star - How to interpret extreme ultraviolet/ x-ray data in the literature?

The EUVE catalog gives you a count-rate in a certain EUV band. To convert this into a flux, you need a flux conversion factor to go from counts per second to energy flux at the Earth per second. This conversion factor, also often known as an "ECF", depends on the intrinsic spectrum of the source and also how much absorption (known as the hydrogen column density) there is between Earth and the source. So there is no one answer that can be given.
I
Your best port of call is the PIMMS flux conversion tool, which has an EUVE module and can do these flux conversions for you if you know something about the spectrum and the absorption. I'd try it for you but I couldn't immediately see how to do it for EUVE, though it claims the information is there...

observation - Calculate time when star is above altitude 30°

To find the best observation time for an object, I'd like to calculate the time when it is 30° or more above the horizon. Local Sideral Time would be sufficient.

To include that in my program, I need the formula.

Example:
On June 4th, Jupiter has the coordinates
RA= 9h 19m 28.0s
Dekl= 16° 32' 0"

It rises at 10:32 and sets at 00:05.

After rise, when is it at altitude 30°, and after transit, when is it at altitude 30° again ?

---

I found this formula at http://www.stjarnhimlen.se/comp/riset.html. Although it's for the sun, it seems to be what I'm looking for.

$$cos (text{LHA}) = frac{sin (text{h}) - sin (text{lat}) times sin (text{Decl})}{cos (text{lat}) times cos (text{Decl})}$$

Applied to the sample assuming a latitude of 45° I get.

Is this the correct approach?

observation - Does CIBER Experiment from Caltech suggest that there can be lots of stars which are not in any galaxy?

Does that suggest that about a half of the stars in the observable universe could not belong to any galaxy?

Not really. A key sentence in the article is "The best interpretation is that we are seeing light from stars outside of galaxies but in the same dark matter halo". So the stars are still within the dark matter halo of a galaxy, but are outside the boundary of the galaxy if the dark matter halo is not considered.

Furthermore the "intrahalo light" explanation is just one of two possible explanations according to Updated analysis of near-infrared background fluctuations which explains:

Two scenarios have been proposed to interpret the clustering excess. The first advocates the contribution from intrahalo light (IHL), i.e. relatively old stars stripped from
their parent galaxies following merging events. These stars
therefore reside in between dark matter halos and constitute a low-surface brightness haze around galaxies. The IHL
is expected to come mostly from low redshifts (1 + z <
∼ 1.5)
systems (Cooray et al. 2012b; Zemcov et al. 2014).

The second scenario is instead based on the presence
of a class of early, highly obscured accreting black holes
of intermediate mass (∼ 10^4−6M⊙) at z >
∼ 13 (Yue et al.
2013b, 2014). As a suitable mechanism to produce such
objects does exist – the so called Direct Collapse Black
Holes (DCBH, for a concise overview of the problem see
Ferrara et al. 2014), and the interpretation of the super-
massive black holes observed at z = 6 seemingly requires
massive seeds (Volonteri & Bellovary 2011), such hypothesis seems particularly worth exploring.

Both scenarios successfully explain the observed clustering excess, albeit with apparently demanding requirements. In fact, if the excess is to be explained by intra-
halo light, then a large fraction of the stars at low-z must
reside outside systems that we would normally classify as
“galaxies” (Zemcov et al. 2014). On the other hand, in the
DCBH scenario the abundance of seed black holes produced
until z ∼ 13 must represent a sizeable fraction of the estimated present-day black hole abundance, as deduced from
local scaling relations (Kormendy & Ho 2013) and recently
revised by Comastri et al. (2015). However, it is important
to outline that both scenarios are not in conflict with any
known observational evidence

Why do planets move in an elliptical orbit?

Not sure if you're looking for a more mathematical answer or just the "why", but to answer the why, I'll start with some history on this.

Everyone who worked out a model for the Solar System, from Aristotle to Copernicus, liked circles. Even though Copernicus correctly reasoned that the Earth moved around the Sun and not the Sun around the Earth, he continued to use circles in his models of the motion of the planets.

