2015

Age and Metallicity determination of young open clusters NGC 7160 and NGC 581

"A dissertation submitted in partial fulfilment of the requirements for B.Sc. Honours Physics with AstrophysicsAlexander Owens, Nottingham Trent University

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CONTENTS Page

1. Abstract 2

2. Introduction/Aims of the study 2

3. Background Information

3.1 Open Galactic Clusters3.2 CCD Photometry3.3 Colour-Magnitude Diagrams3.4 NGC 5813.5 NGC 7160

456911

4. Methodology

4.1 Observations/Data Reduction4.2 Aperture size calculation4.3 Aperture Photometry/Reference Stars4.4 CMD Construction/Isochrone fitting

12151719

5. Results/Discussion

5.1 Photometric Data5.2 Age/Metallicity Determination

2124

6. Conclusion 30

7. References 31

8. Acknowledgements 33

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1. Abstract

Presented in this study is aperture photometry in the B and V filters on 54 stars within young

open galactic cluster NGC 581 and 14 stars within young open cluster NGC 7160. By fitting

stellar evolutionary tracks called isochrones, an age of NGC 581 is deduced, shown to be

21.68±7Myr, agreeing well with previous literature and also an age of NGC 7160 is shown to

be 15±4Myr. The metallicities of NGC 581 and NGC 7160 are found to be (0.025 ±

0.0065)Zʘ and (0.0025 ± 0.00065)Zʘ respectively. A distance of 789pc to NGC 7160 and

2194pc to NGC 581 is assumed. Interstellar reddening for NGC 581 is also deduced and

shown to be E(B-V) = 0.432 ± 0.05mag and for NGC 7160, E(B-V) = 0.2 ± 0.05mag.

2. Introduction/Aims of the study

Stellar evolution theories help us acquire information about the structure and evolution of the

universe. Looking at stellar evolutionary models is a reliable way to make estimates of a

certain objects parameters such as age, distance, chemical abundance and formation. In

particular, isochrones are used and applied on colour-magnitude diagrams (CMD) of clusters

of stars, to help gain an understanding of its age and metallicity along with other factors.

Isochrones are essentially evolutionary tracks that represent a population of stars, with the

same age and distance from the observer. They are often used to date open clusters, as all the

members have approximately the same age, but with a varying initial mass. When applying

an isochrone to a set of data, there are multiple factors to consider such as extinction and

reddening in the UBV photometric system, otherwise known as colour excess. These effects

can alter which isochrone is used for the cluster and therefore giving a different age.

In this study, two relatively young open galactic clusters, NGC 7160 and NGC 581

have been observed at NTU observatory and studied using the UBV Johnson photometric

system. The data is used to plot Colour-Magnitude Diagrams (CMDs) of apparent magnitude, mv against colour (B-V) and the fitting of isochrones from the PARSEC database of stellar

evolutionary tracks is carried out, to determine an age and metallicity for the open clusters.

The choice of clusters to study is limited by the resolution of the telescope in use, which has a

field of view of approximately 6.5 arcminutes. The visibility in Nottingham throughout the

year is also a limiting factor.

The amount of incoming flux in units of ADU from each star is measured using

aperture photometry, which is calibrated with a reference star of known magnitude, to obtain

a magnitude of the star. Aperture photometry has been used in this study as it measures the

brightness of an object whilst taking in to consideration any possible background noise from

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other sources such as bias levels, flats and additional luminous objects. It is beneficial to have

a large annulus that contains the background, to gain a better average of the sky count, but

also it increases the likelihood of the sampling area being a poor representation of the

background closely surrounding the object. Testing of aperture size with relation to signal to

noise ratio (SNR) is also carried out, determining the best aperture size to use on each star

within the cluster images. The gathered information from the photometry is then plotted on

colour magnitude diagrams. Depending on the appearance and general curve of the plots, a

general impression of the age of the cluster can be approximated even at this point, by

looking at what magnitude the red giant branch starts to appear.

Isochrones published by Bressen et al. (1999) through the PARSEC database of stellar

evolutionary tracks, are taken and added to the accumulated CMDs. Extinction and colour

excess and Z-metallicity are also taken in to account to obtain a better fitting of the

isochrones to the data. The isochrones can then be used to determine the corresponding age of

the cluster as well as a value for the distance away from the observer.

The overall objective for this project is to analyse and evaluate the extent to which age

of young clusters can be determined with the limitations of the observatory used in practice.

A CMD age resolution and knowledge of the effectiveness of the photometry is in this

project, can also be deduced.

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3. Background Information

3.1 Open Galactic Clusters

Open galactic clusters are a group of up to a thousand stars, formed from the same molecular

cloud. The stars within the clusters are loosely gravitationally bound and are frequently found

in spiral and irregular shaped galaxies. All of the stars in a cluster have a tendency to be of

the same age and the same distance from the observer. Although the majority of stars within a

cluster have a similar chemical composition, they can vary vastly in initial mass. By plotting

the stars within a cluster on a Colour-Magnitude diagram (CMD) and comparing with stellar

evolution theories, we can start to deduce the age of the cluster. The conventional way of

determining age of a cluster is to fit isochrones to the CMD, using the UBV photometric

system. Absolute V-Magnitude against B-V colour is often used, as shown by Meynet et al

(1993).

There are several parameters that determine a star’s position on a CMD, including

age, initial mass, metallicity, Helium abundance. Primarily, age and metallicity of open

clusters help to understand the star formation process. Bhavya et al. (2012) explain that for

some open clusters, star formation processes can still occur after the most massive stars are

formed. This is supported by the evidence of pre-main sequence stars, implying that stars are

formed with a non-zero duration. Elements of the galactic disk model can also be explained.

