# Density of stars on celestial sphere

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The pattern of stars on the surface of the celestial sphere seems perceptually to have an universally looking structure. If you pick a region of the sky at random, for instance by using the (excellent) set of tools from the stellarium suite you get for example this:

There are bigger structures, like the milky way or more clustered areas, but on a smaller scale (like that you will see in binoculars with a field of view of the size of the moon), you will very often get this similar pattern. This looks to me very much like a self-similar fractal and I am curious to know if anybody knows more about it.

Assuming a given density of stars in this patch of the universe, and omitting inhomogeneities at first, can we derive a mathematical expression for describing the density of stars in a given patch of the sky ?

As a bonus, is there a map estimating this density for different areas of the celestial sphere? Clearly, the milky way is more crowded and would perhaps have more structure…

If stars are uniformly distributed with density $$ho$$ per cubic parsec, out to a distance $$d$$ parsecs, then that volume contains $$4pi ho d^3/3$$ stars spread over the whole sky.

The angular size of the whole sky is 41,252.96125 square degrees, so you would divide by that number to estimate the stellar density in stars per square degree.

This assumes that you can see all the stars. In practice you cannot, because of dust extinction and because stars become fainter the further away they are. You can account for these in any calculation but the details depend on the luminosity function of the stars, the distribution of dust and the instrumental properties of the telescope/detector used to take the picture.

If we consider a 3D Poisson distribution over some 3D volume $$V$$, the rate/density of the orthogonal projection onto a plane will at each point will be the 3D rare $$lambda$$ multiplied by integrated length along the projection that is inside $$V$$. So a unit cube will produce a square with the same rate if projected along one of its axes (and a hexagon with uneven rate along other directions). If the rate is spatially varying $$lambda(x,y,z)$$ the projection will just be $$lambda(x,y)=int lambda(x,y,z) dz$$.

Note that an infinite space with finite $$lambda$$ will produce an infinite point density. Real skies (1) have uneven rates so that most rays stop finding new stars at the edge of the galaxy and remote galaxies are sparse enough that they produce a finite projection, (2) the finite age of the universe allows setting an upper distance limit, and (3) you are actually interested in stars of a certain magnitude range, and remote stars will be dimmed by distance. That means that there is a distance fading factor $$f(z)$$ multiplying the rate, $$lambda(x,y)=int lambda(x,y,z) f(z) dz$$.

Building on the answers from @anders-sandberg and @ProfRob I think I get an answer for my own question. I am most certainly reinventing the wheel, but it has been fun. Please comment or edit if you know any pointer on a similar derivation.

As a (very) rough approximation, one may assume that in a given line of sight, there is locally a uniform, independent and identically distributed density of stars. This can be modeled for instance by a 3D Poisson distribution. A 3D Poisson distribution consists in drawing random positions in space independently for the 3 axis and independently for the different points.

As a consequence, there are stars in all directions, but they have different luminances due to their distance. It is easy to derive the probability distribution of the distance for such a model and by a change of variable, one can find that of luminance as :

$$ext{Pr}(L) propto frac 1 {d^{frac 5 2}}$$

This is what you get with a simple simulation by placing stars at random positions in the universe but also if you plot the distribution of the luminance for stars drawn from a catalog of more than 100k stars (left panel):

In addition, it is also a way to build a very simple model for generating images of the night sky (right panel).

The full details of my musings are available in this blog post.

PS: the other part of my question (can such a model be used to fit the density of stars in different areas of the sky?) will be for another time…

PS2: There is a relation with Olbers' paradox which I discuss in the post…

## Spectral flux density

The flux from an unresolved (point-like) object may be considered to be a parallel beam of light or a plane wave originating at "infinity". It impinges on the telescope with a given amount of energy deposited per second, per square meter, and per unit frequency interval at frequency v (e.g., in the interval v - 0.5 Hz to v + 0.5 Hz). This is known as the spectral flux density,

S(v) = Spectral flux density (W m-2 Hz-1) (8.1)

but it could be more properly called the spectral energy flux density to distinguish it from a photon flux density (photons m-2 Hz-1). In fact it is often called simply the "flux density". Here we reserve that term for another related use.

The definition serves to standardize the values of spectral flux density reported in the literature from telescopes with different areas and frequency bands (band-widths). The standard quantity is simply the observed power divided by the area of the telescope and by the bandwidth in Hz. Thus observations with different equipment of the same source should yield approximately the same value for S.

The motivation for this normalization is similar to that for reporting an automobile speed as distance per unit time, e.g., 100 km/h, rather than in terms of the actual elapsed time of the journey, 20 km/12 min. The standard reference time makes it much easier to compare the average speeds from journeys of different durations.

