The Night Sky of Hong Kong

SO Chu Wing1

The Department of Physics, The University of Hong Kong (HKU)

Received ; accepted

1University No.: 2003254834, Email: socw@hkusua.hku.hk

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Abstract

This project aims at measuring the night sky brightness in Hong Kong.

The night sky brightnesses both in the city (HKU) and countrysides (Sai Kung

East and Lantau Island South) were measured on 21 sets of data taken with

astronomical CCD cameras between November 2004 and March 2006. The sky

brightnesses were measured by relative photometry, the technique of comparing

photon �uxes from the sky background and nearby reference stars. It is found

that the sky brightness near zenith depended on the observing location. On

average, the value of sky brightness in the city was ∼16 mag arcsec−2 while

that in the countryside was ∼20 mag arcsec−2, implying that the night sky in

the city was ∼20-40 times brighter than that in the countryside. Two telescope

systems were used for the measurements and there exists an averaged 0.31 mag

arcsec−2 di�erence on the results obtained. A commercial digital camera was

tested for the project but the performance was unsatisfactory. It is proposed

that the project should be continued as a long-term Hong Kong night sky monitor.

A report submitted for PHYS3531 Physics Project LE 18: Night sky

of Hong Kong to the Department of Physics, the Faculty of Science,

The University of Hong Kong, May 2006.

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Contents

1 Introduction 6

2 Astronomical Photometry 9

3 Apparatus 13

3.1 Telescopes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

3.1.1 TeleVue Pronto Refracting Telescope . . . . . . . . . . . . . . . . . . 13

3.1.2 Optical Guidance System 16" RC Telescope . . . . . . . . . . . . . . 13

3.2 Imaging Devices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

3.2.1 Starlight Xpress MX916 CCD System & SGIG ST8 CCD System . . 14

3.2.2 Nikon Coolpix 4500 Digital Camera . . . . . . . . . . . . . . . . . . . 15

3.3 Mounts, Filters, Focus Reducer, & Diagonal Mirror . . . . . . . . . . . . . . 17

3.3.1 Equatorial Mounts . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

3.3.2 V -band Filters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

3.3.3 OGS Focal Reducer . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

3.3.4 2" Diagonal Mirror . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

3.4 Combinations of Apparatus . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

4 Methodology 19

4.1 Planning for an Observation . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

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4.1.1 Locations of Observation Sites . . . . . . . . . . . . . . . . . . . . . . 20

4.1.2 Target Fields . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

4.1.3 Time of Observation . . . . . . . . . . . . . . . . . . . . . . . . . . . 36

4.2 Data Taking Procedures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38

4.3 Data Pre-processing Procedures . . . . . . . . . . . . . . . . . . . . . . . . . 39

4.4 Data Reduction Procedures . . . . . . . . . . . . . . . . . . . . . . . . . . . 41

5 Results 44

5.1 Critical Aperture Radius Curves . . . . . . . . . . . . . . . . . . . . . . . . . 44

5.2 Linear Fitting Plots . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45

5.3 Testing on Digital Camera . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46

5.4 The Sky Brightness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47

6 Discussion 62

6.1 Sources of Errors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62

6.2 Apparatus . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63

6.3 Time Delay Between Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65

6.4 Light Pollution Problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65

7 Summary 67

A Plate Scale Fitting 71

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B Linear Fitting with Errors on Both Axises 73

C Error Analysis 75

C.1 Error on Photon Counts from Reference Stars . . . . . . . . . . . . . . . . . 75

C.2 Error on Sky Brightness . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76

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1. Introduction

Chinese ancient poet Li Bai described the Milky Way in his poem Watching The Lu

Mountain Falls as:

In the past, people liked to characterize the Milky Way by "heaven's river", "string

of jades", "silver riverside", etc. From their point of views, the Milky Way was huge and

impressive. However, Hong Kong people seldom have the chance to enjoy it nowadays.

Referred to the "Pearl of the Orient", Hong Kong is famous for its attractive non-stopped

fantastic lightings. The stars in the night sky are being dominated by city's lights. When

people in the city look at the sky during cloudless night, there are only few stars hanging on

the "lightened" background. All constellations, deep sky objects, and the Milky Way can

never be seen. Starry night can only be found when people go far away from the city center.

The Milky Way observed though is still far from "spilling to the earth from the heavens".

The growing of city lights increases the light pollution. According to Benn & Ellison

(1998), light pollution is de�ned as "tropospheric scattering of light emitted by sodium-

and mercury-vapor and incandescent street lamps". As human and commercial activities

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are always related to lightings, especially street lamps (see Figure 1), areas with higher

population density means a more serious light pollution problem. The limited availability of

developable land in Hong Kong forces the government to urbanize less light-polluted areas,

e.g. Sai Kung. Furthermore, the development of large-scale constructions, e.g. airport

and West Kowloon Cultural District, bring more and more arti�cial lights to the natural

environment. We should take appropriate actions as soon as possible to protect the priceless

starry night.

Many surveys and observations have been carried out to measure the sky brightness.

There are continuous night sky monitoring and protecting schemes carrying out at

international astronomical observatory sites (e.g. La Palma, Mauna Kea, Benn et al, 1998).

Benn et al (1998) measured the night sky brightness from the images in the electronic data

archive at the Observatorio del Roque de los Muchachos of La Palma in the Canary Island

on 427 CCD images taken with 2.5m Isaac Newton and 1m Jacobus Kapteyn Telescopes

on 63 moonless nights during 1987-1996. Photometric calibration was obtained from the

observations of standard stars (usually from the list of Landolt, 1992) in the archive. It

was found that the median sky brightness at the high elevation, high galactic and ecliptic

latitudes and sunspot minimum was 21.9 mag arcsec−2 at V -band. Taylor et al (2004)

calculated the sky values from stacked galaxy images taken by the Vatican Advanced

Technology Telescope at the Mount Graham International Observatory, Sa�ord, Arizona.

Sky surface brightness values were photometrically calibrated using again the Landolt

(1992) standards and they were averaged to be ∼21.4 mag arcsec−2 at V -band.

Sky brightnesses were also measured in national parks in the US, such as Yellowstone

and Arches. Researchers collected data with a CCD camera, robotic mount, and laptop

computer. The camera would point to pre-determined areas of the sky and make exposures.

The absolute brightness measures would be extracted from the images, provided that data

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had been calibrated to stars of known brightness. Images were stitched and combined

together to form panoramic or �sh-eye view maps on the sky brightness distribution. Night

sky quality monitoring reports for some of the data collected from 2002 to 2005 has been

posted on-line (National Park Service, 2006).

Faint stars can act as indicators to give a quality description on the level of light

pollution. During March and August 1987, with the promotion of the Environmental

Agency of Japan, observers used binocular with a 50mm diameter objective and 7 times

magni�cation to �nd out the magnitude of the faintest star in the selected areas to measure

the relative night sky brightness across Japan (Kosai & Isobe, 1998). Similarly, GLOBE

at Night1 was the international campaign held on 22-31 March 2006 in which students

around the world were invited to make observations on Orion and identi�ed the limiting

magnitude of stars then made online reports. The Gifted Education Section, The Education

and Manpower Bureau of the Hong Kong government joined the campaign and more than

10 primary and secondary schools participated it. The results could re�ect the global

distribution of light pollution(Gifted Education Section, 2006). Densitometer can also be

applied to measure the background darkness on photographic �lms. Japanese observers

took pictures at zenith with standardized focal length and exposure time, and the developed

�lms were collected and reduced. Comparing with the calibrated data, the background

densities of the �lms gave measurements on sky brightness (Kosai et al, 1998).

There was no intensive research or study on how city's lights a�ect Hong Kong's night

sky in the past. Since 2003, HKU started to introduce a scienti�c method of collecting data

on night sky brightness using a small telescope and CCD camera systems. Tam (2004)

attempted to measuring the sky brightness till summer 2004. Using �ve nights of date, It

was found that the average sky brightness in HKU campus was ∼17 mag arcsec−2. This

1O�cial site: http://www.globe.gov/GaN/ .

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current project follows the basic methodology developed by Tam and extends the method

to collect data at di�erent time and locations using di�erent apparatus systems.

In order to provide solid evidence that our night sky is indeed brightening, it is

important to collect data in various locations at the same time, carried out by a term of

amateur astronomers who use their own set of system. This project aims at investigating

these derivations between systems and tries to identify an e�ective and consistent method

for measuring night sky brightness to introduce to the public.

The report was organized in the following way. The theory of astronomical photometry

which leads to the results was summarized in Section 2. All apparatus including telescopes,

CCDs, and mounts used in the project were listed in Section 3. All necessary steps in data

taking, pre-processing, and processing procedures were provided in Section 4. The results

were described in Section 5 and summary and discussion were given in Sections 6 and 7.

2. Astronomical Photometry

Aperture photometry and point spread function modeling (PSF) are the two of the

most popular ways for carrying out astronomical photometry, i.e. measuring the �ux

received from celestial bodies. In this project, the aperture photometry technique was used,

since it is straightforward and the reference star �elds were not crowded. According to

Romanishin (2002), the net counts due to a star is the summed count values of the pixels

within the circular aperture minus the background counts. The circular aperture is chosen

such that it is centered at the star and have the aperture radius equal to 1 to 3 times of

the Full Width Half Maximum (FWHM2) of the star. The value of background counts is

2Full Width at Half Maximum (FWHM) is de�ned as the diameter where the count falls

to half its center value. FWHM is the measurement of the angular size of PSF.

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estimated by the sky annulus which is just right outside the aperture radius. Note that

aperture photometry is suitable for uncrowded �eld only.

Again from Romanishin (2002), the instrumental magnitude mI is de�ned as

mI ≡ −2.5 · log

(Nap − AapSsky

texp

), (1)

where Nap is the total counts in the measuring aperture, Aap is the area of the aperture

in pixel, Ssky is the background counts per pixel and texp is exposure time of the frame in

seconds. In this project, all frames taken within the same night and the same system had

the same exposure time so that an extra constant term 2.5 · log (texp) vanished.

If we assume

foutput ≡ Nap − AapSsky , (2)

where foutput is the output data number from the IRAF3 phot task (Massey P. & Davis L.E.,

1992), then from Romanishin (2002), the actual �ux f from the star is related to the foutput

by:

f =foutput ×G

QE, (3)

where G is the gain in electron per ADU and QE is the quantum e�ciency of the imaging

device.

A number of reference stars in di�erent target �elds were selected and their average

�uxes received fi and log(fi) were calculated. On the other hand, the apparent visual

magnitude mviof the reference star is obtained from the SAO Star Catalog J2000 if the

star has a SAO reference number4 . If it does not, then mviis obtained from the All-sky

3IRAF stands for Interactive Reduction and Analysis Facility.

4The SAO Star Catalog J2000 can be queried from the VizieR Search Page, Simbad

reference database catalog number I/131A, or http://cdsweb.u-strasbg.fr/viz-bin/VizieR?-

source=I/131A .

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Compiled Catalogue of 2.5 Million Stars and the star will be marked by its TYC reference

number of the Tycho-2 Catalogue5.