This shown by Gilmore & Reid (1983) deriving that the luminosity function has a smooth

variation with distance from the galactic plane. They also show that stars with MV < +4 are

more concentrated to the galactic plane.

Janes & Adler (1982) mention that there is a catalogue of up to 1200 known clusters

in the galaxy, but only around 35.5% of those have a CMD, as tabulated by Lyngå (1981).

Since then, that number has risen to 2000 known clusters, in the galactic disk. The youngest

known clusters have a tendency to be of an age of circa several million years, the oldest as

many as several billion years old. The youngest clusters can be seen to still have traces of the

nebula surrounding them, from which they were formed. The less dense clusters are

increasingly disturbed by gravitational interaction with the rest of the galactic disk (Ridpath,

2012).

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3.2 CCD Photometry

For astronomers, there may be a time when obtaining visual pictures of astronomical objects

does not supply enough information. This is where we can use CCD photometry to obtain

more information. A CCD is an electronic chip divided up in to a number of pixels, from

which we can measure the amount of incident electromagnetic radiation. As an output, we get

a matrix numbers that represent a certain amount of light falling within each pixel that is then

converted to a digital image. From this, we can determine the apparent magnitude of an

object. The ultimate task of CCD aperture photometry is to measure the electrons falling

within a certain aperture placed on a CCD image. The original signal from the object will be

blurred or convolved over many pixels, because of the optics in the telescope. This is due to

the seeing quality, affected by diffusion of light through the atmosphere, noise in the

telescopes optics and electronic noise in the CCD. Dome flats and bias images are taken to

help reduce these effects, to produce a clearer image. Full analysis on CCD data reduction

processes can found from Howell (2006).

Henceforth in aperture photometry, there is an aperture or circle around the object in

observation and the total flux is obtained, with units of ADU, within the area. The intensity

average from a nearby sky count is taken and subtracted from the count within the aperture;

the end result can then be converted in to apparent magnitude:

m1−m2=−2.5 log10

I 1

I 2

In the above equation, m1 and m2are the apparent magnitudes of the object and reference star

respectively and I 1and I 2 are the intensities of the object and reference star, measured in

ADU.

CCD cameras typically contain a filter system, in the case for this study the UBVRI

Johnson photometric system is used. The U, B, V, R and I standing for ultraviolet, blue,

visual, red and infrared light. The system was first presented by Harold L. Johnson and

William W. Morgan in the 1950’s. The system is used for filters that have a passband

upwards of 30nm, anything lower are intermediate e.g. The Strömgren 4-colour UVBY

system typically used for stellar classification and narrow band filters.

Equation 3.2.1

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3.3 Colour-Magnitude Diagrams

Open clusters are studied to assist the understanding of stellar evolution, specifically at what

point the main sequence turn-off point is, for varying ages. We can do this by performing

photometric observations on stars within a cluster and plotting the information on a colour-

magnitude diagram. A CMD is essentially a profile of the cluster at a specific age, as shown

in figure 1. There is a distinctive main sequence (MS), which is a continuous band of stars

which are yet to evolve in to Red Giant stars. The MS turn off point for a star in a cluster

depends on its initial mass. Stars with a high initial mass have a tendency to turn off the main

sequence at a brighter magnitude than that of stars with low initial mass. A young open

cluster contains a large range of masses whereas an old cluster encompasses predominantly

low mass stars. A star evolves in to a sub-red giant when Hydrogen fusion stops in the core of

the star consisting of Helium, which then collapses releasing gravitational energy. The

surrounding Hydrogen shell is then hot enough to initiate fusion or Hydrogen shell burning.

The luminosity stays constant but the star becomes redder.

Figure 1 – From Sandage (1958) a colour-magnitude diagram showing evolutionary tracks of 10 open clusters and one globular cluster (M3)

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Photometry carried out in the past has showed that the position a star has in a CMD no longer

has one variable (mass), but several other factors e.g. age, metallicity and Helium abundance

as Twarog (1983) mentions. Factors such as metallicity and Fe/H Metallicity can alter the

shape of an isochrone, hence changing the age of a cluster through the fitting of the

isochrone. Lejeune & Buser (1999) go in to detail about how an isochrone changes with

varying metallicity and present the data shown below in figure 2. The position and the

curvature of the Red Giant Branch is relatively sensitive to a change in metallicity, which is

evident in the figure.

The age of open clusters can be determined by fitting isochrones to a CMD. Isochrones can

be thought of as a set of evolutionary tracks of stars, characteristically representing a

population of stars the same age, with the same initial chemical composition but various

initial masses. Intermediate-age clusters attract the most attention in researchers as they

provide the most useful tests of stellar evolution. This is due to the tendency of the stars

within the clusters to produce ‘convective overshooting’ with masses from 1.0 to 2.2Mʘ (see

Friel, 1995). Overshooting is the advancement of a small convective core in stars with a mass

larger than that of our Sun. Convective elements ‘overshoot’ the boundary between the

convective inner core and the stable outer zone. For a more in-depth look at overshooting, see

Maeder & Meynet (1989). When overshooting occurs, the core mass of the star increases

during its time on the main sequence, yielding more fuel to live longer. This causes the star to

give the impression of a more massive star, hence affecting evolutionary models.

Figure 2 – From Lejeune & Buser (1999) A comparison of the theoretical isochrones for different abundances (Z = 0.0002 to 0.04)

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When putting together colour-magnitude diagrams, we sometimes have to think about

interstellar reddening and extinction. Extinction, notated AV happens when electromagnetic

radiation in the form of light, is absorbed and scattered by dust, gas and other substances that

make up the interstellar medium between the observer and an object. This was first

documented by Trumpler (1930). A number of researchers such as Struve (1847) had noted

the effects of extinction but could not describe why or how it happens. Earth’s atmosphere

can also cause effects of extinction, in some cases so much that space-based telescopes are

preferred. Interstellar reddening occurs because interstellar medium absorbs and scatters blue

light more than it does for red light. This causes a shift towards the red end of the visible

spectrum and the objects appear ‘redder’. A relation between interstellar extinction and

reddening can be found by the following equation:

AV =RV . E(B−V )

RV is the optical extinction ratio and depends on the amount of interstellar material in the line

of sight. For most cases RV = 3.1, assuming a low interstellar medium density. For cases such

as the Cepheus constellation, RV has been found to be up to 6, see Johnson (1965).

