# ¿Es posible calcular el centro de masa del universo visible?

Es fácil deducir que parecemos estar en el centro del universo visible, asumiendo que el universo visible es aproximadamente isótropo y homogéneo en todas sus propiedades, incluidas las de expansión. La luz tiene la misma velocidad finita en todas las direcciones, por lo que no podemos ver ninguna luz, desde ninguna dirección hacia el exterior, lo que tendría que haber tardado más que la edad actual del universo en llegar a nosotros.

Suponiendo que la velocidad finita de la interacción de la fuerza gravitacional es la misma que la de la luz. ¿Qué podemos decir sobre la ubicación del centro de masa del marco del universo visible? Localmente, el supuesto isotrópico y homogéneo no se aplica, ya que en un cálculo de centro de masa, la tierra tiene una masa pequeña en comparación con el resto del sistema solar, la galaxia de la Vía Láctea y un cúmulo de galaxias más amplio, etc. escala donde el supuesto isotrópico y homogéneo vuelve a ser razonable.

1. ¿Podemos, en principio, calcular la posición del centro de masa (el centro del marco de masa) del universo visible (es decir, visible desde la tierra) a partir de las observaciones astronómicas que tenemos hasta la fecha?
2. Si esto es posible, ¿habría alguna conexión entre este marco del centro de masa y el marco que está estacionario en relación con la Radiación Cósmica de Fondo de Microondas (CMBR) observada desde la Tierra?

## ¿Es posible calcular el centro de masa del universo visible? - Astronomía

Las masas de las galaxias se encuentran a partir del movimiento orbital de sus estrellas. Las estrellas de una galaxia más masiva orbitarán más rápido que las de una galaxia de menor masa porque la mayor fuerza de gravedad de la galaxia masiva provocará mayores aceleraciones de sus estrellas. Al medir las velocidades de las estrellas, averigua cuánta gravedad hay en la galaxia. Dado que la gravedad depende de la masa y la distancia, conocer el tamaño de las órbitas de las estrellas le permite derivar la masa de la galaxia.

Para las galaxias espirales, curva de rotacion se usa para medir sus masas como se hace para encontrar la masa de la Vía Láctea. La curva de rotación muestra cómo las velocidades orbitales en una galaxia dependen de su distancia desde el centro de la galaxia. La masa dentro de una distancia dada desde el centro = (velocidad orbital) 2 & # 215 (distancia desde el centro) /GRAMO. La velocidad orbital se encuentra a partir de los cambios Doppler de la línea de radiación de 21 cm del gas hidrógeno atómico. La angular Se mide la distancia de la pieza del disco desde el centro, pero para usar la fórmula de masa incluida, la pieza del disco real lineal se debe encontrar la distancia desde el centro.

Recuerde en el capítulo de ciencia planetaria que la distancia lineal se puede encontrar a partir de la distancia angular si conoce la distancia a ¿el objeto? La distancia lineal desde el centro de la galaxia = [(2& # 215 (distancia a la galaxia) & # 215 (distancia angular en grados)] / 360 & deg. Es por eso que primero debe conocer la distancia a una galaxia si desea medir su masa.

Para las galaxias elípticas, el ancho de las líneas de absorción de todas las estrellas mezcladas se usa para medir la masa de las galaxias elípticas. El ancho de las líneas de absorción depende de la extensión de la distribución de las velocidades --- el dispersión de velocidad. Masa de la galaxia elíptica = k & # 215 (dispersión de velocidad) 2 & # 215 (la distancia entre las estrellas y el centro de la galaxia) /GRAMO, dónde k es un factor que depende de la forma de la galaxia y el ángulo de la galaxia con respecto a la Tierra.

Las estrellas y el gas en casi todas las galaxias se mueven mucho más rápido de lo esperado debido a la luminosidad de las galaxias. En los 1970s, Vera Rubin (vivió entre 1928 y 2016) encontró que en las galaxias espirales, la curva de rotación permanece aproximadamente al mismo valor a grandes distancias del centro (se dice que es  plana ''). Esto significa que la masa encerrada continúa aumentando a pesar de que la cantidad de materia luminosa visible cae a grandes distancias del centro. En las galaxias elípticas, la gravedad de la materia visible no es lo suficientemente fuerte como para acelerar las estrellas tanto como ellas. Algo más debe estar aumentando la gravedad de las galaxias sin brillar.