We also have to take into account the atmospheric extinction. Light from stars may be

dimmed by scattering and absorption. At high airmass, the line of sight intercepts a larger

number of atoms (Benn et al, 1998). Richard (2000) suggested that airmass correction

should be applied as:

mvi+ kvX , (4)

where X is the airmass during observation and kv is the visual extinction coe�cient.

According to Tam (2004), at sea level kv is typically about 0.24 magnitude per airmass and

it is assumed to be a constant. The value of X, up to the �rst order approximation, follows:

X = sec(z) , (5)

if no �lter is applied. Otherwise,

X = sec(z)[(1− 0.0012 · tan2(z)

], (6)

where z is the zenith angle of the reference stars during observation.

Faint stars are measured in a smaller aperture (1.4× FWHM) while bright stars are

measured in a bigger aperture (4 × FWHM). However, since the signal from the faint

star is low and the big aperture yields lots of noise from the sky background, the resultant

signal-to-noise ratio will be decreased. In order to compensate the e�ect, according to

Romanishin (2002), two apertures (1.4×FWHM and 4×FWHM) are selected to measure

5The All-sky Compiled Catalogue of 2.5 Million Stars can be queried from the VizieR

Search Page, Simbad reference database catalog number I/280A, or http://cdsweb.u-

strasbg.fr/viz-bin/VizieR?-source=I/280A .

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a bright reference star. Then apply Equation 1 and de�ne

∆ ≡ mI(4× FWHM)−mI(1× FWHM) , (7)

which yields the aperture correction factor ∆ and it is always negative.

As a result, on one hand we have the independent variables of the reference stars:

mvi+ Xkv − ∆, where ∆ is the average of ∆ and applied only on faint reference stars.

On the other hand we have the dependent variables, which are the logarithmic averaged

�uxes received from the reference stars: log(fi). From the de�nition of apparent magnitude

(Romanishin, 2002)

mapparent ≡ −2.5 log(flux) + c , (8)

we have

log(fi) = −0.4(mvi+ Xkv −∆) + 0.4c . (9)

A linear �tting is performed to �nd the term c, which is di�erent for each set of data. The

detail of the �tting are compiled in Appendix B.

Similarly, the average �ux from the sky background B is plugged into Equation 8:

msky = −2.5 logB

F+ c , (10)

where msky is the sky brightness in mag arcsec−2 and F is the angular �eld of view per

pixel (FOV) in arcsec2.

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3. Apparatus

3.1. Telescopes

3.1.1. TeleVue Pronto Refracting Telescope

Two sets of telescope were used in the project. The �rst set is the TeleVue Pronto

(Pronto)6, a small and highly portable refracting telescope, with the aperture, focal length,

focal ratio, and net weight 70mm, 480mm, f/6.8, and 2.7kg respectively. A soft carry bag is

provided for remote sites data taking. It was used for data taking outside HKU.

3.1.2. Optical Guidance System 16" RC Telescope

The second telescope set is the Optical Guidance System RC16-75F Ritchey-Chretien

telescope (OGS)7. It is the main telescope located at the telescope dome of the Department

of Physics, HKU. The aperture, focal length, and focal ratio are 406.4mm (16.0"), 3,414mm,

and f/8.4 respectively. The OGS-75 Fork mount is used and the whole set is controlled

by the PC-TCS (Personal Computer based Telescope Control System)8 and the Software

Bisque TheSky6 Professional Edition (TheSky6) 9 hosted in the dome's computers.

6Product information: http://www.televue.com/engine/page.asp?ID=5 .

7Product information: http://www.opticalguidancesystems.com/rc16-75f.htm .

8Software information: http://www.opticalguidancesystems.com/computer.htm .

9Software information: http://www.bisque.com/Products/TheSky6/ .

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3.2. Imaging Devices

3.2.1. Starlight Xpress MX916 CCD System & SGIG ST8 CCD System

Two astronomical CCD cameras systems were used in the project. They were Starlight

Xpress MX916 CCD camera (MX916)10, used in association with the Pronto, and Santa

Barbara Instrument Group (SBIG) Dual CCD ST-8XME (ST8)11, used in association with

the OGS. Some of their speci�cations are listed in Table 1.

The MX916 was controlled by either one of the two image processing softwares, namely

STAR_MX9 Version 2.0i or Di�raction Limit Maxlm Version 4.10 (Maxlm)12. STAR_MX9

is the original software came with the CCD camera. The default high sensitivity mode is 2

× 2 binning (i.e. 376 × 290 pixels). Maxlm has more user friendly focusing and imaging

panels and the default binning is 1 × 1 (i.e. 752 × 580 pixels).

The ST8 was controlled by either one of the two image processing softwares, namely

Software Bisque CCDSoft Version 5 (CCDSoft)13 or Maxlm. CCDSoft is the original

software came with the CCD camera. 2 × 2 binning mode was used in order to speed up

the download time.

10Product information: http://www.starlight-xpress.co.uk/mx916.htm .

11Product information: http://www.sbig.com/sbwhtmls/online.htm .

12Software information: http://www.cyanogen.com/products/maxim_main.htm .

13Software information: http://www.bisque.com/Products/CCDSoft/ .

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3.2.2. Nikon Coolpix 4500 Digital Camera

A commercial digital camera (DC), Nikon Coolpix 450014, was tested. Some of the

speci�cations are listed below:

• e�ective Pixels: 4.0 millions

• CCD image format: 2,272 × 1,704 pixels

• CCD size: 25.4 × 45.7 mm

• cooling system: no cooling system

• lens: 4× Zoom

• focal length: 7.85 - 32 mm (non-removable)

• net weight: 360g

Although it has many favorable functions, for example, a full manual mode including the

bulb switch and the fact that a user can apply an adapter for connecting it to the visual

back of the Pronto, many important details (e.g. quantum e�ciency and readout noise) of

the imaging sensor are not disclosed by the manufacturer. As a result, this project assumed

the followings in the data reduction process:

• quantum e�ciency: 100% at all wavelengths

• readout noise: 0 electrons RMS

• data format: 8 bits

14Product information: http://www.nikonusa.com/template.php?cat=1&grp=2&productNr=25503 .

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• full-well capacity: 65,536 electrons

• gain: 1 electron/ADU

In order to minimize the lost of data and maximize the signal, the following settings and

accessories were used during data taking:

• mode: manual (M)

• saturation control: black and white

• image quality: HI (TIFF)

• image size: 2,272 × 1,704 pixels

• �ash: disabled

• focus: manual focus (MF)

• sensitivity: ISO 800

• exposure: 8 seconds

• focal ratio: f/2.6

• remote control: Nikon Remote Cord MC-EU1

• adapter: William Optics DCL-28 24mm Plossol eyepiece (DCL28) (16mm eye relief

and 52◦ �eld of view)15

15Product information: http://www.william-optics.com/wowebs/prod_eyep/dcl_28/features0.htm

.

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Only eyepiece-and-camera-lens projection can be applied since the lens of the DC is

non-removable. A 1.25" V -band �lter, which will be discussed in Subsection 3.3.2, was

mounted inside DCL28. The DC had be given up in the later stage of the project and the

details will be discussed in Section 5.3.

3.3. Mounts, Filters, Focus Reducer, & Diagonal Mirror

3.3.1. Equatorial Mounts

Two sets of equatorial mounts, Vixen Sphinx (SX)16 and Vixen GPE (GP)17, were

used with the MX916 and the DC and associated with the Pronto telescope. SX is a

computerized go-to equatorial mount which is good for pointing to target �elds. Both

mounts can be either powered by 220V AC or 12V DC power sources. An appropriate

polar alignment provides the right tracking and ensures up to 5 minutes exposure without

resulting in distorted stellar images.

3.3.2. V -band Filters

The energies emitted by celestial bodies varies with wavelengths. The total power

output integrated over all wavelengths of the object is called bolometric luminosity and the

resultant magnitude is called bolometric magnitude. However, the bolometric magnitude is

di�cult to �nd and so photometric magnitudes restricted on a speci�c wavelength range

16Product information: http://www.vixen-global.com/TELESCOPE/SX_mount/SXW_mount.html

.

17Product information: http://www.vixen-global.com/TELESCOPE/GP_mount/GPE_mount.html

.

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are quoted more frequently. With the help of a �lter, only photons permitted by the �lter

will be allowed to reach the detector. Photometry on the speci�c wavelength range will

give out di�erent values of magnitude, for example, labeled by U , B, V , R, and I, they

stand for ultraviolet, blue, visual, red and infrared respectively (Romanishin, 2002). The V

magnitude mv is used in this project and so V -band �lter is needed. In the early stage of

the project, no �lter was used and magnitudes of the reference stars are referred to mv. As a

result, non-�ltered measurement is less accurate. Data sets those taken on or after 03/08/05

were all �ltered. A 2" Johnson/Cousins (Bessell) V -band �lter from Custom Scienti�c18

and a 1.25" Johnson V -band �lter from Optec, Inc. (model number: 17133)19 was applied

to measurements. Their transmission curves are shown in Figure 2 and Figure 3.

3.3.3. OGS Focal Reducer

In order to maximize the �eld of view so that more reference stars can be taken within

a single exposure, a focal reducer provided by the Optical Guidance System was applied to

all data sets taken with the OGS. The reducer decreases the focal ratio from f/8.4 to f/5.7.

18Product information: http://www.customscienti�c.com/astroresearch.html .

19Product information: http://www.company7.com/optec/products/�lter.html#Photometric

.

� 19 �

3.3.4. 2" Diagonal Mirror

The William Optics 2" Diagonal Mirror20 was applied between the Pronto and the

MX916 or the DC. The 2" V -band �lter was mounted at the 48mm inside diameter of the

diagonal. The systems can only be focused by applying the diagonal.

3.4. Combinations of Apparatus

Table 2 and Figure 4 show the combinations of apparatus for di�erent sets of data.

Their FOV were tabulated in Table 3 and their relative sizes were compared in Figure 5.

The e�ective focal length and the e�ective focal ratio of the DC system did not calculate as

the system is complicated and the projection distant between the lens and the CCD chip is

unknown. The �eld of views were obtained approximately from the Field of View Indicators

in the TheSky6 software.

4. Methodology

This Section introduces all the procedures of the project, including the selection of

locations and target �elds, time of observation, data taking, pre-processing, and reduction

procedures in details.

20Product information: http://www.william-optics.com/wowebs/prod_diag/dia_mir/features0.htm

.

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4.1. Planning for an Observation

4.1.1. Locations of Observation Sites

Four di�erent observation sites were selected for the project. Their geographical

information are listed in Table 4.

High Island Reservoir and Shui Hau are famous star-grazing sites for amateur

astronomers. Astronomical societies in Hong Kong held lots of observation sessions there

since they have the relatively wider �eld of views. High Island Reservoir consists of two

dams, East and West, and the main sources of light pollution there are city lights from

Sai Kung center and safety lightings from �shing boats parking just outside the dams.

Shui Hau, also known as Lo Kei Wan, is a hillside above the Lo Kei Wan coast. Heavy

light pollution glows from Chek Lap Kok airport to the North while it is relatively dark in

the South. These two observation sites are far away from street lights but can be directly

accessed by taxi. Taxis also make transportation of heavy equipments more convenient.

HKU is located on the Western side of the Hong Kong Island, which is a heavy

light-polluted area. The telescope dome is closely surrounded by tall buildings in East.

