High Mass Black Holes in Soft X-Ray Transients Gap in Black Hole Masses

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黑洞视界下霍金的辐射计算公式

黑洞视界下霍金的辐射计算公式
霍金辐射（Hawking radiation）是指黑洞在量子效应下会自发地发射出粒子和辐射的现象。

霍金于1974年提出了这个理论，它是基于量子场论和黑洞物理学的结合而得出的。

在黑洞视界（event horizon）的边缘，虚粒子和虚反粒子会不断地产生和湮灭。

如果这个过程发生在黑洞视界内部，那么其中一个粒子可能会被吸收到黑洞内部，而另一个粒子则被排斥到黑洞外部。

由于黑洞内部的粒子无法逃脱，这样就会导致黑洞失去质量。

这个过程被称为霍金辐射。

霍金在1974年的论文中给出了霍金辐射的计算公式：
$$
\frac{dE}{dt} = \frac{\hbar c^6}{15360\pi G^2M^2} = \frac{1}{4\pi G^2} \frac{\hbar c^4}{M^2} $$
其中，$E$ 是辐射能量，$t$ 是时间，$\hbar$ 是普朗克常数除以$2\pi$，$c$ 是光速，$G$ 是引力常数，$M$ 是黑洞质量。

这个公式表明，辐射能量与黑洞质量的平方成反比。

也就是说，越小的黑洞辐射的越多，失去的质量也越快。

如果一个黑洞的质量足够小，那么它会在很短的时间内完全辐射掉，这被称为黑洞蒸发。

需要注意的是，霍金辐射的计算公式是基于一些假设和简化的模型，它并不能完全描述黑洞的真实性质。

但是，它仍然是一个非常有趣和重要的理论，它为我们理解黑洞的物理学和量子力学提供了一个新的视角。

黑洞小知识

有关“黑洞”的小知识黑洞的定义根据美国宇航局的说法，黑洞通常被定义为“空间中的一个地方，那里的引力太大，连光都出不去。

”由于光无法逃脱黑洞的引力，它看起来完全是黑色的，因此它被命名为黑洞。

然而，通过对各种望远镜收集到的数据进行一些特殊分析，我们可以“看到”黑洞。

黑洞的形成和种类黑洞的形成取决于它们的类型和起源。

到目前为止，科学家们已经成功地定义了至少四种不同的类型：微型黑洞；恒星黑洞；中型黑洞；超大质量黑洞。

目前的理论认为，微型黑洞(有些甚至只有原子大小)可能在宇宙诞生的最早时刻就形成了。

到目前为止，这些微小的黑洞是纯理论的，被认为是遍布整个宇宙的微小的黑暗漩涡，它们的总质量是太阳的数百倍。

恒星黑洞(质量大约相当于20个太阳或更多)是由大质量恒星自身坍缩而产生的。

在它们的最后阶段，巨大的恒星会发生超新星爆发。

这样的爆炸将恒星物质抛向太空，但留下了恒星的核心。

当这颗恒星还活着的时候，核聚变产生了一种持续的向外推力，平衡了恒星自身质量产生的引力。

然而，在超新星的残骸中，不再有对抗引力的力量，所以恒星核心开始向自身坍塌。

就像微型黑洞一样，中型黑洞只有在理论上才为人所知。

这些黑洞的质量只有几十万个太阳的质量，而不像它们的表亲那样有几百万甚至几十亿个太阳质量。

一些科学家认为，中间黑洞是由小型黑洞合并而成的。

另一些人则认为，如果它们确实存在，它们将是由质量相当于几十万个太阳的恒星坍塌而形成的。

据爱因斯坦的广义相对论预测，超大质量黑洞是在它们所居住的星系形成的同时形成的。

银河系中心有一个超大质量的黑洞，其质量是太阳的400多万倍。

谁首先发现了黑洞虽然现在每个人都听说过黑洞，但你有没有想过是谁首先发现了它们？从技术上讲，我们还没有真正“发现”一个黑洞，但我们可以通过各种技术推断它们的存在。

例如，在1783年，一位名叫约翰·米切尔的业余科学家成功地利用了牛顿万有定律证明了“暗星”的存在，在那里连光都逃脱不出“暗星”的引力。

暮光之城1 中英对照资料

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我是报社的你很有新闻价值可以上头版
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he doesn't hover.

