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Friday, 6 April 2018

Aries Training School in Observational Astronomy (ATSOA) 2018

The 10 days of ARIES Training School in Observational Astronomy (ATSOA) were packed with many activities. Every day we used to have three or four lectures and then data analysis sessions. During these sessions, we first learned about image cleaning i.e. Bias subtraction, Flat correction etc. Different operating systems like Linux, Fedora, and software called IRAF was installed in laptops by guides of each group. At ARIES every computer already had this software so we first tried to practice the image cleaning commands on them. Meanwhile, we also visited different telescopes at ARIES and Devasthal.

Day 2 - A visit to Solar Telescope



Day 6 - A visit to Devasthal telescopes 


1. (3.6m) Devasthal Optical Telescope.
                



  
2. (130 cm) Telescope



3. Liquid Mirror Telescope



Day 7 - A visit to Nainital




Day 10 - Project presentation. The project of our group was to do photometry of star-forming region Sh2-305. Its part of the second catalog made by astronomer Stewart Sharpless that's why the name.
The image we used was taken by Himalayan Chandra Telescope's TIRSPEC instrument, the TIFR infrared spectrometer, an imager which has 1 Mega Pixel CCD.

The data from that telescope was already dark subtracted so we started the cleaning process by making master flat. Then we subtracted the sky image from the raw image and divided it by master flat which gave us the cleaned image.

I happened to click a picture of the computer screen when we were practicing the commands in IRAF.

Next task was to do processing to get the instrumental magnitude of stars. For this, we did aperture photometry using different commands in IRAF. Then to get the standard magnitude of all-stars we did calibration and astrometry which again involved many commands in IRAF. 



Monday, 2 April 2018

ARIES Training School in Observational Astronomy (ATSOA) 2018 - Day 1

Day 1
19th March, 07:30am. 
I was ready with my bags to join the ten days school at ARIES, Nainital - ARIES Training School in Observational Astronomy (ATSOA) 2018 . Luckily it takes only an hour to reach ARIES by car. I looked out of the car window only once or twice during the journey and then I saw the ARIES check-post. Students were already there near the auditorium. I asked where to put my bags. After taking my bags downstairs in the room adjacent to the dining hall, I walked towards the Auditorium. The first lecture was by Prof. Hum Chand. After the welcome talk by ARIES director Dr. Anil Kumar Pandey he talked about celestial coordinates. Next lecture was given by Dr. Brijesh Kumar. He introduced himself as an Optical Astronomer at ARIES and told us about different concepts related to telescopes like focal ratio, plate scale, fast vs. slow telescopes etc. He also told us to read about how our eyes work because no telescope or detector is as good as our eyes. After these two lectures, we came out of the hall for a short break of tea and biscuits. 

The door to the Dining
Hall
Trees as viewed from
outside our rooms




During the tea break, we used to stand outside the auditorium and look at the beautiful site. I used to wonder while watching cars on the road that how small they appear and how small we are as compared to these hills and how small they are as compared to the size of Earth.





In the next lecture, Prof. Amitesh Omar told us about how detectors are arranged in a telescope. He talked for an hour only using the two chalkboards in the hall without any powerpoint slides. For lunch, we walked to the dining hall and after that, we had to attend one more lecture by Anjasha Mam who is the Senior Research Fellow at ARIES. I realized later that what she talked in an hour was equivalent to what we did in the data analysis sessions in the computer lab for a week! Her talk was on photometry and how the IRAF software is used to do image cleaning, processing and then photometry. After her talk, we were divided into groups of four or five students under the guidance of a Ph.D. scholar. Our guide was Rakesh Pandey sir, SRF at ARIES. I met with group members.  

I had only read that telescopes use CCD detectors and the data or image from it can be cleaned using different software including IRAF. I was unfamiliar with the commands used to process or clean the image. 

After a little conversation, all of us headed to see the 104cm Sampurnanand Telescope. It’s really awesome to watch the dome and telescope moving. The CCD used in the telescope has 1300×1340 pixels i.e. it’s a rectangular CCD and not a square one.


Auditorium


104cm Telescope with dome open


104cm Telescope with the dome closed

But the best part of the day came when I saw loads and loads of stars at night. The lights from the faraway houses were also beautiful. It was very very very cold. I can tell this because my roommates were shivering. I was not feeling very cold because I was wearing a lot of clothes plus a jacket with the hood cap and a shawl. I used to remain packed because I knew that I get cold very easily. We spent some time near the auditorium and talked about stars and constellation then we walked to the dining hall and to our rooms.