Que otra cosa se llama materia oscura. Es un material que no produce cantidades detectables de luz pero tiene un efecto gravitacional notable. Los astrónomos no están seguros de qué está hecha la materia oscura. Las posibilidades van desde cosas grandes como planetas, enanas marrones, enanas blancas, agujeros negros hasta una gran cantidad de cosas pequeñas como neutrinos u otras partículas exóticas que aún no se han visto en nuestros laboratorios. Por razones que se explicarán en la siguiente sección y en el capítulo de cosmología, los astrónomos han descubierto que la materia oscura es una combinación de todas esas cosas, pero las partículas exóticas deben constituir la gran mayoría de la materia oscura. De hecho, de la materia total del universo, la masa total de las partículas exóticas es cinco veces la masa total de la "materia ordinaria" con la que estamos más familiarizados (materia hecha de protones, neutrones, electrones, neutrinos, etc.). La naturaleza de la materia oscura es uno de los problemas centrales de la astronomía actual. Aunque se desconoce su naturaleza, la materia oscura parece ser una parte tan integral de las galaxias que la presencia de materia oscura se usa para distinguir una galaxia pequeña de un gran cúmulo globular, los cuales pueden tener el mismo número de estrellas.

## ¿Es posible calcular el centro de masa del universo visible? - Astronomía

El misterio de la materia oscura

• su distancia de la masa central, y
• la masa total encerrada dentro de su órbita.

• encuentre múltiples imágenes de una sola galaxia creadas por la lente gravitacional (las características azuladas en la imagen de arriba). (¿Cómo sabemos que son múltiples imágenes de una sola galaxia?)
• determine la distancia angular a las múltiples imágenes como se ve en la imagen.
• determinar la distancia a la galaxia distorsionada a partir de su velocidad de recesión y la Ley de Hubble
• Determine la distancia al cúmulo de la misma manera, utilizando la Ley de Hubble.
• utilice la teoría de la relatividad general de Einstein para relacionar la separación angular con la masa del cúmulo.
La materia oscura es misteriosa, pero no tiene por qué ser exótica. Una posibilidad es que se trata simplemente de objetos pequeños pero densos de materia ordinaria que son invisibles. Algunos ejemplos son las enanas marrones (demasiado pequeñas para ser estrellas y demasiado débiles para detectarlas en el halo galáctico), enanas negras (viejas enanas blancas que se han enfriado y ya no emiten mucha luz), agujeros negros o quizás alguna otra forma de vida ordinaria. importar. Tal materia se llama bariónico materia, porque está formada por bariones (protones y neutrones). Los astrónomos han llamado caprichosamente a tales objetos como MACHO (Massive Compact Halo Objects). Dado que tales objetos son demasiado débiles para verlos, tenemos que utilizar otros medios para detectarlos. Una forma es buscar pequeños eventos de lentes gravitacionales a medida que pasan frente a fuentes de luz lejanas. De hecho, se han visto eventos de lente tan pequeños, pero no en la gran cantidad que se requeriría para dar cuenta de la materia faltante.

Una posibilidad más exótica es que la materia oscura no está en forma de materia ordinaria, sino que está hecha de algún tipo de partícula subatómica que aún no hemos descubierto. Tales partículas deberían tener mucha masa, pero no interactuar con la luz. Los astrónomos han denominado (de nuevo de forma caprichosa) objetos como WIMP (partículas masivas de interacción débil). Ya hemos conocido un tipo de partícula que interactúa débilmente: el neutrino. Pero los neutrinos, que existen en grandes cantidades, tienen dos problemas. Una es que no tienen suficiente masa (aunque pueden contribuir una pequeña cantidad a la materia oscura fuera de las galaxias), y la otra es que no se acumularían alrededor de los cúmulos de galaxias. Son tan enérgicos que giran alrededor del universo a cualquier lugar al que quieran ir y apenas sienten los centros de masa en los cúmulos de galaxias. En cambio, necesitamos algún tipo de partícula que sea más masiva que los neutrinos, y que sea más lenta para que pueda acumularse alrededor de los centros de masa. Hasta ahora no hemos descubierto tales partículas, pero quizás algún día los experimentos con partículas las identifiquen.