引力波观测原文PhysRevLett.116.061102

Observation of Gravitational Waves from a Binary Black Hole MergerB.P.Abbott et al.*(LIGO Scientific Collaboration and Virgo Collaboration)(Received21January2016;published11February2016)On September14,2015at09:50:45UTC the two detectors of the Laser Interferometer Gravitational-Wave Observatory simultaneously observed a transient gravitational-wave signal.The signal sweeps upwards in frequency from35to250Hz with a peak gravitational-wave strain of1.0×10−21.It matches the waveform predicted by general relativity for the inspiral and merger of a pair of black holes and the ringdown of the resulting single black hole.The signal was observed with a matched-filter signal-to-noise ratio of24and a false alarm rate estimated to be less than1event per203000years,equivalent to a significance greaterthan5.1σ.The source lies at a luminosity distance of410þ160−180Mpc corresponding to a redshift z¼0.09þ0.03−0.04.In the source frame,the initial black hole masses are36þ5−4M⊙and29þ4−4M⊙,and the final black hole mass is62þ4−4M⊙,with3.0þ0.5−0.5M⊙c2radiated in gravitational waves.All uncertainties define90%credible intervals.These observations demonstrate the existence of binary stellar-mass black hole systems.This is the first direct detection of gravitational waves and the first observation of a binary black hole merger.DOI:10.1103/PhysRevLett.116.061102I.INTRODUCTIONIn1916,the year after the final formulation of the field equations of general relativity,Albert Einstein predicted the existence of gravitational waves.He found that the linearized weak-field equations had wave solutions: transverse waves of spatial strain that travel at the speed of light,generated by time variations of the mass quadrupole moment of the source[1,2].Einstein understood that gravitational-wave amplitudes would be remarkably small;moreover,until the Chapel Hill conference in 1957there was significant debate about the physical reality of gravitational waves[3].Also in1916,Schwarzschild published a solution for the field equations[4]that was later understood to describe a black hole[5,6],and in1963Kerr generalized the solution to rotating black holes[7].Starting in the1970s theoretical work led to the understanding of black hole quasinormal modes[8–10],and in the1990s higher-order post-Newtonian calculations[11]preceded extensive analytical studies of relativistic two-body dynamics[12,13].These advances,together with numerical relativity breakthroughs in the past decade[14–16],have enabled modeling of binary black hole mergers and accurate predictions of their gravitational waveforms.While numerous black hole candidates have now been identified through electromag-netic observations[17–19],black hole mergers have not previously been observed.The discovery of the binary pulsar system PSR B1913þ16 by Hulse and Taylor[20]and subsequent observations of its energy loss by Taylor and Weisberg[21]demonstrated the existence of gravitational waves.This discovery, along with emerging astrophysical understanding[22], led to the recognition that direct observations of the amplitude and phase of gravitational waves would enable studies of additional relativistic systems and provide new tests of general relativity,especially in the dynamic strong-field regime.Experiments to detect gravitational waves began with Weber and his resonant mass detectors in the1960s[23], followed by an international network of cryogenic reso-nant detectors[24].Interferometric detectors were first suggested in the early1960s[25]and the1970s[26].A study of the noise and performance of such detectors[27], and further concepts to improve them[28],led to proposals for long-baseline broadband laser interferome-ters with the potential for significantly increased sensi-tivity[29–32].By the early2000s,a set of initial detectors was completed,including TAMA300in Japan,GEO600 in Germany,the Laser Interferometer Gravitational-Wave Observatory(LIGO)in the United States,and Virgo in binations of these detectors made joint obser-vations from2002through2011,setting upper limits on a variety of gravitational-wave sources while evolving into a global network.In2015,Advanced LIGO became the first of a significantly more sensitive network of advanced detectors to begin observations[33–36].A century after the fundamental predictions of Einstein and Schwarzschild,we report the first direct detection of gravitational waves and the first direct observation of a binary black hole system merging to form a single black hole.Our observations provide unique access to the*Full author list given at the end of the article.Published by the American Physical Society under the terms of the Creative Commons Attribution3.0License.Further distri-bution of this work must maintain attribution to the author(s)and the published article’s title,journal citation,and DOI.properties of space-time in the strong-field,high-velocity regime and confirm predictions of general relativity for the nonlinear dynamics of highly disturbed black holes.II.OBSERVATIONOn September14,2015at09:50:45UTC,the LIGO Hanford,W A,and Livingston,LA,observatories detected the coincident signal GW150914shown in Fig.1.The initial detection was made by low-latency searches for generic gravitational-wave transients[41]and was reported within three minutes of data acquisition[43].Subsequently, matched-filter analyses that use relativistic models of com-pact binary waveforms[44]recovered GW150914as the most significant event from each detector for the observa-tions reported here.Occurring within the10-msintersite FIG.1.The gravitational-wave event GW150914observed by the LIGO Hanford(H1,left column panels)and Livingston(L1,rightcolumn panels)detectors.Times are shown relative to September14,2015at09:50:45UTC.For visualization,all time series are filtered with a35–350Hz bandpass filter to suppress large fluctuations outside the detectors’most sensitive frequency band,and band-reject filters to remove the strong instrumental spectral lines seen in the Fig.3spectra.Top row,left:H1strain.Top row,right:L1strain.GW150914arrived first at L1and6.9þ0.5−0.4ms later at H1;for a visual comparison,the H1data are also shown,shifted in time by this amount and inverted(to account for the detectors’relative orientations).Second row:Gravitational-wave strain projected onto each detector in the35–350Hz band.Solid lines show a numerical relativity waveform for a system with parameters consistent with those recovered from GW150914[37,38]confirmed to99.9%by an independent calculation based on[15].Shaded areas show90%credible regions for two independent waveform reconstructions.One(dark gray)models the signal using binary black hole template waveforms [39].The other(light gray)does not use an astrophysical model,but instead calculates the strain signal as a linear combination of sine-Gaussian wavelets[40,41].These reconstructions have a94%overlap,as shown in[39].Third row:Residuals after subtracting the filtered numerical relativity waveform from the filtered detector time series.Bottom row:A time-frequency representation[42]of the strain data,showing the signal frequency increasing over time.propagation time,the events have a combined signal-to-noise ratio(SNR)of24[45].Only the LIGO detectors were observing at the time of GW150914.The Virgo detector was being upgraded, and GEO600,though not sufficiently sensitive to detect this event,was operating but not in observational mode.With only two detectors the source position is primarily determined by the relative arrival time and localized to an area of approximately600deg2(90% credible region)[39,46].The basic features of GW150914point to it being produced by the coalescence of two black holes—i.e., their orbital inspiral and merger,and subsequent final black hole ringdown.Over0.2s,the signal increases in frequency and amplitude in about8cycles from35to150Hz,where the amplitude reaches a maximum.The most plausible explanation for this evolution is the inspiral of two orbiting masses,m1and m2,due to gravitational-wave emission.At the lower frequencies,such evolution is characterized by the chirp mass[11]M¼ðm1m2Þ3=5121=5¼c3G596π−8=3f−11=3_f3=5;where f and_f are the observed frequency and its time derivative and G and c are the gravitational constant and speed of light.Estimating f and_f from the data in Fig.1, we obtain a chirp mass of M≃30M⊙,implying that the total mass M¼m1þm2is≳70M⊙in the detector frame. This bounds the sum of the Schwarzschild radii of thebinary components to2GM=c2≳210km.To reach an orbital frequency of75Hz(half the gravitational-wave frequency)the objects must have been very close and very compact;equal Newtonian point masses orbiting at this frequency would be only≃350km apart.A pair of neutron stars,while compact,would not have the required mass,while a black hole neutron star binary with the deduced chirp mass would have a very large total mass, and would thus merge at much lower frequency.This leaves black holes as the only known objects compact enough to reach an orbital frequency of75Hz without contact.Furthermore,the decay of the waveform after it peaks is consistent with the damped oscillations of a black hole relaxing to a final stationary Kerr configuration. Below,we present a general-relativistic analysis of GW150914;Fig.2shows the calculated waveform using the resulting source parameters.III.DETECTORSGravitational-wave astronomy exploits multiple,widely separated detectors to distinguish gravitational waves from local instrumental and environmental noise,to provide source sky localization,and to measure wave polarizations. The LIGO sites each operate a single Advanced LIGO detector[33],a modified Michelson interferometer(see Fig.3)that measures gravitational-wave strain as a differ-ence in length of its orthogonal arms.Each arm is formed by two mirrors,acting as test masses,separated by L x¼L y¼L¼4km.A passing gravitational wave effec-tively alters the arm lengths such that the measured difference isΔLðtÞ¼δL x−δL y¼hðtÞL,where h is the gravitational-wave strain amplitude projected