After Copernicus, Tycho Brahe, funded by the King of Denmark, had the best equipment at the time for observing the motion of the stars and planets and he was able to make star charts that were ten times as accurate as anyone before him. Brahe used equipment like this mural quadrant, and a large private observatory to take extremely accurate records.

Kepler, who was a better mathematician than Brahe, desperately wanted to get his hands on Brahe's star charts and the use of his observatory and equipment (so much so that when Brahe died, there were rumors that Kepler had poisoned him, though that probably didn't happen). When Kepler finally had everything at his disposal, he was able to work things out and study the Solar System more accurately. However, he still didn't know why the planets moved in ellipses; he'd only worked out that the ellipses fit the movement so well that it almost certainly had to be true, but he had no idea why.

Kepler, in fact, didn't care for ellipses. He liked circles better, but he couldn't deny that ellipses worked. Source.

Nobody knew why planets moved in ellipses until Isaac Newton was asked that question and had to invent calculus to answer it. Calculus explains why planets orbit in ellipses, and that's the real answer.

If "calculus" isn't a satisfying answer, a way to kind of explain it would be to throw a penny out of a space shuttle (which isn't a good idea, but let's say you do). As the penny falls towards the Earth, it falls faster and faster (if we ignore air resistance) until it hits the ground.

Now, if you fling the penny from the space shuttle at a much faster speed and at a different angle, so that it only gets near Earth and misses the planet, it would actually start to orbit Earth. It would fall faster and faster until it passes the Earth, and then, like shooting a bullet into the air, the penny will slow down as it flies past the Earth.

According to Kepler's second law, the penny's fastest speed is at the point closest to the Earth (the perigee). That's essentially how objects in orbits work: as they move closer to the body they orbit, they accelerate faster and faster. Our penny will get so fast that, once it comes around the planet, it will be flung very far away, which will then slow it down. This is what creates an elliptical orbit.

Its motion is like a spring, falling toward the planet then flying away, but at the same time, orbiting in a circular motion with the spring motion, with 1 period per orbit. That motion of moving closer and then further in each orbit forms an ellipse.

It makes the most sense if you think of the velocity being greatest at the closest point and lowest at the furthest point. The low velocity moves it closer while the high velocity moves it back out further. The total energy of the object in orbit (kinetic energy plus potential energy) remains constant.

comets - Does this video catch an Eta Aquarid - Earth skimming meteor?

I did a time-lapse animation looking towards the sunrise from Sydney, Australia on 25th of April. You can see it here around 1m 25s in (that link should jump to just before it appears very near where the Sun is about to rise):

http://www.youtube.com/watch?v=lqr_KuLd2-c&t=1m25s

It then proceeds towards the right of screen over around the next 21 seconds (around 10½ minutes) before disappearing off the right. You might need to send the video to full screen to see the small white 'bullet of haze' that is moving against a very wide background.

One of my first thoughts was that it might be a meteor skimming the upper atmosphere, but I was less confident of that given it seemed to be coming from the general direction of the Sun, and I'd thought that was a direction unlikely to produce meteors.

That was until I read Eta Aquarid Meteor Shower in 2016 which states:

The best time to view the Eta Aquarids is in the early mornings, right before dawn.

Well, at least that pins down the same time of day, if not the direction from which it came.

What is the likelyhood that this feature is a piece of comet debris that skimmed Earth's atmosphere?

the sun - How bright would the sun appear from the hypothetical Planet Nine proposed by Caltech?

Between $1/40,000$ and $1/8,000,000$ of the brightness as seen from Earth, depending on what the actual orbit would turn out to be, and where the planet is in its $15,000$ year orbit period.

Brightness drops as $dfrac{1}{r^2}$ with distance from the light source. Earth is at $1~textrm{AU}.$ The theoretical planet is at $200~textrm{AU}$ when it's closest to the sun, and up to $2800~textrm{AU}$ at the point furthest from the sun at the upper end of the estimated orbit.

So e.g. $1/200^2 = 1/40,000$ of the brightness (luminance) as seen from Earth.

