is what I use to cut the bulk of my dead ends off.
You’ll also need a hair straightener, a hairbrush, 3-4 small hair ties, and 1-2 regular-sized hair ties. I use a regular towel underneath me to catch any hair and just shake it out later for easy clean up. The actual trim time takes me about ten minutes but it would fair to say the first time will take the longest because you’ll be scared (lol).
This is really all you need to cut your own long hair from home, as long as you don’t mind and/or want layers! Below, I share some photos I took after I cut my hair.

Happy hair cutting!



Is science an attack on religion?

Short answer: No. Science is not an attack on religion.

For this post, you are going to hear a lot about Carl Sagan. He was a brilliant astrophysicist who had a way with connecting the public to science. Neil deGrasse Tyson was taught by Carl Sagan. The movie Contact (that has major religious undertones!) with Jodie Foster and Matthew McConaughey is based on Carl Sagan’s book Contact. He wrote several other books including The Variety of Scientific Experience which focuses on the two topics and how they relate: science and religion. I recommend reading this book if you are interested in a different perspective on how to embrace both. 
This is not a celebration of my faith or anyone else’s. This is an essay discussing a different outlook on science and religion than what we popularly know of. Carl Sagan was one of the American scientists to really capture the beauty and human empowerment that we can achieve if we can learn to embrace both science and religion together.
Sources today:

Science is not an attack on religion. I’m going to make some hard-to-swallow statements:The Big Bang theory (not the show) does not suggest there is no God.

The evolutionary theory does not suggest there is no God.

After all, Pope Francis himself suggests these theories don’t prove there is no God but rather that these theories require that there be one. I think that is a very powerful thought. These theories are still being developed, too. This isn’t the final hour but rather just the best guess we humans have at understanding what we have observed. What we provide in these frameworks is what is consistent with what we know and what we observe – there is always room for improvement and even change.

Science is the pursuit of knowledge and truth. It seeks to understand the world around us. For many individual scientists, their pursuit is inspired by their desire to get closer to God and to understand the Heavens. For some it is a quest to understand God’s existence. For others it is a journey of fulfillment; seeking to understand everything they sense, regardless of what religious realms they might uncover.

Scientists often feel a deep connection with science. We may even describe it as a religious experience.

The term [‘God’] means a lot of different things in a lot of different religions. […] To others, for example, Baruch, Spinoza, and Albert Einstein, God is essentially the sum total of the physical laws which describe the universe.
— Carl Sagan

It would be fair to point out that some scientists may even interpret the laws of nature being either the consequence of the existence of a God (i.e. gravity belongs as a inner working to a God) or as the essence of their God (i.e. their God’s powers emerge in the form of nature’s laws).
I would agree that it would be too soon to mark all scientists as athiests. Scientists tend to have minds that are swayed when presented with empirical evidence.

No decent scientist will try to convince you there is no God.

Because we simply do not know enough about the Universe to make such a statement!

If we say “God” made the universe, then surely the next question is, “Who made God?” If we say “God” was always here, why not say the universe was always here? If we say that the question “Where did God come from?” is too tough for us poor mortals to understand, then why not say that the question of, “Where did the universe come from?” is too tough for us mortals?
— Carl Sagan

But in order to be able to embrace both religion and science, we have to be open to learning new information and most importantly, we need to be comfortable not having all of the answers.

We are only human. We do not know anywhere CLOSE to everything there is to know. We may never know it all….

I am extremely uncomfortable with dogmatic atheists, who claim there can be no God; to my knowledge, there is no strong evidence for that position. I’m also uncomfortable with dogmatic believers; to my knowledge, they don’t have any strong evidence either. If we don’t know the answer, why are we under so much pressure to make up our minds, to declare our allegiance to one hypothesis or the other?
–Carl Sagan

For some of you, faith is all you need and I think that is beautiful. You are someone who is so loyal and confident to your God and your God is lucky to have someone like you on their side because you show strength and power. However, I urge you to always remind yourself of the extent of what you put your faith into. Let’s not forget that the Bible was written a very long time ago. It was written and edited hundreds of time since its creation. There are some things we have gotten wrong in it. Just like how scientists have gotten many things wrong before, too.