onto the detector.This differential length variation alters the phase difference between the two light fields returning to the beam splitter,transmitting an optical signal proportional to the gravitational-wave strain to the output photodetector. To achieve sufficient sensitivity to measure gravitational waves,the detectors include several enhancements to the basic Michelson interferometer.First,each arm contains a resonant optical cavity,formed by its two test mass mirrors, that multiplies the effect of a gravitational wave on the light phase by a factor of300[48].Second,a partially trans-missive power-recycling mirror at the input provides addi-tional resonant buildup of the laser light in the interferometer as a whole[49,50]:20W of laser input is increased to700W incident on the beam splitter,which is further increased to 100kW circulating in each arm cavity.Third,a partially transmissive signal-recycling mirror at the outputoptimizes FIG. 2.Top:Estimated gravitational-wave strain amplitude from GW150914projected onto H1.This shows the full bandwidth of the waveforms,without the filtering used for Fig.1. The inset images show numerical relativity models of the black hole horizons as the black holes coalesce.Bottom:The Keplerian effective black hole separation in units of Schwarzschild radii (R S¼2GM=c2)and the effective relative velocity given by the post-Newtonian parameter v=c¼ðGMπf=c3Þ1=3,where f is the gravitational-wave frequency calculated with numerical relativity and M is the total mass(value from Table I).the gravitational-wave signal extraction by broadening the bandwidth of the arm cavities [51,52].The interferometer is illuminated with a 1064-nm wavelength Nd:Y AG laser,stabilized in amplitude,frequency,and beam geometry [53,54].The gravitational-wave signal is extracted at the output port using a homodyne readout [55].These interferometry techniques are designed to maxi-mize the conversion of strain to optical signal,thereby minimizing the impact of photon shot noise (the principal noise at high frequencies).High strain sensitivity also requires that the test masses have low displacement noise,which is achieved by isolating them from seismic noise (low frequencies)and designing them to have low thermal noise (intermediate frequencies).Each test mass is suspended as the final stage of a quadruple-pendulum system [56],supported by an active seismic isolation platform [57].These systems collectively provide more than 10orders of magnitude of isolation from ground motion for frequen-cies above 10Hz.Thermal noise is minimized by using low-mechanical-loss materials in the test masses and their suspensions:the test masses are 40-kg fused silica substrates with low-loss dielectric optical coatings [58,59],and are suspended with fused silica fibers from the stage above [60].To minimize additional noise sources,all components other than the laser source are mounted on vibration isolation stages in ultrahigh vacuum.To reduce optical phase fluctuations caused by Rayleigh scattering,the pressure in the 1.2-m diameter tubes containing the arm-cavity beams is maintained below 1μPa.Servo controls are used to hold the arm cavities on resonance [61]and maintain proper alignment of the optical components [62].The detector output is calibrated in strain by measuring its response to test mass motion induced by photon pressure from a modulated calibration laser beam [63].The calibration is established to an uncertainty (1σ)of less than 10%in amplitude and 10degrees in phase,and is continuously monitored with calibration laser excitations at selected frequencies.Two alternative methods are used to validate the absolute calibration,one referenced to the main laser wavelength and the other to a radio-frequencyoscillator(a)FIG.3.Simplified diagram of an Advanced LIGO detector (not to scale).A gravitational wave propagating orthogonally to the detector plane and linearly polarized parallel to the 4-km optical cavities will have the effect of lengthening one 4-km arm and shortening the other during one half-cycle of the wave;these length changes are reversed during the other half-cycle.The output photodetector records these differential cavity length variations.While a detector ’s directional response is maximal for this case,it is still significant for most other angles of incidence or polarizations (gravitational waves propagate freely through the Earth).Inset (a):Location and orientation of the LIGO detectors at Hanford,WA (H1)and Livingston,LA (L1).Inset (b):The instrument noise for each detector near the time of the signal detection;this is an amplitude spectral density,expressed in terms of equivalent gravitational-wave strain amplitude.The sensitivity is limited by photon shot noise at frequencies above 150Hz,and by a superposition of other noise sources at lower frequencies [47].Narrow-band features include calibration lines (33–38,330,and 1080Hz),vibrational modes of suspension fibers (500Hz and harmonics),and 60Hz electric power grid harmonics.[64].Additionally,the detector response to gravitational waves is tested by injecting simulated waveforms with the calibration laser.To monitor environmental disturbances and their influ-ence on the detectors,each observatory site is equipped with an array of sensors:seismometers,accelerometers, microphones,magnetometers,radio receivers,weather sensors,ac-power line monitors,and a cosmic-ray detector [65].Another∼105channels record the interferometer’s operating point and the state of the control systems.Data collection is synchronized to Global Positioning System (GPS)time to better than10μs[66].Timing accuracy is verified with an atomic clock and a secondary GPS receiver at each observatory site.In their most sensitive band,100–300Hz,the current LIGO detectors are3to5times more sensitive to strain than initial LIGO[67];at lower frequencies,the improvement is even greater,with more than ten times better sensitivity below60Hz.Because the detectors respond proportionally to gravitational-wave amplitude,at low redshift the volume of space to which they are sensitive increases as the cube of strain sensitivity.For binary black holes with masses similar to GW150914,the space-time volume surveyed by the observations reported here surpasses previous obser-vations by an order of magnitude[68].IV.DETECTOR VALIDATIONBoth detectors were in steady state operation for several hours around GW150914.All performance measures,in particular their average sensitivity and transient noise behavior,were typical of the full analysis period[69,70]. Exhaustive investigations of instrumental and environ-mental disturbances were performed,giving no evidence to suggest that GW150914could be an instrumental artifact [69].The detectors’susceptibility to environmental disturb-ances was quantified by measuring their response to spe-cially generated magnetic,radio-frequency,acoustic,and vibration excitations.These tests indicated that any external disturbance large enough to have caused the observed signal would have been clearly recorded by the array of environ-mental sensors.None of the environmental sensors recorded any disturbances that evolved in time and frequency like GW150914,and all environmental fluctuations during the second that contained GW150914were too small to account for more than6%of its strain amplitude.Special care was taken to search for long-range correlated disturbances that might produce nearly simultaneous signals at the two sites. No significant disturbances were found.The detector strain data exhibit non-Gaussian noise transients that arise from a variety of instrumental mecha-nisms.Many have distinct signatures,visible in auxiliary data channels that are not sensitive to gravitational waves; such instrumental transients are removed from our analyses [69].Any instrumental transients that remain in the data are accounted for in the estimated detector backgrounds described below.There is no evidence for instrumental transients that are temporally correlated between the two detectors.V.SEARCHESWe present the analysis of16days of coincident observations between the two LIGO detectors from September12to October20,2015.This is a subset of the data from Advanced LIGO’s first observational period that ended on January12,2016.GW150914is confidently detected by two different types of searches.One aims to recover signals from the coalescence of compact objects,using optimal matched filtering with waveforms predicted by general relativity. The other search targets a broad range of generic transient signals,with minimal assumptions about waveforms.These searches use independent methods,and their response to detector noise consists of different,uncorrelated,events. However,strong signals from binary black hole mergers are expected to be detected by both searches.Each search identifies candidate events that are detected at both observatories consistent with the intersite propa-gation time.Events are assigned a detection-statistic value that ranks their likelihood of being a gravitational-wave signal.The significance of a candidate event is determined by the search background—the rate at which detector noise produces events with a detection-statistic value equal to or higher than the candidate event.Estimating this back-ground is challenging for two reasons:the detector noise is nonstationary and non-Gaussian,so its properties must be empirically determined;and it is not possible to shield the detector from gravitational waves to directly measure a signal-free background.The specific procedure used to estimate the background is slightly different for the two searches,but both use a time-shift technique:the time stamps of one detector’s data are artificially shifted by an offset that is large compared to the intersite propagation time,and a new set of events is produced based on this time-shifted data set.For instrumental noise that is uncor-related between detectors this is an effective way to estimate the background.In this process a gravitational-wave signal in one detector may coincide