# How to derive the redshift of GW150914?

We are searching data for your request:

Forums and discussions:
Manuals and reference books:
Data from registers:
Wait the end of the search in all databases.
Upon completion, a link will appear to access the found materials.

We all know LIGO has detected gravitational wave(GW) directly. prl

The LIGO team argue they detected the merger of two solar mass black holes($36Modot+29Modot-3Modot$) at z=0.09.

My questions are

It seems GW has Doppler shift too. There is a GW spectrum with emission or absorption lines like optical spectrum?

Figure.2 of the PRL paper seems to be very simple. Generally, people take their masses derived seriously? There may be other models which can give different masses. It is different from Taylor binary which was observed many years.

What does a 100HZ GW mean? That is the frequency of the two arms shrink and extend?

What does the frequency stand for in the binary system?

The discovery can not be confirmed. DO you think the team win a Nobel prize only after other facilities like LISA find GW again?

That is a lot of questions, but I can take them in order:

It seems GW has Doppler shift too. There is a GW spectrum with emission or absorption lines like optical spectrum?

Yes, GW has Doppler shift too, as they are travelling at a finite speed, but no, there are no emission or absorption lines we can detect it from. In EM radiation those are caused by the fact that light is quantized, such that certain wavelengths can be absorbed or emitted by atoms. As far as we know, gravity is not quantized, or the effect is too small to be measured. Any irregularity in the signal is then going to be continuous, and not wavelength specific. Detecting a spectra in gravitational waves is unlikely, but would strengthen the theories of quantum gravity and the graviton.

people take their masses derived seriously?

The method for the mass estimate is described well by @Rob Jeffries, but an even simpler point can be made: There are no other ways to measure their mass more accurately.

What does a 100HZ GW mean?

Hertz is the frequency, 1/s. That is the number of waves per second. 100Hz is comparable to normal sound waves.

What does the frequency stand for in the binary system?

As two objects revolve around each other, they would make two waves per orbit,resulting in a double frequency of the system's rotation.

DO you think the team win a Nobel prize only after other facilities like LISA find GW again?

This is almost certainty ending in a Nobel prize, and they do not necessarily have to wait till after the results are confirmed by other experiments. That said, verification by peer researchers is one of the core principles of science.

Too many questions in one question.

The title question: The frequency of the gravitational waves as a function of time give an estimate of the black hole masses; the peak strain amplitude of the waves then tells you how far away the source is based on the expected strain amplitude from a merging binary with the previously derived masses (the amplitude decreases inversely with distance); Hubble's law then gives you the redshift.

Second question - a coalescing binary gives a signal at twice the orbital frequency of the binary, but that frequency rapidly changes (increases) as the binary components get closer together and merge. The redshift of the source cannot be derived directly from the observed frequencies, it is derived as I explained above.

Third question, yes the 100 Hz would mean the arms expand and contract 100 times per second. The binary would be orbiting 50 times per second to produce this signal.

The model that is fitted comes straight out of general relativity. The free parameters are the masses (and spins) of the black holes and the distance to the source. What alternative model were you thinking of?

I think this result will end up in a Nobel prize. The detection was confirmed by two detectors and I would think they will find more in thecoming months - this discovery was found in the first 16 days of data. Further, there will soon be other ground based detectors that are equally capable (e.g. VIRGO).

## Title: Solving puzzles of GW150914 by primordial black holes

The black hole binary properties inferred from the LIGO gravitational wave signal GW150914 posed several serious problems. The high masses and low effective spin of black hole binary can be explained if they are primordial (PBH) rather than the products of the stellar binary evolution. Such PBH properties are postulated ad hoc but not derived from fundamental theory. We show that the necessary features of PBHs naturally follow from the slightly modified Affleck-Dine (AD) mechanism of baryogenesis. The log-normal distribution of PBHs, predicted within the AD paradigm, is adjusted to provide an abundant population of low-spin stellar mass black holes. The same distribution gives a sufficient number of quickly growing seeds of supermassive black holes observed at high redshifts and may comprise an appreciable fraction of Dark Matter which does not contradict any existing observational limits. Testable predictions of this scenario are discussed.

## Contents

Albert Einstein originally predicted the existence of gravitational waves in 1916, [24] [25] on the basis of his theory of general relativity. [26] General relativity interprets gravity as a consequence of distortions in space-time, caused by mass. Therefore, Einstein also predicted that events in the cosmos would cause "ripples" in space-time – distortions of space-time itself – which would spread outward, although they would be so minuscule that they would be nearly impossible to detect by any technology foreseen at that time. [13] It was also predicted that objects moving in an orbit would lose energy for this reason (a consequence of the law of conservation of energy), as some energy would be given off as gravitational waves, although this would be insignificantly small in all but the most extreme cases. [27]

One case where gravitational waves would be strongest is during the final moments of the merger of two compact objects such as neutron stars or black holes. Over a span of millions of years, binary neutron stars, and binary black holes lose energy, largely through gravitational waves, and as a result, they spiral in towards each other. At the very end of this process, the two objects will reach extreme velocities, and in the final fraction of a second of their merger a substantial amount of their mass would theoretically be converted into gravitational energy, and travel outward as gravitational waves, [28] allowing a greater than usual chance for detection. However, since little was known about the number of compact binaries in the universe and reaching that final stage can be very slow, there was little certainty as to how often such events might happen. [29]

### Observation Edit

Gravitational waves can be detected indirectly – by observing celestial phenomena caused by gravitational waves – or more directly by means of instruments such as the Earth-based LIGO or the planned space-based LISA instrument. [30]

#### Indirect observation Edit

Evidence of gravitational waves was first deduced in 1974 through the motion of the double neutron star system PSR B1913+16, in which one of the stars is a pulsar that emits electro-magnetic pulses at radio frequencies at precise, regular intervals as it rotates. Russell Hulse and Joseph Taylor, who discovered the stars, also showed that over time, the frequency of pulses shortened, and that the stars were gradually spiralling towards each other with an energy loss that agreed closely with the predicted energy that would be radiated by gravitational waves. [31] [32] For this work, Hulse and Taylor were awarded the Nobel Prize in Physics in 1993. [33] Further observations of this pulsar and others in multiple systems (such as the double pulsar system PSR J0737-3039) also agree with General Relativity to high precision. [34] [35]

#### Direct observation Edit

Direct observation of gravitational waves was not possible for the many decades after they were predicted due to the minuscule effect that would need to be detected and separated from the background of vibrations present everywhere on Earth. A technique called interferometry was suggested in the 1960s and eventually technology developed sufficiently for this technique to become feasible.

