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Star formation rate (sfr) in the galaxy M51

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in the galaxy M51

Arianna Cattapan, Anna Pegoraro, Yi Hang Zhu

Liceo Scientifico “Eugenio Curiel”, Padova (PD)


The purpose of this experience is to calculate the Star Formation Rate, which is the number of solar masses that annually form, in the galaxy M51, through the acquired spectra from the telescope. It has also been calculated how many ionizing photons are emitted every second, and the theoretical number of stars necessary to warm the whole quantity if them all belong to spectral class O5 or B1.


Figure 1: The Galaxy M51, or Whirlpool galaxy. Image from National Optical Astronomy Observatory, NOAO.

The Whirlpool galaxy M51, discovered on 13th October 1773 by the French astronomer Charles Messier and classified in his catalogue, is a face-on spiral galaxy of type Sc, which form an interacting pair of galaxies with its neighbour, NGC 5195.
Regions where stars form are characterized by strongly visible Hα and Hβ emission lines. It is possible to calculate the Star Formation Rate only in spiral galaxies, because when the density of the proto-galaxy is low, they cool down slowly, the gases condense in the centre forming the bulge’s stars and then distribute themselves on a plane due to the galaxy rotation, continually creating new stars; while in elliptical galaxies stars form roughly at the same time.

In the night of 23rd February 2011, the spectra have been acquired by a composition of the Pennar Telescope 122cm, that has a Newton-Cassegrain configuration, the B&C spectrograph, and the CCD camera, in two different ways: one was horizontal and rotated 90 degrees while the other one was rotated 45 degrees; both spectra were rotated counterclockwise.

Astronomic coordinates of the galaxy are: right ascension 13h 29m 54s, declination 47° 11' 60''; the Whirlpool galaxy is in the costellation Canes Venatici.

Figure 2: The spectrum of the Galaxy M51, rotated 45 degrees counter clockwise. Image elaborated by ds9, originated from Pennar telescope

Figure 3: The Galaxy M51, or Whirlpool galaxy. Image elaborated by ds9, originated from Pennar telescope.


The program IRAF (Image Reduction and Analysis Facility) has been used to analyse the images.

The Hα line has to be identified among the emission lines to individuate the regions to be studied, which in this galaxy represent the arms and the bulge.

The bulge is the highest peak, while the two regions next to it, the westernmost region and the easternmost one are the four arms of M51.

The second peak from West might represent a star located nearby the galaxy.

Figure 4: Emissions from West to East in Hα line. The peaks are the regions of the Whirlpool galaxy.

Figure 5: Correlation of the two spectra by ds9 and IRAF, and the image of the galaxy. Spectra rotated 90 degrees counterclockwise.

For each region it is necessary to calculate the flux of Hα and Hβ lines.

Through the ratio of the two fluxes it is possible to obtain the reddening, that is the absorption of electromagnetic radiation by the atmosphere of our planet and the gases of the Milky Way.

in which:

The mean reddening is Av=1,419; and it is used to find out the real Hα flux valour.

The redshift is calculated only for the bulge, as it should be the same for the whole galaxy.

For λobserved valour has been used the central valour of bulge’s Hα line.(λtheoretical = 6563Å)

From here it can be evaluated the distance thanks to the Hubble's law; where Hubble’s constant is considered 75 km·s-1Mpc-1

The distance, combined with the Hα intensity, is used to derive the luminosity of the Hα line.

The SFR in every region can then be estimated through the Kennicutt’s law.

For each region the area is appossimated to a rectangle, in which the base is the slit’s width and the height is the region's breadth, that is the number of pixels in arcsec, converted in kiloparsec with the two formulas where 1 arcsec=1 pixel.

; k = 4,25 arcsec

; px = region’s width in arcsec


Total area of the galaxy is approssimated to a circle.
Finally the total SFR is figured out by multiplying the total area with the mean density of SFR.
In the second part, to calculate how many ionizing photons are emitted every second, it has been used this relation:

This valour permits to give estimation of how many class O5 stars would be necessary to heat the ionized gas;

and also how many class B1 stars would be needed to achieve the same result.