Equation 3.3.1

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3.4 NGC 581

The first open cluster to be studied is NGC 581 with an apparent size of 6 arcminutes (RA:

01h 33m 23s; Dec: +60° 39’ 00’’), a relatively young cluster in the Milky Way galaxy. It

consists of several thousand stars in the constellation Cassiopeia. Originally discovered in

1781 by Pierre Méchain, it is one of the most distant open clusters known to us, estimated to

be 2884 parsecs away by Sanner et al. (1999) and 2700 parsecs by Sagar & Joshi (1978). 70

stars are found by Steppe (1974) to be hypothetical cluster members, within a field of view of

7.5 arcminutes surrounding the centre of the cluster. Images of NGC 581 are often dominated

by Struve 131 which has an apparent magnitude of 9.9mag (O’Meara, 2014) and also a

noticeable Red Giant star, as you can see in figure 3 it appears to be the brightest red giant

star, with a magnitude of roughly 10.8mag and a spectral type M6 III. Both of these stars are

not classified as cluster members.

Figure 3 – Colour combined image of NGC 581 using R, B and V filters on a Sony ICX285AL CCD, taken at NTU astronomical observatory on the night of 5/12/15. The field of view is 8.65’ x 6.48’. Image combination process was carried out by Dr. Daniel Brown, senior lecturer at NTU.

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There have been very few studies of NGC 581 in the past, so it is difficult to determine

whether the age determinations are reliable or not. Sanner et al. (1999) identifies 77 cluster

members with a brighter magnitude than 14.5 to give an age determination of 16 ± 4 Myr,

from fitting an isochrone to the CMD, as shown in figure 4. For the bright stars, relative

motions were investigated to determine cluster members, as for fainter stars, statistical field

star subtraction is used. This is to gain a more accurate CMD of cluster members, to aid an

improved/more reliable age determination.

Sagar & Joshi (1978) use the UBV photometric system to conclude NGC 581 has an age of

40Myr, by plotting a Colour-Magnitude diagram of absolute-V magnitude (Mv) against (B-V)

colour. This is considerably older than other studies have suggested. It is also stated that one

fifth of the cluster members are still in the pre-main sequence gravitational contraction stage,

or possibly being non-member field stars. Moffat (1972) analyses images of NGC 581 from

Hoag et al. (1961) and Purgathofer (1964) and finds that stars with smaller reddening tend to

lie closer to the centre, rather than further out where the reddening increases to a maximum

value. They imply that NGC 581 may display a dust deficit at its centre. As the age on the

WEBDA database is given as log (t) = 7.336 (taken from Phelps & Janes 1994) which

corresponds to an age of 18.97Myr, you can see by looking at Sagar & Joshi (1978) and

Sanner et al. (1999) that photometric observations have improved significantly over the years.

Figure 4 – From Sanner et al. (1999) Colour magnitude diagram of all members of NGC 581 as determined with the proper motions (V < 14 mag) and the statistical field star subtraction (V > 14 mag)

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The introduction of electronic cameras and CCDs have been the main contributors to this,

providing more accuracy in the measurements.

3.5 NGC 7160

The other cluster that is studied is NGC 7160 (RA: 21h 53m 40s; Dec: +62° 36’ 12’’) with an

apparent size of 7 arcminutes. It is situated in the constellation Cepheus and was first

discovered by William Herschel in 1787. It is the eldest of two young clusters in a neutral

Hydrogen cloud, named the Cepheus OB2 region (Simonson & van Someren Greve 1976).

NGC 7160 is situated in the centre of this region, whereas the other cluster, Trumpler 37 is

positioned at the edge of the gas cloud. It is hypothesised that there may have been a

supernova take place a number of megayears ago, prompting star formation processes,

leading to the formation of the open clusters mentioned. The age of NGC 7160 has been

estimated as 10Myr by Siciliar-Aguilar et al. (2004). This was determined by using optical

photometry in the bands VRI and plotting V against V-I on a CMD with fitted isochrones

from Siess et al. 2000. Siciliar-Aguilar et al. (2004) claim that their age estimate is in

agreement with studies of the hydrogen gas cloud and the upper MS turn off (Patel et al.

1995, 1998). They also find an average cluster extinction of AV = 1.17 ± 0.45 from 39

candidate members. The large uncertainty is thought to be because of ambiguity over spectral

class, colours and photometric error. A constructed CMD for stars in NGC 7160 is shown in

figure 5.

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4. Methodology

4.1 Observations/Data Reduction

Observations of NGC 581 were carried out on the night of 5th December 2014 at Nottingham

Trent Astronomical Observatory, using a 14-inch Meade telescope with focal length

3556mm, connected to a SXV H9 CCD camera with a pixel size of 6.45μm x 6.45μm and a

chip size of 8.95mm x 6.7mm, in V and B broad-band filters mounted in a filterwheel. The

bandwidth of the V-filter is 90nm and the B-filter is 100nm. The field of view in this set-up is

approximately 6.48 arcmin. The details of the images taken are shown in table 1. The images

of NGC 7160 were taken by Pierre Vaurs on the night of 23rd May 2012 at Nottingham Trent

Astronomical Observatory.

