The central hydrogen burning core is called main-sequence. At the core of the star the mass and temperature will be more. Hence the nuclear explosion process takes place at the core of the star. The M-S stars consists of hydrogen to about 70%, its complete conversion into helium. Massive star (>8M) ends its normal evolution with the explosion called Supernova II. Low mass star (<8M) ends as a white dwarf. If the white dwarf is in a binary system, due the mass inflow from the companion star, it's mass can exceed the Chandrasekhar limit (1.44M). At this time it explodes as a Type Ia Supernova. Above the Chandrasekhar mass, the internal electron degeneracy pressure can no longer balance gravity and it collapses. As the density rise the temperature do not increase. Eventually ignites carbon-oxygen burning at high enough density. This begins to generate heat, but no additional pressure to slow the collapse. The extra heat leads to greater fusion, which leads to greater heat. The effect is a runaway nuclear explosion. Fusion of the high elements into iron and nickel. The white dwarf detonates and disrupts completely as a Type Ia SN. SNe Ia leave no remnant behind, and maybe responsible for production of much of the Iron in the environment. For the purpose of this project, I have selected a publicly available catalogue of supernova. By plotting the graph Peak luminosity verses decay time, we calibrated the PL of the Type Ia SN. Since all SN Ia originate from star close to Chandrasekhar limit, they are expected to have the same luminosity. Hence they are considered to be Standard Candles and they become important in cosmology.
Keywords: supernova, nuclear explosion, electron degenerance pressure, white dwarf, Chandrasekhar limit
|P-P Chain||Proton-Proton Chain|
|C-N-O cycle||Carbon-Nitrogen-Oxygen cycle|
|C-M diagram||Color -Magnitude diagram|
|H-R diagram||Hertzsprung-Russell diagram|
|ZAMS||Zero Age Main Sequence|
|SNe Ia||Type Ia Supernova|
|U-B-V Bands||Ultra-violet,Blue, Visible Bands|
|mb||apparent magnitude of blue band|
|mu||apparent magnitude of ultra-violet band|
|mv||apparent magnitude of visibe band|
|SCP||Supernova Cosmology Project|
In order to trace the matter distribution in the universe, a parameter specifying the distance scale is required and hence an accurate value for the fundamental constant in cosmology called hubble constant has to be determined. But the measurement of distance for an object is very complex method. The cosmic distance ladder is a succession method by which the astronomers determine the distance to celestial objects. For the larger distance astronomers can no longer use methods such as parallax or cepheid variables. At such larger distance the parallax shift becomes too small and no longer useful to see the individual stars in galaxies. Astronomers then turned to a new secondary standard candles, that are the objects whose magnitude is known. Standard candles are bright and have some fixed properties and are independent of distance. Based upon the observation we can determine object distance. There are several types of standard candle objects for which we can predict the luminosity from other measurements. Type 1A Supernova are very bright transient events, which can been seen up to large distances. Though being rare they are not observed very near to us and hence direct distance or luminosity determination is not available for any of them. The transient events that occurs in the universe are very bright and can be observed at larger distance. Those are the end point of the stellar evolution.
The stellar evolution is a process by which a star changes over the course of time. Stars are born from collapsing clouds of gas and dust often called nebula (or) molecular clouds. Over the million of years, these protostars settle down into a state of equilibrium, becoming what is known as a main-sequence star. Continuous and distinctive band of stars that appears on plot of stellar color versus brightness. These Color-Magnitude plots are called Hertzsprung Russell Diagram. Stars on this band are known main-sequence star or dwarf stars. Homogenous stars (same structure and chemical compostion) lie along the line in the C-M diagram. This line termed as ZAMS, from which further nuclear evolution proceeds to the Upper-right in the H-R diagram. After condensation and ignition process of star it generates thermal energy in its dense core region through nuclear fusion of hydrogen into helium. During this the star life time it is located on the M-S at a position determined primarily by its mass. The M-S can be divide into upper part based upon that a star uses to generate energy. Star below about 1.5M primarily fuse hydrogen atoms together in a series of stages to form helium sequence called P-P chain. Above this mass in the upper main sequence, the nuclear fusion process mainly uses atoms of carbon, nitrogen and oxygen as intermediates in the C-N-O cycle that produces helium from hydrogen atoms. After the hydrogen fuel at the core has been consumed, the star evolves away from the M-S on the H-R diagram into a supergiant, redgiant or directly into a white dwarf.