Monday, 19 March 2018

12. Very Large Baseline Array

Very Large Baseline Array is a collection of 10 radio telescopes at many different locations in USA and Washington DC. Each telescope has an antenna dish of 25m diameter and it's operated by LBO (Long Baseline Observatory).

astronomy.swin.edu.au

The sensitivity of VLBA can be improved further by adding other radio telescopes. The addition of four radio telescopes and the VLBA telescopes are jointly called HSA (High Sensitivity Array). The four telescopes are Arecibo, Green bank, Effelsberg and VLA.



Thursday, 15 March 2018

11. Very Large Array

Very Large array (VLA) is situated in New Maxico, USA and is operated by NRAO (National Radio Astronomy Observatory).

The red dot is showing position of VLA on earth
Very Large Array is a collection of 27 radio telescopes, each 25m in diameter. They are distributed in a Y-configuration and each of these telescopes can be moved along the railroad tracks. In 2012 it was renamed as Karl G. Janskey Very Large Array after Karl Guthe Jansky who built his own 14.6m rotatable antenna and later in 1931 discovered radio waves coming from the center of our galaxy.

Very Large Array 
APOD May 14, 2006
Credit: Dave FinleyAUINRAONSF
VLA had been used for SETI (Search for Extraterrestrial Intelligence).
We know that our galaxy - Milky Way is the second largest in the Local Group, the first and third are M31 (Andromeda galaxy) and M33 (Triangulum galaxy) respectively. So astronomers pointed the VLA telescopes to look for radio signals of 21cm from these two galaxies but they didn't find any.

VLA radio telescopes also discovered the first Einstein Ring gravitational lens. In gravitational lensing, when a heavy object comes in front of a star, galaxy or quasar it bends the light coming from them and thus distorts is totally. Sometimes it forms a ring and sometimes multiple images. And the first Einstein Ring was made because the image of a quasar was bent by a galaxy in between.

Tuesday, 13 March 2018

10. Australia Telescope Compact Array (ATCA)

Australia Telescope Compact Array or ATCA is located in Australia and is operated by CSIRO.

The red dot on the right end of Australia shows the position of the radio telescopes.

ATCA has six 22m diameter antennas to detect radio waves from space.
Radio waves have the frequency range of 3kHz to 300GHz. These radio telescopes have parabolic dishes to reflect the radio waves to receiver.
The dish of the radio telescope is usually not solid because it would be a waste of money and time to build one. Radio waves can easily get reflected from a mesh just like from a solid surface because of their longer wavelengths.

Another difference that is seen between Radio and optical telescopes is that radio telescopes are usually an array of antennas working together just like ATCA has six Radio antennas.

One of the radio antennas at Australia Telescope Compact Array
www.atnf.csiro.au
The size of these antennas is big because a larger collecting area can help in detecting more faint sources.

Image credit: X-ray: NASA/CXC/Univ. of Hertfordshire/M. Hardcastle et al.; Radio: CSIRO/ATNF/ATCA

The above image is showing the enormous jet of energy released by the Supermassive black hole. It's a composite image showing the data from Chandra X-ray Observatory in blue and the radio data from ATCA in red.

Sunday, 11 March 2018

9. Fermi Gamma Ray Space Telescope

Fermi Gamma Ray Space Telescope orbits around Earth once per 95 minutes.

fermi.gsfc.nasa.gov

Fermi Telescope was launched on 11 June, 2008. And this year it completed 10 years in orbit. Previously it was called Gamma-ray Large Area Space Telescope (GLAST) but later in 2008 it was renamed to honour physicist Enrico Fermi.

It has two instruments on board-
1. Large Area Telescope (LAT)
2. Gamma-ray Burst Monitor (GBM)
Both of these instruments also contain many subsystems.

Fermi has detected the most distant Blazars that are 2.1 billion years old!


Friday, 9 March 2018

8. Suzaku Observatory

Suzaku was an X-ray observatory in a 96 minute orbit around earth.

www.nasa.gov

Suzaku was launched on July 10, 2005. Before its launch it was known as ASTRO-E2. And it was the second launch mission of ASTRO-E observatory which was lost on 10th Feb, 2000 due to rocket failure which crashed into ocean with its payload.