The actual energy received by the telescope per second (power P in watts), in a narrow frequency band Av, is the product of the spectral flux density (averaged over the band Av), the effective area Aeff of the telescope, and the bandwidth Av,

For example, a relatively bright celestial radio source might yield a spectral flux density S(v) at the earth of

S(v) = 1.0 x 10-26 Wm-2Hz-1 = 1.0 Jy (jansky) (8.3)

at frequency v = 100 MHz. This particular spectral flux density is known as 1.0 jansky Carl Jansky was the discoverer of radio radiation from the (MW) Galaxy.

Now, suppose that this signal is detected with a perfect antenna of diameter 16 m (Aeff

200 m2) that is tuned to v = 100 MHz with a narrow bandwidth Av = 104 Hz. This means that the detection system accepts radiation in the frequency band 104 Hz wide at v = 100 MHz, i.e., 99 995 000 Hz to 100 005 000 Hz. Further assume that S(v) is constant, or nearly so, across the band Av so that S(v)

S(v )av. The actual power received by the antenna would then be, substituting into (2),

= 1 x 10-26 x 200 x 104 = 2 x 10-20 W (8.4)

This is a very small amount of energy it would take 0.5 x 1020 s to accumulate the energy of one joule, enough to light a 1 W bulb for 1 s. This time corresponds to about 1013 years or

1000 times the age of the universe! The detection of such small (and even smaller) amounts of power requires high-sensitivity detectors. Do not be misled by such tiny power levels they are associated with tremendous total power outputs from the source, as we demonstrate below.

The calculation above was made under the assumption that the spectral flux density S(v) is constant over the bandwidth of frequencies accepted by the antenna. For a bandwidth narrow compared to the measured frequency, this is often a reasonable assumption. However, it is possible that much of the energy lies in a spectral line, an enhancement of flux in a very narrow, e.g. 10 Hz, frequency band. In this case, the spectral flux density could be close to zero for a large part of the 104 Hz band. A proper calculation of the power received by the antenna for a variable S(v) requires that the product S(v) dv A be integrated (summed) over the frequency band,

J vi where Aeff is the effective area of the telescope, taking into account inefficiencies that dissipate some of the incident energy, and where the integration is over the bandwidth of detected frequencies. In practical cases, the effective area is a function of the frequency Aeff(v), so it too would go inside the integral.

The spectral flux density is properly a vector S, where S = |S|, because the flux at any point in space must have a direction it is a "flow". The direction of the flux may be determined by immersing a test surface of fixed size into the flow and then rotating the surface to various orientations. When the flux through the surface reaches its maximum value, the surface normal lies along the flow lines. This is analogous to the vector current flux density J (A m-2) in electromagnetic theory. Do not confuse the quantity S (W m-2 Hz-1) used in this text with that used in electromagnetic theory for the Poynting vector (W/m2).

The total power flowing across unit area is called the flux density F (W/m2). It is obtained by integrating the spectral flux density S(v) over the frequency band of interest, p v2

F = S(v) dv (W/m2 flux density) (8.6)

Again, this quantity is properly a vector since it is a flow that has direction a surface immersed in the flow can be oriented to give the direction of flow as above. For our purposes, we usually use the scalar quantity F = | F"|. In electromagnetic theory, this vector is the quantity known as the Poynting vector see (7.13).

The flux F can be written in terms of the average over frequency of the spectral flux density S by multiplying and dividing the right side of (6) by Av = v2 - v1 and recalling the definition of an average, Sav = /S dv/Av. Thus, F = Sav Av.

### Luminosity

The luminosity L of a source is, in its usual meaning, the total power output (W) summed over all frequencies. In practice, one usually must specify the band of frequencies (of radiation) that are being measured, e.g., the visual V band, the entire optical band, or the 1-10 keV x-ray band. Normal stars like the sun emit only a tiny fraction of their power in the radio and x ray, and these emissions were long unknown, so these bands were ignored in traditional astronomy. The luminosity over the entire optical band including the spillover into the adjacent infrared and ultraviolet bands is called the bolometric luminosity it is this which is usually given the symbol L where L = L boi.

If the distance r to a source is known, an estimate of the luminosity in a specified band Av is obtained by multiplying the flux density F(W/m2 in the band Av) by the area of a sphere centered on the source with its surface passing through the earth (antenna) as shown in Fig. 1,

LAv = 4nr2FAv (W isotropic emission) (8.7)

= 4nr 2 Sav Av where the (unconventional) subscript Av reminds one that the luminosity is restricted to the chosen band Av.

