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Measuring distances
in the Universe: SNIa
This exercise was initially produced by J.-C. Mauduit & P. Delva, inspired by a work of N.
Ysard, N. Bavouzet & M. Vincendon in France. It is based on 2 images obtained from
professional archives (Digital Sky Survey, photographic plates on a 48-inch (~1.2m) Schmidt
telescope) and by Marc Serreau (a French amateur astronomer with a C8 (8-inch ~ 20cm)
telescope. The quality of the images is moderate, but it is possible to perform astronomical
measurements.
Supernovae of type Ia can be used as standard candles to measure the distance D of galaxies.
It is one method among others (see also the exercise on Cepheid method) to scale the
Universe. This method enables to study very distant objects because supernovae are very
bright. The luminosity of supernovae of type Ia (SNIa later on) at maximum is the same for
all SNIa. SNIa are called “standard candles” and are thus good distance indicators. The
absolute luminosity of a SNIa is L = (1,4±0,4)* 1036 Watts (Allen's Astrophysical Quantities).
The more distant is the SNIa, the weaker is its apparent luminosity. It is thus possible to
determine the distance of a SNIa by comparing its observed flux with its (absolute)
luminosity. More precisely, at a distance D from the star, the luminosity is distributed on a
sphere of radius D and of surface S = 4*π*D². By definition, its flux F (in W/m²) at the
distance D is F = L/S where L is the luminosity in W. One can derive the distance D of the
galaxy: D = √ (L / 4πF)
In 2005, a SNIa has exploded in the NGC691 galaxy. Its name is SN2005W. We are going to
measure the distance of NGC691 with the help of this SN.
1. Open the image file images_snia/NGC691_13111953.fits with SalsaJ. On this image,
taken in November 1953 (i.e. before the explosion of the SN in 2005), one can note a
bright star A on the left hand side of the galaxy.
2. Identify the star A and the reference star, as indicated on the figure above with yellow
arrows.
3. Measure the intensity of the star A and the reference star with the tool Photometry
Check that the radius of the star and that the sky background obtained is coherent with
the pixel values you can see on the image.
4. The flux of the reference star is known: Fref = 5.24×10-14 W/m². Estimate the flux of
the star A: FA =
SN2005W has exploded next to star
A and those two stars are
superimposed on the image. It is not
possible to measure their intensities
separately.
5. Open the image file
images_snia/NGC691_07022
005.fits. This
image has been
taken after the
explosion of SN2005W
(located very close to the star
A).
6. Identify the objects in the 2
images
In order to identify the various
objects in the field adjust the contrast with ImageAdjustBrightness/Contrast
If you are not sure of the identification of the object, you can measure distances and angles
between different point sources. For this, select an image, click on
Analyse/Tools/ROI manager, a ROI manager window opens, draw
a straight line selection and click on add [it], then repeat the
operation. Once you have drawn several lines you click on Measure
and you will have a measure window displaying the positions, lengths
and angles of all the lines. This enables to compare the features
between the 2 images.
7. Measure the total intensity of SN2005W and the star A. Check the sky background
obtained is coherent with the pixel values you can see on the image.
8. As before, derive the combined flux of SN2005W and of the star A.
Ftot = FSN2005W + FA =
using the measurement of the intensity of the
reference star and the combined stellar image (S20005W and A).
9. Estimate FSN2005W =
10. The absolute luminosity L of the SNIa is given in the introduction, estimate the
distance1 to NGC691: DNGC691 = ............ m = ............. Mpc.
11. As you know the error on L, estimate the error on DNGC691.
12. You can compare your results with the professional measurements obtained for this
galaxy, available on the NASA/IPAC Extragalactic Database (NED)
http://nedwww.ipac.caltech.edu/forms/byname.html
Star A
Reference star &
supernova position
th
Epoch 1 (13 November 1953)
Intensity
measurement2
A =
Ref =
Flux (Wm-2)
F A=
FRef =5.24×10-14
Supernova
not detected
Epoch 2 (7th February 2005)
1
2
Intensity
measurement2
A + SN =
Ref =
Flux (Wm-2)
FA+ FSN =
FRef =5.24×10-14
FSN =
Luminosity (W)
LSNmax = 1.4±0.4 1036
Distance
D= √ (LSN / 4πFSN)=
1 parsec = 3.086 1016m; 1 light year = 9.461.1015m
Instrumental unit
History
Saul Perlmutter
Supernova
Cosmology Project
Brian Schmidt
Adam Riess
High- z Supernova Search Team
In 1998, both teams started to study the positions of SNIa in the far
Universe. The challenge was difficult: there is only one SNIa occurring per
galaxy per millennium!
Fortunately, there are a lot of galaxies in the Universe. By studying
thousands of galaxies, they managed to found enough SNIa, and began to
realize something: the furthest ones appear less bright than expected!
At the same time, the two teams realized that only a Universe in accelerated
expansion can explain this effect, and published their results in scientific
papers.
Their discovery implied that the Universe was filled by an energy that “pulls”
the galaxies apart, called the Dark Energy. It opened so many new
perspectives in cosmology that in 2011, both teams were awarded a Nobel
prize.
Basics on stellar photometry
In SalsaJ, we can perform photometry of stars. The idea is to compute the instrumental
flux3 (or intensity) of one star. As they are very distant, stars are (even from space) point
sources for the observer. However, our instruments (refractor or telescope) have a
transfer function: it includes the diffraction limit and the imperfections of the mirrors
(quality of the surface, etc.), and the atmosphere (turbulence) further enlarges it.
The photometry tool computes the sum of the pixel flux (or intensity) and subtracts the
contribution of the background (moon and various parasite lights). The column entitled
Star’s intensity provides this quantity.
You have to check the other parameters to be sure that your measurements are correct.
The sky intensity can be checked with the pixel values of your images (by scrolling the
mouse on the image in SalsaJ), while you can check what is inside the sky’s radius if
there are unexpected results.
In principle, you should use the same Star’s radius for all your measurements on a single
image, as the resolution (and the transfer function) is in principle the same all over the
image (unless there are some distortions). Checking the value of the Sky’s intensity is
important in crowded fields or if there is a strong background (e.g. a gradient).
You can check the resolution of your image with a slice on one star: for one image the
full width half maximum should be the same for all stars.
Plot profile of one star: this displays the transfer
function. The Full Width Half Maximum (FWHM)
is about 4-5 pixels, and is the same all over the
image.
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We measure a quantity proportional to the number of photons that reaches the instrument of observation
(camera CCD mounted in a telescope).
SalsaJ determines the photometric parameters automatically. In some cases, it is
necessary to further tune or fix them.
To change the star’s radius, you should use the Photometry Settings, and click on Forced
Star Radius. It is then possible to change it and check it interactively on the image.
Similarly, you can modify the other parameters: this is usually necessary for special
cases (if there are perturbations close to your star).
It is possible to save the content of the Photometry window as an excel file
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This project has been funded with support from the European Commission.
This publication [communication] reflects the views only of the
author, and the Commission cannot be held responsible for any use which may be made of the information contained therein.