Mientras tanto, estamos atascados sin una explicación segura y sin demasiadas pistas. Una pista importante que parece favorecer a los WIMP sobre los MACHO es la distribución de la materia oscura. La materia bariónica ordinaria se ha acumulado en los centros de concentraciones de masa, como las galaxias y los cúmulos de galaxias, por lo que, sea lo que sea la materia oscura, debe resistir la acumulación en estas escalas. Los WIMP satisfacen esta expectativa muy bien, ya que habrían nacido bastante calientes (alta velocidad) en el Big Bang. Los bariones también estaban calientes, pero interactúan con la luz y, por lo tanto, producen radiación que les permite derramar su energía, enfriarse y acumularse en galaxias, etc. Los WIMP, por otro lado, no tienen forma de perder energía, por lo que permanecerían más agrupados libremente en halos de galaxias.

En la primera conferencia discutimos el hecho de que nuestra galaxia es parte del Grupo local de galaxias, que comprenden la Vía Láctea, la Galaxia de Andrómeda, las Nubes de Magallanes y unas 20 más. También dijimos que el Grupo Local era parte de una colección más grande de galaxias llamada el Supercluster local . Cuando miramos hacia el cielo nocturno, vemos un gran número de galaxias en todas las direcciones, y a partir de sus velocidades de recesión y la Ley de Hubble podemos determinar su distancia. A partir de esto, podemos construir un mapa tridimensional de ubicaciones de galaxias. Lo que encontramos es que las galaxias no se distribuyen uniformemente en el espacio, sino que forman estas enormes estructuras llamadas supercúmulos, que se mantienen unidas por la gravedad.

Al medir las velocidades peculiares de las galaxias (sus velocidades después de restar su velocidad de recesión), encontramos que parecen estar reuniéndose en concentraciones de masa. Aquí está la Figura 21.13 del texto La perspectiva cósmica, que traza las velocidades peculiares de las galaxias cercanas a la nuestra (la Vía Láctea está en el centro).

Fig 21.13 desde la perspectiva cósmica, por Bennet, Donahue, Schneider & amp Voit, Addison Wesley (1998)

Las galaxias parecen moverse "cuesta abajo" en varias concentraciones de masa. Cuando miramos más lejos en el universo, la estructura a gran escala del universo se hace evidente. Hay regiones de supercúmulos y otras regiones llamadas vacíos , que no contienen galaxias en absoluto. La estructura general aparece como una esponja, con vacíos esféricos separados por membranas de masa.

Figura 21.14a
Figura 21.14b

Para explorar cómo se creó esta estructura, podemos comenzar con el Big Bang e imaginar algunas pequeñas fluctuaciones en el universo temprano. Estas fluctuaciones habrían sido ligeramente más frías y hubieran permitido que la masa se acumulara y colapsara, lo que enfrió aún más la región (al irradiar el exceso de energía), de modo que las áreas donde se acumula la materia se concentran más. Entonces, la estructura a gran escala que vemos nos muestra cómo debió ser el universo primitivo. Podemos ejecutar simulaciones y ver qué condiciones iniciales se necesitan para que el universo aparezca como lo hace hoy.

El destino del universo está ligado a esta cuestión. ¿Continuará expandiéndose el universo para siempre, o eventualmente dejará de expandirse y comenzará a colapsar (para terminar en el " Gran crujido , "que es lo opuesto al Big Bang)? La respuesta a esta pregunta depende de la densidad del universo. Hay un densidad crítica en el que el universo se ralentizará pero no dejará de expandirse, simplemente equilibrándose en el borde entre expandirse para siempre y colapsar. Si el universo es menor que la densidad crítica, continuará expandiéndose para siempre (lo que lleva a una universo abierto ), mientras que si es más que la densidad crítica, eventualmente dejará de expandirse (lo que lleva a una universo cerrado ). Exactamente a la densidad crítica, el universo seguirá expandiéndose para siempre, pero irá cada vez más lentamente para que finalmente se detenga después de que haya pasado un tiempo infinito. A esto se le llama universo plano .