An assumption implicitly adopted in (7) is that the emission from the source is isotropic, that is, the energy is radiated equally into all directions. Only in this case does our antenna get its expected share of the total radiation that leads to the factor 4nr2 in (7). The assumption of isotropy is a common one because an antenna on

Figure 8.1. A point-like source at distance r from an antenna radiates equally in all directions. The luminosity of the source in a given frequency band is the flux density (W/m2) detected in that band multiplied by 4nr2.

the earth can sample only one emission direction, and isotropy is often the most reasonable guess. Some objects, e.g., pulsars, active galactic nuclei and gamma-ray bursts, emit beams of radiation that are demonstrably non-isotropic in these cases, (7) is clearly incorrect.

Consider the luminosity of a hypothetical radio source radiating isotropically with a constant spectral flux density at the earth of S = 1.0 Jy over the 50-150 MHz band. If it is at the center of the Galaxy, at a distance of

25 000 LY (2.4 x 1020 m), its luminosity from 50 to 150 MHz (Av = 108 Hz) would be

This is a lot of watts, equivalent to almost 10 billion trillion 100-watt light bulbs! It is about 1/600 of the sun's luminosity of 4 x 1026 W. The quasar 3C273 at a distance of 2.1 MLY with spectral flux densities ranging from 100 to 50 Jy over the range 100 to 1000 MHz, has a radio luminosity of

1036 W. Inclusion of optical, x-ray and gamma-ray radiation raises this to more than 1038 W, or

1012 L Q (solar luminosities). This would be in error, probably an overestimate, if the radiation is beamed.

Over a wide bandwidth, such as a factor of two change in frequency, the spectral flux density S(v) is likely to change substantially in this case one must integrate over frequency to obtain the luminosity,

L = 1.0 x 10-26 x 108 x 4n x (2.4 x 1020)2 = 7 x 1023 W (8.8)

+ L = 4nrFAv = 4nr2 S(v) dv (W isotropic emission) (8.9)

One can often estimate roughly the luminosity without integrating by substituting for the integral the product of the bandwidth Av and a typical or average value of the spectral flux density Sav in that band. If the functional form of S(v) is simple, formal integration is quite straightforward.

### Fluence

Some astronomical sources emit occasional isolated bursts of radiation which might last for 10-100 seconds. It is convenient to define a quantity that gives the flux of energy integrated over the duration of the burst. This is called the fluence S (J m-2), or more precisely, the energy fluence, which is defined as the time integral of the flux density, ft2 2 S = & dt (J m-2 fluence) (8.10)

Again this quantity is properly a vector S = S |. A spectral fluence (J m-2 Hz-1) could also be defined if desired.

Note that the quantities above are all derived from an integrations of S(v) over one or more of the variables: area, frequency, and time.

## Astronomy Methods

Astronomy Methods is an introduction to the basic practical tools, methods and phenomena that underlie quantitative astronomy. Taking a technical approach, the author covers a rich diversity of topics across all branches of astronomy, from radio to gamma-ray wavelengths. Topics include the quantitative aspects of the electromagnetic spectrum, atmospheric and interstellar absorption, telescopes in all wavebands, interferometry, adaptive optics, the transport of radiation through matter to form spectral lines, and neutrino and gravitational-wave astronomy. Clear, systematic presentations of the topics are accompanied by diagrams and problem sets. Written for undergraduates and graduate students, this book contains a wealth of information that is required for the practice and study of quantitative and analytical astronomy and astrophysics.

Hale Bradt is Professor Emeritus of Physics at the Massachusetts Institute of Technology. Over his forty years on the faculty, he carried out research in cosmic ray physics and x-ray astronomy, and taught courses in Physics and Astrophysics. Bradt founded the MIT sounding rocket program in x-ray astronomy, and was a senior or principal investigator on three NASA missions for x-ray astronomy. He was awarded the NASA Exceptional Science Medal for his contributions to HEAO-1 (High Energy Astronomical Observatory 1), the 1990 Buechner Teaching Prize of the MIT Physics Department, and shared the 1999 Bruno Rossi prize of the American Astronomical Society for his contributions to the RXTE (Rossi X-ray Timing Explorer) program.

Solutions manual available for instructors by emailing [email protected]

Views of the entire sky at six wavelengths in galactic coordinates. The equator of the Milky Way system is the central horizontal axis and the galactic center direction is at the center. Except for the x-ray sky, the colors represent intensity with the greatest intensities lying along the equator. In all cases, the radiation shows an association with the galactic equator and/or the general direction of the galactic center. In some, extragalactic sources distributed more uniformly are evident. The captions below are listed in frequency order (low to high). The maps are also in frequency order as follows: top to bottom on the back cover followed on the front cover by top inset, background map, lower inset.