Arti�cial lightings from the residence buildings in Kowloon to the North are also a�ect the

site. It is relatively dark in the South-west (See Figure 6).

4.1.2. Target Fields

Target �elds containing reference stars were selected for data taking. Basic selection

criteria for a good �eld are as follows:

• It should contain more than 3 reference stars located near the center of the �eld of

view. More data points produce better �tting and stars near the image center are

� 21 �

least likely to su�er from �eld curvature and other optical aberrations.

• The target �eld should not be a crowded �eld where the aperture photometry is

di�cult to carry out.

• The visual magnitude of the reference star should be within the range mv ≈ 6-9

for the MX916, while it should be mv > 8 (i.e. dimmer) for the ST8 and mv < 5

(i.e. brighter) for the DC. The main criteria for the selection of the magnitude range

for the reference star is that the star should have maximium signal-to-noise ratio,

while not getting the CCD saturated or nearly saturated in the observed data. (For

example, the counts should be smaller than 60,000 for a 16 bits data format imaging

device).

• The reference stars should be in a wider range of magnitudes so that a better �tting

can be obtained.

• The reference stars should be main sequence stars but not variable stars or red

giants, those do not have constant magnitudes. In this project, relative photometry

was carried out with respect to the �ux from reference star. Reliable results on sky

brightness can only be obtained if the �uxes from the reference stars are constant, i.e.

non-variable stars.

• The reference stars should not be close binary systems otherwise the aperture

photometry is hard to conduct.

• The reference stars should not be close to the zodiac (i.e. high ecliptic latitude) and

extended objects such as the Milky Way (i.e. high galactic latitude), planets, clusters,

planetary nebula, supernova remnants, or galaxies to avoid contamination of the data

by their inter-stellar gases or dusts, or the objects themselves.

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• The target �eld should pass as close as possible near the zenith because there are

least light pollution and atmospheric extinction at the zenith.

• At least one �eld is needed for one season because this project was carried over the

entire year and di�erent target �elds will pass through the meridian at di�erent times.

Tables 5 and 6 list the details on all CCD target �elds and the corresponding date

taking dates. Information on reference stars with SAO reference numbers came from SAO

Star Catalog J2000, while information on reference stars with TYC reference numbers came

from the All-sky Compiled Catalogue of 2.5 Million Stars. The �eld star maps used in

Spring, Summer, Autumn, and Winter were shown in Figures 7 to 10 respectively. Notice

that the North direction is not stated in the maps and only reference stars were labeled.

Labels start with s and follow by �ve or six digits denote the SAO reference numbers.

Otherwise, the labels are TYC reference numbers from the All-sky Compiled Catalogue of

2.5 Million Stars. Sometime, �elds might be taken with slightly di�erent orientations and

had di�erent selections of reference stars, as labeled with the last su�x of the �eld identi�er

in Table 6, a or b. Reference stars may be rejected during the data pre-processing if they

were not suitable for performing aperture photometry, for example, saturated or distorted.

The FOV of the Pronto+MX916 and the OGS+ST8+reducer are di�erent and the target

�elds recorded in the two systems were thus di�erent.

� 23 �

Fig. 1.� Typical spectrum of moonless sky taken at the Los Muchachos Observatory, La

Palma, Spain. Several lines show the distinctive features due to airglow. The NaD emission

line at 5890-6Å and the Hg emission lines at 4358Å and 5461Å, originated from low and

high pressure sodium street lamps, and mercury-contained light bulbs or incandescent lamps

respectively. (adopted from Benn et al (1998))

� 24 �

Table 1. Speci�cations of Imaging Devices

properties MX916 ST8

CCD type Sony ICX083AL SuperHAD CCD Kodak KAF-1603ME + TI TC-237

CCD image format 752 × 580 pixels 1,530 × 1,020 pixels

CCD size 8.7 × 6.5 mm 13.8 × 9.2 mm

quantum e�ciency 60% peak at 520nm 60% peak at 520nm

readout noise <15 electrons RMS 15 electrons RMS

data format 16 bits 16 bits

full-well capacity 65,536 electrons 65,536 electrons

gain 5 electron/ADU 2.3 electron/ADU

cooling system single-stage thermoelectric cooler single-stage thermoelectric cooler

weight 250g 900g

Fig. 2.� Transmission Curve of 2" V -band Filter (adopted from:

http://www.customscienti�c.com/astroresearch.html)

� 25 �

Fig. 3.� Transmission Curve of 1.25" V -band Filter (adopted from:

http://www.company7.com/optec/graphics/�lter_graphs/17133.gif)

Fig. 4.� Combinations of Apparatus (�lters and the OGS focal reducer are not shown):

OGS+ST8 (left); GP+Pronto+DC+DCL28 (middle); GP+Pronto+MX916 (right)

� 26 �

Table 2. Apparatus Combinations and Data Taking Locations

date location system V -band �lters

(DD/MM/YY) (size)

20/11/04 West Upper Dam SX+Pronto+MX916 NO

10/12/04 West Lower Dam SX+Pronto+MX916 NO

06/03/05 Shui Hau SX+Pronto+MX916 NO

04/07/05 Shui Hau SX+Pronto+MX916 NO

03/08/05 HKU GP+Pronto+MX916 YES(2")

04/08/05 HKU GP+Pronto+MX916 YES(2")

04/08/05 HKU GP+Pronto+DC+DCL28 YES(2")

29/09/05 HKU GP+Pronto+MX916 YES(2")

06/10/05 HKU GP+Pronto+MX916 YES(2")

25/10/05 HKU GP+Pronto+MX916 YES(2")

28/10/05 HKU GP+Pronto+MX916 YES(2")

02/11/05 HKU GP+Pronto+MX916 YES(2")

02/11/05 HKU OGS+ST8+reducer YES(2")

06/11/05 HKU GP+Pronto+MX916 YES(2")

06/11/05 HKU OGS+ST8+reducer YES(2")

02/12/05 HKU OGS+ST8+reducer YES(2")

23/12/05 HKU GP+Pronto+MX916 YES(2")

23/12/05 HKU OGS+ST8+reducer YES(2")

02/02/06 HKU OGS+ST8+reducer YES(1.25")

03/02/06 HKU OGS+ST8+reducer YES(1.25")

15/02/06 HKU OGS+ST8+reducer YES(2")

04/03/06 West Upper Dam SX+Pronto+MX916 YES(2")

Table 3. FOV of Apparatus Combinations

system projection method focal length (mm) focal ratio FOV

OGS+ST8+reducer direct 2316 f/5.7 22′ × 14′

Pronto+MX916 direct 480 f/6.8 63′ × 47′

Pronto+DC+DCL28 eyepiece-and-camera-lens ? ? ∼ 120′ × 120′

� 27 �

Fig. 5.� FOV of Apparatus Combinations

Table 4. Observation Sites

location longitudea latitudea approx. altitude

(from East to West) above sea level (m)

West Upper Dam, High Island Reservoir, Sai Kung East 114o20′E 22o23′N 85

West Lower Dam, High Island Reservoir, Sai Kung East 114o20′E 22o23′N 5

Telescope Dome, Chong Yuet Ming Physics Building, HKU 114o08′E 22o17′N 80

Shui Hau, Lantau Island South 113o55′E 22o13′N 50

aadopted from the sites data base of http://www.heavens-above.com/

� 28 �

Fig. 6.� Views of HKU Observation Site in Four Directions

� 29 �

Table 5. CCD Target Fields and Data Taken Dates

season identi�er constellation system date

(DD/MM/YY)

sp1a Leo Minor Pronto+MX916 06/03/05

Spring sp1b Leo Minor Pronto+MX916 04/03/06

sp2 Leo Minor OGS+ST8+reducer 03/02/06

su1 Hercules Pronto+MX916 04/07/05

Summer su2 Hercules Pronto+MX916 04/08/05, 29/09/05, 06/10/05

su3 Hercules Pronto+MX916 03/08/05

au1 Andromeda Pronto+MX916 10/12/04

au2a Andromeda Pronto+MX916 02/11/05

Autumn au2b Andromeda Pronto+MX916 25/10/05, 28/10/05

au3 Andromeda OGS+ST8+reducer 02/11/05

au4a Andromeda Pronto+MX916 06/11/05

au4b Andromeda OGS+ST8+reducer 06/11/05, 02/12/05

wi1 Lepus Pronto+MX916 20/11/04

Winter wi2 Orion Pronto+MX916 23/12/05

wi3 Orion OGS+ST8+reducer 23/12/05, 02/02/06, 15/02/06

� 30 �

Fig. 7.� Spring CCD Target Fields (FOV ≈ 63′ × 47′ (sp1a, sp1b), 22′ × 14′ (sp2) )

� 31 �

Fig. 8.� Summer CCD Target Fields (FOV ≈ 63′ × 47′)

� 32 �

Fig. 9.� Autumn CCD Target Fields (FOV ≈ 63′ × 47′ (au1, au2a, au2b, au4a), 22 × 14

(au3, au4b))

� 33 �

Fig. 10.� Winter CCD Target Fields (FOV ≈ 63′ × 47′ (wi1, wi2), 22′ × 14′ (wi3))

� 34 �

Table 6. CCD Target Fields and Reference Stars

�eld SAO or TYC mv σmv RA(J2000) DEC(J2000) spectral type bright or fainta

identi�er reference no. (hh mm ss) (dd mm ss)

sp1a s62018 7.3 0.1 10 24 05.98 +34 11 34.9 K0 bright

s62021 7.3 0.1 10 24 22.08 +34 10 34.1 M0 bright

s62010 5.8 0.1 10 23 06.34 +33 54 29.1 A3 bright

s62019 5.8 0.1 10 24 08.56 +33 43 06.6 K0 bright

s61999 8.9 0.1 10 21 48.75 +33 50 35.3 ? faint

sp1b s62018 7.3 0.1 10 24 05.98 +34 11 34.9 K0 bright

s62021 7.3 0.1 10 24 22.08 +34 10 34.1 M0 bright

s62010 5.8 0.1 10 23 06.34 +33 54 29.1 A3 bright

s62019 5.8 0.1 10 24 08.56 +33 43 06.6 K0 bright

s62038 4.8 0.1 10 25 54.86 +33 47 45.7 F0 bright

sp2 2503:1096 10.85 0.08 10 11 51.37 +31 33 33.8 ? bright

2503:816 10.206 0.043 10 11 55.79 +31 30 44.6 ? bright

2510:1017 13.015 0.372 10 12 16.78 +31 32 54.7 ? faint

2510:983 10.575 0.061 10 12 25.46 +31 33 42.8 ? bright

2510:961 11.284 0.108 10 12 26.34 +31 36 53.6 ? faint

2510:761 9.87 0.037 10 12 25.53 +31 27 21.1 ? bright

2510:872 12.125 0.143 10 12 30.76 +31 23 41.8 ? faint

su1 s66377 8.0 0.1 17 50 39.02 +39 33 17.4 G5 bright

s66374 8.2 0.1 17 50 34.21 +39 31 31.9 G0 bright

s66361 8.0 0.1 17 49 40.68 +39 36 27.7 K0 bright

su2 s66361 8.0 0.1 17 49 40.68 +39 36 27.7 K0 bright

s66377 8.0 0.1 17 50 39.02 +39 33 17.4 G5 bright

s66374 8.2 0.1 17 50 34.21 +39 31 31.9 G0 bright

s66428 7.4 0.1 17 53 05.63 +39 41 14.1 K5 bright

s66441 8.7 0.1 17 53 30.26 +39 27 10.8 F8 bright

su3 s67171 7.7 0.1 18 36 48.80 +38 31 14.9 F5 bright

3105:152 9.833 0.032 18 36 29.34 +39 04 11.8 ? bright

s67149 8.6 0.1 18 35 36.84 +39 03 41.3 ? bright

s67142 8.7 0.1 18 35 20.55 +39 17 51.1 ? bright

s67141 9.0 0.1 18 35 17.53 +39 03 14.9 ? bright

s67143 6.9 0.1 18 35 21.54 +38 53 41.2 A0 bright

� 35 �

Table 6�Continued

�eld SAO or TYC mv σmv RA(J2000) DEC(J2000) spectral type bright or fainta

identi�er reference no. (hh mm ss) (dd mm ss)