The instruments on board Suzaku are-
1. X-ray Telescope (XRT)
2. X-ray Spectrometer (XRS)
3. X-ray Imaging Spectrometer (XIS)
4. Hard X-ray Detector (HXD)

Suzaku detected chromium and manganese elements in the intergalactic space - the space between galaxies of Perseus Cluster. The gas in cluster was very hot thus emitting X-rays. Suzaku's instruments detected these X-rays and split them into its component wavelengths. As every element has a different spectrum, the two atoms were identified.

This video describes more details about the discovery-


The mission was deactivated on 2nd September, 2015.

Wednesday, 7 March 2018

7. Swift Observatory

Swift observatory is in a 95.74 minute orbit around earth. Its NASA's Multi-wavelength space telescope.

NASA E/PO, Sonoma State University/Aurore Simonnet

It was launched on 20th November, 2004. Swift is named after a small bird. One of its mission is to detect Gamma Ray Bursts and their afterglows in X-ray and visible light. For this, there are three instruments on board Swift -

1. Burst Alert Telescope (BAT)
2. X-Ray Telescope (XRT)
3. Ultraviolet/Optical Telescope (UVOT)
Swift detects ~100 GRBs per year.

This year in January, Swift was renamed as Neil Gehrels Swift Observatory to honour Cornelis A. Neil Gehrels, an astrophysicist who left us on February 6, 2017.

swift.gsfc.nasa.gov

It was the first image captured by the UVOT instrument - the pinwheel galaxy in UV and visible light.


Tuesday, 6 March 2018

6. RXTE

Rossi X-Ray Timing Explorer (RXTE) was a spacecraft in low-earth circular orbit of 90 minutes.

wikipedia.org

RXTE was launched on December 30, 1995. Its mission was to study time variation of astronomical X-ray sources. The spacecraft was named after an Italian physicist Burno Benedetto Rossi.
The mission was deactivated on 5th January, 2012 after working for 16 years and 6 days.

RXTE solved one of the deepest mysteries in Astronomy.

It was known through observations that the galactic plane glows in X-rays whose brightness increases towards the galactic center.

Other observatories like Chandra and XMM-Newton were not able to give details of what's causing the glow. So, it was assumed by astronomers that the X-rays were coming from hot, diffuse Interstellar gas.

RXTE had mapped the X-ray background for 10 years since February, 1996. And NASA's another satellite COBE (Cosmic microwave Background Explorer) in early 1990s had also mapped the near-Infrared glow from our galaxy. The data from two satellites were matched.

Credit: NASA/RXTE-COBE/Revnivtsev et al.

As lots of individual stars glow in near-Infrared, it was suggested that X-ray emission in the galactic plane came from cataclysmic variables (a binary system with a star and a white dwarf).

White dwarfs are cores of dead stars and if they are in a binary, they will accrete gas from their companion star. Due to this process very high energy X-rays are released.

(New Map of Milky Way Reveals Millions of Unseen Objects - March 2006. heasarc.gsfc.nasa.gov)

Monday, 5 March 2018

5. INTEGRAL

ESA's INTEGRAL (INTErnational Gamma Ray Astrophysics Laboratories) is orbiting in a highly elliptical orbit around Earth. And it takes three days to orbit once around Earth.

Credit: ESA/ D. Ducros

INTEGRAL was launched on 17th October, 2002. Its mission is to study black holes, neutron stars, pulsars, active galactic nuclei, Supernovae, Gamma Ray Bursts etc.

It's the most sensitive gamma-ray Observatory ever launched. To detect Gamma rays from the objects in the universe an instrument needs to go in space because Earth's protective layer prevents them from reaching the ground.

INTEGRAL can observe objects in gamma-rays, X-rays and visible light. There are two detectors on INTEGRAL to detect gamma rays from space - an imager (IBIS - Imager on-board INTEGRAL) and an spectrometer (SPI - Spectrometer on INTEGRAL). Other two instruments are JEM-X (Joint European X-ray Monitor) and OMC (Optical monitoring Camera). OMC can detect stars with visual magnitude up to 19.7. It's a standard optical refractor with 5-cm lens and a CCD of 2055×1056 pixels in the focal plane.

On 14th August, the merger of two neutron stars that triggered the LIGO detectors fifth time also triggered the instruments on board INTEGRAL. And It was recorded as a 2 second gamma-ray-burst prior to the gravitational wave detection.

It became the first event to be observed in gravitational waves and in electromagnetic spectrum by lots of ground based and space based Telescopes in addition to the LIGO detectors.