Radio sky at 408 Hz exhibiting a diffuse glow of synchrotron radiation from the entire sky. High energy electrons spiraling in the magnetic fields of the Galaxy emit this radiation. Note the North Polar Spur projecting above the equator to left of center. [From three observatories: Jodrell Bank, MPIfR, and Parkes. Glyn Haslam et al., MPIfR, SkyView]

Radio emission at 1420 MHz, the spin-flip (hyperfine) transition in the ground state of hydrogen, which shows the locations of clouds of neutral hydrogen gas. The gas is heavily concentrated in the galactic plane and shows pronounced filamentary structure off the plane. [J. Dickey (UMn), F. Lockman (NRAO), SkyView ARAA 28, 235 (1990)]

Far-infrared (60-240 |im) sky from the COBE satellite showing primarily emission from small grains of graphite and silicates ("dust") in the interstellar medium of the Galaxy. The faint large S-shaped curve (on its side) is emission from dust and rocks in the solar system. Reflection of solar light from this material gives rise to the zodiacal light at optical wavelengths. [E. L. Wright (UCLA), COBE, DIRBE, NASA]

Optical sky from a mosaic of 51 wide angle photographs showing mostly stars in the (Milky Way) Galaxy with significant extinction by dust along the galactic plane. Galaxies are visible at higher galactic latitudes, the most prominent being the two nearby Magellanic Clouds (lower right). [(©Axel Mellinger]

X-ray sky at 1-20 keV from the A1 experiment on the HEAO-1 satellite showing 842 discrete sources. The circle size represents intensity of the source and the color represents the type of object. The most intense sources shown (green, larger, circles) represent accreting binary systems containing a compact star, either a white dwarf, neutron star, or a black hole. Other objects are supernova remnants (blue), clusters of galaxies (pink), active galactic nuclei (orange), and stellar coronae (white) [Kent Wood, NRL see ApJ Suppl. 56, 507 (1984)]

Gamma-ray sky above 100 MeV from the EGRET experiment on the Compton Gamma Ray Observatory. The diffuse glow from the galactic equator is due to the collisions of cosmic ray protons with the atoms of gas clouds the nuclear reactions produce the detected gamma rays. Discrete sources include pulsars and jets from distant active galaxies ("blazars"). [The EGRET team, NASA, CGRO]

## Density of stars on celestial sphere - Astronomy

The School of Astronomy and Space Science of Nanjing University was established in March 2011, and its predecessor, the Department of Astronomy, was founded in 1952. It earns the longest history and a high reputation of all the astronomy departments in China. The school has cultivated many astronomers who are currently active in academic circles.

Today the school has 2 undergraduate programs, respectively under 2 departments, the Department of Astronomy and the Department of Space Science & Technology. It also consists of several laboratories, such as Key Laboratory of Modern Astronomy and Astrophysics, named by the Ministry of Education, Central Laboratory for Teaching, Solar Tower Laboratory, Center for Nonlinear Sciences, and Planetary Science and Deep Space Exploration Laboratory. Furthermore, the school owns the national first-level key discipline of astronomy, including two national second-level key disciplines: Astrophysics and Astrometry & Celestial Mechanics.

The school’s current research activities cover high-energy astrophysics, solar physics, galaxies and cosmology, extra-solar planets, aerospace dynamics, astrometry and space science.

The School has a strong faculty consisting of both distinguished senior scholars and a large number of young academic leaders. There are 44 faculty members in total, including 20 professors, with 4 academicians of the Chinese Academy of Science, 4 Cheung Kong Scholars, 1 Chief Scientist for the National 973 Basic Research Program, 7 National Science Fund for Distinguished Young Scholars Winners, 7 China Cross-Century Talent Raising Program Winners, and 4 Youth Qianren Professors. Sponsored by the National Science Foundation of China and National Key Fundamental Research Programs, the school has obtained fruitful academic achievements and won many national/provincial awards.

In order to foster a new collaborative mode between universities and observatories, in 2010, Nanjing University, Purple Mountain Observatory and Nanjing Institute of Astronomical Optics & Technology signed an agreement aimed at jointly establishing the Center for Astronomy and Space Science on the Xianlin Campus of Nanjing University.

Moreover, after a series of discussions and consultations, Nanjing University, Peking University, National Astronomical Observatories, Purple Mountain Observatory and University of Science & Technology of China co-founded the Collaborative Innovation Center of Modern Astronomy and Space Exploration in December 2012.

The school also explores the channels of cooperation with overseas partners to push forward the process of internationalization and has established friendly and cooperative relationship with over 20 institutes of higher education in the USA, UK, Australia, Japan and so on. Its partners include Harvard University, California Institute of Technology, Massachusetts Institute of Technology, Kyoto University, University of California Santa Cruz, University of California Los Angeles, University of Tokyo, University of Sydney, and Paris Observatory.