In the present approach used by LIGO, a laser beam is split and the two halves are recombined after travelling different paths. Changes to the length of the paths or the time taken for the two split beams, caused by the effect of passing gravitational waves, to reach the point where they recombine are revealed as "beats". Such a technique is extremely sensitive to tiny changes in the distance or time taken to traverse the two paths. In theory, an interferometer with arms about 4 km long would be capable of revealing the change of space-time – a tiny fraction of the size of a single proton – as a gravitational wave of sufficient strength passed through Earth from elsewhere. This effect would be perceptible only to other interferometers of a similar size, such as the Virgo, GEO 600 and planned KAGRA and INDIGO detectors. In practice at least two interferometers would be needed because any gravitational wave would be detected at both of these but other kinds of disturbance would generally not be present at both. This technique allows the sought-after signal to be distinguished from noise. This project was eventually founded in 1992 as the Laser Interferometer Gravitational-Wave Observatory (LIGO). The original instruments were upgraded between 2010 and 2015 (to Advanced LIGO), giving an increase of around 10 times their original sensitivity. [36]

Initial LIGO operations between 2002 and 2010 did not detect any statistically significant events that could be confirmed as gravitational waves. This was followed by a multi-year shut-down while the detectors were replaced by much improved "Advanced LIGO" versions. [37] In February 2015, the two advanced detectors were brought into engineering mode, in which the instruments are operating fully for the purpose of testing and confirming they are functioning correctly before being used for research, [38] with formal science observations due to begin on 18 September 2015. [39]

Throughout the development and initial observations by LIGO, several "blind injections" of fake gravitational wave signals were introduced to test the ability of the researchers to identify such signals. To protect the efficacy of blind injections, only four LIGO scientists knew when such injections occurred, and that information was revealed only after a signal had been thoroughly analyzed by researchers. [40] On 14 September 2015, while LIGO was running in engineering mode but without any blind data injections, the instrument reported a possible gravitational wave detection. The detected event was given the name GW150914. [41]

### Event detection Edit

GW150914 was detected by the LIGO detectors in Hanford, Washington state, and Livingston, Louisiana, USA, at 09:50:45 UTC on 14 September 2015. [4] [11] The LIGO detectors were operating in "engineering mode", meaning that they were operating fully but had not yet begun a formal "research" phase (which was due to commence three days later on 18 September), so initially there was a question as to whether the signals had been real detections or simulated data for testing purposes before it was ascertained that they were not tests. [42]

The chirp signal lasted over 0.2 seconds, and increased in frequency and amplitude in about 8 cycles from 35 Hz to 250 Hz. [3] The signal is in the audible range and has been described as resembling the "chirp" of a bird [4] astrophysicists and other interested parties the world over excitedly responded by imitating the signal on social media upon the announcement of the discovery. [4] [43] [44] [45] (The frequency increases because each orbit is noticeably faster than the one before during the final moments before merging.)

The trigger that indicated a possible detection was reported within three minutes of acquisition of the signal, using rapid ('online') search methods that provide a quick, initial analysis of the data from the detectors. [3] After the initial automatic alert at 09:54 UTC, a sequence of internal emails confirmed that no scheduled or unscheduled injections had been made, and that the data looked clean. [40] [46] After this, the rest of the collaborating team was quickly made aware of the tentative detection and its parameters. [47]

More detailed statistical analysis of the signal, and of 16 days of surrounding data from 12 September to 20 October 2015, identified GW150914 as a real event, with an estimated significance of at least 5.1 sigma [3] or a confidence level of 99.99994%. [48] Corresponding wave peaks were seen at Livingston seven milliseconds before they arrived at Hanford. Gravitational waves propagate at the speed of light, and the disparity is consistent with the light travel time between the two sites. [3] The waves had traveled at the speed of light for more than a billion years. [49]

At the time of the event, the Virgo gravitational wave detector (near Pisa, Italy) was offline and undergoing an upgrade had it been online it would likely have been sensitive enough to also detect the signal, which would have greatly improved the positioning of the event. [4] GEO600 (near Hannover, Germany) was not sensitive enough to detect the signal. [3] Consequently, neither of those detectors was able to confirm the signal measured by the LIGO detectors. [4]

### Astrophysical origin Edit

The event happened at a luminosity distance of 440 +160
−180 megaparsecs [1] : 6 (determined by the amplitude of the signal), [4] or 1.4 ± 0.6 billion light years, corresponding to a cosmological redshift of 0.093 +0.030
−0.036 (90% credible intervals). Analysis of the signal along with the inferred redshift suggested that it was produced by the merger of two black holes with masses of 35 +5
−3 times and 30 +3
−4 times the mass of the Sun (in the source frame), resulting in a post-merger black hole of 62 +4
−3 solar masses. [1] : 6 The mass–energy of the missing 3.0 ± 0.5 solar masses was radiated away in the form of gravitational waves. [3]

During the final 20 milliseconds of the merger, the power of the radiated gravitational waves peaked at about 3.6 × 10 49 watts or 526dBm – 50 times greater [50] than the combined power of all light radiated by all the stars in the observable universe. [3] [4] [15] [16]