Remember when we found Pluto and we thought it was ten times the mass of the Earth? Today we understand it to be 0.2% of the Earth’s mass! And remember when we thought that because the Earth is made of dirt and rocks, that the stars had to be made of it, too? Today we understand that stars are hot balls of hydrogen and helium! Remember when we tried to measure the speed of light by taking lanterns on top of mountaintops and trying to time the on/off of the lights? Haha! Today we understand that light can travel the Earth’s surface in seven seconds! Remember when we legitimately thought the Moon had intelligent alien life on it? And then Mars? I mean really. Very distinguished and beloved scientists believed plenty of outlandish things. Not to mention we have used science for really, incredibly inhumane things (ahem, nuclear weapons, biological warfare, etc.).

Science is not perfect. A decent person won’t tell you that science has it all figured out and that religion has it all wrong. Though we have presented evidence over time that says, “Hey, you know how we’ve been interpreting the Earth as being merely a few thousand years old? Well we just found evidence [tons of it] that suggests it is much more exciting and dynamic than we thought!”

This evidence in no way suggests there is no God. It just means we are learning about our world. We are learning that we are only human and therefore, we do not hold all of the answers. If you want to think of it this way, God has given us clues along the way to help us grow closer to him. He has given us this information. He is helping us understand our own, collective purpose. Sometimes he even does things to save us from ourselves.

He can manifest himself as laws of nature. He can manifest himself as the Big Bang that led to the existence of this Universe. He can be the divine intervention in the evolutionary theory that ignites genetic mutation. He can be all of these things.

Science doesn’t say He can’t be a part of this newfound evidence. ​

My guess is that there has to be some deeper explanation. But that doesn’t mean the explanation has to be what the people themselves report—that they went to heaven and saw a god or gods.
​–Carl Sagan

Do you agree that worshipping can be different for everyone? Do you agree that branches of christianity stem from varying interpretations of statements in the bible? This is the same thing. Science and religion are not mutually exclusive pools of thought and the two topics have quite a lot they could learn from each other.

For one, religion can provide science a deeper meaning in research endeavors. Human values and scientific goals should be at the forefront of any endeavor, and never with malice.

Science has something to share with religion in how to interpret evidence and seeing beyond the surface, revealing the inner workings of life itself, its beauty, and what it has to offer us. Science can help awaken our religious experience as we walk through life.

This is a learning moment for us all. Not one of us has all of the answers. We are simply all searching for the answers in different ways.

Merging science and religion can be a powerful, unstoppable force. But currently the two are at odds globally, which can have devastating consequences. Over human history, religious conflict has killed so many and scientific advancements have been taken advantage of costing the lives of many more.

This is not necessary.

It is not the teachings of any God and it is written nowhere in the scientific method. Moving forward, let’s be mindful of our experiences and the information we absorb. Whether you are a religious scientist or a religious science skeptic, keep these things in mind to help yourself (and others) to grow their relationship between science and religion:

1. There are many real mysteries that not even science can explain. Go deeper. Keep asking questions. But most importantly, be okay with not having an explanation. Do not invent explanations that have no support.

Imagine our ancestors looking at the moon, the planets, the stars and making up stories to answer their need to understand. In many cases, the stories involved deities, such as the moon as a god. Now is that myth about the moon deeper because it was wrong? Should we waffle, and say, “Well, if we can redefine what we mean by a god, then we can still call the moon a god?” No. Let’s admit that the moon is not a god and move on. It seems to me that it is a much greater achievement to understand what the moon is really about—4½ billion years old, cratered by enormous explosions in its earliest history, a desolate world on which life never arose.
​–Carl Sagan

2. Be kind to others even when they don’t think like you.
3. Be skeptical. Ask for verification (constantly!).

 If someone claims a thing happens in a certain way, you do the experiment to check it out, to see if, in fact, it works as claimed. You examine the internal coherence of the idea. You test its logical structure. You see how well it agrees with other things which are reliably known. And only then do you start accepting new ideas.
​–Carl Sagan