In August 2014, the school moved into a new building which covers 12,000 square meters. The new building well meets the needs of research, experiments, teaching and academic activities, and will play a significant role in the school’s development in the decades to come.

### History

In 1952, the Department of Astronomy, Nanjing University, was established, integrating the Department of Astronomy of Sun Yat-sen University and the Astronomy & Arithmetic Department of Qilu University. The director was Professor Zhao Que-min.

In 1955, the Department of Astronomy and the Department of Mathematics, Nanjing University, merged into the new Department of Mathematics & Astronomy.

In 1962, the Department of Astronomy was re-established and was headed by professor Dai Wen-sai.

From 1972 to 1976, the department enrolled 183 students. In 1977, the National College Entrance Examination was resumed, and the department began to recruit graduate students since 1978 and doctoral students since 1987.

In 1993, the Department of Astronomy was granted the title “National Training Bases of Astronomy Talents” and began to be funded by the National Natural Science Foundation of China.

In March 2011, the School of Astronomy and Space Science was established.

### Discipline Construction

#### High Energy Astrophysics Group

Focus on supernovae and supernova remnants, Gamma-ray bursts and GRB cosmology, compact stars, high-energy cosmic rays and other relevant astronomical phenomena. The faculty plans to involve the most violent outbreaks in outer space, which will be quite significant for the study of evolution of stars, galaxies and the universe.

Prof. Dai Zigao, Prof. Li Xiangdong, Prof. Huang Yongfeng, Prof. Wang Xiangyu, Prof. Chen Yang, Dr. Wang Fayin, Dr. Jiang Bing, Dr. Xu Xiaojie XU, Dr. Zhou Ping, Dr. Shao Yong

Self-organized criticality in X-ray flares of gamma-ray-burst afterglows, F.Y., Wang and Z.G., Dai, 2013, Nature Physics, 9, 465

Discovery of the transient magnetar 3XMM J185246.6+003317 near supernova remnant Kesteven 79 with XMM-Newton, P., Zhou et al. 2014, ApJL, 781, L16.

#### Solar Physics Group

The research addresses the origin, structure and evolution of solar activities, especially the physical mechanisms of the most energetic solar eruptions such as solar flares and coronal mass ejections. The theoretical part includes MHD and radiative hydrodynamic simulations, and the observational part covers a wide range from radio to hard X-ray.

Prof. Fang Cheng, Prof. Ding Mingde, Prof. Chen Pengfei, Dr. Dai Yu, Dr. Li Chuan, Dr. Cheng Xin, Dr. Guo Yang, Dr. Hao Qi

SDO/AIA 131 A images showing the early eruption of magnetic flux rope.

X., Cheng et al. 2011, ApJL, 732, L25 2012, ApJ, 745, L5 2013, ApJ, 763, 43 ApJL, 769, L25

#### Galaxies and Cosmology Group

The research focuses on the galaxy-center black hole activities, starburst galaxies and active galactic nucleus, chaos in the galaxy and cluster dynamics, stellar structure and galactic-disk thickness of neighbor galaxies. The research uses observational data from large ground and space telescopes and theoretical models to establish the physical processes that is, triggering, evolution and inter-relation of neighbor galaxies stellar activities and nuclear activities.

Prof. Gu Qiusheng, Prof. Shi Yong, Prof. Qiu Keping, Prof. Li Zhiyuan, Prof. Luo Bin, Dr. Luo Xinlian, Dr. Chen Yanmei, Dr. Wang Tao

Inefficient star formation in extremely metal poor galaxies, Shi et al. 2014, Nature, 514, 335

#### Celestial Mechanics and Planetary Dynamics Group

The team focuses research on the formation and evolution of exo-planetary systems and dynamics of small objects in the Solar system. It studies formation mechanism and dynamical evolution of the solar system and extrasolar planetary systems, nonlinear Hamiltonian dynamics theory and its applications in celestial mechanics, orbit and motion stability of small solar-system bodies and satellites and its application in the field of aerospace.

Prof. Sun Yisui, Prof. Zhou Jilin, Prof. Zhou Liyong, Dr. Xie Jiwei, Dr. Li Jian, Dr. Zhang Hui, Dr. Liu Huigen

The team confirmed 54 Kepler exoplanet candidates by TTV(right), which is about half of the No. confirmed by TTV before 2014.

J.W., Xie, 2013, ApJS, 208, 22 J.W., Xie, 2014, ApJS, 210, 25Yang et al. 2013, ApJ, 778, 110 S.H., Wang et al. 2014, ApJS, 211, 26.

Planetary transit candidates in the CSTAR field: Analysis of the 2008 data, S.H., Wang et al. 2014, ApJS, 211, 26.