Across the 0.2-second duration of the detectable signal, the relative tangential (orbiting) velocity of the black holes increased from 30% to 60% of the speed of light. The orbital frequency of 75 Hz (half the gravitational wave frequency) means that the objects were orbiting each other at a distance of only 350 km by the time they merged. The phase changes to the signal's polarization allowed calculation of the objects' orbital frequency, and taken together with the amplitude and pattern of the signal, allowed calculation of their masses and therefore their extreme final velocities and orbital separation (distance apart) when they merged. That information showed that the objects had to be black holes, as any other kind of known objects with these masses would have been physically larger and therefore merged before that point, or would not have reached such velocities in such a small orbit. The highest observed neutron star mass is two solar masses, with a conservative upper limit for the mass of a stable neutron star of three solar masses, so that a pair of neutron stars would not have had sufficient mass to account for the merger (unless exotic alternatives exist, for example, boson stars), [2] [3] while a black hole-neutron star pair would have merged sooner, resulting in a final orbital frequency that was not so high. [3]

The decay of the waveform after it peaked was consistent with the damped oscillations of a black hole as it relaxed to a final merged configuration. [3] Although the inspiral motion of compact binaries can be described well from post-Newtonian calculations, [51] the strong gravitational field merger stage can only be solved in full generality by large-scale numerical relativity simulations. [52] [53] [54]

In the improved model and analysis, the post-merger object is found to be a rotating Kerr black hole with a spin parameter of 0.68 +0.05
−0.06 , [1] i.e. one with 2/3 of the maximum possible angular momentum for its mass.

The two stars which formed the two black holes were likely formed about 2 billion years after the Big Bang with masses of between 40 and 100 times the mass of the Sun. [55] [56]

### Location in the sky Edit

Gravitational wave instruments are whole-sky monitors with little ability to resolve signals spatially. A network of such instruments is needed to locate the source in the sky through triangulation. With only the two LIGO instruments in observational mode, GW150914's source location could only be confined to an arc on the sky. This was done via analysis of the 6.9 +0.5
−0.4 ms time-delay, along with amplitude and phase consistency across both detectors. This analysis produced a credible region of 150 deg 2 with a probability of 50% or 610 deg 2 with a probability of 90% located mainly in the Southern Celestial Hemisphere, [2] : 7 : fig 4 in the rough direction of (but much farther than) the Magellanic Clouds. [4] [11]

### Coincident gamma-ray observation Edit

The Fermi Gamma-ray Space Telescope reported that its Gamma-Ray Burst Monitor (GBM) instrument detected a weak gamma-ray burst above 50 keV, starting 0.4 seconds after the LIGO event and with a positional uncertainty region overlapping that of the LIGO observation. The Fermi team calculated the odds of such an event being the result of a coincidence or noise at 0.22%. [58] However a gamma ray burst would not have been expected, and observations from the INTEGRAL telescope's all-sky SPI-ACS instrument indicated that any energy emission in gamma-rays and hard X-rays from the event was less than one millionth of the energy emitted as gravitational waves, which "excludes the possibility that the event is associated with substantial gamma-ray radiation, directed towards the observer". If the signal observed by the Fermi GBM was genuinely astrophysical, INTEGRAL would have indicated a clear detection at a significance of 15 sigma above background radiation. [59] The AGILE space telescope also did not detect a gamma-ray counterpart of the event. [60]

A follow-up analysis by an independent group, released in June 2016, developed a different statistical approach to estimate the spectrum of the gamma-ray transient. It concluded that Fermi GBM's data did not show evidence of a gamma ray burst, and was either background radiation or an Earth albedo transient on a 1-second timescale. [61] [62] A rebuttal of this follow-up analysis, however, pointed out that the independent group misrepresented the analysis of the original Fermi GBM Team paper and therefore misconstrued the results of the original analysis. The rebuttal reaffirmed that the false coincidence probability is calculated empirically and is not refuted by the independent analysis. [63] [64]

Black hole mergers of the type thought to have produced the gravitational wave event are not expected to produce gamma-ray bursts, as stellar-mass black hole binaries are not expected to have large amounts of orbiting matter. Avi Loeb has theorised that if a massive star is rapidly rotating, the centrifugal force produced during its collapse will lead to the formation of a rotating bar that breaks into two dense clumps of matter with a dumbbell configuration that becomes a black hole binary, and at the end of the star's collapse it triggers a gamma-ray burst. [65] [66] Loeb suggests that the 0.4 second delay is the time it took the gamma-ray burst to cross the star, relative to the gravitational waves. [66] [67]

### Other follow-up observations Edit

The reconstructed source area was targeted by follow-up observations covering radio, optical, near infra-red, X-ray, and gamma-ray wavelengths along with searches for coincident neutrinos. [2] However, because LIGO had not yet started its science run, notice to other telescopes was delayed. [ citation needed ]

The ANTARES telescope detected no neutrino candidates within ±500 seconds of GW150914. The IceCube Neutrino Observatory detected three neutrino candidates within ±500 seconds of GW150914. One event was found in the southern sky and two in the northern sky. This was consistent with the expectation of background detection levels. None of the candidates were compatible with the 90% confidence area of the merger event. [68] Although no neutrinos were detected, the lack of such observations provided a limit on neutrino emission from this type of gravitational wave event. [68]

Observations by the Swift Gamma-Ray Burst Mission of nearby galaxies in the region of the detection, two days after the event, did not detect any new X-ray, optical or ultraviolet sources. [69]

### Announcement Edit

The announcement of the detection was made on 11 February 2016 [4] at a news conference in Washington, D.C. by David Reitze, the executive director of LIGO, [6] with a panel comprising Gabriela González, Rainer Weiss and Kip Thorne, of LIGO, and France A. Córdova, the director of NSF. [4] Barry Barish delivered the first presentation on this discovery to a scientific audience simultaneously with the public announcement. [70]