Tenga en cuenta que cada uno de estos escenarios indica que la expansión debería ralentizarse, incluso si nunca se detiene. Cuando hacemos mediciones diseñadas para determinar si nuestro universo está abierto o cerrado, siempre parece indicar que estamos muy, muy cerca de un universo plano. Eso significa que nuestro universo está cerca de la densidad crítica. Sin embargo, cuando contamos toda la materia, encontramos que no es suficiente para hacer que el universo sea plano, incluso si incluimos la materia oscura. De hecho, si llamamos a la densidad crítica r critico , entonces la densidad de la materia parece estar alrededor de 0.3 r critico . Sin embargo, deberíamos poder decir si el universo estaba tan abierto (tan por debajo de la densidad crítica), y nuestras observaciones no lo demuestran. Durante muchos años hemos tenido esta aparente contradicción: el universo parece ser plano, pero hay muy poca materia (incluida la materia oscura) para que lo sea.

Recientemente, las cosas se han vuelto aún más extrañas. Al medir las supernovas más distantes, que creemos que son velas estándar, parece que el universo una vez se expandió más lentamente que ahora. En otras palabras, la tasa de expansión parece estar acelerándose ! Los astrónomos ahora están jugando con la idea de que existe una forma exótica de energía que está separando el espacio: una especie de gravedad negativa. Esta forma de energía se llama energía oscura , y es posible que, si hay suficiente energía oscura, podría explicar por qué el universo parece plano.

La próxima vez (nuestra última conferencia) analizaremos la cuestión de la cosmología, el Big Bang y el comienzo del universo.

## Contenido

Al informar sobre NGC 3115, Jan Oort escribió que "la distribución de masa en el sistema parece no tener casi ninguna relación con la de la luz. Uno encuentra que la proporción de masa a luz en las partes externas de NGC 3115 es de aproximadamente 250". [11] En las páginas 302-303 de su artículo de revista, escribió que "El sistema luminoso fuertemente condensado aparece incrustado en una masa grande y más o menos homogénea de gran densidad" y aunque continuó especulando que esta masa puede ser estrellas enanas extremadamente débiles o gas y polvo interestelar, había detectado claramente el halo de materia oscura de esta galaxia.

El telescopio Carnegie (Carnegie Double Astrograph) estaba destinado a estudiar este problema de la rotación galáctica. [12]

Si se supone que la mecánica newtoniana es correcta, se deduciría que la mayor parte de la masa de la galaxia tenía que estar en la protuberancia galáctica cerca del centro y que las estrellas y el gas en la porción del disco deberían orbitar el centro a velocidades decrecientes con la distancia radial. desde el centro galáctico (la línea discontinua en la Fig. 1).

Sin embargo, las observaciones de la curva de rotación de las espirales no lo confirman. Más bien, las curvas no disminuyen en la relación de raíz cuadrada inversa esperada, sino que son "planas", es decir, fuera del abultamiento central la velocidad es casi constante (la línea continua en la Fig. 1). También se observa que las galaxias con una distribución uniforme de materia luminosa tienen una curva de rotación que se eleva desde el centro hasta el borde, y la mayoría de las galaxias de bajo brillo superficial (galaxias LSB) tienen la misma curva de rotación anómala.

Las curvas de rotación podrían explicarse planteando la hipótesis de la existencia de una cantidad sustancial de materia que impregna la galaxia fuera del bulbo central que no emite luz en la relación masa / luz del bulbo central. El material responsable de la masa extra se denominó materia oscura, cuya existencia fue planteada por primera vez en la década de 1930 por Jan Oort en sus mediciones de las constantes de Oort y Fritz Zwicky en sus estudios de las masas de los cúmulos de galaxias. La existencia de materia oscura fría (CDM) no bariónica es hoy una característica importante del modelo Lambda-CDM que describe la cosmología del universo.