This experience had the aim to estimate the Star Formation Rate, number of solar masses annually formed, of the galaxy M51, through two acquired spectra from the telescope. Another purpose was to calculate how many ionizing photons are emitted every second, and the theoretical number of stars necessary to heat the ionized gas if all the stars belong to spectral class O5 or B1.
The Star Formation Rate of the galaxy results 7 solar masses per year, that means that in the warmest regions of the arms and in the bulge, every year could be created on average 7 stars dimensioned as our Sun.

The mean SFR in spiral galaxy is about 5 solar masses per year; although the datum found out can be accepted, because the error might be due to the imprecision of the distance value, in fact there is still a difference of about 1 Mpc between the closest and the furthest arm of the galaxy.

The mean quantity of ionizing photons is 8·1049, that is also the amount of the ionized gas.

The number of stars which belong to O5 spectral class, needed to warm all the ionized gas is nearly 12 stars.

In the same way the number of stars which belong to B1 spectral class, needed to warm all the ionized gas is nearly 2·105 stars.

The second valour is higher than the first because B1 spectral class’ stars are cooler (12000K < T < 25000K) and smaller than O5 class’ stars (25000K < T < 50000K); so more stars B1 than O5 are needed to warm the same quantity of gas.

From the other relations it is possible to conclude that:

-the redshift of the galaxy’s centre is 0,001545;

-the M51’s distance is 6,1794 Mpc equivalent to about 20 millions light year (1pc = 3,26 ly);

-the mean valour of the reddening is 1,419.

In the bulge the star density is very elevated so the resultant spectrum is a composition of the stars’ continuum spectrum in absorption and the bulge’s emission spectrum.

To find out the bulge’s emission spectrum, the star's continuum spectrum has to be subtracted from the rilevated spectrum. Without the subtraction, the Hα line’s intensity results very lower than the theoretical valour, because the emission lines and the absorption lines are summed up.

Figure 6: Bulge spectrum in which emission lines and absorption lines are summed up.

Figure 7: Bulge spectrum without the stars’ continuum spectrum; the emission lines of the bulge are here higher.

The bulge's spectrum of the Whirlpool Galaxy,rotated 90 degrees counterclockwise, without the stars’ continuum spectrum: the emission lines of the bulge are here higher. Image elaborated by IRAF and another softwere to substracted absorption spectra of stars in the bulge, originated from Pennar telescope.
The spectrum presents a strange peak, the second western one, which might not correspond to a galaxy’s arm.

It could be the emission track of a star which is located near the galaxy. However it has been considered in the calculations.



{} & z & D & A_v & L & SFR & Q_ion & Stars O5 & Stars B1 \\


WestRegion1 & 0.00167 & 668.60294 & 0.30248 & 1.384013E38 & 0.00109 & 1.010329E50 & 2.02066 & 33677.63931 \\


WestRegion2 & 0.0016 & 639.34837 & 1.98374 & 9.262033E38 & 0.00732 & 6.761284E50 & 13.52257 & 2.253761E5 \\


WestRegion3 & 0.00156 & 624.73596 & 1.97388 & 8.550906E38 & 0.00676 & 6.242161E50 & 12.48432 & 2.080720E5 \\


Bulge & 0.00163 & 653.99054 & -0,5099 & 1.889587E38 & 0.00149 & 1.379399E50 & 2.7588 & 45979.69185 \\


EastRegion2 & 0.00161 & 645.44927 & 3.23785 & 4.140938E39 & 0.03271 & 3.022885E51 & 60.45769 & 1.007628E6 \\


EastRegion1 & 0.00149 & 597.29678 & 1.44279 & 3.619560E38 & 0.00286 & 2.642279E50 & 5.28456 & 88075.95796 \\


Star & 0.00162 & 649.73478 & 0.66646 & 2.887590E38 & 0.00228 & 2.107941E50 & 4.21588 & 70264.68701 \\


\caption{The summary of calculated data}




-Report on a stage at the Astrophysical Observatory in Asiago, M. Lazzari, M. Rocchetto, I. Vidal, "Misura della Star Formation Rate nelle galassie NGC 1569, NGC 2798 e NGC 3227", 2006/2007 Edition;


-Material given by the coordinators of the project.

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