The initial announcement paper was published during the news conference in Physical Review Letters, [3] with further papers either published shortly afterwards [19] or immediately available in preprint form. [71]

### Awards and recognition Edit

In May 2016, the full collaboration, and in particular Ronald Drever, Kip Thorne, and Rainer Weiss, received the Special Breakthrough Prize in Fundamental Physics for the observation of gravitational waves. [72] Drever, Thorne, Weiss, and the LIGO discovery team also received the Gruber Prize in Cosmology. [73] Drever, Thorne, and Weiss were also awarded the 2016 Shaw Prize in Astronomy [74] [75] and the 2016 Kavli Prize in Astrophysics. [76] Barish was awarded the 2016 Enrico Fermi Prize from the Italian Physical Society (Società Italiana di Fisica). [77] In January 2017, LIGO spokesperson Gabriela González and the LIGO team were awarded the 2017 Bruno Rossi Prize. [78]

The 2017 Nobel Prize in Physics was awarded to Rainer Weiss, Barry Barish and Kip Thorne "for decisive contributions to the LIGO detector and the observation of gravitational waves". [79]

The observation was heralded as inaugurating a revolutionary era of gravitational-wave astronomy. [80] Prior to this detection, astrophysicists and cosmologists were able to make observations based upon electromagnetic radiation (including visible light, X-rays, microwave, radio waves, gamma rays) and particle-like entities (cosmic rays, stellar winds, neutrinos, and so on). These have significant limitations – light and other radiation may not be emitted by many kinds of objects, and can also be obscured or hidden behind other objects. Objects such as galaxies and nebulae can also absorb, re-emit, or modify light generated within or behind them, and compact stars or exotic stars may contain material which is dark and radio silent, and as a result there is little evidence of their presence other than through their gravitational interactions. [81] [82]

### Expectations for detection of future binary merger events Edit

On 15 June 2016, the LIGO group announced an observation of another gravitational wave signal, named GW151226. [83] The Advanced LIGO was predicted to detect five more black hole mergers like GW150914 in its next observing campaign from November 2016 until August 2017 (it turned out to be seven), and then 40 binary star mergers each year, in addition to an unknown number of more exotic gravitational wave sources, some of which may not be anticipated by current theory. [11]

Planned upgrades are expected to double the signal-to-noise ratio, expanding the volume of space in which events like GW150914 can be detected by a factor of ten. Additionally, Advanced Virgo, KAGRA, and a possible third LIGO detector in India will extend the network and significantly improve the position reconstruction and parameter estimation of sources. [3]

Laser Interferometer Space Antenna (LISA) is a proposed space based observation mission to detect gravitational waves. With the proposed sensitivity range of LISA, merging binaries like GW150914 would be detectable about 1000 years before they merge, providing for a class of previously unknown sources for this observatory if they exist within about 10 megaparsecs. [19] LISA Pathfinder, LISA's technology development mission, was launched in December 2015 and it demonstrated that the LISA mission is feasible. [84]

A current model predicts LIGO will detect approximately 1000 black hole mergers per year after it reaches full sensitivity planned for 2020. [55] [56]

### Lessons for stellar evolution and astrophysics Edit

The masses of the two pre-merger black holes provide information about stellar evolution. Both black holes were more massive than previously discovered stellar-mass black holes, which were inferred from X-ray binary observations. This implies that the stellar winds from their progenitor stars must have been relatively weak, and therefore that the metallicity (mass fraction of chemical elements heavier than hydrogen and helium) must have been less than about half the solar value. [19]

The fact that the pre-merger black holes were present in a binary star system, as well as the fact that the system was compact enough to merge within the age of the universe, constrains either binary star evolution or dynamical formation scenarios, depending on how the black hole binary was formed. A significant number of black holes must receive low natal kicks (the velocity a black hole gains at its formation in a core-collapse supernova event), otherwise the black hole forming in a binary star system would be ejected and an event like GW would be prevented. [19] The survival of such binaries, through common envelope phases of high rotation in massive progenitor stars, may be necessary for their survival. [ clarification needed ] The majority of the latest black hole model predictions comply with these added constraints. [ citation needed ]

The discovery of the GW merger event increases the lower limit on the rate of such events, and rules out certain theoretical models that predicted very low rates of less than 1 Gpc −3 yr −1 (one event per cubic gigaparsec per year). [3] [19] Analysis resulted in lowering the previous upper limit rate on events like GW150914 from

140 Gpc −3 yr −1 to 17 +39
−13 Gpc −3 yr −1 . [85]

### Impact on future cosmological observation Edit

Measurement of the waveform and amplitude of the gravitational waves from a black hole merger event makes accurate determination of its distance possible. The accumulation of black hole merger data from cosmologically distant events may help to create more precise models of the history of the expansion of the universe and the nature of the dark energy that influences it. [86] [87]

The earliest universe is opaque since the cosmos was so energetic then that most matter was ionized and photons were scattered by free electrons. [88] However, this opacity would not affect gravitational waves from that time, so if they occurred at levels strong enough to be detected at this distance, it would allow a window to observe the cosmos beyond the current visible universe. Gravitational-wave astronomy therefore may some day allow direct observation of the earliest history of the universe. [3] [18] [19] [20] [21]

### Tests of general relativity Edit

The inferred fundamental properties, mass and spin, of the post-merger black hole were consistent with those of the two pre-merger black holes, following the predictions of general relativity. [7] [8] [9] This is the first test of general relativity in the very strong-field regime. [3] [18] No evidence could be established against the predictions of general relativity. [18]

The opportunity was limited in this signal to investigate the more complex general relativity interactions, such as tails produced by interactions between the gravitational wave and curved space-time background. Although a moderately strong signal, it is much smaller than that produced by binary-pulsar systems. In the future stronger signals, in conjunction with more sensitive detectors, could be used to explore the intricate interactions of gravitational waves as well as to improve the constraints on deviations from general relativity. [18]