Object Filter No. of exposures Exposure time (s)

NGC 581 B 3 5

5 60

V 3 3

5 60

NGC 7160 B 20 3

2 60

V 10 1

2 60

Table 1 – Photometric details of observations of NGC 581 and NGC 7160

Bias and dome flat images were also taken in order to perform the necessary data reduction.

Bias subtraction is performed because the electronics in the CCD need an offset in order to

evade a negative current that cannot be converted. This offset (bias) then needs to be

subtracted from each image. Flat images are taken because each pixel within a CCD chip

does not have equal sensitivity to photons i.e. does not have the same quantum efficiency

Figure 5 – Taken from Monroe & Pilachowski (2010) CMD showing dereddened stars in NGC 7160. Photometry data from Sicilia-Aguilar et al. (2005), probability of star being a cluster member is judged on individual extinction values. The CMD shows 3 different isochrones of 1, 10 and 100Myr (Siess et al. 2000).

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across the CCD. Dust grains on the CCD and the filters can also cause unnecessary noise on

the images and block out light. To counteract this, an image of an ideally evenly illuminated

area is obtained as the ‘flat’ image. A summary of the calibration images taken for the

observations in this study is shown in table 2.

Object Image Type Filter Exposures Comment

NGC 581 Bias - 10 x 0 seconds OK

Dome Flat B 5 x 15 seconds Good

V 5 x 20 seconds Bright

NGC 7160 Bias - 20 x 0 seconds OK

Dome Flat B 9 x 12 seconds Bright

V 10 x 3 seconds Good

Table 2 – Photometric details of calibration images for NGC 581 and NGC 7160

The quality of bias or flat images can be judged on its variation across the image. A dome flat

with a variation of more than 2% is thought to be a cause for concern. For the case of the

CCD used in these observations, a dome flat with an ADU count range of 20,000 to 40,000 is

sufficient to obtain an adequate signal to noise ratio on the final object image. For the ‘good’

dome flats, an average ADU of ~28,000 is observed and for a ‘bright’ image, an average

ADU of over 30,000 is observed. The single bias images are combined using a median option

with no normalisation, to produce a master bias. This is then taken away from the individual

dome flat images. The dome flats are then combined using a median option in the relevant

filters. The resulting master flat is then normalised by diving each pixel by the average pixel

intensity across the image. An example of a master bias and master flat image used in the

data reduction, can be seen in figures 6 and 7. The individual cluster images are then

subtracted by the master bias and flat division is performed.

Figure 6 – Combined master bias of 10 x 0 second Figure 7 – Combined and normalised master

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Once data reduction is carried out, the object images are then combined in their separate

filters and exposures, using a median option with auto-star matching to track the stars across

the different images. At first, an averaging option was used to combine the images but it

resulted in a tracking of ‘dead’ pixels across the image that could interfere with the

photometry, by drastically altering the intensity value of the pixels. The cluster images are

then ready to be analysed. Both image reduction and aperture photometry is carried out using

the software MaxIm DL.

The cluster members for NGC 581 and NGC 7160 are identified before the

photometry process, using finding charts from the SIMBAD astronomical database (Wenger

et al. 2000). The problem with using a database to identify cluster members is that it may not

classify all of the stars within the field of view. At that point, photometry is typically done on

all stars in the image, to see which ones fit the CMD and which ones are just field stars.

Diagrams of each finding chart can be found in figure 8 and 9.

4.2 Aperture Size Calculation

Once the cluster members are identified in the gathered images, a process to determine the

optimum aperture radius is carried out. The aperture radius is increased from 2 pixels, by

intervals of 2 pixels, on a selection of stars in the image and the signal-to-noise ratio (SNR) is

Figure 8 – From SIMBAD astronomical database, finding chart of NGC 581, red circles showing archived objects.

Figure 9 – From SIMBAD astronomical database, finding chart of NGC 7160, showing labels of objects.

Figure 6 – Combined master bias of 10 x 0 second Figure 7 – Combined and normalised master

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noted along with a magnitude value. The stars which were used for the aperture calculation

represented a range of magnitudes, so that the data analysis was not done on only bright stars

or dim stars, but the whole spectrum of magnitudes within the image. This helps determine a

radius at the highest SNR simultaneously without losing too much intensity of the object

from the sky count subtraction. Ideally, a big aperture radius is preferred to make sure all of

the light from the object is accounted for, but there comes a problem where a lot of the sky

count can contribute to the counts within the aperture. There is also the possibility of the light

in the aperture coming from different sources other than the desired object. This is called

contamination (Romanishin, 2006). Figure 10 and 11 show the aperture radius against

apparent magnitude of an object in an image and also against the SNR. Note that this is

before calibration with a reference star.

By

looking at the figure 10, there is a region after an aperture size of 9 pixels where the data

becomes saturated. We use an upper limit of 8.6 pixels and a lower limit of 6 pixels. If a

radius of 4 pixels is chosen i.e. where the SNR is largest, the full amount of incoming light is

not measured. We derive a median aperture radius of 7.3 pixels and perform error analysis

taking the uncertainty as a third of the difference between the upper and lower limits. An

Figure 10 – measurement of apparent B-magnitude against an increasing aperture radius, for one selected star in NGC 7160. Image of 3s exposure.

Figure 11 – measurement of SNR against an increasing aperture radius, for selected star as in figure 7.

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optimum aperture radius of 7.3±0.87 pixels is calculated. It is noticeable in figure 11 that this

radius does not produce the best SNR possible, but a compromise is taken to make sure all of

the light in the aperture is accounted for. This aperture size is used on every star in during the

photometry. The same process is carried out for NGC 581 and an optimum aperture radius of

12±1.3 pixels is found.

4.3 Aperture Photometry/Reference Stars

After identifying cluster objects using finding charts, 54 stars in NGC 581 are identified to

perform aperture photometry on. The selected objects can be seen below in figure 12.