Sunday, 4 March 2018

4. Chandra X-ray Observatory

Chandra X-ray Observatory (CXO) is orbiting around Earth in a highly elliptical orbit of 64 hours.

Artistic image of CXO: wikipedia.org

Chandra Observatory was launched on the space shuttle Columbia in July 23, 1999.

There are lots of objects which emit X rays, for example Stars, Supernovae, Supernova remnants, gases falling into neutron stars and black holes etcetera.

But the mirrors used in Chandra Observatory are not like in any optical telescope where parabolic mirrors are used. If the X rays fall directly on a mirror they'll be absorbed. So the mirrors are shaped like a hollow cylinder which narrows the X rays until they are focused on an electronic detector, as shown in the video.


Last year in December Chandra released a new image of the 11 thousand light years distant Supernova remnant named Cassiopeia A. In this image different colours show different elements. Silicon is shown in red, Sulfur in yellow, Calcium in green and Iron in purple.

chandra.harvard.edu

A similar but more colorful composite image was also released using the data from Spitzer Space Telescope, Hubble Space Telescope and Chandra X ray Observatory.

The best thing about these images is that you can see the remaining core of the star as a dot (white or blue) in the center which is a neutron star.

Saturday, 3 March 2018

3. XMM-Newton

XMM-Newton is a space telescope that is orbiting around Earth in an elliptical orbit of 48 hours.

Artistic Image of XMM-Newton - ESA - D. Ducros

It was launched on December 10, 1999.  
Later on February 9, 2000 European Space Agency (ESA) presented the first image taken by XMM and also announced its new name : XMM-Newton after the originator of the field of spectroscopy - Issac Newton. It's now called X-ray Multi-Mirror mission. One of its goals was to identify black hole candidates. 

Some of its major instruments are-
1. European Photon Imaging Cameras (EPIC) : It has two MOS-CCD cameras of total resolution 2.5 MegaPixel to detect low energy X-rays and a single pn-CCD camera to detect high energy X-rays.
2. Reflection Grating Spectrometers (RGS)
3. Optical Monitor 

XMM-Newton and NASA's NuSTAR measured the spin rate of a Supermassive Black Hole for the first time which is at the center of galaxy NGC 1365.

Last year in December the mission was extended for two years and is expected to operate till the end of 2020.

Friday, 2 March 2018

2. Keck Telescopes

W.M. Keck Observatory has two Telescopes in the Hawaii Island which lies in the middle of the Pacific Ocean.

The red dot shows the position of Keck Telescopes on Earth

The two Keck telescopes can see both infrared and visible light. Each telescope has a diameter of 10m and weigh 300 tons. The mirror used is made of 36 Hexagonal segments and a single segment is 1.8m in diameter which is only a little bit greater than the average human height.

Keck Telescopes

Keck1 telescope started observing in May 1993 and Keck2 telescope in October 1996.

A recent science news released by Keck Observatory tells us about a star orbiting the supermassive black hole at the centre of our galaxy, which was thought to be binary. The star named S0-2 is now proved to be single.

The orbit of S0-2 is shown in blue in the image below.

CREDIT: S. SAKAI/A.GHEZ/W. M. KECK OBSERVATORY/ UCLA GALACTIC CENTER GROUP

There are several theories which describe how S0-2 can form near the black hole and the theory that S0-2 should be a binary is one of them.

But the news that S0-2 does not have a companion deepens the mystery of its formation.

Thursday, 1 March 2018

1. Very Large Telescope Array (VLT)

European Southern Observatory has advanced observational facilities at three sites in northern Chile - La Silla, Paranal and Chajnantor.

The red dot shows the position of VLT on Earth

Very Large Telescope (VLT) at Paranal has four 8.2m telescopes and four 1.8m telescopes.
These telescopes can work together to form a giant interferometer.
The 8.2m telescopes are mostly used individually but the 1.8m telescopes are available to allow VLTI to operate every night.

The large 8.2 telescopes are named Antu, Kueyen, Melipal, Yepun. Out of four Antu was the first telescope to begin routine observations from 1st April, 1999.

There are many discoveries and scientific firsts by VLT.

1. The accelerating expansion of the universe.

For this discovery Nobel Prize in physics was awarded in 2011. ESO's two observatories also contributed to the discovery and VLT was one of them.

Hubble's observation of red shifted galaxies led to the theory of expanding universe and the observation of Type1a Supernova led to the theory of accelerating expansion of the universe.

