Main Sequence

I must wait until a supernova appears that is close/bright enough for me to accurately observe it in reasonable time. This range is around magnitude 11-14. Magnitude, the unit that astronomers use for an object’s brightness. There are two types of magnitude: relative and absolute. Relative magnitude is the measure of how bright something appears to be and is dependent on distance. Absolute magnitude, or luminosity, measures how bright an object would appear to be from a set distance of 10 parsecs. This absolute magnitude can be thought of as the real or intrinsic brightness of an object. There are two things to keep in mind going forward regarding magnitudes. The first is that the scale of magnitudes is not linear. A change in one magnitude results in a change in brightness of a factor of about 2.5. This means that an object five magnitudes brighter than another is really 100 times brighter. Additionally, the scale works in reverse. Higher numbers refer to dimmer objects, and lower numbers refer to brighter objects. The naked eye can see down to magnitude 6. My telescope allows me to see down to magnitude 12-13, and with my camera I can image down to 18, which is millions of times dimmer than what I can see looking up. But, for accurate photometry—the measure of how bright something looks, I must observe things no dimmer than 14. But also no brighter than 10-11 because it would saturate my sensor. Once a supernova fits that range, I observe it once or twice a week over the course of a few months to cover the entire life cycle of the curve—the variability in its brightness over time. 

Each night I image, I go outside at sunset, and begin setting up. My telescope weighs well over 100 pounds so I bring it out in several parts. I ensure that it is facing directly north and that the initial orientation points it at an angle in the sky that’s the same as the latitude where I am (39-40º). This ensures that Polaris, the north star, is in view. At that point, I level it and then begin the aligning process. I align it by using the electronic controller that’s built into the telescope and allows me to move it around. On my computer, I used a software called Astroimager, a popular option for amateurs. I can view the live view that my camera sees in the telescope, and by centering the stars, my telescope creates a map of the sky so it knows where it is. I then polar align it using the physical adjustments on the mount, and then redo the normal alignment for accuracy. Once that is down, I slew it to the object, generally a galaxy, that I need to be imaging. Due to the alignment, it now rotates at the exact same rate that the earth does which keeps the object framed all night, at least for the most part as I do have to make minor adjustments here and there. Once the object is framed, I set an exposure time and spend hours taking hundreds of individual frames of the object. Once done, before I go inside, I wrap the aperture of my telescope with a white t-shirt and use a ring light to evenly illuminate it. Then I take 100 1-second long exposures that I can then use as calibration frames to account for the dust and vignetting that appears over the night. I take similar frames in the dark called dark flat, bias, and dark frames which reduce the inherent noise in my camera and the thermal noise from the sensor to minimize the image’s artifacts when I am analyzing it later. Once I go inside, that’s when I analyze my data. 

Single frame in Siril

First, I must stack the data using a program called Siril, another common amateur stacking software. Any individual image alone isn’t a very strong image. There is lots of noise and not very much signal. So I stack the images together, effectively adding all of the information together to create a master image that I then use to analyze. I take that image, and I put it into another software that allows me to perform differential photometry. This process basically allows me to assign known magnitudes to stars in the frame so that it can deduce the brightness of the object I am interested in knowing about, in this case the supernova. This brightness value, I then plot, along with every other night throughout the whole time to make a time vs. magnitude graph. This graph is what I will use to statistically determine, with the help of Dr. Igel, when and how bright the peak magnitude was based on my data. This is the actual value—only one for each object compiled from many nights of imaging and analysis—that I use to determine the distance. I then take the brightness I found, factor in the galactic extinction (dust obstruction), and get the final “peak brightness I observed.” I plug it into the distance luminosity equation knowing that the literature says that the supernova peaks around -19.3 as an absolute magnitude (it would look -19.3 from 10 parsecs or 32 light years) and that pops out a distance. That distance is the distance to the supernova, and also the host galaxy of the supernova. Then, I will find a literature value of what the professionals have determined the distance to be to that supernova, and compare my number to theirs to determine if it is close or not. This will answer, very simply, if amateurs can or cannot determine the distances accurately. 

Stacked image in Siril

Part of accurate distance measurement is accurate photometry, so before the supernova was imaged, I set out to prove the accuracy of amateur photometry. This would allow me to be as accurate and transparent as possible about this step of the process before I calculate the distance to a supernova. Specifically, I tested photometry on two open star clusters in the northern constellation of Auriga known as Messier 36 and Messier 38. The images of Messier 36 and Messier 38 that I took for analysis are shown in figure 5 and figure 6 respectively. Open star clusters are a good way of testing photometric accuracy because they provide a relatively bright accumulation of stars with similar properties. As these clusters are relatively young, the stars were born in similar conditions at similar times meaning their temperature, color, and compositions are alike. In this case, nearly every star in the frame is a young, hot, blue star. Because of the way each color on my camera’s sensor interacts differently, keeping to just one color of star eliminates any photometric inaccuracy that could come from comparing different colored stars to one another. 

Though photometry is intended to find an unknown apparent magnitude by comparing it to reference stars, it can still be used in a cluster of stars of known apparent magnitudes. By “pretending” that one is unknown, the software can treat all but one star in the frame as a reference star to estimate the magnitude of the remaining star. By comparing this experimental apparent magnitude for the remaining star to the magnitude from Gaia’s DR3, the accuracy of the process can be determined. I repeated this process 100 times across the two images, focusing on the difference between my values and Gaia’s. 

My images of M36 and M38 that I analyzed

Before reviewing cluster my data statistically, I decided to reject the five worst outliers. The reason for this decision is that all five outliers were subject to two large sources of error that diminished their measurement accuracy. The first source of error was their proximity to the border of my image. Though my optics are designed to reduce distortion and light gradients, the edge still contains more optical problems. Additionally, and more importantly, though most stars in the images were blue, the five I reject are all red. This is no surprise due to the previously discussed high photometric inaccuracy that comes with comparing different colored stars.