#### Astronomical Reference System and Astrometry Group

The research focuses on the astronomical reference system. Recently the team reconsidered the definition of the Galactic coordinate system. The team also studies relativistic astrometry and the Galactic dynamics and kinematics

Prof. Zhu Zi, Dr. Zhang Hong, Dr. Wan Xiaosheng, Dr. Liu Jiacheng, Dr. Xie Yi

The density distribution of 2MASS point source on the celestial sphere where the Galactic belt can be clearly seen.

J.C., Liu et al. 2011, A&A, 516, A16 J.C., Liu et al. 2011, A&A, 536, A102

#### Space Weather

The research focuses on solar activity mechanisms, solar activity monitoring and forecasting, and causes of disastrous space weather.

Prof. Fang Cheng, Prof. Chen Pengfei, Dr. Dai Yu, Dr. Li Chuan, Dr. Hao Qi

Extreme ultraviolet imaging of three-dimensional magnetic reconnection in a solar eruption, J.Q., Sun et al. 2015,

Nature Com. , 6, 7598.

#### Spacecraft Orbit Design and Control

Mainly research is dynamics of solar system main-belt asteroids, small near-earth bodies and methods of artificial earth satellite, interplanetary probes, orbital mechanics, etc.

Prof. Bo XU, Dr. Xi-Yun HOU, Dr. Jing-Shi TANG, Dr. Han-Lun LEI

Space Science Laboratories

### Facility

The Optical & Near-Infrared Solar Eruption Tracer (ONSET), located at Fuxian Lake, Yunnan Province.

Construction of the Time Domain Survey Telescope (TDST)

TDST focuses on searching of planets around bright star (Vmag<12) near North ecliptic Pole. It will provide the light curves of these bright stars with a high precision. Utilizing the light curves of G, K, F stars, planet candidates with period 1-5 year can be detected.

TDST will give star catalogues around North Ecliptic Pole before TESS, and is helpful to TESS mission. Additionally, the long period planets detected by TDST will be an important complementary for TESS and Plato. Planets around dwarfs are also expected. All these planets are suitable to be followed up by worldwide telescopes.

## Definitions

If you want to complete some additional reading beyond what is in our Lesson 1 pages, I recommend:

In this lesson, we will be using some vocabulary that may be either unfamiliar or may be used differently, in an astronomical context, from your usual usage. Normally, I advocate for discussing vocabulary in the context of a lesson, instead of presenting it like this to begin the lesson. In our case, though, I'm going to break my own rule so that we can start discussing the sky immediately and make sure that we agree on the meaning of these terms. The vocabulary you will encounter in this lesson includes:

• Altitude
• Azimuth
• Meridian (and transit of the meridian)
• Horizon
• Zenith

All of these terms are used to describe the location or behavior of objects in the sky. For example, you can refer to the altitude of the Sun. Or, when the Sun passes from one side of the meridian to the other, you can talk about the Sun "transiting the meridian." These terms and their meanings are illustrated using the following two diagrams. Read over the list of terms and definitions in the list and/or mouse over the terms in the image to view their definitions.

## How Ancient Star Maps Gave Rise to Modern Astronomy

Scientists have incredibly advanced tools to look at the stars today, but in the era before light pollution, star-gazing was much easier and simpler for the average person—just step outside at night. Pretty early on, and in a variety of cultures, people realized that they could chart the stars and their movements for navigation. The Greek constellations, which were tied to their myths, illustrate how this information moved through time. But humanity’s early star maps are much more than ancient artifacts—they became part of our history and culture, and continue to inform modern science to a surprising degree.

The first complete star map that still exists today was made in 650 A.D. in Dunhuang, western China, a city on the Silk Road. There, a star atlas was meticulously drawn onto a piece of paper, then filed away with other documents in a temple alcove. The space was sealed off at some point, and wasn’t re-discovered until 1907, when a Taoist monk, the self-appointed guardian of the temple, accidentally crashed through a wall to find the hidden cache, which contained sculptures, piles of documents, and the now-famous star map.

“[The map] was most likely made by someone highly educated like a scholar or a court astronomer,” cosmologist Dr. Khee-Gan Lee , a NASA Hubble Fellow at the Lawrence Berkeley National Lab, tells Gizmodo. “This was definitely not amateur work, but was professional for the time.”

Lee is an expert on ancient star maps who has given several presentations on them at U.C. Berkeley over the past few months. The history of star maps matters to him personally, because even today, maps of the cosmos help guide his research.

“Mapping out what we can observe. is one way of inferring some of the fundamental parameters of the universe,” Lee said. A good example of how this works is the recent Dark Energy Survey, which used information about the shapes and distribution of galaxies to “infer the density of gravitational matter in the Universe—one of the fundamental parameters of the Universe,” Lee said. That Survey’s results were also a test of Einstein’s theory of general relativity.