Figure 12 – Marked inverted image of NGC 581 to show cluster members for photometry. The image has been rotated 90° clockwise.

Ref star

Figure 13 – Reduced image of NGC 581 in V filter with 60 seconds exposure. Field of view of 8.65’ x 6.48’, image taken on 5/12/14 at NTU Observatory. The image has been rotated 90° clockwise.

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As previously mentioned, images with 60s exposure are used for both B and V filters and a

bright reference star (RA: 01h 33m 41.9s; Dec: +60° 42’ 19.6’’) of spectral type B3 is

chosen, to calibrate the relative intensities of the objects to an apparent magnitude. A bright

star is chosen as the reference, to make sure of getting a highest SNR possible, but not too

bright that the star becomes saturated. It is also ideal that the reference star chosen is of a

similar magnitude to the objects on which the photometry is implemented. The little variation

between the reference and the object can help produce a more accurate calibration. The SNR

for the reference star is found to be 1610.6 for the B-filter and 1966.3 for the V-filter. This

corresponds to an uncertainty of ~0.05% which predicts the photometry results to be accurate

within reason. The star has an apparent visual B-magnitude of 11.61 and V-magnitude of

11.35, taken from SIMBAD database (Wenger et al. 2000). Aperture photometry is then

performed, using the software MaxIm DL, on the images of 60s exposure, in the B and V

filter. A selection of stars within the image have other objects very close to them, meaning

the standard gap size of 10 pixels between the aperture and annulus is too small to obtain an

accurate reading of the background, due to contamination. Therefore the gap size is increased

depending on the stars surroundings.

Only 14 stars in NGC 7160 are identified as cluster objects as the images obtained are

assumed to be of the centre of the cluster, rather than the whole cluster. This limits the

amount of cluster members we can perform aperture photometry on and hence the amount of

data plotted on the CMD. This can lead to a higher uncertainty when fitting the isochrones.

The stars acknowledged as members are presented in figure 14.

Figure 14 - Marked inverted image of NGC 7160 to show cluster members for photometry. Image has been rotated 90° clockwise.

Ref Star

Figure 15 - Reduced image of NGC 7160 in V filter with 90 seconds exposure. Field of view of 8.65’ x 6.48’, image taken by Pierre Vaurs on 23/5/12 at NTU Observatory.

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For the photometry, exposure time of 3s is used for the B-filter and 1s exposures are used for

the V-filter. A variable blue giant star (RA: 21h 53m 53.3s; Dec: +62° 36’ 00.75’’) named

HD 208440 of spectral type B1, is used as a reference for the magnitude calibration. This is

one of the brightest non-cluster stars and so produces a high SNR which is important for

magnitude calibration. The star has a known V-magnitude of 7.91 and a B-magnitude of 7.93

(Wenger et al. (2000) through SIMBAD astronomical database). The photometry is carried

out with the short exposure images i.e. 3s exposure in the B-filter and 1s exposure in the V-

filter, as a number of the cluster members are saturated in the long exposures.

4.4 CMD Construction/Isochrone Fitting

Once the photometric data is obtained from each cluster, it is plotted on a colour-magnitude

diagram of apparent-V magnitude against B-V colour. The relevant error bars are also

plotted, estimated from the SNR (explained further in chapter 5.1). Once the CMDs are

constructed, the age and metallicity of each cluster can be found by adding stellar

evolutionary tracks otherwise known as isochrones, from the PARSEC database of stellar

evolutionary tracks (Bressen et al. 1999). The database contains an input form where any

metallicity can be entered along with any age, to gain data containing absolute magnitudes in

the U, B, V, R, I, J, H and K filters along with other information such as luminosity,

temperature, bolometric magnitude and initial mass function (IMF). For this purpose of this

study, only the magnitudes of B and V are needed for the colour-magnitude diagram. The

magnitudes from the isochrone data presented are absolute magnitudes, MV and MB whereas

in this study, apparent magnitude, mV and mB are used. Therefore the distance modulus

equation below is used to convert the isochrone data.

m−M=5 log10( d10 pc )

m=M +5 log10( d10 pc )

Equation 4.5.1

Equation 4.5.2

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In the above equation, d represents the distance to the cluster in parsecs, which for NGC 581

is given as 2194pc and 789pc for NGC 7160. These values are taken from WEBDA database

of galactic open clusters through Phelps & Janes (1994) and Hoag et al. (1961) (II). Changing

the value of the distance can alter the position of the V-magnitude on the CMD, shifting the

position of the MS turn off and hence, the age of the cluster. There is a relatively small

systematic error in the distance as each star in the cluster is not at exactly the same point, but

because the cluster is so far away, we can assume the distances to be the same for each star

i.e. the distance between two stars in a cluster is insignificant or negligible compared to the

distance between the observer and cluster. When applying the isochrones to the CMDs,

extinction (AV) and colour-excess E(B-V) have to be taken in to consideration, to make sure

the tracks fit the data accurately. Once we obtain an estimation of the colour-excess from the

data, we can calculate the extinction, AV, using equation 3.3.1 stated in chapter 3.2. In this

case along with most other studies, we assume a low-density ISM, which has a value of

RV~3.1, described by Fitzpatrick (1999). Realistically, assuming a constant distance to the

cluster from the observer, instead of shifting the isochrone using an estimated distance

modulus and calculating a distance, would increase the uncertainty when the extinction is

applied, as the uncertainty in the distance also has to be taken in to account.