with time-shifted noise transients in the other detector,thereby contributing to the background estimate.This leads to an overestimate of the noise background and therefore to a more conservative assessment of the significance of candidate events.The characteristics of non-Gaussian noise vary between different time-frequency regions.This means that the search backgrounds are not uniform across the space of signals being searched.To maximize sensitivity and provide a better estimate of event significance,the searches sort both their background estimates and their event candidates into differ-ent classes according to their time-frequency morphology. The significance of a candidate event is measured against the background of its class.To account for having searchedmultiple classes,this significance is decreased by a trials factor equal to the number of classes [71].A.Generic transient searchDesigned to operate without a specific waveform model,this search identifies coincident excess power in time-frequency representations of the detector strain data [43,72],for signal frequencies up to 1kHz and durations up to a few seconds.The search reconstructs signal waveforms consistent with a common gravitational-wave signal in both detectors using a multidetector maximum likelihood method.Each event is ranked according to the detection statistic ηc ¼ﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃ2E c =ð1þE n =E c Þp ,where E c is the dimensionless coherent signal energy obtained by cross-correlating the two reconstructed waveforms,and E n is the dimensionless residual noise energy after the reconstructed signal is subtracted from the data.The statistic ηc thus quantifies the SNR of the event and the consistency of the data between the two detectors.Based on their time-frequency morphology,the events are divided into three mutually exclusive search classes,as described in [41]:events with time-frequency morphology of known populations of noise transients (class C1),events with frequency that increases with time (class C3),and all remaining events (class C2).Detected with ηc ¼20.0,GW150914is the strongest event of the entire search.Consistent with its coalescence signal signature,it is found in the search class C3of events with increasing time-frequency evolution.Measured on a background equivalent to over 67400years of data and including a trials factor of 3to account for the search classes,its false alarm rate is lower than 1in 22500years.This corresponds to a probability <2×10−6of observing one or more noise events as strong as GW150914during the analysis time,equivalent to 4.6σ.The left panel of Fig.4shows the C3class results and background.The selection criteria that define the search class C3reduce the background by introducing a constraint on the signal morphology.In order to illustrate the significance of GW150914against a background of events with arbitrary shapes,we also show the results of a search that uses the same set of events as the one described above but without this constraint.Specifically,we use only two search classes:the C1class and the union of C2and C3classes (C 2þC 3).In this two-class search the GW150914event is found in the C 2þC 3class.The left panel of Fig.4shows the C 2þC 3class results and background.In the background of this class there are four events with ηc ≥32.1,yielding a false alarm rate for GW150914of 1in 8400years.This corresponds to a false alarm probability of 5×10−6equivalent to 4.4σ.FIG.4.Search results from the generic transient search (left)and the binary coalescence search (right).These histograms show the number of candidate events (orange markers)and the mean number of background events (black lines)in the search class where GW150914was found as a function of the search detection statistic and with a bin width of 0.2.The scales on the top give the significance of an event in Gaussian standard deviations based on the corresponding noise background.The significance of GW150914is greater than 5.1σand 4.6σfor the binary coalescence and the generic transient searches,respectively.Left:Along with the primary search (C3)we also show the results (blue markers)and background (green curve)for an alternative search that treats events independently of their frequency evolution (C 2þC 3).The classes C2and C3are defined in the text.Right:The tail in the black-line background of the binary coalescence search is due to random coincidences of GW150914in one detector with noise in the other detector.(This type of event is practically absent in the generic transient search background because they do not pass the time-frequency consistency requirements used in that search.)The purple curve is the background excluding those coincidences,which is used to assess the significance of the second strongest event.For robustness and validation,we also use other generic transient search algorithms[41].A different search[73]and a parameter estimation follow-up[74]detected GW150914 with consistent significance and signal parameters.B.Binary coalescence searchThis search targets gravitational-wave emission from binary systems with individual masses from1to99M⊙, total mass less than100M⊙,and dimensionless spins up to 0.99[44].To model systems with total mass larger than 4M⊙,we use the effective-one-body formalism[75],whichcombines results from the post-Newtonian approach [11,76]with results from black hole perturbation theory and numerical relativity.The waveform model[77,78] assumes that the spins of the merging objects are alignedwith the orbital angular momentum,but the resultingtemplates can,nonetheless,effectively recover systemswith misaligned spins in the parameter region ofGW150914[44].Approximately250000template wave-forms are used to cover this parameter space.The search calculates the matched-filter signal-to-noiseratioρðtÞfor each template in each detector and identifiesmaxima ofρðtÞwith respect to the time of arrival of the signal[79–81].For each maximum we calculate a chi-squared statisticχ2r to test whether the data in several differentfrequency bands are consistent with the matching template [82].Values ofχ2r near unity indicate that the signal is consistent with a coalescence.Ifχ2r is greater than unity,ρðtÞis reweighted asˆρ¼ρ=f½1þðχ2rÞ3 =2g1=6[83,84].The final step enforces coincidence between detectors by selectingevent pairs that occur within a15-ms window and come fromthe same template.The15-ms window is determined by the10-ms intersite propagation time plus5ms for uncertainty inarrival time of weak signals.We rank coincident events basedon the quadrature sumˆρc of theˆρfrom both detectors[45]. To produce background data for this search the SNR maxima of one detector are time shifted and a new set of coincident events is computed.Repeating this procedure ∼107times produces a noise background analysis time equivalent to608000years.To account for the search background noise varying acrossthe target signal space,candidate and background events aredivided into three search classes based on template length.The right panel of Fig.4shows the background for thesearch class of GW150914.The GW150914detection-statistic value ofˆρc¼23.6is larger than any background event,so only an upper bound can be placed on its false alarm rate.Across the three search classes this bound is1in 203000years.This translates to a false alarm probability <2×10−7,corresponding to5.1σ.A second,independent matched-filter analysis that uses adifferent method for estimating the significance of itsevents[85,86],also detected GW150914with identicalsignal parameters and consistent significance.When an event is confidently identified as a real gravitational-wave signal,as for GW150914,the back-ground used to determine the significance of other events is reestimated without the contribution of this event.This is the background distribution shown as a purple line in the right panel of Fig.4.Based on this,the second most significant event has a false alarm rate of1per2.3years and corresponding Poissonian false alarm probability of0.02. Waveform analysis of this event indicates that if it is astrophysical in origin it is also a binary black hole merger[44].VI.SOURCE DISCUSSIONThe matched-filter search is optimized for detecting signals,but it provides only approximate estimates of the source parameters.To refine them we use general relativity-based models[77,78,87,88],some of which include spin precession,and for each model perform a coherent Bayesian analysis to derive posterior distributions of the source parameters[89].The initial and final masses, final spin,distance,and redshift of the source are shown in Table I.The spin of the primary black hole is constrained to be<0.7(90%credible interval)indicating it is not maximally spinning,while the spin of the secondary is only weakly constrained.These source parameters are discussed in detail in[39].The parameter uncertainties include statistical errors and systematic errors from averaging the results of different waveform models.Using the fits to numerical simulations of binary black hole mergers in[92,93],we provide estimates of the mass and spin of the final black hole,the total energy radiated in gravitational waves,and the peak gravitational-wave luminosity[39].The estimated total energy radiated in gravitational waves is3.0þ0.5−0.5M⊙c2.The system reached apeak gravitational-wave luminosity of3.6þ0.5−0.4×1056erg=s,equivalent to200þ30−20M⊙c2=s.Several analyses have been performed to determine whether or not GW150914is consistent with a binary TABLE I.Source parameters for GW150914.We report median values with90%credible intervals that include statistical errors,and systematic errors from averaging the results of different waveform models.Masses are given in the source frame;to convert to the detector frame multiply by(1þz) [90].The source redshift assumes standard cosmology[91]. Primary black hole mass36þ5−4M⊙Secondary black hole mass29þ4−4M⊙Final black hole mass62þ4−4M⊙Final black hole spin0.67þ0.05−0.07 Luminosity distance410þ160−180MpcSource redshift z0.09þ0.03−0.04。