### Speed of gravitational waves and limit on possible mass of graviton Edit

The speed of gravitational waves (vg) is predicted by general relativity to be the speed of light (c). [89] The extent of any deviation from this relationship can be parameterized in terms of the mass of the hypothetical graviton. The graviton is the name given to an elementary particle that would act as the force carrier for gravity, in quantum theories about gravity. It is expected to be massless if, as it appears, gravitation has an infinite range. (This is because the more massive a gauge boson is, the shorter is the range of the associated force as with the infinite range of electromagnetism, which is due to the massless photon, the infinite range of gravity implies that any associated force-carrying particle would also be massless.) If the graviton were not massless, gravitational waves would propagate below lightspeed, with lower frequencies (ƒ) being slower than higher frequencies, leading to dispersion of the waves from the merger event. [18] No such dispersion was observed. [18] [28] The observations of the inspiral slightly improve (lower) the upper limit on the mass of the graviton from Solar System observations to 2.1 × 10 −58 kg , corresponding to 1.2 × 10 −22 eV/c 2 or a Compton wavelength (λg) of greater than 10 13 km, roughly 1 light-year. [3] [18] Using the lowest observed frequency of 35 Hz, this translates to a lower limit on vg such that the upper limit on 1-vg /c is

## 3 TIME DELAYS FOR MASSIVE BBH MERGERS

To link the SFR, progenitor metallicity, and host mass evolution discussed above with BBH mergers that are detectable by LIGO, we compute a set of BPS models. Many phases in the evolution of binary stars remain poorly understood and previous BPS studies have shown that this results in large uncertainties in the BBH merger rate (e.g. Lipunov, Postnov & Prokhorov 1997 Sipior & Sigurdsson 2002 Dominik et al. 2013). Since this Letter focuses on host galaxies, and not binary evolution, we consider a simple, single set of standard assumptions consistent with observational constraints. We note that our models do not include the recently proposed massive overcontact binary BBH formation channel (Mandel & de Mink 2016 Marchant et al. 2016). We focus on field binaries and neglect BBHs that are dynamically formed in globular clusters (e.g. Downing et al. 2011 Rodriguez et al. 2015), which would typically form at high redshifts and preferentially reside in more massive galaxies. Lacking observational constraints, we also neglect BBH stemming from Pop III stars (Kinugawa et al. 2014), which are not likely candidates for GW 150914 (Hartwig et al. 2016) and which contribution to the gravitational wave background is still uncertain (Dvorkin et al. 2016).

The BPS models are computed with the binary star evolution code bse described in Hurley, Tout & Pols ( 2002), which we have updated to improve the treatment of massive binaries. We use the weaker, metallicity-dependent wind mass-loss prescriptions from Belczynski et al. ( 2010). Updated remnant mass prescriptions are taken from Belczynski et al. ( 2008). BH birth kicks are modelled following Dominik et al. ( 2013). This results in the production of BBHs with component masses ≳ 25M that are not disrupted by powerful natal kicks. The kicks are drawn from a Maxwellian distribution of width 265 km s −1 , reduced according to the amount of material that falls back after core collapse.

We have also updated the treatment of some mass transfer scenarios in bse . We force systems that experience a common envelope phase while the mass donor is in the Hertzsprung gap to merge. 2 For stars that have evolved beyond the Hertzsprung gap, we take the common envelope efficiency to be unity, and compute the envelope binding energies with the bse -default, evolutionary-state-dependent formulae. Furthermore, we allow stable Roche lobe overflow mass transfer to be non-conservative and assume that only half of the mass lost by the donor is accreted by the companion (Dominik et al. 2013). With this updated version of bse we are able to produce a reasonable estimate for the BBH merger delay time distribution given an initial population of binary stars.

We construct the delay time distribution from a Monte Carlo ensemble of 2.5 × 10 6 binaries. Primary masses range from 25 to 150M and are drawn from the initial mass function (IMF) given by Kroupa ( 2001). This allows for a wider mass distribution than the GW150914 event, which will be representative for future massive black hole binary detections. When we select a narrow mass range, set by the uncertainties on the GW150914 detection ( ⁠|$M_1=36_<-4>^<+5> m M_<>$| and |$M_2=29_<-4>^<+4> m M_<>$|⁠ ), we find qualitatively very similar trends. The initial mass ratios and orbital periods are drawn from the distributions measured by Sana et al. ( 2012). Initial eccentricities are drawn from a thermal distribution f(e) ∝ 2e. We evolve the same population of binaries for the 11 metallicity bins we consider.

Fig. 2 shows the number of BBH mergers per solar mass of stars formed that occur at time tdelay after the stellar binary forms. We only considered BBH mergers with total mass larger than 40M. Due to the metallicity dependence of the wind mass-loss rates, binaries formed at |$Z_mathrm = 0.01 m Z_<>$| produce the most massive BHs. Accordingly, these extremely low-metallicity stars have the largest number of massive BBH mergers per unit stellar mass. However, at very late times higher metallicity stars account for a comparable number of mergers.

Number of massive BBH mergers per solar mass of star formation Nm as a function of time since formation for a stellar population with a Kroupa IMF and BBH mass >40 M. The upper limit in tdelay = tmtf is the Hubble time. For massive BBH mergers, only the 0.01Z population follows the standard dNm/dtt −1 evolution, shown with a red line.

Number of massive BBH mergers per solar mass of star formation Nm as a function of time since formation for a stellar population with a Kroupa IMF and BBH mass >40 M. The upper limit in tdelay = tmtf is the Hubble time. For massive BBH mergers, only the 0.01Z population follows the standard dNm/dtt −1 evolution, shown with a red line.