2. First image of an extrasolar planet.

3. Tracking of individual stars that are moving around Supermassive Black Hole at the center of Milky Way.

Saturday, 3 February 2018

Transcendental Numbers

"...Pi wasn't the only transcendental number. In fact there was an infinity of transcendental numbers. More than that, there were more transcendental numbers than ordinary numbers, even though pi was the only one of them she had heard of. In more ways than one, pi was tied to infinity."

These beautiful lines are from the book, Contact by Carl Sagan.

Even though there are infinite transcendental numbers most of us have heard of only e and pi.
e = 2.718281828459045...
Pi = 3.1415926535...

Transcendental numbers are irrational. That is, they cannot be expressed as the ratio of two integers.

The abc book of e : mathwithbaddrawings.com

But all irrational numbers are not transcendental.
Its because, transcendental numbers cannot be expressed as a solution of a polynomial equation. In other words they are not the solution of any polynomial equation with integer coefficients.
So square root of 2 is an irrational number but not transcendental.


In this Numberphile video a simple proof is shown that pi is transcendental. The proof was given by Ferdinand von Lindemann in 1882.

1. He first proved that e^a is transcendental where a is nonzero. In 1873 Charles Hermite had already proved that e is transcendental.

2. Next, he used Roger Cotes' identity (famously but inaccurately known as Euler's identity). And using proof by contradiction he proved that i(pi) and pi are transcendental.

mathwithbaddrawings.com

There is a conjecture in transcendental theory which indirectly implies that above equation is the only nontrivial relation between e, pi and i.

Hilbert's seventh problem is also about transcendental numbers:

If a is an algebraic number such that a>1 and b is an irrational algebraic number, is a^b necessarily transcendental?

It was eventually proved and now known as Gelfond-Schrieder theorem in 1934.

Here are some of the numbers and functions that are proved to be transcendental.


Sunday, 28 January 2018

Charge Coupled Device and Astronomy

This post is about Charge Coupled Device or CCD and how it changed Astronomy.

The concept of CCD was invented by Willard S. Boyle and George E. Smith at Bell Telephone Laboratories.

In their lab notebook, on 19 October, 1969 they developed the idea of a memory device which they named as 'Charge Bubble Device' because it was an electronic analog of magnetic bubble device.
And few weeks later a device was designed, fabricated and tested.

Charge Coupled Device is now used in digital cameras and Smartphones as an image sensor. 

The functioning of a CCD can be divided in two phases-


1. Exposure – CCD is made of lots of individual pixels which collect light. Each of these pixels is actually a photodiode that converts light into electricity. When light falls on a pixel a free electron is released. If there are lots of electrons in a pixel it means there were lots of photons which hit the pixel. The amount of time till the shutter remains open is called the exposure time. In astronomy many exposures are taken with the CCD shutter closed and open. The dark frame average image is then subtracted from the open shutter image to remove dark current and other factors.

2. Readout – The electrons thus accumulated in each pixel are read out or counted electronically. In this process the electrons are shifted along the semiconductor surface from one storage capacitor to another and thus the information is stored. During the shifting process pixels continue to collect light. So the shifting process should be fast otherwise light may fall on a pixel already containing a charge. And it can lead to Vertical Smear which is a vertical bright line that extends from a bright source. During the readout time CCD cannot collect light. Only when all the electrons are counted the CCD again becomes ready to accumulate another set of electrons for the new image.


The digital cameras are described by the number of pixels they contain. CCD cameras can have pixels in multiple of one million. An M×N pixel camera tells us the number of rows (M) and columns (N) in a CCD. 

So a 1 megapixel camera with square shaped CCD will have 1024×1024 pixels.


It’s very interesting to notice that even before the concept of CCD was invented, NASA planned some projects which required an electronic solid state detector.
One of the project proposed in 1965 was, Large Space Telescope which was later called Hubble Space Telescope.

And the first Wide field Planetary Camera (WF/PC) in Hubble Space Telescope used 8 Texas Instruments backside-illuminated 800×800×15 mu meter pixel three-phase CCDs.

Here the backside illumination is the technique used in CCDs. In this, the image is focused on the back side of Silicon so that the maximum amount of photons are detected. But for this the thick wafer on which CCD is built must be very thin.


The CCD used in ACS (Advanced Camera for Surveys) - www.spacetelescope.org

The WF/PC produced many beautiful images. And it was replaced by WF/PC 2 in December, 1993.