For how a human would experience it, we can convert to exposure value as used in photography: The difference in exposure value (photographic 'stops') is $log 2$ of the luminance ratio, so we would have $15$ to $23$ stops less light than on Earth.
Sunny noon on Earth is $15~textrm{EV}.$

So the brightness at noon on the planet surface would be:

• At $200~textrm{AU},$ planet orbit is closest to the sun: About $0~textrm{EV},$ roughly the same as a dimly lit interior




• $400~textrm{AU},$ lower bound on semi-major axis: $-2 ~textrm{EV},$ similar to a landscape lit by the full moon




• $1500~textrm{AU},$ upper bound on semi-major axis: $-6~textrm{EV},$ similar to landscape lit by a quarter moon




• $2800~textrm{AU},$ upper bound on aphelion (the point on orbit most distant from the sun): $-8~textrm{EV}.$ This would be dark, but you would probably still see enough to avoid running into things.

constellations - Which is really larger, Big Dipper or Small Dipper, in 3D

This obviously depends on which stars you choose, but in general Ursa Major is likely to win by a factor of about five(ish), since it occupies a much larger chunk of the sky (1280 square degrees) than Ursa Minor (256 square degrees). At a fixed magnitude, and therefore at a fixed visibility radius for each intrinsic luminosity, the volume will be (very roughly) proportional to the area of each constellation on the celestial sphere. (There are subtleties, such as these, and this only rigorously holds when there are many stars, but it is a good rule of thumb.)

The volumes themselves can quite easily be calculated in Mathematica using the curated data. There is one easy way, which selects what Wolfram Research thinks are the 'bright stars' in each constellation. If you do that, you get

$$mathrm{Vol}(mathrm{UMa})=9.20133times 10^{20}mathrm{AU}^3,
mathrm{Vol}(mathrm{UMi})=1.7105times 10^{20}mathrm{AU}^3$$

which is the volume of the convex hull of the stars shown here:

If you have Mathematica (v10+ only, I think) and you want to tinker with the code, here it goes:

RegionMeasure[
   ConvexHullMesh[
    StarData[
     ConstellationData[Entity["Constellation", #], 
      EntityProperty["Constellation", "BrightStars"]], 
     "HelioCoordinates"]]
] & /@ {"UrsaMajor", "UrsaMinor"}

---

What one should really do is set a threshold magnitude and only count stars brighter than this, and then see the dependence of the volumes on the magnitude threshold. If you do this, you get pretty similar results:

That is, Ursa Major has a consistently higher volume at all naked-eye magnitude thresholds.

For the curious, here's the code.

nakedEyeStarProperties = 
 StarData[#, {"Name", "Constellation", "ApparentMagnitude", 
     "HelioCoordinates", "RightAscension", "Declination"}
] & /@ StarData[EntityClass["Star", "NakedEyeStar"]]
constellationVolume[constellation_, magnitude_] := 
 Block[{selectedStars},
  selectedStars = 
   Select[nakedEyeStarProperties, 
    And[#[[2, 2]] == constellation, #[[3]] < magnitude] &];
  RegionMeasure[ConvexHullMesh[selectedStars[[All, 4]]]]
  ]
ListLogPlot[
 Table[
   {{m, constellationVolume["UrsaMajor", m]}, {m, 
     constellationVolume["UrsaMinor", m]}}
   , {m, 3, 6.5, 0.1}][Transpose]
 , AxesLabel -> {"magnitude threshold", 
   "constellation volume/!(*SuperscriptBox[(AU), (3)])"}
 , PlotLegends -> {"Ursa Major", "Ursa Minor"}
 ]

the moon - Appearance of the Cresent

Yes it does. If you are at a high latitude the crescent Moon will set looking like a reversed C orientation but in the tropics it will set more like a U orientation. Though the time of the year will also have some effect due to the angle of the ecliptic to the horizon.

big bang theory - Was time different before the great inflation?

Food for thought on density and time dilation. Density isn't gravity. We tend to think it is, but it's not. Variation in density gives us gravity.

If you have an infinite universe, very young, hot and dense, but it's uniform, then you have no time dilation. One way to think about this is to ask if light passing through the universe is red shifted or blue shifted. If the universe is uniform and infinite, it's the same in all directions around the photon, so the photon is neither red nor blue shifted, so, contrary to what our intuition about relativity tells us, there might not have been a great deal of time dilation in the very young universe.