Low mass star (<8M) are the smallest, coolest and dimmest Main Sequence stars and orange, red or brown in color. Low mass stars use up their hydrogen fuel very slowly and consequently have long lives. Low mass stars simply die by burning up their fuel to leave behind. White dwarfs (contracted low mass stars about the size of the Earth) which themselves cool and contract further to black dwarfs.
High mass star (>8M) are largest, hottest and brightest Main sequence stars and blue, blue-white or white in color. High mass stars use up their hydrogen fuel rapidly and consequently have short lives. High mass stars pass through a Red Supergiant stage before dying catastrophically in supernovae explosions. Remnant stellar cores which survive supernovae can be sufficiently dense to form neutron stars (a star composed almost entirely of neutrons about 10 to 20 kilometres in diameter), pulsars (rapidly rotating neutron stars) or black holes (objects smaller than neutron stars with a gravitational attraction so strong that not even light can escape). Supernovae events are important, if rare, within galaxies. All elements heavier than hydrogen and helium are produced within stars at different stages in their life cycles. Supernovae release these elements into space making them available to be incorporated within later generations of stars.
A white dwarf is a star that has used all its hydrogen and helium and it too cool to burn carbon. It has therefore collapsed into a highly dense state. With no source of energy, it glows only because of residual heat, and over billions of years it will cool down and become a black dwarf, if it is left undisturbed.
Limits on stellar evolution
In 1935, the Indian astrophysicist Subrahmanyan Chandrasekhar famously showed that a star would not form a white dwarf if its mass was greater than 1.44 solar masses because the core temperature would be sufficient to ignite carbon fusion. If a star's mass increased beyond this "Chandrasekhar limit" of 1.44 solar masses after it has collapsed to form a white dwarf, the star shrinks still further. The loss in gravitational potential energy causes an increase in temperature, and a runaway fusion process begins, creating a massive thermonuclear explosion that obliterates the star in seconds.
Because type Ia supernova are almost always formed by the thermonuclear explosion of an object with about the same mass, they almost always have about the same brightness. Observations of distant type Ia supernovae proved the expansion of the universe was accelerating, a discovery rewarded with the 2011 Nobel Prize for physics. However, there have been a small number of troubling observations recently of nearby type Ia supernovae that are abnormally bright, and which appear to have been formed by the detonation of a white dwarf well above the Chandrasekhar limit. The absence of a satisfactory model for how these could be produced has placed a question mark over the use of type Ia supernova as standard candles for observing distant galaxies.
Statement of the Problems
- We selected the U-B-V bands in the light curves of type Ia supernova from the catalogue. Then we analyzed the curves to find the distance of an object.
- But we could not collect the more data. We collected about 300 data, from that we tried to get the distance of bright points.
- Since Supernova Ia is a primary candles. Some astronomers may find the star at large distance and some star at the smaller distance.
- Analyse the U-B-V data for Supernova Ia in the catalogue which are sampled well, and study the relationship between peak flux and time of decline in all the three bands.
- Use this analysis to classify the Supernova Ia and calibrate them.
- In our project we collected about 300 data points by analyzing the curves. We got the bright points in the range of 2 to -2 magnitude from the stretch factor graph.
- If some other research on the basis of this concept they may get the best results and also can be able to find the distance of standard candles.
Objectives of the Research
- To determine the distance of the Standard Candles.
- To verify the distance of the bright points using light curves of supernova.
Supernova explosions are one the most energetic events in the universe. Supernova explosions play an important role for the evolution of galaxies and for driving turbulence in the interstellar medium. They are so powerful that supernova can potentially blow away the clouds in which they formed, and compress nearby gas to such high densities that new stars can form. Type Ia supernovae, caused by exploding white dwarfs, are often used by astronomers as "standard candles" to calculate the distance to a point in space because they are extremely bright and usually have similar luminosity.