As discussed above, the MS turn off point is influenced by the age of a cluster and

also the metallicity. Conventionally, the higher the magnitude of the turn off point the older

the cluster. If an open cluster is old, the main sequence stars tend to be of low mass i.e.

towards the bottom of the Zero Age Main Sequence (ZAMS). An increase of metallicity in a

star generally means that it is fainter and cooler. This is supported by Kotoneva et al. (2002)

deriving a linear relationship between luminosity and metallicity, for stars on the lower main

sequence. This compensates for the fact that high metallicity stars have a longer lifetime. For

an isochrone with a high metallicity, it becomes redder by shifting to the right of the B-V

scale and the turn off point becomes redder and fainter. A range of metallicities is tested for

NGC 7160 and NGC 581, to see which isochrone best fits the data. Once the age of the

clusters are determined, an knowledge of the quality of the photometry used in this study can

be deduced, and an approximation to the resolution of the CMD can be made and to what

extent a spread of ages can be distinguished using the optics in this study.

20

5. Results

5.1 Photometric Data

Aperture photometry is carried out on 54 stars in NGC 581 and a sample of the data is shown

below in table 3.

star no. mB

(mag)mV

(mag)B-V

(mag)ΔmB

(mag)ΔmV

(mag)ΔB-V (mag)

α (RA) δ (Dec)

1 12.370 10.980

1.390 0.001278 0.000416 0.0016946 01h 33m 34s +60° 42' 59''

2 14.887 14.401

0.486 0.01252 0.010045 0.022565 01h 33m 12s +60° 42' 23''

3 13.732 13.501

0.231 0.005941 0.004704 0.0106441 01h 33m 13s +60° 41' 53''

4 13.225 12.965

0.260 0.002719 0.002485 0.0052036 01h 33m 22s +60° 41' 59''

5 13.649 13.234

0.415 0.003891 0.003312 0.0072031 01h 33m 29s +60° 41' 52''

6 15.496 15.044

0.452 0.022885 0.017415 0.0403002 01h 33m 21s +60° 41' 44''

7 16.062 15.551

0.511 0.037478 0.028654 0.0661314 01h 33m 20s +60° 41' 00''

8 13.528 13.267

0.261 0.003492 0.003236 0.0067279 01h 33m 30s +60° 41' 19''

9 14.529 14.134

0.395 0.009103 0.007118 0.0162212 01h 33m 27s +60° 41' 06''

10 11.930 11.75 0.174 0.000865 0.000888 0.0017532 01h 33m 19s +60° 40' 47''

21

611 12.052 11.84

70.205 0.005036 0.004282 0.0093188 01h 33m 16s +60° 40' 48''

12 12.534 12.301

0.233 0.001436 0.001415 0.0028504 01h 33m 25s +60° 40' 33''

13 14.744 14.070

0.674 0.017123 0.009233 0.0263554 01h 33m 13s +60° 40' 00''

The uncertainties ΔmB, ΔmV and Δb-v are determined using the following derivation:

m=−2.5 log ( S )

∆ m=−2.5 log (S )+2.5 log (S+N )

∆ m=2.5 log( S+NS )

∆ m=2.5 log (1+ NS )

Where S is the signal intensity and N is the noise measured in ADU. It is clear from the data

that there is a relationship between brightness of a star and uncertainty, in which dimmer stars

produce an increased amount of error. This is because for fainter stars, there is less light

within the aperture actually coming from the object and an increased amount of background

flux. Once the data is collected, a CMD can then be constructed. The CMD for NGC 581

without added isochrones is shown below in figure 16.

Equation 5.1.1

Equation 5.1.2

Table 3 - A sample of photometric data obtained from NGC 581, with given errors and respective position in the sky

22

From the accumulated CMD, you can see clearly the main sequence spread of stars towards

the left hand side of the diagram. The spread of data points from mV > 13 mag can be

considered as probable field stars as they do not fit the main sequence pattern shown. Another

justification is that the stars could be pre-main sequence stars that are yet to undergo

gravitational contraction and hence develop on to the main sequence. Comparing the obtained

CMD to CMDs which other studies have produced e.g. in figure 4, the main sequence lies

between B-V = 0 and B-V = 0.5 and you can see the same result in figure 16. This increases

confidence in the data even before it comes to fitting the isochrones. The data presented here

is without the effects of reddening and extinction as that will come in to consideration when

applying the isochrones.

Figure 16 – Colour-Magnitude diagram showing photometric data from NGC 581

23

For photometry on NGC 7160, 14 stars are analysed. The data is shown in table 4.

Star no. mB mV B-V ∆mB ∆mV ∆B-V α (RA) δ (Dec)

1 10.068 10.023 0.045 0.000721 0.00238 0.00310 21h 53m 53.3s +62° 36' 01''

2 11.702 11.560 0.142 0.003076 0.008908 0.0120 21h 53m 57.9s +62° 37' 32''

3 12.919 12.800 0.119 0.009954 0.028586 0.0385 21h 52m 52.8s +62° 38' 04''

4 13.937 13.602 0.335 0.025306 0.064006 0.0893 21h 53m 44.4s +62 38' 17''

5 14.442 13.922 0.520 0.039785 0.080325 0.120 21h 53m 37.2s +62° 38' 09''

6 11.654 11.548 0.106 0.003476 0.010603 0.0141 21h 53m 33.3s +62° 37' 20''

7 12.701 12.627 0.074 0.007849 0.023663 0.0315 21h 53m 13.8s +62° 36' 13''

8 14.087 13.703 0.384 0.030851 0.066918 0.0977 21h 53m 40.2s +62° 36' 35''

9 13.114 12.705 0.409 0.013377 0.029463 0.0428 21h 53m 41.8s +62° 36' 30''

10 11.852 11.819 0.033 0.003625 0.012661 0.0163 21h 53m 40.1 s +62° 35' 26''

11 9.390 9.347 0.043 0.000463 0.001318 0.00178 21h 53m 34.1s +62° 35' 55''

12 10.000 9.893 0.107 0.00078 0.002176 0.00296 21h 53m 29.7s +62° 35' 54''

13 12.333 12.211 0.122 0.005694 0.017719 0.0234 21h 53m 55.7s +62° 34' 23''

14 12.484 12.408 0.076 0.007069 0.020536 0.0276 21h 54m 00.4s +62° 33 56''

The given errors in magnitude are calculated using the same method as for NGC 581, using

the signal to noise ratio. As mentioned before, the sample of data is very small for NGC 7160

as the images are of the centre of the cluster and so not an accurate representation of the

whole cluster. Nonetheless the CMD is still plotted to obtain an estimate of the age and

metallicity. The CMD without isochrones can be found in figure 17.