Following the Dunhuang map, there wasn’t another more complete star map for hundreds of years (at least, none that have been discovered yet). All civilizations were limited by technology—they could record what was observed by the naked eye, like the brightest stars and planets. For almost a thousand years, that limitation halted a further understanding of the cosmos. To get more detailed information, humans needed a better eye.

When the first telescopes were developed in The Netherlands in the early 1600s, amateurs and experts alike were excited to try them, even though they only had weak magnifications of 3X or 4X. From Galileo’s early models, to Newton’s, to the 1500-foot-long model designed by Johannes Hevelius, astronomers of the 16th and 17th centuries were limited by the quality of the glass needed to make more powerful telescopes. Not much more could be learned about the stars until higher magnifications were achieved.

In late 1770s, German/Czech/Jewish musician William Herschel turned to designing telescopes. After some failures, he developed a powerful enough ‘scope to make brand-new observations, and immediately began a systematic search and recording of the night sky above Bath, England. In 1781, he was able to discern that Uranus wasn’t another star, but a planet. Following that discovery, he was appointed Court Astronomer by the British king, George III, and paid to study the stars full time. His sister Caroline Herschel, who started her career in astronomy by recording her brother’s observations, soon moved on to making her own when she got her own telescope. Her observations on comets became widely published, and she was also employed by the Crown, the first woman in British history to be recognized in this way.

Putting their observations together, William and Caroline Herschel published On the Construction of the Heavens in 1785, which painted a basic picture of The Milky Way. “The Herschels were the first people to systematically chart the heavens. “From my perspective as a modern cosmologist, it’s the earliest echo of what I do—charting out and analyzing the positions of objects in the sky, then inferring the properties of the universe through the process,” said Lee.

“That the Milky Way is a most extensive stratum of stars of various sizes admits no longer of the least doubt, and that our Sun is actually one of the heavenly bodies belonging to it is evident. I have now viewed and gauged this shining zone in almost every direction, and find it composed of stars whose number, by the account of these gauges, constantly increases and decreases in proportion to its apparent brightness to the naked eye.” -Herschel

In the 1800s, humanity’s understanding of the universe exploded thanks to several key advances, which improved star mapping by revealing the distances between and relative movement of stars (not just their fixed location at a given time of observation). Going from knowing where a star is to knowing how it behaves over time is the cosmological difference between a two-dimensional representation of the Universe and a three-dimensional one.

The first advance came in 1838, when the Astronomical Distance Scale was established, using the breakthrough parallax method developed by Friedrich Bessel—this meant that distances between stars and other objects could be measured much more accurately.

Then, in the 1850s and 1860s, the development of astronomical spectroscopy (analyzing starlight by wavelength) allowed astronomers to access even more information. Lee calls it the “key to astrophysics,” since now observers could learn about the spin, magnetic fields, composition, and relative motion of stars. Together, the distance scale and spectroscopy gave scientists the ability to make a star map with much greater detail and three-dimensional perspective: “We were no longer confined to plotting two-dimensional positions on the ‘celestial sphere,’” says Lee.

In the late 1800s, astrophotography advanced the field yet again. No longer were humans reliant on what could be observed with the eye and a telescope: astrophotography can reveal nebulae, galaxies, and dimmer stars using a longer exposure time for the film in a camera. Direct recordings were now possible: “. where before we had to manually write down the positions of objects and sketch their appearance by hand,” said Lee.

In 1920, the National Academy of Sciences sponsored a “Great Debate” about whether the sun was at the outskirts of the Milky Way or toward the center (and how spiral nebulae related to our galaxy). Harlow Shapley, a Princeton astronomer, argued that the Milky Way was the extent of the universe, and the sun was in the outer arms of it Heber Curtis, the director of the Allegheny Observatory, disagreed, presenting evidence that there were many galaxies, and the sun was at the center of the Milky Way. “It was such a huge question at the heart of where we are in the universe, and nature of the universe itself,” Lee said. Though it seems odd to us that people were arguing about whether the sun was at the center of our galaxy or not less than a hundred years ago, Lee explained, “It was an honest debate in terms of what they knew and there were good reasons for either camp to argue for what they did—at that point it was such a universal question.”

Just a few years later, in 1923, American Cosmologist Edwin Hubble calculated the location of the Andromeda galaxy using astrophotography . “Hubble could not have discovered the Cepheid variable ‘standard candle’ stars in the Andromeda galaxy if he wasn’t able to photograph it and record the exact position and brightness of the stars in that galaxy at different times,” says Lee. This measurement allowed him to prove that Andromeda was outside our galaxy and settled the question—there were more galaxies than our own (probably trillions, we know now) as Curtis has argued. But Shapely was correct about the placement of the sun in the outer arms of the Milky Way. The photographic plates from Hubble’s astrophotography make a whole new kind of map—one made from photographs representing a three-dimensional universe.