If we include BBH mergers of all masses (not shown here), dNm/dt at each metallicity considered here approaches the standard t −1 dependence (e.g. Dominik et al. 2013 Belczynski et al. 2016). This agreement with previous work is encouraging because, for our purposes, it is most important to properly capture the shape of the delay time distributions. When we restrict our study to BBH mergers with total mass larger than 40M, only the |$Z_mathrm = 0.01 m Z_<>$| delay time distribution dNm/dt follows the t −1 dependence, as is shown by the flat line for Nm(t). At higher metallicity, short mergers are absent because of larger stellar radii, which make many systems merge as stellar binaries before producing a BBH. On top of that, some binaries contract less during the common envelope phase, because of the lower envelope binding energy, resulting in BBHs that merge at later times. Except for the very low metallicity progenitors, we do not expect mergers from recently formed stars.

## How to derive the redshift of GW150914? - Astronomy

COVID-19 has impacted many institutions and organizations around the world, disrupting the progress of research. Through this difficult time APS and the Physical Review editorial office are fully equipped and actively working to support researchers by continuing to carry out all editorial and peer-review functions and publish research in the journals as well as minimizing disruption to journal access.

We appreciate your continued effort and commitment to helping advance science, and allowing us to publish the best physics journals in the world. And we hope you, and your loved ones, are staying safe and healthy.

Many researchers now find themselves working away from their institutions and, thus, may have trouble accessing the Physical Review journals. To address this, we have been improving access via several different mechanisms. See Off-Campus Access to Physical Review for further instructions.

#### Images

###### Figure 1

The left plot shows the strain sensitivity during the first observation run (O1) of the Advanced LIGO detectors and during the last science run (S6) of the initial LIGO detectors. The O1 strain noise curve is shown for H1 (dark red) and L1 (light red) the two detectors have similar performance. The Advanced LIGO design sensitivity, as well as a possible future upgrade [13], are shown to highlight the discovery potential in the coming years. The right plot shows the single detector signal-to-noise ratio (SNR) under optimal orientation as a function of redshift z —for two merging black holes with mass 30 M ⊙ each. GW150914 was not optimally orientated and was detected with a single detector SNR of 13 to 20 at z = 0.09 this event would not have been seen in S6.

###### Figure 2

Interferometer configuration and test mass setup. Each arm of the Michelson interferometer includes two suspended test masses. The two test masses are placed 4 km apart and form an optical resonator with a gain of 300. The suspension system is shown on the right, each test mass is at the bottom of a quadruple pendulum. It provides high isolation above the resonance frequencies which range from 0.4 to 13 Hz. The test mass is attached to the penultimate mass through fused silica fibers providing a high mechanical quality factor which lowers the thermal noise. The other stages use steel wire. The attachment point to the seismic isolation system as well as stages 1 and 2 implement cantilever springs for vertical isolation. Each test mass is accompanied by its own reaction chain to minimize actuation noise. Coil actuators are mounted to the upper stages of the reaction chain, and an electrostatic actuator is implemented at the bottom stage. Shown on the left are the other optics of the Michelson interferometer with the beam splitter and the perpendicular arm. The two optics at the interferometer input and output port comprise the coupled resonator system which amplifies the response of the optical transducer.

###### Figure 3

The displacement sensitivity of the Advanced LIGO detector in Hanford during the first observation run O1 the Livingston detector has a similar sensitivity, as shown in Fig. 1. The sum of all known noise sources accounts for most of the observed noise with the exception of the frequency band between 20 and 100 Hz. This will be the focus of future commissioning to full sensitivity. The quantum noise includes both shot noise and radiation pressure noise. Thermal noise includes terms due to the suspensions, the test masses, and the coatings. Seismic noise is the ground displacement attenuated through the seismic isolation system and the suspensions. Cross couplings from the autoalignment system and from the auxiliary lengths are combined into the trace labeled “other DOF” (degrees of freedom). Newtonian gravitational noise is estimated from density perturbations due to surface ground motion. The strong line features are due to the violin modes of the suspension wires, the roll and bounce modes of the suspensions, the AC power line and its harmonics, and the calibration lines. Not shown are numerous noise sources that do not contribute significantly—such as laser frequency, intensity and beam jitter noise, sensor and actuation noise, and Rayleigh scattering by the residual gas [19].

## ASTROPHYSICAL IMPLICATIONS OF THE BINARY BLACK HOLE MERGER GW150914

We study prospects for detecting extragalactic binary black holes similar to GW150914 by evolved Laser Interferometer Space Antenna (eLISA). We find that the majority of detected binary black holes will not merge within reasonable observation periods of eLISA in any configuration. While long-arm detectors are highly desired for promoting multiband gravitational-wave astronomy by increasing the detections of merging binaries, the number of total detections can be increased also by improving the acceleration noise. A monochromatic approximation works well to derive semiquantitative features of observational prospects for non-merging binaries with clearly indicating the parameter dependence. Our estimate also suggests that the number of galaxies in the error volume is so small that the host galaxy may be determined uniquely with high confidence.

The first detection of a binary-black hole merger, GW150914, opened the door to gravitational-wave astronomy (Abbott et al. 2016a). The masses of the black holes, ∼29 and ∼36 M, are larger than ∼10–15 M previously expected from galactic observations (Özel et al. 2010 Kreidberg et al. 2012), and this finding prompts a vigorous debate regarding their origin. At the same time, The LIGO Scientific Collaboration et al. ( 2016) suggest a very high merger rate of binary black holes in our Universe based on a part of Advanced LIGO's O1 observation run. These facts immediately mean that space-based gravitational-wave detectors, such as evolved Laser Interferometric Space Antenna (eLISA: see Armano et al. 2016, for LISA Pathfinder), would have a fair chance to detect extragalactic stellar-mass binary black holes as well as galactic compact binaries (Abbott et al. 2016b Sesana 2016).