Para acomodar una curva de rotación plana, un perfil de densidad para una galaxia y sus alrededores debe ser diferente a uno que está concentrado centralmente. La versión de Newton de la tercera ley de Kepler implica que el perfil de densidad radial esféricamente simétrico ρ(r) es:

ρ (r) = v (r) 2 4 π G r 2 (1 + 2 re log ⁡ v (r) re log ⁡ r) < Displaystyle rho (r) = < frac > <4 pi Gr ^ <2> >> left (1 + 2

dónde v(r) es el perfil de velocidad orbital radial y GRAMO es la constante gravitacional. Este perfil coincide estrechamente con las expectativas de un perfil de esfera isotérmica singular donde si v(r) es aproximadamente constante, entonces la densidad ρr −2 a algún "radio del núcleo" interno donde la densidad se supone constante. Las observaciones no concuerdan con un perfil tan simple, como lo informan Navarro, Frenk y White en un artículo fundamental de 1996. [17]

Los autores luego señalaron que una "pendiente logarítmica que cambia suavemente" para una función de perfil de densidad también podría acomodar curvas de rotación aproximadamente planas en escalas grandes. Encontraron el famoso perfil de Navarro-Frenk-White, que es consistente tanto con las simulaciones de N-cuerpos como con las observaciones dadas por

donde la densidad central, ρ0 , y el radio de escala, Rs , son parámetros que varían de un halo a otro. [18] Debido a que la pendiente del perfil de densidad diverge en el centro, se han propuesto otros perfiles alternativos, por ejemplo, el perfil de Einasto, que ha mostrado una mejor concordancia con ciertas simulaciones de halo de materia oscura. [19] [20]

Las observaciones de velocidades orbitales en galaxias espirales sugieren una estructura de masa de acuerdo con:

Dado que las observaciones de la rotación de galaxias no coinciden con la distribución esperada de la aplicación de las leyes de Kepler, no coinciden con la distribución de la materia luminosa. [15] Esto implica que las galaxias espirales contienen grandes cantidades de materia oscura o, alternativamente, la existencia de física exótica en acción a escalas galácticas. El componente invisible adicional se vuelve progresivamente más conspicuo en cada galaxia en los radios exteriores y entre las galaxias en las menos luminosas. [ aclaración necesaria ]

Una interpretación popular de estas observaciones es que aproximadamente el 26% de la masa del Universo está compuesta de materia oscura, un tipo hipotético de materia que no emite ni interactúa con la radiación electromagnética. Se cree que la materia oscura domina el potencial gravitacional de las galaxias y los cúmulos de galaxias. Según esta teoría, las galaxias son condensaciones bariónicas de estrellas y gas (a saber, hidrógeno y helio) que se encuentran en los centros de halos mucho más grandes de materia oscura, afectados por una inestabilidad gravitacional causada por fluctuaciones de densidad primordial.

Muchos cosmólogos se esfuerzan por comprender la naturaleza y la historia de estos omnipresentes halos oscuros investigando las propiedades de las galaxias que contienen (es decir, sus luminosidades, cinemática, tamaños y morfologías). La medición de la cinemática (sus posiciones, velocidades y aceleraciones) de las estrellas observables y el gas se ha convertido en una herramienta para investigar la naturaleza de la materia oscura, en cuanto a su contenido y distribución en relación con los diversos componentes bariónicos de esas galaxias.