Of-course the ray of light passing through expanding space is enormously red-shifted, but that doesn't affect time dilation. The gravitational red or blue shift in the very young universe might still be close to zero meaning very little time dilation anywhere.

As the early universe grew less uniform then you had time dilation variations in denser parts of the early Universe but with FTL expansion and gravity limited by the speed of light, it's unclear if there ever was massive time dilation in the young universe (at least, unclear to me, if somebody here knows 100%, feel free to post and/or correct me).

Now if we assume the universe is finite and flat and the big bang happened at a point, which, generally isn't the model most people like these days, then you could run into enormous time dilation inside the tiny young and dense universe, but it still expanded FTL, so the calculations get weird and too hard for me. If the expansion of space happens faster than gravity can keep up, gravitational time dilation might not apply, at least not until after the rate of expansion slowed down enough for gravity to permeate the local regions. I couldn't even begin to run the math on this and you'd have different answers for different models too, I'd think. I agree with Andy though, it would need to be accounted for or the models wouldn't be much good.

star - Why can't this be the simple (and obvious) explanation for the dimming of KIC 8462852?

As others have said, there is repeated dimming of the star, that suggests something in orbit around the star. But in addition to that, you are having the perfectly reasonable and common failure to comprehend the vastness and emptiness of space.

Now, comets, planets and the like are quite common going around stars, but in interstellar space they are very rare and to line up exactly with a distant star is incredibly unlikely. To get an idea of the scale, think of the shadow cast by a flea in London, from a light bulb in Beijing, being seen in New York. It just doesn't happen. Because the distances are too vast (even this example is wrong, by a factor of about 1000). Space is just too big and too empty for random debris to exactly line up with a star.

Now if the debris is near the Sun, as is passes in front of a star, the light from that star is abruptly cut out. This is called an occulation, and they happen very often. The conclusion is that whatever is causing the dimming of this star must be close to it. Probably a cloud of dust in orbit around the star, but this doesn't explain how that dust got there, and why it doesn't appear in the infrared.

positional astronomy - Question on Equatorial and Galactic coordinate systems

I'm currently working with proper motions and have needed to convert my galactic longitude and latitude into right ascension and declination (ie from galactic to equatorial coordinates). This is fine since NED have a tool to do this, however once I convert into Cartesian coordinates I do not get the same results as I had for the galactic-cartesian conversion.

I understand that the conversion from galactic to cartesian is

x = Dcos(l)cos(b)

y = Dcos(b)sin(l)

z = Dsin(b)

where D is the distance to the galaxy in question in my case.

Also for the equatorial to cartesian transformation

x = Dcos(RA)cos(DEC)

y = Dcos(DEC)sin(RA)

z = Dsin(DEC)

I have done this for both my galactic coordinates and converted equatorial coordinates, but I do not get the same x,y and z. Should this be happening?

planet - mountains higher than atmosphere

This is a bit of a gray area, as an atmosphere doesn't have a clear boundary. That being said, Olympus Mons on Mars is so tall, the atmospheric pressure on top of it is only 12% the average pressure on the surface of Mars. That's near vacuum by terrestrial standards.

https://en.wikipedia.org/wiki/Olympus_Mons#Description

In general, for this to happen you need:

• a pretty thin atmosphere to begin with


• some exceptional geology that ends up producing very tall anomalies like Olympus

It's not a very likely combination, but it can happen, as seen on Mars.

Focusing light through fiber optic cable to extend telescope viewer

I want to build a system to view my telescope without being uncomfortable. Currently I have to stand up and bend over to view the eye piece.

I want to build a system that allows me to 'pipe' the output of the view piece in a non-digital format along a flexible fiber optic cable to my eye and possible split the view into two for a sort of VR headset.

I know the cable will transfer the light, but will it be just burly light or break down too much (one meter or less) or will I be able to focus it into view-able picture?

I could just try it, but the cable itself is really expensive to get, and I want to know if this is worth trying before I spend.