浅说中等质量黑洞

“ 遗迹 ”。可见，恒星级黑洞乃是大质量恒星在
３中等质量黑洞
２０年前有人注意到，超大质量黑洞的质量与母星系（或其核球）的蓝波段光度￡线性相关，即存在一关系，并很快为随后的相关工作所证实。５年后，一系列的工作进而发现，
和运动学状态，会因黑洞对其强大的引力作用而改变。或者，黑洞在吸积周围物质的过程中，被吸积物质会发出很强的ｘ射线辐射和射电辐射。黑洞的这些效应为探测黑洞是否存在提供了间接的、然而是有力的观测判据。
实质上，黑洞决非什么黑色之物，更称不上是一种 “ 洞 ”，实质上是一类具有封闭边界的
一
个质子的大小！作为比较，一个地球质量黑洞
的尺度只有乒乓球那么大，而１个太阳质量黑洞
的引力半径约为２．９ｋｍ，黑洞世界的奇妙之处可
见一斑。
中子星（原有质量介于１Ｏ￣２０Ｍｅ之间）和黑洞（原有质量大于２０）。这３类天体都可称为恒星的
超大质量黑洞的与其母星系核区恒星的速度
弥散度（即统计学上的均方差）强相关，即存在
天体。黑洞的边界就是外部观测者视线所不能及的范围，称之为 “ 视界 ”。可以把黑洞视界所包容的空间想象为大致呈圆球形，球的半径是为黑洞的引力半径，俗称黑洞半径。黑洞视界之外的物质和辐射可进入视界之内（称为黑洞吸积），但视界内的任何物质和辐射都不能逸出视界，于是

高中语文人教版必修3 4.13黑洞简介

黑洞简介黑洞（Black hole）是现代广义相对论中，宇宙空间内存在的一种密度无限大，体积无限小的天体，所有的物理定理遇到黑洞都会失效。

1916年，德国天文学家卡尔·史瓦西（Karl Schwarzschild，1873～1916年）通过计算得到了爱因斯坦引力场方程的一个真空解，这个解表明，如果将大量物质集中于空间一点，其周围会产生奇异的现象，即在质点周围存在一个界面——“视界”一旦进入这个界面，即使光也无法逃脱。

这种“不可思议的天体”被美国物理学家约翰·阿奇巴德·惠勒（John Archibald Wheeler）命名为“黑洞”。

“黑洞是时空曲率大到光都无法从其视界逃脱的天体”。

黑洞是由质量足够大的恒星在核聚变反应的燃料耗尽而死亡后，发生引力坍缩产生的。

黑洞的质量极其巨大，而体积却十分微小，它产生的引力场极为强劲，以至于任何物质和辐射在进入到黑洞的一个事件视界（临界点）内，便再无法逃脱，甚至目前已知的传播速度最快的光（电磁波）也逃逸不出。