Shortly after that, advances in photography and electronics set humanity up to double our knowledge of the known universe—and expand ideas of the universe itself. “Electronic detectors are a critical part of what’s been possible in modern times, providing the quantum leap to get to where we are now” Lee said. In the 1940s and 1950s, scientists sat inside giant telescopes taking photographic plates each night of star movements—it took years to gather a data set. Electronic detectors are much, much faster.

Lee cites the “CfA stickman” map as a good example of the new type of star map (or now, galaxy map) that came out of the mid-late 20th century data from electronic detectors. Published in 1986, by Valerie de Lapparent, Margaret Gellerit, and John Huschra, it was the first real evidence for the cosmic web. (It got the “stickman” moniker from the anthropomorphic cluster of stars at its center.) It includes thousands of galaxies and was the precursor to other important maps like the Great Wall, from 1989.

Now, cosmologists like Lee can collect and analyze data sets that scientists 75 years ago could only dream about. Still, Lee sees his work as connected to the people in this history—he says his work is built on their foundations, even though he’s looking at places that are 10 billion light years away, in the Cosmos field targeted by the Hubble telescope. “I’m old-fashioned in that I actually do make maps and stare at them,” Lee said. “I see what I’m doing is giving this extremely distant and remote, early part of the Universe a sense of place by mapping it.”

A geologist in her first career, Starre is now freelance science writer—but she still picks up rocks wherever she goes.

## 219 Million Stars Create the Most Detailed Catalogue of our Milky Way Yet

On the darkest of nights, thousands of stars are sprinkled across the celestial sphere above us. Or, to be exact, there are 9,096 stars observable across the entire sky. Divide that number in half, and there are 4,548 stars (give or take a few) visible from horizon to horizon.

But this number excludes the glowing band stretching across the night sky, the Milky Way. It’s the disk of our own galaxy, a system stretching 100,000 light-years across. The naked eye is unable to distinguish individual specks of light, but the Isaac Newton Telescope (INT) on La Palma in the Canary Islands has recently charted 219 million separate stars in this disk alone.

For the last 10 years a team of astronomers led by Geert Barentsen from the University of Hertfordshire has been collecting and compiling light from all stars brighter than 20 th magnitude, or one million times fainter than the human eye can see (at 6 th magnitude).

They created a beautiful density map of the Milky Way, giving them new insight into the structure of this vast system. The black, fog-like regions are galactic dust, which blocks more distant light. The brighter regions are densely packed stars.

The INT took measurements in two broad filters, which captured light at the red end of the visible spectrum, and in one narrow filter, which captured light only from the hydrogen emission line, H-alpha. The inclusion of H-alpha enables exquisite mapping of nebulae, glowing clouds of hydrogen gas.

The production of the catalogue is an example of modern astronomy’s exploitation of “big data.” But it would also grace the walls of any art studio.

## Astrochemistry

Spanning across the disciplines like chemistry, chemical biology, planetary sciences astrochemistry is one of the most prominent branches of astronomy. The field involves experimental as well as computational laboratory studies for generating data regarding interpretation or explanation of multiple astronomical observations which provide data input for models. These data theories help in the formation or evolution of small or large particles in varied astrophysical. The Astrochemists use satellites, telescopes along with other space vehicles to collect the spectroscopic data. They also put in use the computer visualizations that help them in elucidating the collected observations in terms of physical as well as chemical principles.

## Density of stars on celestial sphere - Astronomy

Our SC001 star map is similar to these Mercator projections of the globe. The celestial equator divides the map in half top-to-bottom: north hemisphere at the top and south hemisphere at the bottom) with right ascensions running from 0 h at the map's center to 12 h at the left edge. The run of RA picks up at the right edge again at 12 h , and continues to 23 h and finally back to 0 h =24 h at the center. Note that RA increases to the left, which is eastward. Yes, eastward is to the left, not right as on most maps of the globe. The reason is one of perspective. World maps are made as if God was looking down from space on the outside surface of the globe. Sky maps are made looking out from Earth toward the inside surface of the celestial sphere. Indeed if you think about facing south, and pointing the south-part (bottom) of the SC001 toward the south celestial pole, and the north-part (top) of the SC002 toward the north celestial pole, the left side of the map is toward the east. Declination ranges from -60° at the bottom to +60° at the top.

The below drawing shows how we can project the inside surface of the celestial sphere onto the inside surface of a cylinder, which we can then cut into a large rectangle. The red and green stars are on the far side of the celestial sphere, in the northern hemisphere they end up above the blue celestial equator.