I'm thinking of using this 14 mm 'solid core' cable

Star versus Black Hole - Astronomy

A black hole (BH) never sucks anything in. 'Sucking' requires gas pressure, but a black hole only acts via its gravity. A non-rotating (=Schwarzschild) black hole attracts all massive objects, very much like the Sun attracts the planets.
Yet, the planets are not falling into the Sun. This is because the planets move on near-circular orbits when the centrifugal force balances the gravitational attraction. The planets orbital angular momemtum is conserved (because the Solar force field is purely radial [to good approximation]) and these orbits are stable.

The difference to a black hole is that very close to the event horizon no such stable circular orbits exist anymore. At those distances, nothing can orbit the BH without falling in.

However, an object orbiting a BH on a stable orbit (including passing trajectories) is still subjected to the BH's tidal forces. These distort the object, very much like the Moon's gravity distorts the Earth, generating tides.
In case, the trajectory passes sufficiently close to the BH and the object is rather big and fluffy, like (some) stars, the tidal forces may not merely distort the object, but rip it apart.

Such tidal disruption of stars must happen if a star passes close to a supermassive BH. This can hardly be directly observed, but the it is thought that some of the stellar matter forms an accretion disc around the BH and produces a characteristic light curve. An observed light curve in agreement with this model is often interpreted as circumstantial evidence for a stellar disruption event.

solar system - Planets and Pluto? Neptune?

I answered this same question at physics.SE. I specifically joined this part of the SE network to address this duplicate question at this site.

The astronomy community faced two crises with regard to what constitutes a "planet", first in the mid 19th century, and more recently at the start of the 21st century. The first crisis involved the asteroids. The second involved trans-Neptunian objects. Both crises challenged astronomers to question what a "planet" was.

1 Ceres, 2 Pallas, 3 Juno, and 4 Vesta were discovered in quick succession during the first decade of the 19th century. There was no international astronomical organization at the time of these discoveries; the International Astronomical Union wouldn't be formed for another century. Instead, the designation of what constituted a "planet" fell on the major astronomical almanacs such as the Berliner Astronomisches Jahrbuch (BAJ). Those discoveries at the start of the 19th century were treated as newly discovered "planets". This situation remained static for about 40 years.

That changed in 1845 with the discovery of 5 Astraea. During the 1850s, the list of objects orbiting the Sun grew to 50, and during the 1860s, the list grew to over 100. The response of the BAJ and others was to demote Ceres, Pallas, Juno, and Vesta from planethood status to some lesser status, either minor planet or asteroid. Astronomers didn't have a clear-cut concept of what constituted a planet other than that they should somehow be large. Ceres, the largest of the bunch, is not very large. The end result of all of these discoveries starting in 1845 was that the first four discovered asteroids were demoted from planethood status.

The second crisis started in 1992 with the discovery of (15760) 1992 QB₁. By 2006, the number of trans-Neptunian objects had grown significantly. Were these things "planets", or something else? Some astronomers, notably Alan Stern, wanted the term "planet" to be extremely inclusive. Most astronomers balked at this idea.

Paradoxically, it was Alan Stern himself, along with Harold Levison, who provided the key criterion of "clearing the neighborhood" that lies at the heart of what the IAU deems to constitute a "planet." Their paper, Stern and Levison, "Regarding the criteria for planethood and proposed planetary classification schemes," Highlights of Astronomy 12 (2002): 205-213 suggested splitting "planet" into two categories, "überplanet" (Mercury, Venus, Earth, Mars, Jupiter, Saturn, Uranus, and Neptune) and "unterplanet" (Pluto+Charon, Eris, Ceres, Sedna, and a host of others).

Stern is being quite hypocritical when he rants that there is no clear-cut boundary between "planets" and "dwarf planets." The boundary is huge, and Stern knows this. The ratio of the square of an object's mass to its orbital radius about the Sun is key in determining whether an object can clear most of the junk from the vicinity of the object's orbit. There is a five order of magnitude difference between the smallest of the planets and the largest of the dwarf planets in terms of this ratio. This five order of magnitude difference figures predominantly in that paper by Stern and Levison.