4. Be more open to science and religion. After all, just look at all the advancement we have made in science. We have extended life expectancies, developed life saving equipment for thousands of medical conditions, developed communication that has made the entire globe more connected than ever before, we have sent humans not only into space but on the moon for Christ’s sake ;-). Religion has brought us a deep sense of purpose, community, and morality. We are in touch with what is right and wrong. We discuss what is right and wrong and how to establish moral code all of the time. We grow as a species in both respects because of this.

In short, ​pursue truth while practicing love. 

My deeply held belief is that if a god of anything like the traditional sort exists, our curiosity and intelligence are provided by such a god. We would be unappreciative of those gifts (as well as unable to take such a course of action) if we suppressed our passion to explore the universe and ourselves. On the other hand, if such a traditional god does not exist, our curiosity and our intelligence are the essential tools for managing our survival. In either case, the enterprise of knowledge is consistent with both science and religion, and is essential for the welfare of our species.
​–Carl Sagan

Search for



We saw last time a plot just like this:



We plot the “spectral flux” or “spectral density” or “spectral flux density” versus the energy. Why do we do it this way?
The plot comes straight from this paper published in September 2019 (and I’ve linked the free version!). The y-axis (the vertical) is plotted using E^{2} \frac{dN}{dE} in units of ergs/cm ^{2} /s. This is the spectral flux density in units of energy per area per second. But why E^2 dN/dE? What does that even mean to us? How does it relate to the total flux from a source at a given frequency? And what are the perks to defining and plotting the spectral flux density? 


Linked are two sources:
1) This source is designed for astrophysics graduate students. It explains when the common \nu F_\nu is useful and why that is so. 

2) This source is more user friendly and explains things a little more generally.

First, let’s get a handle on one thing: the relationship between frequency and energy.
Recall the relationship between frequency, we will call \nu (or nu, a greek letter), and wavelength, \lambda (or lambda, ​another greek letter):

c = \nu \lambda

where c is the speed of light. Recall that the energy of a single photon with wavelength \lambda is:

E = h \nu = h\frac{c}{\lambda}

where is Planck’s constant


Now, net flux is defined as the intensity at a given wavelength observed over all directions. In theory, we assume the intensity is isotropic, or the same in any direction. That means the net flux observed in a given wavelength is assumed to be isotropic in all directions, too. This is not necessarily true across the light spectrum though, because this only defines the net flux measurement in one given wavelength!!

This can be mathematically expressed as the following.

F_\nu = I_\nu Cos[\theta] d\theta d\phi

Where the intensity is variable on frequency and thus, so is the flux. Integrating over all angles like this gives you the net flux.

To find the total flux observed in a given frequency range (i.e. from frequency v to some other frequency v’ ) in units of ergs/cm^2/s is

F = \int F_\nu d\nu

You might be thinking: Well, oh okay, this is the same units as the plot above so we must be done and that’s how we plot spectral energy distributions. Sorry, but you would be wrong! You certainly can plot F vs. v but you wouldn’t be able to look right at the plot and see what frequency ranges dominate the flux density, i.e. what frequencies of light are more abundant from this source than other frequencies. 

Now, if you plot F_\nu (the net flux over a given frequency) against the frequency and integrate the area under the subsequent data (see the figure below), you simply get back the total flux in that range. That’s really it. There’s no safe way to guess how much of say, the X-ray flux, compares to the gamma-ray flux just by plotting it this way. You’d have to sit down and do the math using the equations above.


Taken from the textbook Radiative Processes in Astrophysics written by George Rybicki and Alan Lightman. I’ve kept the page number and chapter (Bremsstrahlung) for your reference.

This is where our funky notation and definition for the spectral flux density comes in!