Astronauts installing the WFC 3 


The second generation WF/PC 2 camera system with corrective optics had four Lockheed frontside-illuminated 800×800×15 mu meter pixel three-phase CCDs. Then a new camera named ACS (Advanced Camera for Surveys) was installed in 2002. And it was also replaced in 2009 by WFC 3.

spacetelescope.org : A gravitational lens captured by WF/PC 2


WF/PC 2

Out of all the images taken with the cameras installed in Hubble Space Telescope, the deepest view of the universe was provided with the Hubble Deep Field images.


The first Hubble Deep Field image was captured with three WF/PC 2 CCD detectors. Separate images in blue, red and infrared were captured to make the true-color image.



After many such Deep Field images, Hubble Ultra Deep Field image was taken with the Advanced Camera for Surveys (ACS) in the Fornax constellation. In 2009 Hubble Ultra Deep Field (HUDF) was taken with the Wide Field Camera 3 in infrared. Later in 2012 Hubble eXtreem Deep Field was released which was just the combination of many exposures of UDF. 

The last HUDF was released in 2014. It’s a composite image of the exposures taken from 2002 to 2012 with the Advanced Camera for Surveys and Wide Field Camera 3 of Hubble Space Telescope. The project was called the Ultraviolet coverage of the Hubble Ultra Deep Field (UVUDF).

> You can see what Hubble Space Telescope is observing right now with WFC 3. 

   Spacetelescopelive.org



Saturday, 20 January 2018

Apparent Size

One of the units used in astronomy is degree.

1 degree = 1/360 of a circle
1 arc minute = 1' = 1/60 of a degree
1 arc second = 1'' = 1/60 of an arcminute

The size of a planet or other astronomical objects is described using their angular diameter as seen from Earth, or simply their apparent size.

And apparent size is the angle subtended by an object which is usually measured in degrees, arcminutes or arcseconds.

Sun and Moon appear similar as seen from earth so their apparent size is almost same, 1/2 degree.

Another interesting example is the Hubble deep field which is an image of a small region in the constellation Ursa Major (Big Dipper).

wikipedia.org

It covers an area of about 2.6 arcminutes. And the image was taken with the Wide Field and Planetary Camera 2 of Hubble Space Telescope.  342 exposures were taken from 18 to 28 December, 1995.

wikipedia.org : Hubble Deep Field (1995)



Friday, 12 January 2018

Brightness of stars

One of the units used in Astronomy is Magnitude (or brightness). It tells us about the brightness of stars or other astronomical objects.

Magnitude is actually divided in two types, apparent and absolute.

1. Apparent Magnitude tells us how bright a star is as seen from Earth. And its inversely proportional to the square of distance.

The measurement of apparent brightness is called photometry.

























Image Credit: www.windows2universe.org

If we assume that stars are at same distance from us then we can compare their brightness. And that's what absolute magnitude tells us.

2. Absolute Magnitude gives us the brightness of stars as seen from 10 parsecs (32.6 light years).

Greek Astronomer Hipparchus categorized the stars according to their brightness more than 2000 years ago. According to him the brightest stars were of first magnitude and faintest were of sixth magnitude.
The first magnitude stars were two times brighter than second magnitude stars.

Later, as the instruments became more sensitive, astronomers found that the magnitude scale was not accurate.
But instead of abandoning it, they refined it.

In the Modern Magnitude System, first magnitude stars are about 2.512 times brighter than second magnitude stars. And second magnitude stars are (2.512)^2 times brighter than third magnitude stars.

So faint stars have bigger magnitude.

https://en.m.wikipedia.org/wiki/Luminosity

For example let's take two stars of Orion constellation, Rigel and Betelgeuse.

1. Rigel
    Apparent magnitude (m) = +0.12
2. Betelgeuse
    m = +0.50
The difference between their magnitude is
0.50 - 0.12 = 0.38

So Rigel is about (2.512)^0.38 times brighter (apparent brightness) than Betelgeuse.

Absolute magnitude, apparent magnitude and distance are interrelated. So if two are known, another can be calculated.

To study brightest stars (as seen from Earth) BRITE (BRIght Target Explorer) a set of 6 nano satellites were launched in 2013.

www.brite-constellation.at

Out of six, two satellites UniBRITE-1 and TUGSAT-1 (BRITE-Austria) were launched by PSLVC-20 on February 25, 2013 from ISRO's Satish Dhawan Space Centre, Sriharikota, Andhra Pradesh.

Image credit : ww.isro.gov.in