Observing gravitational waves at low frequency will be important to understand the origin of massive black holes like GW150914. Facing massive black holes with ≳30 M unexpected for end products of stellar evolution with the solar metallicity (Abbott et al. 2016b), possible formation channels of the binary are actively discussed. One plausible scenario is the evolution of low-metallicity stars with weak stellar winds in an isolated field binary (see Postnov & Yungelson 2014, for reviews). Another scenario is dynamical formation in dense stellar environments like galactic nuclei or globular clusters (see, e.g. Benacquista & Downing 2013 Rodriguez et al. 2015, 2016). It is also pointed out that a binary of primordial black holes satisfying current observational constraints is also consistent with GW150914 (Bird et al. 2016 Sasaki et al. 2016). Because these scenarios predict different distribution of binary parameters such as the eccentricity, which is determined to higher accuracy at lower frequency (see section 1 of Nishizawa et al. 2016b, for the discussion), multiple detections could statistically clarify the formation scenario (see also Breivik et al. 2016 Nishizawa et al. 2016a). Moreover, precise localization of the binary by the annual modulation of the detector with the distance estimation will be beneficial to determine the host galaxy, information of which is also invaluable to infer the origin.

In this paper, we study prospects for detecting extragalactic binary black holes by eLISA, enhancing the previous investigation for Galactic binary black holes by one of the authors (Seto 2016). The possibility of detecting extragalactic binary black holes is mentioned briefly by LIGO Scientific Collaboration immediately after the detection of GW150914 (Abbott et al. 2016b). Various authors conducted follow-up studies of this possibility by Monte Carlo simulations (Nishizawa et al. 2016b Sesana 2016 Vitale 2016), primarily focusing on the aspects of multiband gravitational-wave astronomy, i.e. simultaneous detections of the same binary by eLISA and ground-based interferometric detectors such as Advanced LIGO. Here, we analytically evaluate the expected number of detections and put more emphasis on extragalactic binary black holes that do not merge during the operation of eLISA than previous studies do, because such binaries inevitably dominate the detection. We also show that a monochromatic approximation works well to derive semiquantitative features of observational prospects for non-merging binaries.

Our assumptions and parameter choices are summarized as follows. We treat all the binary black holes as circular, and denote the gravitational-wave frequency by f, which is twice the orbital frequency. This is justified to the accuracy of our discussion, because the eccentricity is not expected to be very high. We apply the quadrupole formula for point masses neglecting the black hole spin as well as higher order post-Newtonian effects, and the cosmological redshift is also neglected. We take the fiducial chirp mass of binary black holes to be |$mathcal = 28 ,mathrm_$| according to the estimate from GW150914 (Abbott et al. 2016a), and later show that our estimate applies approximately to distribution of chirp masses once averaged over the weight |$mathcal ^<10/3>$|⁠ . We take the fiducial comoving merger rate to be R = 100 Gpc −3 yr −1 motivated by the estimate from a part of O1 (The LIGO Scientific Collaboration et al. 2016).

## How to derive the redshift of GW150914? - Astronomy

Context. Redshifts are fundamental for our understanding of extragalactic X-ray sources. Ambiguous counterpart associations, expensive optical spectroscopy, and/or multimission multiwavelength coverage to resolve degeneracies often make estimation difficult in practice.
Aims: We attempt to constrain redshifts of obscured active galactic nuclei (AGN) using only low-resolution X-ray spectra.
Methods: Our method for determining redshifts from the X-ray spectrum (XZ) fits AGN X-ray spectra with a moderately complex spectral model incorporating a corona, a torus obscurer, and a warm mirror. Using the Bayesian X-ray Astronomy (BXA) package, we constrain redshift, column density, photon index, and luminosity simultaneously. The redshift information primarily comes from absorption edges in Compton-thin AGN, and from the Fe Kα fluorescent line in heavily obscured AGN. A new generic background fitting method allows us to extract more information from limited numbers of source counts.
Results: We derive redshift constraints for 74/321 hard-band detected sources in the Chandra deep field South. Comparing with spectroscopic redshifts, we find an outlier fraction of 8%, indicating that our model assumptions are valid. For three Chandra deep fields, we release our XZ redshift estimates.
Conclusions: The independent XZ estimate is easy to apply and effective for a large fraction of obscured AGN in today's deep surveys without the need for any additional data. Compared to different redshift estimation methods, XZ can resolve degeneracies in photometric redshifts, help detect potential association problems, and confirm uncertain single-line spectroscopic redshifts. With high spectral resolution and a large collecting area, this technique will be highly effective for Athena/WFI observations.

## Conclusion

What do we conclude? Einstein’s general relativity is further strengthened as good operational science with no fudge factors. Any change in the speed of light is rejected. Nevertheless there exist other much more plausible solutions to the biblical creationist starlight-travel-time problem. 26 – 29 With a constant speed of light, general relativity theory gives us the needed clue that time is not an absolute in the universe, which means that much more time could have been available for light to travel to earth from the most distant sources, even within the 6,000 years since creation. There are no other implications that impact on biblical creationist explanations for the origin of the universe.

## LIGO Detects Third Black Hole Merger

By: Camille M. Carlisle June 1, 2017 2

### Get Articles like this sent to your inbox

Scientists with the gravitational-wave observatory announce another discovery, this time of a black hole merger twice as far away as previous detections.

This illustration shows two black holes about to merge, similar to those detected by LIGO. In this illustration, the black holes are spinning on axes that are tilted with respect to their orbital plane.
LIGO / Caltech / MIT / Sonoma State (Aurore Simonnet)

What was once a pipe dream is becoming old hat. Scientists with the Laser Interferometer Gravitational-Wave Observatory (LIGO) have announced their discovery of another black hole merger, revealed when the gravitational waves that were created by the cosmic consolidation changed the length of the two LIGO sites’ arms by approximately one-thousandth the width of a proton.

Gravitational waves are ripples in the fabric of spacetime, created by accelerating masses. Along with black holes, gravitational lenses, and other fun phenomena, they’re a prediction of Einstein’s masterwork vision of gravity, the general theory of relativity.