au1 s73770 8.2 0.1 00 08 52.53 +28 48 01.0 K2 bright

s73745 8.9 0.1 00 06 41.06 +28 49 42.9 G0 bright

s73748 9.0 0.1 00 06 49.16 +28 56 55.5 F2 bright

s73747 9.0 0.1 00 06 48.72 +29 07 24.2 K0 bright

1735:96 10.135 0.042 00 07 29.92 +29 31 50.9 ? bright

1735:11 10.26 0.048 00 07 20.04 +29 28 48.5 ? bright

au2a s74181 9.0 0.1 00 39 56.72 +29 22 14.8 K0 bright

s74179 9.5 0.1 00 39 46.76 +29 20 20.0 F0 faint

1744:612 10.009 0.046 00 38 51.34 +29 08 53.9 ? faint

s74165 9.0 0.1 00 38 35.67 +29 07 33.2 K0 bright

1744:783 9.842 0.054 00 37 48.32 +29 12 53.0 G5 bright

s74151 9.4 0.1 00 37 31.14 +29 13 50.5 F8 bright

s74144 9.0 0.1 00 36 46.74 +29 11 01.4 K0 bright

au2b s74181 9.0 0.1 00 39 56.72 +29 22 14.8 K0 bright

s74179 9.5 0.1 00 39 46.76 +29 20 20.0 F0 faint

1744:612 10.009 0.046 00 38 51.34 +29 08 53.9 ? faint

s74165 9.0 0.1 00 38 35.67 +29 07 33.2 K0 bright

1744:783 9.842 0.054 00 37 48.32 +29 12 53.0 G5 bright

s74151 9.4 0.1 00 37 31.14 +29 13 50.5 F8 bright

au3 1736:811 10.18 0.038 00 16 38.84 +29 14 51.1 K0 bright

1736:1807 9.666 0.024 00 16 23.01 +29 14 21.6 ? bright

s73867 9.2 0.1 00 16 54.97 +29 22 29.4 A0 bright

s73864 9.5 0.1 00 16 33.61 +29 20 22.4 F5 bright

1736:800 11.364 0.1 00 17 02.44 +29 25 51.9 ? bright

1736:993 10.955 0.068 00 16 52.21 +29 25 58.9 ? bright

au4a s72650 7.3 0.1 22 42 54.24 +37 26 50.4 A2 bright

s72579 7.7 0.1 22 39 31.92 +37 44 36.8 A2 bright

s72603 8.2 0.1 22 40 13.74 +37 31 40.1 F8 bright

s72583 8.0 0.1 22 39 37.32 +37 23 50.6 K2 faint

au4b s72578 6.7 0.1 22 39 31.28 +37 21 14.0 K0 bright

s72569 6.7 0.1 22 39 04.52 +37 22 31.6 B3 bright

� 36 �

4.1.3. Time of Observation

Weather is the main concern for planning the observations. Obviously, observations

could not be preformed during cloudy condition. Hazy or thin layer of cloud such as cirrus

should also be avoided. The most important rule is the atmospheric conditions should

be stable during the whole data taking processes, in order to minimize the e�ects due to

atmospheric variations.

Roughly two time slots, naming early mid-night (before 12 o'clock mid night) and

late mid-night (after 12 o'clock mid night), within a night were divided. From experience,

since the human activities mainly concentrate on early mid-night, the light pollution

during the late mid-night period is expected to be less severe. Data sets taken on

02/02/06 and 03/02/06 show this e�ect on sky brightness and it will be discussed in

Sectionsection:skyresult.

The phase of the moon during observation may increase the sky brightness measured,

so it should be taken into account. The best observation is done when the moon is well

below the horizon, that is, it has not risen or at least the moon phase is small and the moon

is far away from the target �elds.

In order to minimize the e�ect due to atmospheric absorption, data were taken when

the target �eld passes as close as possible near the zenith (i.e. smallest zenith angle) or the

meridian. Targets �elds were selected according to these restrictions.

As a whole, observation was done when the weather was �ne, the moon was absent,

and the target �elds passed close to the zenith. Since the weather was di�cult to predict

and the subtropic climate of Hong Kong made astronomical observations di�cult, data

were taken at random time intervals.

� 37 �

Table 6�Continued

�eld SAO or TYC mv σmv RA(J2000) DEC(J2000) spectral type bright or fainta

identi�er reference no. (hh mm ss) (dd mm ss)

s72583 8.0 0.1 22 39 37.32 +37 23 50.6 K2 bright

s72603 8.2 0.1 22 40 13.74 +37 31 40.1 F8 bright

wi1 s150550 8.2 0.1 05 33 00.79 -17 15 30.5 K5 bright

s150536 8.6 0.1 05 32 00.06 -17 46 02.2 F8 bright

s150560 8.4 0.1 05 33 39.38 -17 47 11.1 K0 bright

s150581 8.8 0.1 05 34 36.25 -17 33 13.0 A3 bright

s150561 8.8 0.1 05 33 43.60 -18 11 43.0 K0 bright

wi2 s94357 8.7 0.1 05 09 29.77 +14 21 20.9 Ma bright

710:596 9.071 0.022 05 07 58.39 +14 14 59.8 K7 bright

s94334 8.8 0.1 05 07 39.28 +14 13 12.2 A2 faint

s94323 8.1 0.1 05 06 43.09 +14 05 04.3 F8 bright

s94336 8.2 0.1 05 07 43.91 +14 21 33.4 A0 bright

s94341 8.3 0.1 05 08 06.34 +14 31 57.4 G5 bright

s94322 7.3 0.1 05 06 42.40 14 26 44.8 G5 bright

s94327 8.3 0.1 05 06 56.74 +14 30 12.0 K0 bright

wi3 s94322 7.3 0.1 05 06 42.40 +14 26 44.8 G5 bright

s94336 8.2 0.1 05 07 43.91 +14 21 33.4 A0 bright

s94327 8.3 0.1 05 06 56.74 +14 30 12.0 K0 bright

aif the reference star is consider as "faint", aperture correction was applied, otherwise no aperture correction was

applied, notice that a star considered as "faint" in the target �elds of the Pronto+MX916 may considered as "bright"

in the target �elds of the OGS+ST8+reducer since the aperture of OGS is much greater and so "faint" stars became

"bright" stars under OGS

� 38 �

4.2. Data Taking Procedures

For observations taken in remote countryside sites outside HKU, transport of

equipments including telescope, CCD camera, and mount was essential. Taxi was the best

transportation choice due to the heavy equipments and the limited observation time. On

the another hand, for the HKU site, equipments were ready and only initial setups were

needed.

Similar to usual astronomical observations and astrophotographies by amateur

astronomers, the equatorial mount was setup on a hard and �at surface. Since long-time

CCD exposures would be preformed, appropriate polar alignment was necessary. It was

possible as long as the Polaris was visible.

For the observations with the Pronto, the diagonal mirror and the V -band �lter

needed �rst to be mounted. At the same time, the MX916 and a notebook computer were

connected and powered up. A bright star was chosen for careful focusing. The system was

then pointed to the selected target �eld. The auto-slew go-to system of the SX mount

helped the pointing tremendously provided that it had been aligned since the Pronto has

no �nderscope. With the GP mount, it may take more time to point to the target �eld.

Several test frames were taken to make sure that the system performed normally and the

appropriate exposure time was estimated. The initialization for the OGS and the ST8 was

similar, except that the OGS system was ready and only �ne pointing alignments were

needed. The whole setting up and initialization process took less than 20 minutes.

The systems would have achieved thermal equilibrium when the above processes were

�nished. Thermal equilibrium means that the temperatures of both the CCD (cooled) and

optical systems are stabilized and the air current inside the telescope is steady. Three dark

frames were taken each at the beginning, middle, and end of the observation. The black

metal Pronto's lens cover was used to cover the objective of the telescope. For the ST8,

� 39 �

an internal shutter helped to take dark frames. Normally, a total of ten raw data frames

and nine dark frames were taken under the same setting including the exposure time and

roughly the same atmospheric condition. Normally 2 × 2 binning (i.e. 376 × 290 pixels

for the MX916 and 765 × 510 pixels for the ST8) was adapted to fasten the downloading

time, which is roughly a second after binning. Exposure times of 10-20 seconds were used

according to di�erent atmospheric conditions, target �elds, and CCD devices. All �les were

saved in FIT or FITS format21. The sizes of the �les were less than 800KB for the ST8 data

and 250KB for the MX916 data. Headers of all frames were also saved. The data taking

procedures took less than 20 minutes for each system. It was important to shorten the time

intervals between frames and systems, in order to minimize the e�ects due to atmospheric

variations.

4.3. Data Pre-processing Procedures

Frames in FIT or FITS format were processed by the IRAF software. A set of dark

frames was median combined using the IRAF task imcombine and a master dark frame

was created. Each raw data frame was subtracted by the master dark frame by using the

task imarith. For each data set, the corresponding master dark frame was used. No scaling

or weighting was performed in combining and subtracting since the exposure times for all

frames were identical. Bias and �at �eld calibration frames were not taken so far as the bias

value had been included in the dark frame and it is di�cult to obtain a good �at frame.

All dark-subtracted data frames (data frames for short) were displayed with a FITS

21FIT or FITS - Flexible Image Transport System, which is a standard data format used

in astronomical data processing, see http://�ts.gsfc.nasa.gov/ for details.

� 40 �

viewer namely SAOImage DS922 (DS9) using the command display. Appropriate bottom

and upper gray scale levels (z1 and z2) were chosen by displaying the same image on Maxlm

and adjusting the gray scale levels such that all reference stars were easy to identify and a

good contrast of the background was obtained. Using the command epar display, the gray

scale levels were set. Figure 11 provides a sample display. Judging by eyes, 4 to 5 data

frames with least variation on sky background and show no faults on reference stars (e.g.

oval in shape, over-exposured, near the edge of the CCD, out-focused, etc) were selection

out of ten of them. One of the selected frames was set as a standard. It would been used to

�nd the FOV per pixel and the critical aperture radius.

For each target �eld, a number of reference stars were choices. They were marked by

either their SAO reference numbers or TYC reference numbers. The standard data frame

was compared with the TheSky6 electronic star chart and so reference stars were identi�ed.