We like to use

\nu F_\nu\, \text{vs.}\, \nu

Note: this is essentially the same as using wavelength (\lambda), converting by just using the relationship above using the speed of light. This is also essentially the same as 

E^2 \frac{dN}{dE}

by making a few rearrangements using the relationship between energy and frequency. In my field of high energy astrophysics, we don’t really talk about photon energies in terms of wavelength or frequency. I don’t really know why – I suppose because frequencies are really large and wavelengths are very, very small in the high energy regime. Instead, we speak of its energy. This is why, in all of my posts, I refer to the X-ray range in energy units. For example, the soft energy range of X-rays (i.e. low energy X-rays) are defined as 0.5-10keV. keV means kilo-electronvolt. It’s just another unit of energy. Any unit of energy can be converted into another. ergs is also a unit of energy. And Joules. And Calories! 


1\,\text{eV} = 1.6\times10^{-19}\,\text{Joules}
1\,\text{keV} = 1,000\,\text{eV}
(the prefixes here are just referencing the orders of magnitude. They can be Googled easily!)
1\,\text{eV} = 1.6\times10^{-12}\,\text{ergs}
For good measure,
1\,\text{MeV} = 1\,\text{million eV or}\, 1\times10^6\, \text{eV}

Now this next section will also tie in why we use logarithms (in addition to the huge spans of measurements which I discuss below). 


We want

\nu F_\nu

Start with

F = \int F_\nu d\nu

Get a fancy one in there (i.e. 3/3 = 1 so \frac{\nu}{\nu} = 1)

F = \int F_\nu \frac{\nu}{\nu} d\nu


F = \int F_\nu \nu \frac{d\nu}{\nu}

You might need more math to understand this next jump but you can trust me it’s a solid thing to say.

d Log[\nu]= \frac{d\nu}{\nu}

Such that

F = \int \nu F_\nu dLog(\nu)

To generalize, recall the slope of a curve is m and is related to the axes by y=mx. In this case, F=m, y=\nu F_\nu, and x=Log[\nu].

You can plot \nu F _\nu versus the Log[\nu] and get a lot more information (over a wider range of frequencies!). There are a lot of special things about this trick but the main one I want to emphasize is that plotting this way, we can see where the total flux is being dominated. Look at the example of another spectral energy distribution (SED) shown below.



This plot is from the analysis of a pulsar wind nebula in the SNR G327.1-1.1, Temim et al. 2013.
The plot is coming from this paper (again, free version!). The peaks show us where the flux is being dominated. For example, most of the overall flux from this given source above is being dominated in the X-ray regime (where Chandra has measured the spectral flux density in this energy range).

You can tell just by looking at the graph – no calculations necessary! This is a huge perk. ​

In short, plotting \nu F_\nu\,\text{vs.}\, \nu enables us to immediately understand what part of the electromagnetic spectrum being generated from some source is dominating the observed flux. i.e. how bright is it in one energy range from another? 


From this we can show

\nu F_\nu \propto E^2 \frac{dN}{dE}

because N(E) is the photons per area per second, thus \frac{dN}{dE} is the change with energy, and E and \nu are related. I’ll leave this up to you to ponder (and the pdf linked at the beginning has some extra insight to this!)

More on the logarithmic scales….

Take a look at the plots above (specifically the very first figure). How many magnitudes are we plotting along the y- and x- axes? Let’s see…


The y-axis is plotted from order 10^{-12} to more than 10^{-9} ergs/cm^2/s. That’s THREE orders of magnitude! 
The x-axis is plotted from 1 MeV to over 10^{8} MeV. That’s EIGHT orders of magnitude!

To put this into perspective, take the ratios. For the y-axis,

\frac{10^{-9}}{10^{-12}} = 1000

and for the x-axis,

\frac{10^{8}}{10^{0}} = 10^8 = 100\, \text{million}

These are huge ranges we are trying to plot over. This is exactly why you see the plot axes looking so funky. It’s plotted in logarithmic scale to be able to fit all of this measured data onto one plot. Plotting in logarithm base ten allows us to plot fluxes versus their corresponding energies over a wide range of energies by creating equally spaced axes based on their order of magnitude​.