The only difference between the proposal by Stern and Levison versus the voted-upon IAU resolution is that while Stern and Levison wanted to designate hundreds (and perhaps thousands) of objects into subcategories of "planet" ("überplanet" and "interplant"). On the other hand, the IAU chose to designate those objects as the mutually exclusive terms "planets" and "dwarf planets". This is consistent with how astronomers dealt with that first crisis. Planets should be "large." Stern and Levison provided the necessary ammunition to distinguish large from not so large.

Is Earth unique in its fairly clear atmosphere?

No, the clarity of the Earth's atmosphere cannot be considered unique. We don't have to speculate about exoplanets.

You could argue the answer is no, because both the Moon and Mercury have (very, very) thin atmospheres, and these are obviously "clear".

If you regard that argument as tricksy, then we can turn to Mars. Yes Mars has occasional dust storms. In normal conditions, the optical depth of the Martian atmosphere is usually somewhere between 0.5 and 1 per airmass. (Petrova et al. 2012; Lemmon et al. 2014). Most of this extinction is caused by dust and is nearly wavelength independent. i.e. between 60% and 37% of light would travel through it's atmosphere from outside. This compares with typical extinctions of about 0.2-0.4 magnitudes of visual extinction per airmass on Earth (0.1 mag at the best astronomical sites in the world), corresponding to 80% to 69% of light passing through the Earth's atmosphere from outside (to sea level). Most of this extinction is due to dust, though there is some absorption by water and other aerosols).

Thus, though Mars is dustier than Earth on average, it is not outrageously so. It would be stretching the use of the word unique to say that the clarity of the Earth's atmosphere was "unique".

gravity - Spinning black hole vs non spinning black hole

It makes a difference, but not to the strength of the gravity.

Around a spinning black hole (or any other spinning mass) space time is dragged. This effect has been measured around the (spinning) Earth by Gravity Probe B. It would cause a plumb line not to point directly at the centre of the Earth, but slightly forward.

For a rotating black hole, there is a region close to the event horizon, but outside it, in which the gravity (a combination of downwards and sideways accelerations) is so strong that it is not possible to remain stationary, relative to a distant observer, for to do so one would have to travel faster than the speed of light (relative to the local spacetime)

A similar situation exists in a non-rotating black hole, but only behind the event horizon.

So a rotating black hole does not have stronger gravity, but it is different: It is sideways.

neutron star - Cosmic events as standard candles

_{Intro for the uninformed: A standard candle is an important concept in astronomy, helping to map out distances in the Universe. Since the observed flux $F$ of a light source decreases with distance $r$ by a known factor ($r^2$), if we know its intrinsic luminosity L, we can calculate the distance. For large distances, where bright sources are needed, we usually use supernovae (SNe). But the luminosity of a SN depends on the mass of its progenitor star which is not known in general. However, for a specific type of SNe — "type Ia" — it is known: This type are SNe that explode when a white dwarf accreting mass from a companion star exceed the mass threshold for explosion of $1.4,M_odot$.}

---

In addition to the gravitational waves discussed by Rob Jeffries, I can mention the following candidates for standard candles:

Type II supernovae

Type Ia SNe are so similar in luminosity because they all have (almost) the same mass when they go off. But there is also evidence that type II SNe can act as standard candles. As is also to some extent the case with Ia, their lightcurves (how the luminosity changes with time) are not identical, but can be standardized using the so-called Philips relation (see e.g. Kasen & Woosley 2009).

GRB supernovae

Gamma-ray bursts as a whole are too diverse to be used as standard candles, but when an associated SN is detected, it becomes a standard(izable) candle (Li & Hjorth 2014).

Quasars

My favorite candidate are quasars. This technique doesn't rely on the Philips relation. Quasars are caused by gas accreting onto a supermassive black hole in the center of galaxies, resulting in an "active galactic nuclus" (AGN) with extreme energy outputs (easily over $10^{12},L_odot$, and even up to $10^{14}$–$10^{15},L_odot$; Ibata et al. 1999). It turns out that there is a correlation between the absolute luminosity of the AGN and the size of its broad-line region (BLR), i.e. the region around the quasar where fast-moving gas clouds absorb the continuum$^1$ of the quasar and emit lines$^2$, e.g. H$alpha$ (Watson et al. 2011). The reason is that the size of the BLR is determined by the depth that the ionizing radiation from the quasar can penetrate into the BLR, which is proportional to the square root of the luminosity. The figure below (from Watson et al. 2011) shows the relation between distances ($D_L$) determined by this technique and distances obtained from type Ia SNe.