The first indication of the origin of supernova is provided by their occurrence in galaxies of different types. Supernova Ia are the only type which occur in all kind of galaxies, in particular also in elliptical galaxies and in the halos of spiral galaxies. In contrast, the SN II and SN Ib/c are observed only in spiral and irregular galaxies, where they are mainly concentrated in the spiral arms. It therefore can be presumed that supernovae of types SN II and SN Ib/c are to be attributed to young massive Population I stars. The origin of the SNe Ia must be from the old objects.
The total energy release E from the explosion of a supernova can be estimated on the one hand by integration of the light curve with an approximate bolometric correction, in favorable cases also using observations in the ultraviolet and infrared, to be obtain the total emitted radiation.
In systematic searches over the last 12 years the supernova Cosmology Project (SCP) has discovered and studied over 100 supernova, most of which have been spectroscopically identified as a Type 1A Supernova at redshift upto z=1.20. An important element of these studies has been recognition of homogeneity within a one-parameter family of SN1A light curves. Several approaches has been used to characterize the SN1A light - curves family. Philips (1993) first suggested that range of a SN 1A light curves might be grouped into a single family of curves parameterized by their initial rate of decline. Further observed that the absolute magnitudes of SNe 1A at maximum light were tightly correlated with this decline rate in the B-band light curve brighter SNe 1A have wider light curves that decline slowly.
Sample Collection and Data Reduction
The data was collected from the publicly available Supernova Catalogue. i.e.
It consists of more than 60,000 supernova light curves data. For the purpose of our project we seperated supernova Ia from the above catalogue. We used python scripts to get the necessary results.
The Scripts and data sheet can be found in the repository given below:
Light curve analysis
The diversity of Type Ia Supernova photometry is explored using a grid of 130 one-dimensional models. It is shown that the observable properties of SNe Ia resulting from the Chandrasekhar-mass explosions are chiefly determined by their final composition and some measure of mixing in the explosion. Light curves are calculated for each model using two different approaches to the radiation transport problem. Within the resulting templates are models that provide good photometric matches to essentially the entire range observed SNe Ia on the whole. On the whole, the gride of models spans a wide range in B-band peak magnitude and decline rates and does not obey a phillips relation.
The Light curves of Supernova is constructed by plotting its magnitude as a function of time. For Type Ia Supernova corresponds to the time of maximum light in the bands with negative numbers indicating the days before peak brightness. The graph verses the (X-axis) Time of decay in julian days and (Y-axis) Absolute Magnitude.
After the separation of Type Ia SNe, We calculated around 300 mpc of light curves. We plotted the graph of time of decay versus absolute magnitude. To find the time of decay we considered the epoch of each light curves. Using the difference of epoch values of the peak point and the point at 2 magnitude away from it in the light curves, we found the time of decay for each of the 300 light curves.
The points which we have considered as (about 2 mag) peak and lowest are shown in the above graphs.
To find the Absolute Magnitude of the optical curves, we used the following formula of absolute magnitude, i.e.,
M = m - 5 log(dL/10 pc
where, M = absolute magnitude of the star
m = apparent magnitude of the star
dL = distance between star and earth
For calculating Mu ,Mb, Mv, we need the distance between star and earth and the apparent magnitude of the star. We got the dL value for each star from the catalogue. Using the graphs present in the catalogue for the corresponding star, we can determine the values of mu ,mb, mv.
We have considered 3 bands U-B-V and have calculated the values of M for the same. From the above calculated data we plotted a graph of Peak luminosity versus time of decay which gave us the light curves for each U-B-V Band.
Best-fitting method analysis
For these obtained scatter plots of supernova, we appled the Best Fit Straight Line method. A line of best fit can be roughly determined using an eyeball method by drawing a straight line on a scatter plot so that the number of points above the line and below the line is about equal. The line of best fit is often useful to attempt to represent with in the equation of straight line in order to predict values which may not be displayed on the plot. The line of best fit is determined by the correlation between the two variables on a scatter plot.