Information for each star such as RA(J2000), DEC(J2000), mv, σmv and spectral type were

obtained from online databases23. Using IRAF task imexamine with keystroke a, the peak

count values and the center pixel coordinates of all reference stars were outputted. The

aim of checking the peak counts was to ensure that the reference stars had not saturated or

near saturated. (For example, the counts should be smaller than 60,000 for a 16 bits data

format imaging device).

A C program, namely lsf.c24, used the center pixel coordinates and the RA and DEC

of reference stars to compute the plate scales, a1 and a2, and so the FOV, F . Plate scale

is the angular length of the sky in which a dimension of the pixel covered. It has the unit

22Software information: http://hea-www.harvard.edu/RD/ds9/ .

23Simbad reference database catalog, either the SAO Star Catalog J2000 or the All-sky

Compiled Catalogue of 2.5 Million Stars.

24See Appendix A for details.

� 41 �

arcsec. Since the pixels on the CCD are not perfectly square and there is a �eld curvature

of the optical system, a1 and a2 are not necessary the same but should be close to. FOV,

which has the unit arcsec2, is the area of sky covered by a pixel and has the following

relation:

F = a1 · a2 . (11)

Tables 7 and 8 listed the values of a1, a2, F , and σF for all sets of CCD data. Also notice

that the value of F vary for di�erent �elds. The value of σF was big when the seeing was

bad, otherwise, it was close to zero.

4.4. Data Reduction Procedures

From now on, aperture photometry was applied to �nd the counts from reference stars.

The photons from a star will distribute on several pixels on the CCD in the form of a

so-called point spread function (PSF). Theoretically, PSF is circularly symmetric and the

photons from star will extend to in�nity with decreasing intensity. In order to measure as

much as possible the counts from the star, while not introducing extra noise from the sky

background, a suitable aperture radius should be determined. If we plot the log(counts)

against the aperture radius, a critical radius, where the counts level o�, should be observed.

This critical radius means that most of the counts from the star are included within that

radius.

Using the task imexamine with keystroke r, FWHM was measured from the best

performed brightest reference star (set it as the standard star) in the standard data frame

for each set of data. From the task phot under the package noao > diaphot > apphot and

input the radii of the centering box and the sky annulus as 2.5×FWHM and 4×FWHM

radius respectively, aperture photometries of aperture radii listing from 0.00 to 10.0 pixels

in the interval of 0.50 pixel were performed and the outputs were used to plot log(counts)

� 42 �

Table 7. FOV per Pixel of the Pronto+MX916

date a1 a2 F σF

(DD/MM/YY) (arcsec) (arcsec) (arcsec2) (arcsec2)

20/11/04 10.0 9.70 97.5 0.1

10/12/04 10.0 9.67 97.1 0.0

06/03/05 10.0 9.71 97.5 0.0

04/07/05 10.1 9.68 97.6 0.1

03/08/05 10.0 9.72 97.7 0.1

04/08/05 10.1 9.70 97.7 0.1

29/09/05 10.1 9.64 97.1 0.2

06/10/05 10.1 9.69 97.5 0.1

25/10/05 10.0 9.81 98.3 2.6

28/10/05 10.1 9.81 99.5 1.7

02/11/05 10.2 9.75 99.5 1.3

06/11/05 10.1 9.71 97.6 0.2

23/12/05a 5.03 4.86 24.4 0.0

04/03/06 10.0 9.71 97.6 0.0

aThis set of data was taken by 1 × 1 binning mode of instead of 2

× 2 binning mode as usual, so a1, a2, and F were smaller.

Table 8. FOV per Pixel of the OGS+ST8+reducer

date a1 a2 F σF

(DD/MM/YY) (arcsec) (arcsec) (arcsec2) (arcsec2)

02/11/05 1.61 1.60 2.57 0.0

06/11/05 1.62 1.62 2.64 0.0

02/12/05 1.45 1.44 2.09 0.0

23/12/05 1.45 1.45 2.10 0.0

02/02/06 1.44 1.43 2.07 0.0

03/02/06 1.43 1.43 2.06 0.0

15/02/06 1.44 1.43 2.06 0.0

� 43 �

against aperture radius by Origin Pro 7.0 (Origin)25. The critical radius from the plot was

used as the aperture radius of the photometries of other reference stars later on.

If some of the reference stars in the target �eld were faint, then the aperture correction

factor ∆ was needed to calculated according to Equation 7 where the FWHM was obtained

from the standard star on each data frames.

Next, the �ux from the sky background B was needed. Using the task imexamine with

keystroke m, within the region where had no star and the background was uniform, median

counts from the box of 100× 100 pixels with the smallest standard deviation were obtained.

Notice that this output data number was not the actual �ux from the background, but

had to be converted according to Equation 3. The �uxes of the sky background B from

individual 4 to 5 data frames were averaged, yielded B. The error of the sky background

σB was simply set as the standard deviation of the values of individual B.

Finally the photometries on the reference stars were performed. For bright reference

star, the task phot was performed with the radius of the centering box equaled to

2.5× FWHM radius and the radii of the sky annulus and apertures were set as the critical

radius found before from the standard star. Notice that the inner radius of the sky annulus

was set to be equal to the aperture radius to get the best estimation of the background.

The width of the sky annulus was 10 pixels.

For faint star, the task phot was performed with the same values on radius of the

centering box and the width of the sky annulus as bright star, but the radii of the sky

annulus and aperture were both set as 1.4× FWHM radius, i.e. the smaller aperture size.

Some remarks at this point: 1) A number of parameters could be set for the task phot,

but they were all kept as default and important parameters such as aperture radius were

25Software information: http://www.originlab.com/index.aspx?s=8#pro .

� 44 �

set interactively when running the task. 2) The above procedures were applied to all sets of

data as long as the target �eld was not crowded. 3) Equation 3 was still had to apply to all

output data number to get the actual �uxes from stars. 4) The actual �uxes of all reference

stars fi from individual 4 to 5 data frames were averaged, yielded fi. The error of the

them was simply set as the standard deviation of the values of individual fi. 5) Aperture

correction was applied to all faint reference stars only.

With the �uxes and visual magnitudes from all reference stars and the sky backgrounds'

�uxes in hand, �ttings were performed according to Equation B7, see Appendix B for

details. The �tted plots of log(fi) against mvi+ kvX − ∆ were generated by Origin for

visualizations.

Finally, the value of the sky brightness msky in the unit of mag arcsec−2 was computed

for each set of data by using Equation 10.

5. Results

5.1. Critical Aperture Radius Curves

A suitable aperture radius for photometry was needed to determine so that the

maximum signals from the stars were included without introducing extra noise from the sky

background. For each data set, the counts from the standard reference star of the standard

image were measured. All the plots of integrated �ux against aperture radius are shown in

Figures 12 to 14.

Notice here that the �ux values, i.e. the output data number from the phot task, foutput

which follows Equation 2, are not the actual �uxes from the stars. However, since the actual

�uxes follows Equation 3 which is directly proportional to foutput, it made no e�ect on the

critical aperture radius determination.

� 45 �

Each plots showed a radius such that the log(flux) value level o�. Theoretically, as the

size of the aperture radius increase, more and more counts from star are included, so the

the curves should be monotonic increasing. However, some curves has strength behavior,

especially data taken by the MX916 in HKU site during bad atmospheric conditions.

The curves �uctuate below the maximum values and even there are drops in values with

increasing aperture radius. I speculated the bad seeing in HKU site and the relatively poor

quality of the MX916 CCD camera may a�ected them.

5.2. Linear Fitting Plots

After gathering the �uxes and visual magnitudes from all reference stars and the sky

backgrounds' �uxes, a linear �tting was performed to determine the best �t parameters c

and its error σc. The formulae and procedures of the �tting are outlined in Appendix B.

Figures 15 to 17 are log(fi) against mvi+ kvX −∆ plots. Each set of data corresponds to

one plot and the scales of the axises of the plots were optimized. Notice that the aperture

correction factor was ∆ = 0 for bright reference stars. Each data point corresponds to one

reference star but the number of reference stars varied from target �elds.

From the plots, generally we see that the �ttings are acceptable. In some plots, like

data taken on 04/07/05, 06/11/05 and 23/12/05 by the Pronto+MX916, show an increasing

error on y-axis (i.e.σlog(fi)) with increasing star magnitude mvi

(i.e. fainter star). This

re�ects the signal-to-noise ratio decreases with faint star. The �ttings depend on the

spectral types, the magnitude distribution of the reference stars and the application of

V -band �lters.

� 46 �

5.3. Testing on Digital Camera

A commercial digital camera (DC), namely Nikon Coolpix 4500, was tested in the

project. The aim of using this DC is to �nd out the deviation on the result of the sky

brightness between low-prized (around HKD$4,000) and low-grade pocket-size commercial

digital camera and high-prized (around HKD$30,000) and high quality astronomical CCD

camera system. We were hoping to introduce the sky brightness measuring method to the

public who are using such pocket-size DCs.

We believe that the astronomical CCD systems, the MX916 and the ST8 in this

project, provides a more reliable result since all important properties on CCD chip, such as

quantum e�ciency and gain ratio, are provided by the manufacturer. One set of data using

the DC (through the 2" V -band �lter) was taken on 04/08/05 at HKU using the Pronto

and the GP mounts. The results were compared to those taken by the MX916 (through the

same V -band �lter) at the same location in the same evening.

The data taking procedures with the DC were similar to those with the MX916 CCD,

except that the DC data were taken approximately 45 minutes before those with the

MX916. In addition, data (actually images in 11Mb TIFF format in 2,272 × 1,704 pixels

size) were saved in Compact Flash (CF) cards and the DC does not need a notebook

computer to operate it. The various settings of the DC were listed in Subsection 3.2.2.

A special target �eld was needed for the DC as it hardly got a good signal-to-noise

ratio with a 8-second exposure for reference stars with magnitude greater than 7. Table 9

and Figure 18 shows the details and the map on this �eld.

I processed the DC data by assuming the CCD has 100% quantum e�ciency at all

wavelength, gain equal to 1 electron/ADU and most importantly, no special pre-precessing

on the outputted data, i.e. linear respond on incoming photons and generated electrons

� 47 �

over the whole range.

Although the DC data were taken with a black and white saturation mode, it was also

necessary to combine RGB channels into gray-scale by using Image > Mode > Grayscale

under The GIMP 2.2.826. Each combined pixel has 65, 536 electrons full-well capacity. In

order to process the data under IRAF, TIFF data format must be converted to FITS and it

was achieved by The GIMP as well. Apart from these special treatments on the DC data,

the others data reduction procedures are the same as the MX916 and the ST8 data.

The the FOV per pixel, F and its error, σF of this DC data were found out to be

18.5 arcsec2 and 0.1 arcsec2 respectively. The critical aperture radius curve and linear

�tting plot are showed in Figure 19. The data showed an acceptable critical aperture

radius at 4.0 pixels. After the �tting it yielded the sky brightness as 13.04±0.120 mag

arcsec−2. Comparing it with MX916 data taken during the same night, the sky brightness

is 15.65±0.050 mag arcsec−2, there is a 2.61 mag arcsec−2 di�erence between them.

5.4. The Sky Brightness

Table 10 and Figures 20 to 22 summarizes the sky brightnesses against data taken

during November 2004 and March 2006 both in the city and countrysides using various

telescope and camera combinations. Several points can be interpreted from the results.