黑洞无法直接观测，但可以借由间接方式得知其存在与质量，并且观测到它对其他事物的影响。

借由物体被吸入之前的因高热而放出紫外线和X射线的“边缘讯息”，可以获取黑洞存在的讯息。

推测出黑洞的存在也可借由间接观测恒星或星际云气团绕行轨迹取得位置以及质量。

科学家最新研究理论显示，当黑洞死亡时可能会变成一个“白洞”，它不像黑洞吞噬邻近所有物质，而是喷射之前黑洞捕获的所有物质。

演化过程黑洞就是中心的一个密度无限大、时空曲率无限高、体积无限小的奇点和周围一部分空空如也的天区，这个天区范围之内不可见。

依据阿尔伯特-爱因斯坦的相对论，当一颗垂死恒星崩溃，它将聚集成一点，这里将成为黑洞，吞噬邻近宇宙区域的所有光线和任何物质。

黑洞的产生过程类似于中子星的产生过程：某一个恒星在准备灭亡，核心在自身重力的作用下迅速地收缩，塌陷，发生强力爆炸。

当核心中所有的物质都变成中子时收缩过程立即停止，被压缩成一个密实的星体，同时也压缩了内部的空间和时间。

地球与拟态黑洞的洛希极限

地球与拟态黑洞的洛希极限
地球与拟态黑洞的洛希极限。

随着科技的不断进步，人类对于宇宙中黑洞的认识也越来越深入。

其中，拟态黑洞是一种比较特殊的黑洞类型，它与地球之间的洛希极限
也有着密切的联系。

一、什么是洛希极限？
洛希极限，又称为洛希半径，是指一个星体因为引力作用而无法稳定
存在于另一个星体的周围的距离。

这个距离取决于两个星体的质量和
距离。

二、什么是拟态黑洞？
拟态黑洞，是一种假想的天体，其质量可以非常小，同时也具有与黑
洞相似的外观和引力场。

其名字来源于拟态效应（mimicry effect），
即表现出与另一种物体或动物相似的特征，以达到欺骗或保护的目的。

三、拟态黑洞的洛希极限
根据现有理论，拟态黑洞与地球之间的洛希极限大约在15万公里左右。

这也就意味着，如果拟态黑洞距离地球的距离小于这个数值，那么它
就很容易被地球的引力所捕获，成为地球的附属天体。

四、洛希极限的应用
除了在黑洞和拟态黑洞的研究中有着重要意义外，洛希极限在天文学
中还有着广泛应用。

例如，它可以用来解释为什么在太阳系行星轨道
上存在着一些小行星和彗星，以及为什么卫星轨道上不能太过密集等
问题。

总之，地球与拟态黑洞的洛希极限是一项十分有趣的领域，它不仅让
我们更深入地了解了洛希极限的概念和应用，还有助于深入探索黑洞、拟态黑洞等神秘天体的奥秘。

黑洞到底有多大

黑洞到底有多大：
目前已知最大黑洞名为SDSS J140821.67+025733.2，质量为太阳的1960亿倍，是芬兰科学家发现的一个巨大的双黑洞系统。

这个宇宙最大黑洞是之前天文学所记录最大黑洞的6倍，它的质量很大，相当于一个小型星系，它距离地球35亿光年，形成于OJ287类星体的中心位置。

类星体是一种极端明亮的星体，它的物体将持续螺旋状进入一个大型黑洞并释放大量辐射线。

然而，十分特殊的是，OJ287类星体包含着两个黑洞，除此之外还有一个质量略小的黑洞，这样的星体组合使天文学家能够更为精确地对宇宙中最大的黑洞"量体重"。

最小黑洞位于天蝎座方向，这个黑洞系统包含一个拥有14倍太阳质量的黑洞，它不断发出具有非常精确特定模式的X射线辐射，脉冲的持续时间从数秒到数小时不等。

相比之下，这次观测到的黑洞脉动信号要比之前那个案例要暗弱20倍，并且其脉动信号周期重复的时间也要比前者快8倍左右，最短持续时间仅5秒左右。

黑洞：
黑洞是恒星的残余，是演变到最后阶段的恒星，它们以超新星的形式结束了自己的生命。

它们的特征是一个空间区域，在这个空间中重力非常强，甚至光都无法逃逸。

这个区域的边界被称为视界，在黑洞的中心是奇点，死恒星的质量被压缩到一个零大小和无限密度的单一点。

正是这个奇点产生了黑洞强大的引力场，使得它所发射的任何电磁波都无法向外传播，变成看不见的孤立天体，人们只能通过引力作用来确定它的存在，故名黑洞。

《飞向人马座》(课件)

求出。 • 旋转不带电黑洞：称克尔黑洞。时空结构由克尔于1963年求出。 • 旋转带电黑洞：称克尔-纽曼黑洞。时空结构于1965年由纽曼求出
发现“超大”黑洞
• 2015年3月1日，北京大学吴学兵教授等人在一个发光类星体里发现了一片质量为太阳120亿倍的黑洞，并且该星体早在宇宙形成的早期就已经存在。科学家称，如此巨大的黑洞的形成无法用现有黑洞理论解释。
• 超新星是某些恒星在演化接近末期时经历的一种剧烈爆炸。这种爆炸都极其明亮，过程中所突发的电磁辐射经常能够照亮其所在的整个星系，并可能持续几周至几个月才会逐渐衰减。由于在一个星系中超新星是很少见的事件，银河系大约每隔50年发生一次。
超新星的搜寻分为两大类
一些侧重于相对较近发生的事件，另一些则寻找更早期的爆炸。
由于宇宙的膨胀，一个已知发射光谱的远程对象的距离可以通过测量其多普勒频移（或红移）来估计。平均而言，较远的物体比较近的物体以更大速度减弱，因此具有更高的红移。因此，搜寻分为高红移和低红移，其边界约为z = 0.1–0.3之间——其中z是频谱频移的无量纲量度。
超新星的发现
怎么来的呢？
• 在20世纪30年代，沃尔特·巴德和弗里茨·兹威基在威尔逊山天文台时 [19] ，起初的工作相信这只是一种新类型的新星。“超新星（super-novae）”这个名词在1931年巴德和兹威基在加州理工学院的一场演讲中首度被使用，然后在1933年在美国物理学会的会议中被大众使用
怎么发现的？
• 恒星从中心开始冷却，它没有足够的热量平衡中心引力，结构上的失衡就使整个星体向中心坍缩，造成外部冷却而红色的层面变热，如果恒星足够大，这些层面就会发生剧烈的爆炸，产生超新星。大质量恒星爆炸时光度可突增到太阳光度的上百亿倍，相当于整个银河系的总光度。