Using this method we calculated the slope and intercept values of U-B-V bands. The Best Fit line obtained passed through the most brightness points. For obtaining the best fit curve we have excluded the zero values. Here zero value implies the absence of respective band curve. The slope and intercept values of U-B-V mentioned below.
1. U-Band :
slope = 0.0254 ; intercept = -18.90
2. B-Band :
slope = 0.0151 ; intercept = -18.72
3. V-Band :
slope = 0.0136 ; intercept = -19.02
The scripts to get the best fit straight line can be found in the GitHub repository provided above.
Stretch factor method analysis
Stretch factor method describes the light curves by a simple stretch time. Stretch factor is a method can efficiently describes almost all the diverse range of U-B-V band light curve shapes over the peak weeks. The stretch factor method was introduced and tested without the benefit of either detailed or early data. We can test whether it applies to the entire curves, rather than just to the post maximum decline, and determine the scatter about the scaled curve.
Using this method we plotted two graphs for regular points and for the brightest points. However, there appear to be some data points systematically well above and below the best-fit line, in all the three bands. This is not expected for a homogeneously sampled data of single type of objects. We analysed the brightest points separately. Unfortunately both samples appear to have same data. But we could not find that much difference between those two graphs. This was the major limitation.
RESULTS AND DISCUSSION
Light Curves Scatter Graphs
- The following three are the scatter plots of 300 supernova for U,B,V band. We can see the distribution of supernova in the graphs. The brightest points are accumulated more in −18 to −20 magnitude in the U_Band. Similarly in B-Band about −17 to −20 mag and in V-Band about −18 to −21 mag.
Best-Fit Straight Line Graphs
Stretch Factor Graphs
There are about 10% Bright Supernova Ia in the B-V plot of color versus stretch factor. We studied light curves and the color - magnitude, but we could'nt find much difference. The mean value and scatter appears to be similar for SNe Ia.
- By considering the standard candles we can find the distance of celestial objects present at larger distance.
- Through the light curves we can easily find the luminosity of each supernova Ia. And from the color-magnitude diagram we are able to find the stretch factor of U-B-V bands of the supernova.
- We could'nt find much difference between the stretch factor graph of regular and brightest points. The major limitations in the graph is about 1 mpc. We could not collect more data. Unless very accurate Light curve is studied we do not seem to have two separate bright points.
It was the wonderful opportunity. I got in my early stage of career. I am exposed to the world of research field of Astrophysics. I would like to thank to my guide, Dr. D Narasimha for teaching me and making me to understand the fundamentals of Astrophysics in these 2 months of summer fellowship program. I met research scholars who are working in the field, they have helped a lot to understand concepts. From this program, I got enough confidence to pursue my research in the astrophysics field.
1. A.Unsold, B.Baschek, Springer, THE NEW COSMOS An Indroduction to Astronomy and Astrophysics, 5th Edition, Heidelberg, December 2004.
2. G.Goldhaber, D.E.Groom, TIMESCALE STRETCH PARMETRRIZATION OF TYPE Ia SUPERNOVA B-BAND LIGHT CURVE, The Astrophysical Journal, 558:359-368, 2001 September 1
3. S. E. Woosley, D. Kasen,S. Blinnikov, and E. Sorokina, TYPE Ia SUPERNOVA LIGHT CURVES, THE ASTROPHYSICAL JOURNAL, 2007.
I sincerely acknowledge the Indian Academy of Sciences, Bangalore for giving me this incredible opportunity of working at Indian Institude of Technology. This research fellowship has been a phenomenal learning experirence.
I would like to thank Indian Institude of Technology for giving an opportunity to carry our project.
I am genuinely thank to my guide Dr. D Narasimha, whose hard work, motivation and consolation have been inestimable.
I extend my special gratitude to Prof. Rajshekar, Prof. Naveen M.B and Mayur Atkade who helped me in python scripts.
I wish to express my sincere thank to Prof. Ramesh Naik, Dean of Student Welfare Section of Karnataka University Dharwad. who gave me the permission to stay in the Working Women's Hostel.