First, the measured night sky brightness depended on location. Sky brightness on the

HKU's observatory dome was 16.39±0.71 mag arcsec−2 measured with the Pronto+MX916

system (averaged over 9 sets of �ltered data) and 16.33±0.66 mag arcsec−2 measured with

the OGS+ST8+reducer system (averaged over 7 sets of �ltered data). Sky brightness in

26Software information: http://www.gimp.org/windows/ .

� 48 �

the countryside (West Dam and Shui Hau) was 19.73±0.60 mag arcsec−2 measured with

the Pronto+MX916 system (averaged over 5 sets of non-�ltered and �ltered data). Notice

that the error on the averaged sky brightness was given by the standard deviation of the

individual values, since it is greater than the square sum of individual errors. As a result,

there is a di�erence of ∼3.4 mag arcsec−2 on sky brightness between city and countryside.

In other words, the surface brightness of the city night sky was ∼22-23 times brighter in

�ux than that in the countryside.

Also notice that, from Figure 22, sky brightness result on 10/12/04 showed a relatively

large (∼1 mag) deviation from the averaged value. This data set was taken at the West

Lower Dam of the High Island Reservoir and it was close to the Chong Hing Water Sports

Center where lightings there contributed to the sky brightness. I suggest that the West

Lower Dam was the relatively "bright" site compared with the West Upper Dam and Shui

Hau. So that if we excluded the result of this data set, the averaged sky brightness in

the countryside (West Upper Dam and Shui Hau) was 20.0±0.22 mag arcsec−2 measured

with the Pronto+MX916 system (averaged over 4 sets of non-�ltered and �ltered data,

and the error on the averaged sky brightness was given by the standard deviation of the

individual values, same as before) Another signi�cant deviation was data taken on 06/11/05

by OGS+ST8+reducer at HKU. Its result marked a ∼1.3 mag di�erence with the average.

I doubt that the frost on the ST8's CCD chip a�ected the result. As the CCD camera was

electronically cooled to maintain a low-electron-noise environment, frosts may form if the

desiccating agent inside the camera body was degraded. Frosts condensed on the surface

of the CCD and decreased the contrast of the sky background and thus increased the sky

brightness. The desiccant of the camera were regenerated afterward and no frost formed so

far.

Second, the sky brightness at both HKU's observatory dome and countryside showed

� 49 �

variation over time with a range of 1.5 to 2.4 mag arcsec−2. This re�ected the varying

atmospheric conditions, changing of target �elds, at di�erent epochs. Interestingly, two sets

of data taken on 02/02/06 and 03/02/06 showed change of measured sky brightness between

early mid-night and late mid-night. The sky brightness was 16.20±0.06 mag arcsec−2 at

21:00 and 16.81±0.037 mag arcsec−2 at 02:30. Approximately half magnitude or 1.6 times

in �ux di�erence was observed. We assumed here that the atmospheric condition remained

unchanged over time and the change of target �eld had negligible e�ects. This is consistent

with experience that human activities mainly concentrate on early mid-night, and thus the

light pollution during early mid-night is more serious.

Third, the sky brightness depended on the systems used to take the data. Two

telescope systems, i.e., the Pronto+MX916 and the OGS+ST8+reducer, were used and

there was a small di�erence in the results. Using the data taken on 02/11/05, 06/11/05 and

23/12/05, di�erence in 0.31, 0.47, and 0.14 mag arcsec−2 were recorded. Average di�erence

was 0.31 mag arcsec−2. Only these three data sets were compared as others data sets were

taken within the same night using only one set of system.

Finally, obviously the Moon is one of many factors a�ecting the sky brightness.

Krisciunas (1991) proposed that the moonlight is a function of its phase, its zenith distance,

the zenith distance of the target, the angular separation of it and the target, and the local

extinction coe�cient k. However, as the data sets in this project were collected during

moonless nights, except for data taken on 06/10/05, 25/10/05 and 02/02/06, there were not

enough data to make reasonable correlation between the moonlight and the sky brightness.

� 50 �

Fig. 11.� Display a Dark-Subtracted Data Frames by DS9

� 51 �

Fig. 12.� Critical Aperture Radius Curves of the MX916 data obtained on DD/MM/YY:

20/11/04, 10/12/04, 06/03/05, 04/07/05, 03/08/05, 04/08/05, 29/09/05 and 06/10/05.

(from top left to bottom bright)

� 52 �

Fig. 13.� Critical Aperture Radius Curves of the Pronto+MX916 data obtained on

DD/MM/YY: 25/10/05, 28/10/05, 02/11/05, 06/11/05, 23/12/05 and 04/03/06. (from

top left to bottom bright)

� 53 �

Fig. 14.� Critical Aperture Radius Curves of the OGS+ST8+reducer data obtained on

DD/MM/YY: 02/11/05, 06/11/05, 02/12/05, 23/12/05, 02/02/06, 03/02/06 and 15/02/06.

(from top left to bottom bright)

� 54 �

Fig. 15.� Linear Fitting Plots of the Pronto+MX916 data obtained on DD/MM/YY:

20/11/04 (no �lter), 10/12/04 (no �lter), 06/03/05 (no �lter), 04/07/05 (no �lter), 03/08/05,

04/08/05, 29/09/05 and 06/10/05. (from top left to bottom bright)

� 55 �

Fig. 16.� Linear Fitting Plots of the Pronto+MX916 data obtained on DD/MM/YY:

25/10/05, 28/10/05, 02/11/05, 06/11/05, 23/12/05 and 04/03/06. (from top left to bottom

bright)

� 56 �

Fig. 17.� Linear Fitting Plots of the OGS+ST8+reducer data obtained on DD/MM/YY:

02/11/05, 06/11/05, 02/12/05, 23/12/05, 02/02/06, 03/02/06 and 15/02/06. (from top left

to bottom bright)

� 57 �

Table 9. The DC Target Fields and Reference Stars

�eld SAO mv σmv RA(J2000) DEC(J2000) spectral type bright or fainta

identi�er reference no. (hh mm ss) (dd mm ss)

dc�eldc s47009 6.5 0.1 17 51 14.04 +40 04 20.8 G0 bright

s66402 6.1 0.1 17 52 04.70 +39 58 55.4 K0 bright

s47037 5.1 0.1 17 53 18.06 +40 00 28.6 K0 bright

aif the reference star is consider as "faint", aperture correction was applied, otherwise no aperture correction was

applied

bthis �eld is located in constellation Hercules and closed to �eld su1 or su2

Fig. 18.� The DC Target Field (FOV ≈ 120′ × 120′)

� 58 �

Fig. 19.� Critical Aperture Radius Curve (right) and Linear Fitting Plot (left) of the

Pronto+DC+DCL28 data obtained on DD/MM/YY: 04/08/05

Fig. 20.� The Sky Brightness against Date (City Pronto+MX916 Data with msky =

16.39±0.71 mag arcsec−2)

� 59 �

Fig. 21.� The Sky Brightness against Date (City OGS+ST8+reducer Data with msky =

16.33±0.66 mag arcsec−2)

Fig. 22.� The Sky Brightness against Date (Countryside Pronto+MX916 Data with msky =

19.73±0.60 mag arcsec−2)

� 60 �

Table10.

Resultson

SkyBrightness

date

time

%moonphase

locationb

system

cnumber

ofred-

target

�eld

�tted

parameter

msk

yV-band�lter

(DD/MM/YY)

(hhmm-hhmm)

(altitude◦

a)

-ucedframes

c(m

ag

arcs

ec−

2)

(mag

arcs

ec−

2)

(size)

20/11/04

0159-0210

56(-20)

WDU

P+M

4wi1

22.2±0.06

20.04±0.059

No

10/12/04

2100-2116

3.5(-66)

WDL

P+M

5au1

21.8±0.03

18.71±0.043

No

06/03/05

0015-0018

28(-28)

SH

P+M

5sp1a

20.3±0.05

20.24±0.094

No

04/07/05

0018-0034

8(-33)

SH

P+M

5su1

22.4±0.06

19.94±0.061

No

03/08/05

2220-2247

2.4(-34)

UD

P+M

5su3

21.4±0.03

16.45±0.046

Yes(2")

04/08/05

2115-2145

0.53(-15)

UD

P+M

5su2

21.0±0.05

15.65±0.050

Yes(2")

29/09/05

1938-1955

14(-35)

UD

P+M

5su2

21.0±0.05

15.50±0.051

Yes(2")

06/10/05

1921-1941

10(3)

UD

P+M

5su2

21.5±0.05

16.61±0.052

Yes(2")

25/10/05

0023-0052

54(14)

UD

P+M

5au2b

21.6±0.05

16.50±0.065

Yes(2")

28/10/05

2325-2346

19(-43)

UD

P+M

4au2b

22.2±0.05

17.46±0.050

Yes(2")

02/11/05

2246-2315

0.4(-69)

UD

P+M

5su2a

22.2±0.04

17.18±0.043

Yes(2")

06/11/05

2121-2137

23(-0.3)

UD

P+M

5au4a

21.0±0.06

15.51±0.062

Yes(2")

23/12/05

2245-2304

52(-19)

UD

P+M

5wi2

21.6±0.05

16.66±0.059

Yes(2")

04/03/06

0047-0053

19(-34)

WDU

P+M

5sp1b

18.6±0.05

19.72±0.120

Yes(2")

02/11/05

2326-2342

00.4(-64)

UD

S+O

4au3

23.4±0.04

16.87±0.063

Yes(2")

06/11/05

2018-2053

23(-0.3)

UD

S+O

5au4b

22.7±0.05

15.04±0.055

Yes(2")

02/12/05

1850-1911

1(-11)

UD

S+O

5au4b

22.6±0.05

16.01±0.053

Yes(2")

23/12/05

2330-2347

52(-19)

UD

S+O

5wi3

23.1±0.06

16.80±0.071

Yes(2")

02/02/06

2104-2123

22(11)

UD

S+O

5wi3

23.0±0.06

16.20±0.064

Yes(1.25")

03/02/06

0234-0253

24(-55)

UD

S+O

5sp2

23.3±0.03

16.81±0.037

Yes(1.25")

15/02/06

1937-2003

96(-5)

UD

S+O

5wi3

23.3±0.06

16.61±0.069

Yes(2")

04/08/05

2030-2055

0.56(-10)

UD

PDC

5dc�eld

14.5±0.11

13.04±0.120

Yes(2")

� 61 �aapproximate

moonaltitudeatthemiddleofthedata

takingprocess

bWDU=WestUpper

Dam;WDL=WestLow

erDam;SH=ShuiHau;UD=HKUTelescopeDome

cP+M

=Pronto+MX916;O+S=OGS+ST8+reducer;PDC=Pronto+DC+DCL28(m

ountwasomittedhereandbutlisted

inTable2)

� 62 �

6. Discussion

6.1. Sources of Errors

These are a number of error sources in the calculation of the sky brightness. The

most dominate source of error is σfiduring the photometric data reduction processes. It is

obviously that di�erent values of counts (i.e. the output data number from IRAF, foutput) of

a reference star will be obtained for di�erent data frames. This �uctuation was due to the

varying atmospheric condition, i.e. seeing, and the statistical error on electrons, i.e. Poisson

noise. Seeing, as de�ned by Romanishin (2002), means "the smearing and shimmering of

light from celestial objects due to its passage through the Earth's atmosphere". The e�ects

of it are re�ected on the �uctuation of photons counts. On the other hand, electrons obey

Poisson noise which is a counting statistic and follows

σ =√

n (12)

and

n = foutput ×G (13)

where n, foutput, and G are the number of electrons, the output data number, and the gain

of the CCD respectively (Romanishin, 2002).