The Soft X-ray Imager(SXI)on the SMILE Mission

The Soft X-ray Imager(SXI)on the SMILE MissionS.Sembay;A.L.Alme;D.Agnolon;T.Arnold;A.Beardmore;A.Belén BaladoMargeli;C.Bicknell;C.Bouldin;G.Branduardi-Raymont;T.Crawford;J.P.Breuer;T.Buggey;G.Butcher;R.Canchal;J.A.Carter;A.Cheney;Y.Collad o-Vega;H.Connor;T.Crawford;N.Eaton;C.Feldman;C.Forsyth;T.Frantzen;G.Galgóczi;J.Garcia;G.Y. Genov;C.Gordillo;H-P.Gröbelbauer;M.Gu edel6.Guo;M.Hailey;D.Hall;R.Hampson;J.Hasiba;O.Hetherington;A.Holl and;S-Y.Hsieh;M.W.J.Hubbard;H.Jeszenszky;M.Jones;T.Kennedy;K.Koch-Mehrin;S.Kögl;S.Krucker;K.D.Kuntz;kin;ky;O.Lylund;A.Martindale;J.Miguel Mas Hesse;R.Nakamura;K.Oksavik;N.Østgaard;H.Ottacher;R.Ottensamer;C.Pagani;S.Parsons;P.Pa tel;J.Pearson;G.Peikert;F.S.Porter;T.Pouliantis;B.H.Qureshi;W.Raab;G.Randal;A.M.Read;N.M. M.Roque;M.E.Rostad;C.Runciman;S.Sachdev;A.Samsonov;M.Soman;D.Sibeck;S.Smit;J.Sønd ergaard;R.Speight;S.Stavland;M.Steller;TianRanSun;J.Thornhill;W.Thomas;K.Ullaland;B.Walsh;D.Walton;C.Wang;S.Yang【期刊名称】《Earth and Planetary Physics》【年(卷),期】2024(8)1【摘要】The Soft X-ray Imager(SXI)is part of the scientific payload of the Solar wind Magnetosphere Ionosphere Link Explorer(SMILE)mission.SMILE is a joint science mission between the European Space Agency(ESA)and the Chinese Academy of Sciences(CAS)and is due for launch in 2025.SXI is a compact X-ray telescope with a wide field-of-view(FOV)capable of encompassing large portions of Eart h’s magnetosphere from the vantage point of the SMILE orbit.SXI is sensitive to the soft X-rays produced by theSolar Wind Charge eXchange(SWCX)process produced when heavy ions of solar wind origin interact with neutral particles in Earth’s exosphere.SWCX provides a mechanism for boundary detection within the magnetosphere,such as the position of Earth’s magnetopause,because the solar wind heavy ions have a very low density in regions of closed magnetic field lines.The sensitivity of the SXI is such that it can potentially track movements of the magnetopause on timescales of a few minutes and the orbit of SMILE will enable such movements to be tracked for segments lasting many hours.SXI is led by the University of Leicester in the United Kingdom(UK)with collaborating organisations onhardware,software and science support within the UK,Europe,China and the United States.【总页数】10页(P5-14)【作者】S.Sembay;A.L.Alme;D.Agnolon;T.Arnold;A.Beardmore;A.Belén Balado Margeli;C.Bicknell;C.Bouldin;G.Branduardi-Raymont;T.Crawford;J.P.Breuer;T.Buggey;G.Butcher;R.Canchal;J.A.Carter;A.C heney;Y.Collado-Vega;H.Connor;T.Crawford;N.Eaton;C.Feldman;C.Forsyth;T.Frantzen;G.Galgóczi;J.Garcia;G.Y.Genov;C.Gordillo;H-P.Gröbelbauer;M.Guedel6.Guo;M.Hailey;D.Hall;R.Hampson;J.Hasiba;O.Heth erington;A.Holland;S-Y.Hsieh;M.W.J.Hubbard;H.Jeszenszky;M.Jones;T.Kennedy;K.Koch-Mehrin;S.Kögl;S.Krucker;K.D.Kuntz;kin;ky;O.Lylund;A.Martindale;J.Miguel MasHesse;R.Nakamura;K.Oksavik;N.Østgaard;H.Ottacher;R.Ottensamer;C.Pagan i;S.Parsons;P.Patel;J.Pearson;G.Peikert;F.S.Porter;T.Pouliantis;B.H.Qureshi;W. Raab;G.Randal;A.M.Read;N.M.M.Roque;M.E.Rostad;C.Runciman;S.Sachdev;A.Samsonov;M.Soman;D.Sibeck;S.Smit;J.Søndergaard;R.Speight;S.Stavland; M.Steller;TianRanSun;J.Thornhill;W.Thomas;K.Ullaland;B.Walsh;D.Walton;C.Wang;S.Yang 【作者单位】School of Physics and Astronomy of Leicester;Space Park Leicester of Leicester;Mullard Space Science Laboratory College London;Centre for Electronic Imaging University Keynes AA;Birkeland Centre for Space Science of Physics and Technology.of Bergen-5007 Bergen;University of Vienna-1010 Vienna;Space Research Institute Academy of Sciences-8042 Graz;National Institute of Aerospace Technology;ESTEC Space Agency AZ Noordwijk;State Key Laboratory of Space Weather Space Science Centre 100190;University of Applied Sciences and Arts Northwestern Switzerland-5210 Windisch;Koegl Space GmbH-8157 Dielsdorf;Space Acoustics GmbH-8157 Dielsdorf;Zurich University of Applied Sciences Winterhur;Genov Solutions-5172 Loddefjord;STM Engineering-5165 Laksevag;John Hopkins University Applied Physics Laboratory 20723;NASA/Goddard Space Flight Centre 20771;Center for Space Physics University 02215;Department of Theoretical Physics and Astrophysics University Brno Republic;Institute of Physics¨otvo¨s Lor´and Univ ersity Budapest;Aerospace InformationResearch Institute Academy of Sciences 100045;Centro de Astrobiologia(CAB)-INTA【正文语种】中文【中图分类】P35【相关文献】1.Hard X-ray Imager (HXI) onboard the ASO-S mission2.Estimating the subsolar magnetopause position from soft X-ray images using a low-pass image filter3.Simulation of the SMILE Soft X-ray Imager response to a southward interplanetary magnetic field turning4.On the apparent line-of-sight alignment of the peak X-ray intensity of the magnetosheath and the tangent to the magnetopause,as viewed by SMILE-SXI5.SMILE soft X-ray Imager flight model CCD370 pre-flight device characterisation因版权原因，仅展示原文概要，查看原文内容请购买。

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arXiv:astro-ph/9909270v1 15 Sep 1999HIGHMASSBLACKHOLESINSOFTX-RAYTRANSIENTSGapinBlackHoleMasses?