Advantages over supernovae

A huge advantage of quasars over SNe is that they don't disappear after a few weeks, meaning that if e.g. we want to refine some measurement, we can go back and observe it again at any time. Another advantage is that quasars, being so luminonous, can be detected out to much larger distances (roughly to $zsimeq4$) than SNe (which are only observed ut to $zsimeq2$).

Reverberation mapping

Since quasars are so far away, the BLR, being less than a parsec in size, cannot be resolved. But luckily, a technique call "reverberation mapping" allows us to determine the size:

The spectrum of the quasar consists of a continuum with spectral lines. Quasars vary in luminosity on rather short timescales. If we measure a quasar's luminosity regularly over some period of time, we get a so-called "lightcurve". But since the lines are created at a distance from the source, a given "bump" in the lightcurve (i.e. a temporary increase in luminosity) does't show up in the continuum and the lines at the same time. Instead, there is a delay, corresponding to the extra distance that the light had to travel from the quasar to the cloud reflecting$^3$ it.

In the figure below, blue shows the continuum, while red shows the lines. The lines are seen to lag behind the continuum, since they first had to travel from the quasar (black) to the clouds (magenta).

Since the clouds lie at a range of distances, they exhibit different time lags, effectively broadening the line:

So, in the figure above, showing observed flux as a function of time, the light in the line increased in luminosity roughly 1.5 days later than the light in the continuum. This means that the BLR is roughly 1.5 lightdays (or ~250 AU) in radius.

---

$^1$_{I.e. the continuous and relatively featureless spectrum of many different atomic transitions and physical processes.}

$^2$_{I.e. features in the spectrum resulting from strong atomic transitions. For instance, an eletron falling from the second to the first excited states of a hydrogen atom emits a photon with the wavelength 6563 Å, called "H$alpha$".}

$^3$_{The light isn't really "reflected". Instead, it is the high-energy photons (UV and X-rays) of the continuum that ionize the atoms in the clouds. When the ions recombine, they emit spectral lines.}

jupiter - What would happen to a gas planet if its core mass goes beyond the Chandrasekhar limit?

Hypothetically, let's say we had a gas giant that continued to accrete mass. I've heard that the cores of gas giants are electron degenerate. So if the planet continued to accrete mass and the core mass went beyond the Chandrasekhar limit, what would happen?

In white dwarfs, the result is dependent on the composition. Carbon-oxygen white dwarfs will undergo carbon fusion, leading to a type 1a supernova. Oxygen-magnesium-neon white dwarfs will undergo rapid oxygen fusion, leading to a rapid ignition and supernova but leaving behind a neutron degenerate core.

So would the composition of a gas giant's core play a similar role, if it went beyond the Chandrasekhar limit? What would happen if, say, Jupiter somehow accreted a core mass beyond the limit?

What is the maximum transmission distance of the radio signal in the outer space which could still be understood?

It cannot be said correctly, since we humans have hardly traveled to the moon and sent space probes to explore other planets in our solar system. So, theoretically anything might be possible. I'm trying to be a bit practical here. The only man made object that has gone really far is Voyager 1, which is at a distance of 18.7 billion kilometers (125.3 AU) from the sun. Although launched in 1977, it is the only live transmitter and receiver which is that far.

The radio communication system of Voyager 1 was designed to be used up to and beyond the limits of the Solar System. The communication system includes a 3*.7 meters (12 ft) diameter parabolic dish high-gain antenna* to send and receive radio waves via the three Deep Space Network stations on the Earth. Voyager 1 normally transmits data to Earth over Deep Space Network Channel 18, using a frequency of either 2296.481481 MHz or 8420.432097 MHz, while signals from Earth to Voyager are broadcast at 2114.676697 MHz.
As of 2013, signals from Voyager 1 take over 17 hours to reach Earth.

I agree that there are powerful transmitters in the world than what is present in the Voyager 1, but, most of them still remain untested. So, we can be exact with the measurements.