For example, the data taken by the OGS+ST8+reducer on 23/12/05, the number of

electrons n responded from three reference stars in �ve data frames were given in Table 11.

These frames were taken within 4 minutes under the same setting included the exposure

time. It is clearly that√

n were much smaller than σn those were the standard deviation of

n. As as result, varying atmospheric condition was the dominant component of the source

of error.

Another source of error is the error on the derived magnitude of the reference stars,

σmvi. Photometry should be conducted with �lters and instrumental magnitudes of

� 63 �

various bands obtained are converted to standard photometry system with several color

transformation equations (Romanishin, 2002). But in this project, no transformation was

performed as only V -band �lters were used. Errors rose from this and the instrumental

magnitudes obtained had not converted the standard system yet. There is no idea at this

moment whether omitting color transformation signi�cantly a�ects the results.

Using di�erent targets �elds may also introduce systematic error. The �uxes from

reference stars (calibrators) were used to calibrate the �ux from the sky brightness.

However, various magnitudes of these calibrators would give systematic errors on log(fi)

against (mvi+ Xkv − ∆) �tting and so the sky brightness. Due to the limitation on the

apparatus and time, the calibration between di�erent �elds had not been carried out at this

stage yet.

6.2. Apparatus

Since the 2004 summer, the Pronto+MX916 system had been used for the night

sky brightness project, �rst by Tam (2004), and later by this work. Since 02/11/05, a

research-graded OGS 16" RC telescope and a bigger format SBIG ST8 CCD were used

together with the former system. The Pronto has a much shorter prime focal length

(480mm against the OGS 3414mm) so that it has a much greater FOV (Pronto+MX916,

63' × 47' against the OGS+ST8+reducer, 22' × 14', Table 3 and Figure 5). More reference

stars could be captured within a single exposure if the FOV was greater. Better linear

�tting can be obtained with more reference star data points. For this project, on average

5 and 4 reference stars were selected for the MX916 and the ST8 target �elds respectively.

The relatively small FOV of the OGS+ST8, even after using a focal reducer, signi�cantly

increase the di�culties and limitation on selecting its target �eld. However, the light

collecting area (ignored the central obstruction due to the secondary mirror) of the OGS

� 64 �

is 33 times greater than that of the Pronto, so high signal-to-noise ratio can be obtained

by the OGS on fainter (say, 10 mag) stars. The results from these two systems had been

discussed in Subsection 5.4. There exists an averaged 0.31 mag arcsec−2 di�erence on the

results obtained. No further deduction can be found as there were only three related data

sets at this stage.

A commercial digital camera (DC) was tested but the performance was unsatisfactory.

It is not designed for taking image with long exposure time so that the maximum exposure

time is 8 seconds. Without cooling, which is essential in reducing dark current, in addition

to low sensitivity, the DC can hardly record high enough signal-to-noise ratios for reference

stars, even for the bright (say, 3 mag) stars. Moveover, the lens of the DC is non-removable

and so the magni�ed image can only be taken with an eyepiece-and-camera-lens projection.

On 04/08/05, both the Pronto+DC+DCL28 and the Pronto+MX916 data with the

same V -band �lter were taken. From Table 10, the DC's data shows the sky brightness of

13.04±0.120 mag arcsec−2 while the MX916's data shows 15.65±0.050 mag arcsec−2, so a

di�erence of 2.61 mag arcsec−2 or about 11 times in sky brightness's �ux was recorded.

Apart from �tting with di�erent target �elds, I suggest such a large deviation is mainly

due to the unknown processing or treatments applied on the DC image before the image is

outputted. We have no idea whether the counts of the pixels of the DC's CCD truly re�ect

the amount of photons from reference stars. So that the result on the sky background

measured by the DC was highly uncertain. We had given up using this DC in the project.

Results from di�erent systems are di�erent. It is because di�erent CCDs must have

di�erent behaviors over optics and it is di�cult to calibrate them unless we have extensive

testing. However the deviation is acceptable except the result for the DC data.

� 65 �

6.3. Time Delay Between Data

It is important that the time interval between data taking with di�erent systems

within the same night should be as short as possible. The atmosphere is not stable � cloud

or haze may develop over �ne. Unstable atmospheric condition a�ects the sky brightness

measured. For example, invisible thin layer of cloud along high altitude masks the sky

and decrease the �uxes from stars. Haze, which re�ects the city night, increases the sky

brightness. Shortening the time delay means minimizing the e�ects from the atmospheric

variation. On 04/08/05, 02/11/05, 06/11/05 and 23/12/05, two systems were used in each

night and there were time delays of 35 to 50 minutes, due to reset of apparatus, including

focusing and pointing. It is currently technically not possible to take data by di�erent

systems simultaneously with a signal observer.

6.4. Light Pollution Problem

How much is the Hong Kong's night sky polluted? The values of sky brightness over

observatories around the world are listed in Table 12. The darkest sky can reach down to

∼22 mag arcsec−2. Comparing with this, it was found that the night sky of Hong Kong's

city and countryside are ∼6 and ∼2 mag arcsec−2 brighter respectively. In other words,

the surface brightness of the Hong Kong's city night sky was ∼250 times brighter in �ux

than that in the darkest sky, while the surface brightness of the Hong Kong's countryside

night sky was ∼6 times brighter in �ux than that in the darkest sky. We may not able to

conclude that the brightened night sky of Hong Kong was only due to the light pollution,

as the air quality and weather may accounted to the e�ect. Discuss on this can be found on

Section 7.

Is light pollution in Hong Kong getting worse? This project was carried out since

� 66 �

Table 11. Examples on Fluctuations on the Numbers of Electrons n from IRAF of the

OGS+ST8+reducer 23/12/05 Data

SAO number

s94322 s94336 s94327

frames n n n

15data1ds.�t 2613668 1951587 2053027

15data2ds.�t 2619570 1915020 2062827

15data3ds.�t 2577773 1884942 2088183

15data4ds.�t 2517436 1845405 2047653

15data5ds.�t 2504671 1915594 1987978

n 2566624 1902509 2047934

σn 53382 39705 36954√

n 1602 1379 1431

Table 12. Near-zenith Moonless V -band Sky Brightness Measured at various International

Observatoriesa

place year V -band sky brightness (mag arcsec−2)

McDonald 1960, 1973 21.7

Junipero Serra 1966, 1971 21.9

San Pedro Martir 1970 21.9

San Benito 1976, 1985-7 21.9

La Silla 1978 21.7

Sacramento Peak 1978 21.9

Kottamia 1980 21.9

Kitt Peak 1987 21.9

Cerro Tololo 1987 22.0

La Palma 1987 21.8

Mauna Kea 1989-91, 1995-6 21.9

Calar Alto 1990 21.5

apartly adopted from Benn et al, 1998

� 67 �

late 2004 and the sky brightness at the HKU's observatory dome was roughly constant

between August 2005 and February 2006. The results obtained by Tam (2004) were

tabulated in Table 13. He used the similar data taking and reduction procedures in his

project except that linear �ttings which including the errors on both axises and the V -band

�lter were applied in this current project. If we compare Tam's results, which is averaged

to be 16.49±1.28 mag arcsec−2 (standard deviation is taken to be the error), with my

result, which is averaged to be 16.39±0.71 mag arcsec−2 (standard deviation is taken to

be the error), there is still no signi�cantly variation. Similarly, for the sky brightness of

countryside, the values remained stable at 19.72±0.18 mag arcsec−2 throughout November

2004 and March 2006. We may conclude that the light pollution of Hong Kong had not

getting worse at least within these 16 months.

7. Summary

A number of sources contribute to the night sky glow. For example, airglow, aurora

(which is negligible at latitude less than 40◦), zodiacal light, stars (with magnitudes greater

than 20), starlight scattered by interstellar dust, extragalactic light and light pollution

increase the night sky brightness during moonless night and at sunspot minimum (Benn

et al, 1998). All the above factors should be take into the account in the presentation of

results. Below are some recommendations and suggestions on the project:

• Replace the DC to other common middle-priced digital cameras, e.g. digital single

lens re�ector (DSLR), which have the higher sensitivity in dark environment and

primary projection can be applied so as to broaden the choice of target �elds, increase

the signal-to-noise ratio and more amateur astronomers are able to contribute to the

project.

� 68 �

• Take �at �eld frames associate with the raw data, in order to calibrate the non-

uniformities of the CCD chips. Flat �eld frames can be obtained by taking images of

the twilight sky or an arti�cial uniformly illuminated screen inside the observatory

dome (Romanishin, 2002).

• More studies should be conducted to calibrate more combinations of apparatus and

more varieties of apparatus.

• It is important to investigate the systematic errors in the project. They may a rise

from the apparatus and can a�ect calculations on the sky brightness. It may be

achieved by calibrating all the possible factors especially the systematic shift between

standard and instrumental magnitudes. One way to do the calibration is to perform

the full color transformation through multi-bands �lters. B- and R- bands �lters are

being considered by the department and hope they can be applied in the future works,

although V -bands �lters were applied since 03/08/05.

• In order to have a more comprehensive and systematic monitor of the light pollution

of Hong Kong, data should be taken at various observation sites at the same time and

for su�cient long periods of time. HKU should promote this project to the public

such that interested parties are able to involve in it, provided that we had developed

an e�ective and systematic means to coordinate, collect and reduce data from various

sources.

It is clear that increase in the arti�cial city lights make the light pollution problem

worse. however air quality may a�ect the sky brightness as well. Recently, the air pollution

in Hong Kong is deteriorating. Hazy skies are common especially when Northern wind bring

� 69 �

pollutants from mainland China27. These pollutants include aerosols of size range from 0.05

to 1,000µm. Part of them originated from human activities, such as combustion of fossil fuel

by vehicles' engines and power plants, and dust from construction sites. Aerosol particles

in size range from 0.1 to 2-3µm remain 8 days in the lower troposphere and scattering

sunlight so the visibility will be decreased. At night, aerosols may also scatter city lights

and increase the sky brightness (Nichols, 1998). The Environmental Protection Department

has set up air monitoring systems to provide air quality data hourly at 14 stations around

Hong Kong. Collected air pollutants' data include sulphur dioxide, respirable suspended

particulates, nitrogen oxides, nitrogen dioxide, ozone and PM2.5 (particulate matter that

is 2.5µm or smaller in size) (Environmental Protection Department, 2005). The results of

sky brightness may be compared with the air quality data. High Island Reservoir Sai Kung

is the potential testing site as it is near Tap Mun station which collects air quality data

regularly. Further studies should be conduct in order to �nd out whether the city lights or

the air pollutants contribute to the sky brightness most.

Focus on the light pollution of Hong Kong, guidelines should be given to the general

public for the protection of the starry night. Pedani (2004) suggested that high-pressure

sodium (HPS) and mercury lamps should be replaced by low-pressure sodium (LPS) lamps.