G.E.BROWN,C.-H.LEEDepartmentofPhysicsandAstronomy,SUNYatStonyBrook,NY11794,USA

ANDH.A.BETHEFloydR.NewmanLaboratoryofNuclearStudies,CornellUniversity,Ithaca,NewYork14853,USA

Abstract.1Wesuggestthathigh-massblackholes;i.e.,blackholesofseveralsolarmasses,canbeformedinbinarieswithlow-massmain-sequencecompanions,providedthatthehydrogenenvelopeofthemassivestarisremovedincommonenvelopeevolutionwhichbeginsonlyafterthemassivestarhasﬁnishedHecoreburning.Ourevolutionscenarionaturallyexplainsthegap(lowprobabilityregion)intheobservedblackholemasses.

1.IntroductionInthistalkwesuggestthathigh-massblackholes;i.e.,blackholesofsev-eralsolarmasses,canbeformedinbinarieswithlow-massmain-sequencecompanions,providedthatthehydrogenenvelopeofthemassivestarisre-movedincommonenvelopeevolutionwhichbeginsonlyafterthemassivestarhasﬁnishedHecoreburning(Brown,Lee,&Bethe1999).Thatis,themassivestarisinthesupergiantstage,whichlastsonly∼104years,soeﬀectsofmasslossbyHewindsaresmall.Sincetheremovalofthehy-drogenenvelopeofthemassivestaroccurssolate,itevolvesessentiallyasasinglestar,ratherthanoneinabinary.Thus,wecanuseevolutionarycalculationsofWoosley&Weaver(1995)ofsinglestars.Weﬁndthathigh-massblackholescanbeformedinthecollapseofstarswithZAMSmass∼>20M⊙.Masslossbywindsinstarssuﬃciently

1TalkgivenbyC.-H.LeeattheNATOAdvancedStudyInstituteon“TheNeutron

Star-BlackHoleConnection”,June7-18,1999,Elounda,Crete,Greece2G.E.BROWN,C.-H.LEEANDH.A.BETHE

TABLE1.ParametersofsuspectedblackholebinariesinsoftX-raytransientswithmeasuredmassfunctions(Brown,Lee,&Bethe1999).Nmeansnova,XNmeansX-raynova.Numbersinparenthesisindicateerrorsinthelastdigits.

namesname(s)qKoptiMX

(Mopt/MX)(kms−1)(degree)(M⊙)

massivetoundergotheLBV(luminousbluevariable)stagemayseriouslyaﬀecttheevolutionofstarsofZAMS>35−40M⊙,wetaketheupperlimitfortheevolutionoftheso-calledtransientsourcestobe∼35M⊙

ZAMSmass.BothPortegiesZwart,Verbunt&Ergma(1997)andErgma

&VandenHeuvel(1998)havesuggestedthatroughlyourchosenrangeofZAMSmassesmustberesponsibleforthetransientsources.Webelievethatthehigh-massblackholelimitofZAMSmass∼40M⊙suggestedbyVandenHeuvel&Habets(1984)andlaterrevisedto≥50M⊙(Kaperetal.1995)appliestomassivestarsinbinaries,whichundergoRLOF(RocheLobeOverﬂow)earlyintheirevolution.Themostcopioushigh-massblackholesofmasses∼6−7M⊙havebeenfoundinthetransientsourcessuchasA0620.Thesehavelow-masscompanions,predominantlyof∼<1M⊙,suchasK–orM–stars.IntheHIGHMASSBLACKHOLESINSOFTX-RAYTRANSIENTS3Figure1.Comparisonofthecompactcoremassesresultingfromtheevolutionofsin-glestars(ﬁlledsymbols,CaseBofWoosley&Weaver1995),andnakedheliumstars(Woosley,Langer&Weaver1995)withmassesequaltothecorrespondingHecoremassofsinglestars.10.020.030.040.0ZAMS mass0.00.51.01.512C/16OFigure2.Ratioofproductionratesof12Cand16Oresultingfromtheevolution

ofsinglestars(ﬁlledsymbols),caseofsolarmetallicityofWoosley&Weaver(1995).

progenitorbinariesthemassratiosmusthavebeentiny,sayq∼1/25.FollowingtheevolutionaryscenariofortheblackholebinaryofDeKooletal.(1987),weshowthatthereasonforthissmallq-valueliesinthecommonenvelopeevolutionofthebinary.Thesmallerthecompanionmass,thegreatertheradiusRgthegiantmustreachbeforeitsenvelopemeetsthecompanion.Thisresultsbecausetheorbitofalow-masscompanionmustshrinkbyalargefactorinordertoexpeltheenvelopeofthegiant,hencetheorbitmustinitiallyhavealargeradius.(ItsﬁnalradiusmustbejustinsideitsRocheLobe,whichsetsalimittothegravitationalenergyitcanfurnish.)AlargeradiusRginturnmeansthattheprimarystarmustbeinthesupergiantstage.ThusitwillhavecompleteditsHecoreburningwhileitisstill“clothed”withhydrogen.ThispreventsexcessivemasslosssothattheprimaryretainsessentiallythefullmassofitsHecorewhenitgoessupernova.WebelievethisiswhyK–andM–starcompanionsofhigh-massblackholesarefavored.

2.FormationofHigh-MassBlackHolesWeﬁndthattheblackholesintransientsourcescanbeformedfromstarswithZAMSmassesintheinterval20−35M⊙(Brown,Lee,&Bethe1999).TheblackholemassisonlyslightlysmallerthantheHecoremass,typically∼7M⊙(Bethe,Brown,&Lee1999).CrucialtoourdiscussionhereisthefactthatsinglestarsevolveverydiﬀerentlyfromstarsinbinariesthatlosetheirH-envelopeeitheronthe