Table 4 – Photometric data of NGC 7160 with given photometric errors and relative positions in the sky

24

The error bars for the dimmer stars are significantly bigger than for the brighter ones, as a

much shorter exposure time was used for NGC 7160 compared to the exposure time for NGC

581, due to the saturation in some stars. This reduces the amount of light that is taken in

through the CCD, meaning less light within the aperture. The sky count dominates the area of

the aperture, hence decreasing the signal to noise ratio and increasing the uncertainty.

5.2 Age/Metallicity determination

The next stage is to apply isochrones to the obtained CMDs in section 5.1. We can alter a

number of parameters to gain the best fit to the data, including distance modulus, age,

metallicity, extinction and reddening. By using the distance modulus, equation 4.5.1

mentioned in chapter 4.5, the V magnitudes from the isochrones, are converted from absolute

to apparent magnitude. The isochrones are then applied to the CMD of NGC 581, as shown in

figure 18. As the data does not seem to show an apparent main sequence turn off from which

the age can best be determined, we use an isochrone of age t = 21.68Myr as given by

WEBDA (Phelps & Janes 1994) and vary the metallicity to gain a best fit.

Figure 17 - Colour-Magnitude diagram showing photometric data from NGC 7160

25

The age of the isochrone appears to fit the data appropriately as it sits appropriately along the

main sequence of the cluster. To make the isochrone fit superiorly, reddening and extinction

effects are added. NGC 581 was found to have a reddening or colour excess E(B-V) of 0.432

± 0.05mag and AV extinction of 1.382 ± 0.016mag, by using equation 3.3.1 in chapter 3.1.

Studies in the past of NGC 581 such as Sanner et al. (1999) find a colour excess E(B-V) of

0.41 ± 0.02mag which corresponds to an AV extinction of 1.312 ± 0.0064. The WEBDA

database of open clusters (Phelps & Janes 1994) gives a reddening value of 0.382mag and

Sagar & Joshi (1977) also find the value of reddening to be 0.38mag. The value considering

the uncertainty given for colour excess E(B-V) and extinction AV is in respectable agreement

with the literature values given, as the upper and lower bounds of the uncertainty cover the

values in the other studies. The uncertainty is marginally larger for this study but that is due

to personal judgement as to what point the isochrone best fits the data. One reason that there

is not enough data to see the MS turn off could be that the field of view used in this study,

does not cover the whole NGC 581 and so we do not see some of the stars that could

potentially fill the gaps on the CMD. Therefore, there is a large error in determining the age

of the cluster, as one can only assume where the RGB might be, subject to the data available.

Figure 18 – CMD of NGC 581 with fitted isochrones of age, t = 21.68Myr and metallicity varying from 0.01 to 0.04. Reddening E(B-V) of 0.41 and extinction, AV = 1.382

26

A limit to which isochrones best fit the data can be deduced by eye. In figure 19, the CMD

for NGC 581 is presented with the upper and lower bounds to the age of the cluster. The

metallcity used is the mean metallicity calculated further on. Any age that is older or younger

and the main sequence of the isochrones realistically do correspond with the data. If an

isochrone of a much older or younger age is used, other parameters such as distance modulus,

extinction and reddening would have to be changed in order for the isochrones to fit the data.

A range of metallicity from 0.01 to 0.04 is given, in the units of solar metallicity, Zʘ. This is

the range of metallicities that accommodates the data and hence we can calculate a mean

metallicity, <Z> and a standard error, S. The calculation is given below:

¿ Z>¿∑i

Zi

N→<Z>¿0.025

Variance , σ2=∑i

N

¿¿¿¿

Standard Deviation , σ=√variance=0.01118

Standard Error= σ√N−1

=0.00645From this we can say that the metallicity of NGC 581 is

(0.025 ± 0.0065)Zʘ. Previous studies such as Sanner et al. (1999) show a Z-metallicity of

0.02 and Eggenberger (2002) calculates a metallicity of 0.015. When we compare the value

Figure 19 – CMD of NGC 581 showing upper and lower bounds of uncertainty in age of the cluster.

27

obtained in the study to the literature values given, we can assume a high level of accuracy in

the approximation.

The uncertainty comes from judgement to where the isochrone best fits the data.

The same process carried out for NGC 581 is carried out NGC 7160. Isochrones of

age t = 15Myr are added to the CMD and a range of metallicities are tested. The obtained

CMD with isochrones can be seen in figure 20.

Once more, there is not sufficient data present to show the RGB, so the age determination can

only be estimated. The age given by Hoag et al. (1961) (II) of t = 18.97Myr did not appear to

give a correct fit for the data so instead, an isochrone of age t = 15Myr is used, through a

process of trial and error to see at what age, the isochrone best fits the data. The uncertainty

in this determination is analysed further on. Values of reddening and extinction are found to

be E(B-V) = 0.2 ± 0.05mag and AV = 0.64 ± 0.16mag. The uncertainty is an estimate from the

judgement of how well isochrone fits the photometric data. The value for reddening on

WEBDA is stated to be E(B-V) = 0.375mag with a corresponding extinction of AV = 1.2.