It is because the emission of LPS concentrated in NaD 5890-6Å which adds natural sky glow

and show no continuum emission. There is no data on what kind of lamps are used in Hong

Kong's street lamps. However, there is even a simpler way to reduce light pollution: use as

less arti�cial lightings as possible, or in other words, use lighting if only if it is necessary. It

is typical that buildings around the Victoria Harbor release unnecessary light energy to the

27The Environmental Protection Department once pointed out that Pearl

River Delta accounts 80% to 95% of total pollutants emissions (adopted from:

http://www.epd.gov.hk/epd/).

� 70 �

sky (Figure 23 shows an impassive example), this make almost no astronomical observation

can be conducted around the city center. Careful design and the operation time of the

buildings' illumination are important in reducing light pollution.

Fig. 23.� The Victoria Harbor is �lled of light pollution. The center tall building is

International Finance Center (IFC) and it is the Hong Kong's tallest o�ce building. IFC,

as a serious source of light pollution, lights up the clouds above it.

With the development of urban area, it is unavoidable that Hong Kong's sky is

getting "brighter" and "more hazy". As far as amateur astronomers are concerned, the

government should preserve observation sites, e.g. Shui Hau and High Island Reservoir, for

undevelopment. Starry night is a precious natural resource.

� 71 �

A. Plate Scale Fitting

This Section introduces the procedures which aims at �tting the plate scales per pixel,

a1 and a2 so as the �eld of view per pixel, F . See Figures 24, and 25 for the source codes.

The relation between a1, a2, and the angular separation Ai of a pair of reference stars

follows

(a1 ·∆xi)2 + (a2 ·∆yi)

2 = A2i , (A1)

where ∆xi and ∆yi are the di�erence on the pixel center coordinates of the star pair i.

Notice that i runs from 1 to γ = nC2 where n is the number of reference stars. This γ

ensures that all combination of star pairs are included.

Ai for stars pair with RA and DEC center coordinates (δj, αj) and (δk, αk) is de�ned as

cos Ai = cos δj cos αj cos δk cos αk + cos δj sin αj cos δk sin αk + sin δj sin δk . (A2)

We would like to �t the best parameters, a1 and a2. According to Press (1992), de�ne

χ2 ≡γ∑

i=1

[(a1 ·∆xi)

2 + (a2 ·∆yi)2 − A2

i

]2(A3)

or

χ2 ≡∣∣∣−→∆ · −→a −−→A

∣∣∣2 , (A4)

where

−→∆ =

(∆x1)

2 (∆y1)2

(∆x2)2 (∆y2)

2

......

(∆xγ)2 (∆yγ)

2

γ×2

, (A5)

−→a =

a21

a22

2×1

, (A6)

� 72 �

and,

−→A =

A2

1

A22

...

A2γ

γ×1

. (A7)

By SVD decomposition, the solution is given by the equation as

−→a =2∑

k=1

(−−→U(k) ·

−→A

ωk

)−→V(k) , (A8)

where−−→U(k) is the column of

−→U which is a 2 × γ column-orthogonal matrix,

−→V(k) is the

column of−→V which is a γ× γ orthogonal matrix and ωk are the singular values of this linear

least-squares problem.

Since the measurement errors on δ,α, x and y are not known and assumed to be small,

here de�ned the values of σa1 and σa2 as

σ2a ≡ σ2

a1≡ σ2

a2≡ χ2/(γ − 2) . (A9)

Then from Equation 11 and the error propagation equation

(σz)2 =

(∂f

∂x1

)2

(∂x1)2 +

(∂f

∂x2

)2

(∂x2)2 + ...... , (A10)

where z is a function of x1, x2,......, i.e. z = f (x1, x2, ......).

Yield

z ≡ F ≡ f(a1, a2) = a1 · a2 (A11)

and

(σz)2 =

(∂f

∂a1

)2

(∂a1)2 +

(∂f

∂a2

)2

(∂a2)2 (A12)

also

σF =√

a22 · σ2

a + a21 · σ2

a . (A13)

� 73 �

B. Linear Fitting with Errors on Both Axises

This Section introduces the procedures which aims at �tting c in Equation 10.

According to Press (1992), below performs the �tting:

Consider a straight-line model

y(x) = a + bx , (B1)

and a merit function

χ2(a, b) ≡N∑

i=1

(yi − a− bxi)2

σ2yi

+ b2σ2xi

, (B2)

where σxiand σyi

are the x and y standard deviations for the ith point respectively.

Consider the variance

V ar(yi − a− bxi) = V ar(yi) + b2V ar(xi) = σ2yi

+ b2σ2xi

(B3)

and de�ne

σ2yi

+ b2σ2xi≡ 1/ωi . (B4)

We want to minimize equation with respect to a. ∂χ2

∂a= 0 is linear and yields

a =

[∑i

ωi(yi − bxi)

]/∑

i

ωi . (B5)

The error on the parameters a and b are de�ned from Taylor series expansion as

∆χ2 ≈ 1

2

[∂2χ2

∂a2(∆a)2 +

∂2χ2

∂b2(∆b)2

]+

∂2χ2

∂a∂b∆a∆b . (B6)

In this project, the constant c in the equation

log(f) = −0.4(mv + Xkv −∆) + 0.4c (B7)

is required to �nd. xi is set as (mvi+ Xkv − ∆), where ∆ is only for faint star applied

with aperture correction, yi is set as log(fi), b (i.e. slope) is set as -0.4, σyiis set as σlog(f i)

,

� 74 �

and σxiis set as 0.1 which is equal to the σmv from the SAO Star Catalog J2000 or the

corresponding error from the All-sky Compiled Catalogue of 2.5 Million Stars.

The relations between a and c are

c = 2.5a (B8)

and

c = 2.5 ·∑

i [ωi(yi − bxi)]∑i ωi

. (B9)

From equation B6 and since the parameter b is �xed, put σb = ∆b = 0 yields

∆χ2 ≈ 1

2

[∂2χ2

∂a2(∆a)2

]. (B10)

Set ∆χ2 = 1 and ∆a = σa and consider

χ2(a, b) ≡N∑

i=1

(yi − a− bxi)2

σ2yi

+ b2σ2xi

(B11)

⇒ ∂χ2

∂a= −2

N∑i=1

yi − a− bxi

σ2yi

+ b2σ2xi

(B12)

⇒ ∂2χ2

∂a2=

N∑i=1

2

σ2yi

+ b2σ2xi

, (B13)

so

1 =1

2

[N∑

i=1

2

σ2yi

+ b2σ2xi

(σa)2

]= (σa)

2N∑

i=1

ωi (B14)

⇒ σa = 1/

√√√√ N∑i=1

ωi (B15)

� 75 �

so

σc = 2.5/

√√√√ N∑i=1

ωi . (B16)

A C + + program named result.cpp (the source codes are included in Figures 26 to 28)

is written according to Equations B4, B9 and B16 to get the value of c and σc so as the

sky brightness msky, according to Equation 10, and its error σmsky, which will be discuss in

Appendix C.2.

C. Error Analysis

In order to get the error on the result of the sky brightness σmsky, a number of terms

should be considered. They include errors on the photon counts from reference stars σlog(f i),

errors on the stars' derived magnitudes σmvi(those were listed in Table 6 and obtained

directly from the related data bases), error on the airmass σX , error on the visual extinction

coe�cient σkv , error on the aperture correction factor σ∆, errors on the �tted parameters

σc (those were listed in Table 10 and calculated from the C + + linear �tting program),

errors on the FOV σF (those were listed in Tables 7 and 8 and calculated from the C plate

scale �tting program), and error on averaged �ux from the sky background σB. In this

project, σX , σkv and σ∆ were ignored and the treatments on σlog(f i), σB, and σmsky

were

being analysis as below.

C.1. Error on Photon Counts from Reference Stars

Counts from the reference stars were measured by IRAF and from Equation 3 the

actual �uxes f were obtained, assumed no error on G and QE. For each reference star, the

actual �uxes of it from individual 4 to 5 dark subtracted data frames were averaged and

� 76 �

took logarithm for base 10 (i.e. log10 fi)). The error of it is derived from the Equation A10

and set

z ≡ log10 f =ln f

ln 10(C1)

yield∂z

∂f=

∂

∂f

(ln f

ln 10

)=

1

ln 10· 1

f(C2)

and

(σz)2 =

(1

ln 10· 1

f

)·(σf

)2, (C3)

σlog(fi) =1

ln 10·σf

f. (C4)

Notice that σlog(f i)contains statistical errors, including Poisson and readout noises.

Similarly for the �uxes of the sky background B and the values of the aperture

correction factor ∆, they were averaged from individual 4 to 5 dark subtracted data frames.

The errors of the sky background σB was simply set as the standard deviation of the values

of B. σ∆ was ignored.

The dependent variable log(fi), which has the error σlog(f i), together with the

independent variables (mvi+ Xkv − ∆), which has the error σmv obtained from the star

catalogs, were �tted linearly according to log(f) = −0.4(mv +Xkv−∆)+0.4c by the C ++

Program.

C.2. Error on Sky Brightness

The error on the sky brightness σmskywas found according to Equation 10,

msky = −2.5 log BF

+ c which was bring transformed by

log10 x ≡ ln x

ln 10, (C5)

� 77 �

where x = B/F , yields

msky = − 2.5

ln 10· ln x + c . (C6)

From the Equation A10 yields

(σmsky)2 =

(−2.5

ln 10

)2 (σx

x

)2

+ (σc)2 , (C7)

where

(σx)2 =

(σB

F

)2

+

(B

F 2

)2

(σF )2 . (C8)

� 78 �

Table 13. Results on Sky Brightness obtained by Tam (2004) using the Pronto+MX916 at

the HKU Observation Site

date time % moon phase msky

(DD/MM/YY) (hhmm-hhmm) (altitude◦a ) (mag arcsec−2)

13/07/04 2155-2201 14(-44) 17.61± 0.26

14/07/04 2232-2239 8(-41) 17.17± 0.12

24/07/04 2107-2114 43(42) 16.81± 0.16

02/08/04 2105-2121 96(-6) 14.87± 0.15

03/08/04 2236-2242 89(5) 15.44± 0.16

aapproximate moon altitude at the middle of the data taking process

� 79 �

Fig. 24.� C Source Codes for Plate Scale Fitting

� 80 �

Fig. 25.� C Source Codes for Plate Scale Fitting (con't)

� 81 �

Fig. 26.� C + + Source Codes for Linear Fitting with Errors on Both Axises

� 82 �

Fig. 27.� C + + Source Codes for Linear Fitting with Errors on Both Axises (con't)

� 83 �

Fig. 28.� C + + Source Codes for Linear Fitting with Errors on Both Axises (con't)

� 84 �

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Benn C.R. & Ellison S.L. (1998). La Palma Technical Note n.115

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Garstang R.H., 2004, The Observatory, Vol. 124, p.14-21

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15th April, 2006, from http://resources.emb.gov.hk/gifted/GaN/index.htm

Kosai H. & Isobe S. (1998). Organized Observations of Night Sky Brightness in Japan. IAU

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University Press.

� 85 �

Richard B. (2000). The Handbook of Astronomical Image Processing, 1st edition. US:

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This manuscript was prepared with the AAS LATEX macros v5.2.