The newly announced event, called GW170104, squeezed and stretched LIGO’s 4-km-long arms on January 4th, during the observatory’s (ongoing) second observing run. The larger of the two black holes had a mass between 25 and 40 times that of the Sun the smaller, between 13 and 25 Suns. The resulting black hole has a mass of about 50 solar masses, with a couple of solar masses carried away as gravitational radiation, the collaboration reports June 1st in Physical Review Letters.

Based on how “loud” the signal was, the researchers conclude that the merger happened roughly 3 billion light-years away, somewhere in a long, skinny region on the sky spanning roughly 1200 square degrees.

One of the important revelations from LIGO's discoveries is that stellar-mass black holes can be more massive than many astronomers expected. Previously, mass estimates based on the X-ray emission from black holes in binary systems with stars (purple) did not exceed 20 solar masses. But the three confirmed LIGO detections (GW150914, GW151226, GW170104) and one candidate detection (LVT151012) point to a population of stellar-mass binary black holes that surpass the 20-solar-mass limit.
LIGO / Caltech / Sonoma State (Aurore Simonnet)

This is the third firm detection of gravitational waves. LIGO scientists detected the previous two events in September and December 2015, announcing them each in 2016. (A third iffy detection, in October 2015, was not strong enough to rise above “candidate” status.) These events all appear to come from the final moments of the merger of two black holes, each object having about ten or more solar masses.

Before LIGO, astronomers could only “see” this type of black hole when it siphoned gas from a companion star, heating the gas up to X-ray-emitting temperatures. The objects LIGO first detected, with masses of more than 20 Suns, came as a surprise — many theorists didn’t think such beefy stellar-mass black holes existed. (Supermassive black holes, the ones skulking in galaxies’ cores, are a distinct population: Unlike the LIGO objects, they haven’t reached their current sizes by forming from a single star.)

The final mass of the black hole produced by the latest merger lies betwixt those of the previous two LIGO discoveries. It also happened approximately twice as far away as those events.

GW170104 is the first discovery from LIGO’s second observing run, at least that we know of. The team has circumspectly noted that they’ve identified seven “triggers,” but deputy spokesperson Laura Cadonati (Georgia Tech) cautions that she and her colleagues cast a wide net when looking for potential gravitational waves, so many triggers may not pan out.

### Deciphering the Gravitational-Wave Wiggle

A comparison of the reconstructed waveforms of the three LIGO detections (GW150914, GW151226, GW170104) and one unverified candidate (LVT151012). Although these binary systems have been producing gravitational waves for millions or even billions of years, LIGO can only detect them when the members move close enough to produce gravitational waves of a high enough frequency. In this figure, the zero-second point corresponds to a 30-Hz detection threshold. The more massive the black holes involved, the shorter the amount of time their measurable signal lasts in LIGO's detectors.
LIGO / Caltech / MIT / University of Chicago (Ben Farr)

Scientists derive things like the black holes’ masses, spin, and distance based on a careful breakdown of the gravitational wave signal. The frequency of the gravitational waves, for example, is inversely proportional to the total mass of the black holes: Higher frequency means lower mass.

One aspect of GW170104’s signal has astrophysicists excited: the black holes’ spins. Although the team can’t determine the exact direction and speed of the two black holes’ spins before the merger, the gravitational wave pattern does indicate that at least one of the black holes was spinning in the opposite direction from the one in which the two objects were orbiting each other.

The reasoning goes something like this: If the two black holes were spinning exactly aligned with the axis of their orbit, they would have needed to shed some of the system’s total rotational energy before they could merge. Such a merger would take a few more orbits than if the spins weren’t aligned, Cadonati explains. But the team didn’t see this “hang-up” effect, so they think things weren’t perfectly lined up.

Shown are two projections of the probable sky locations for the three confirmed LIGO detections and the candidate detection, over an optical image of the Milky Way. The top is a 3D projection meant to mimic the celestial sphere, and the bottom is an Aitoff projection of the same map. The outer contour for each represents the 90% confidence region. All the sky localizations are shifted to the sidereal time of GW151226.
Contours: LIGO / Caltech / MIT / Leo Singer, Milky Way Image: Axel Mellinger

This hint of a misalignment is tantalizing. If the two black holes formed from two stars that began life together as a binary system, then it’s more likely that they would be spinning in roughly the same way. But if the black holes joined up after they formed — say, by sinking to the center of a dense stellar cluster — then their two spins could easily be totally different. “This is an important clue in understanding how black holes form,” Cadonati says.

The spin values themselves might provide another clue. All three of the final black holes whose birth LIGO has detected spin at rates that are about 70% of the maximum allowed. This result matches recent calculations by Maya Fishbach (University of Chicago) and others, suggesting that when black holes of similar masses merge, the resulting object will have a spin rate around this value. If this correlation holds up, then whenever we find a black hole with this spin, we might be able to say that it’s the product of a merger.

Part of the great allure in studying black holes is that, as gravitational objects, they’re perfect laboratories for testing our understanding of gravity. Thus far, all the gravitational-wave events detected are cookie-cutter examples of what scientists expected to see, based on Einstein’s general theory of relativity. Despite murmurs of exotic echoes in the first event’s gravitational wave signal, the LIGO team is skeptical of that analysis. As of yet, scientists have found no clear deviation from Einstein’s gravity.

But what they have found is just as cool: excellent evidence that black holes are real.

Maya Fishbach, Daniel E. Holz, Ben Farr. “Are LIGO's Black Holes Made from Smaller Black Holes?” Astrophysical Journal Letters. May 10, 2017.

If you’d like to know more, read the behind-the-scenes story of the first gravitational-wave detection and what we’ve learned from these spacetime ripples in our September issue, on newsstands August 1st.

## Watch the video: Warped Spacetime and Horizons of GW150914 (May 2022).

yes that's for sure, the spam topic blooms and smells :)

2. Eduard

In my opinion, they are wrong. We need to discuss.

3. Nash