Mentioned in the chapter 3.5, Siciliar-Aguilar et al. (2004) give an extinction value of AV =

1.17 ± 0.45. Comparing the literature values given to the values obtained in this study, it can

Figure 20 – CMD of NGC 7160 with fitted isochrones of age, t = 15Myr and Z-metallicity varying from 0.001 to 0.004. Reddening E(B-V) = 0.2, extinction AV = 0.64

28

be deduced that the accuracy of the measurement is relatively poor. This is mostly due to the

lack of data and that it only represents a small proportion of the cluster. It is also

hypothesised that the majority of stars within the cluster have a magnitude of V>18 which we

cannot resolve in this study, due to limitations of the photometry. The values for reddening

and extinction are expected to be much higher as it is hypothesised that there is a large

amount of interstellar medium between the observer and NGC 7160, because of the

knowledge that it lies in a cloud of Hydrogen, as mentioned in the background information of

NGC 7160 given in chapter 3.5. The cloud would be expected to shift the wavelength of the

light towards the red end of the spectrum and hence increase the value of interstellar

reddening and extinction. The CMD in figure 20 shows a range of metallicities of 0.001 to

0.004. An error analysis is carried out, the same as for NGC 581 and is shown below.

¿ Z>¿∑i

Zi

N→<Z>¿0.0025

Variance ,σ2=∑i

N

¿¿¿¿

Standard Deviation ,σ=√variance=1.118 ×10−3

Standard Error= σ√N−1

=0.000645

The metallicity of NGC 7160 can now be given as Z = (0.0025 ± 0.00065)Zʘ. Due to the lack

of studies on NGC 7160, there is no literature value given of the metallicity. Therefore solar

metallicity, Z=0.02 is assumed as a first estimate and a trial and error process is conveyed for

the process of isochrone fitting. Further analysis of the NGC 7160 spectra is needed to gain a

more reliable estimate on the metallicity.

An estimation to the uncertainty of the age determination is carried out by changing

the age parameter of the isochrone to indicate at which extreme the track correspond with the

data. The CMD showing the upper and lower bounds of the age estimate are given in figure

21.

29

From figure 21 the upper and lower bounds of the age of NGC 7160 are 19Myr and 11Myr

respectively. This is subject to debate as the uncertainty is so large for reasons mentioned

previously e.g. lack of data, no visible RGB and large error bars for dimmer stars. A larger

field of view is needed to obtain further data on the remaining stars in the cluster, this would

help gain a better understanding of the age and metallicity. Studies that have analysed NGC

7160 such as Siciliar-Aguilar et al. (2004) and Mayne et al. (2007) all give an age estimate of

t = 10Myr with large uncertainty. Both suggest a lack of confidence is due to the absence of

data, similar to this study. These studies predict an age of NGC 7160 that is slightly lower

than the estimate given in this project due to having access to supplementary data on the stars

within the cluster, which has not been available in this study. The only tangible deduction we

can make from this project that is the age of NGC 7160 is less than 20Myr due to the

significant error. This leads to much room for improvement in further studies.

6. Conclusion

Figure 21 - CMD of NGC 7160 showing upper and lower bounds of uncertainty in age of the cluster.

30

NGC 581 is a young open cluster with age 21.68±7Myr. A CMD is derived from carrying out

aperture photometry in B and V filters on 54 stars. The distance to NGC 581 is assumed to be

2194 parsecs and a metallicity of (0.025 ± 0.0065)Zʘ is found, along with an interstellar

reddening of E(B-V) = 0.432 ± 0.05mag and interstellar extinction of AV = 1.382 ± 0.016mag.

These values are in agreement with the literature with a suitable uncertainty. The error in the

age estimation is slightly larger than most studies due to the absence of stars on the RBG in

the data collected. This can be improved using a wider field of view in the future and instead

of only selecting stars that are given as cluster members from a database, photometry can be

done on each object within the image to see if any of the stars fit in with the rest of the CMD.

But overall, the photometry appears to be of a good standard as the main sequence data fits

suitably in agreement with data given in other studies.

NGC 7160 is an open cluster which appears to be at a younger age than NGC 581. An

age of (15 ± 4)Myr is given, with a distance of 789 parsecs assumed and a metallicity of

(0.0025 ± 0.00065)Zʘ. Interstellar reddening for NGC 7160 is found to be E(B-V) = 0.2 ±

0.05mag and interstellar extinction is found to be AV = 0.64 ± 0.16mag. There is less

confidence in the parameters specified for NGC 7160 for the reason mentioned in chapter 4.3,

that there is a lack of data. The uncertainty can be improved in further studies by expanding

the field of view and using an improved technique of identifying cluster members from field

stars. This can provide more data on the open cluster and in turn help build a better

representation of the CMD. From this, a more accurate approximation of the age can be

deduced.

The photometry in this study has proven to be substantially reliable as we can deduce

suitable errors on measurements that do not cause too much concern or doubt. The only

difficulty encountered was that in NGC 7160, some of the stars were over exposed and as a

result, became saturated. As the shorter exposed images were used, this decreased the

magnitude of the dimmest stars visible to us, limiting the data available for photometry.

It has been shown that it is relatively difficult to provide an accurate estimate of the

age of a young open cluster, as often there are very few stars that have developed in to red

giants and so it is hard to identify the stars in the images.

In future studies of open clusters using NTU telescope, it would be beneficial to

determine the age of older clusters to help gain a resolution of the CMD. This was not

feasible due to the lack of visibility throughout the year.

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33

8. Acknowledgements

I’d like to thank Dr. Daniel Brown, Senior lecturer at Nottingham Trent University, also my

project supervisor, for his assistance during this project and providing the colour combined

image (figure 3) given in chapter 3.1.

Thank you to Pierre Vaurs, for the image data for cluster NGC 7160 which was analysed in

this project.