La dinámica de rotación de las galaxias está bien caracterizada por su posición en la relación Tully-Fisher, que muestra que para las galaxias espirales la velocidad de rotación está relacionada de manera única con su luminosidad total. Una forma consistente de predecir la velocidad de rotación de una galaxia espiral es medir su luminosidad bolométrica y luego leer su tasa de rotación desde su ubicación en el diagrama de Tully-Fisher. Por el contrario, conocer la velocidad de rotación de una galaxia espiral da su luminosidad. Por tanto, la magnitud de la rotación de la galaxia está relacionada con la masa visible de la galaxia. [22]

Si bien el ajuste preciso de los perfiles de densidad de abultamiento, disco y halo es un proceso bastante complicado, es sencillo modelar los observables de las galaxias en rotación a través de esta relación. [23] [ se necesita una mejor fuente ] Entonces, aunque las simulaciones cosmológicas y de formación de galaxias de última generación de materia oscura con materia bariónica normal incluida pueden compararse con las observaciones de galaxias, todavía no hay una explicación sencilla de por qué existe la relación de escala observada. [24] [25] Además, investigaciones detalladas de las curvas de rotación de las galaxias de bajo brillo superficial (galaxias LSB) en la década de 1990 [26] y de su posición en la relación Tully-Fisher [27] mostraron que las galaxias LSB tenían que tienen halos de materia oscura que son más extendidos y menos densos que los de las galaxias con alto brillo superficial y, por lo tanto, el brillo superficial está relacionado con las propiedades del halo. Tales galaxias enanas dominadas por la materia oscura pueden ser la clave para resolver el problema de la formación de estructuras de las galaxias enanas.

Muy importante, el análisis de las partes internas de las galaxias de brillo superficial bajo y alto mostró que la forma de las curvas de rotación en el centro de los sistemas dominados por materia oscura indica un perfil diferente del perfil de distribución de masa espacial NFW. [28] [29] Este llamado problema del halo cuspy es un problema persistente para la teoría estándar de la materia oscura fría. En este contexto, se invocan con frecuencia simulaciones que involucran la retroalimentación de energía estelar en el medio interestelar para alterar la distribución de materia oscura predicha en las regiones más internas de las galaxias. [30] [31]

Ha habido varios intentos de resolver el problema de la rotación de las galaxias modificando la gravedad sin invocar la materia oscura. Una de las más discutidas es la Dinámica Newtoniana Modificada (MOND), propuesta originalmente por Mordehai Milgrom en 1983, que modifica la ley de la fuerza newtoniana a bajas aceleraciones para mejorar la atracción gravitacional efectiva. MOND ha tenido un éxito considerable en la predicción de las curvas de rotación de las galaxias de bajo brillo superficial, [32] coincidiendo con la relación bariónica Tully-Fisher, [33] y las dispersiones de velocidad de las pequeñas galaxias satélites del Grupo Local. [34]

Utilizando datos de la base de datos de Spitzer Photometry and Accurate Rotation Curves (SPARC), un grupo descubrió que la aceleración radial trazada por las curvas de rotación podría predecirse solo a partir de la distribución bariónica observada (es decir, incluidas las estrellas y el gas, pero no la materia oscura). [35] La misma relación proporcionó un buen ajuste para 2693 muestras en 153 galaxias en rotación, con diversas formas, masas, tamaños y fracciones de gas. El brillo en el infrarrojo cercano, donde domina la luz más estable de las gigantes rojas, se utilizó para estimar la contribución de densidad debida a las estrellas de manera más consistente. Los resultados son consistentes con MOND y ponen límites a las explicaciones alternativas que involucran solo a la materia oscura. Sin embargo, las simulaciones cosmológicas dentro de un marco Lambda-CDM que incluyen efectos de retroalimentación bariónica reproducen la misma relación, sin la necesidad de invocar nuevas dinámicas (como MOND). [36] Así, una contribución debida a la propia materia oscura puede ser completamente predecible a partir de la de los bariones, una vez que se tienen en cuenta los efectos de retroalimentación debidos al colapso disipativo de los bariones. MOND no es una teoría relativista, aunque se han propuesto teorías relativistas que se reducen a MOND, como la gravedad tensorial-vectorial-escalar (TeVeS), [5] [37] la gravedad escalar-tensor-vectorial (STVG) y la f ( R) teoría de Capozziello y De Laurentis. [38]

También se propuso un modelo de galaxia basado en una métrica de relatividad general, que muestra que las curvas de rotación de la Vía Láctea, NGC 3031, NGC 3198 y NGC 7331 son consistentes con las distribuciones de densidad de masa de la materia visible, evitando la necesidad de una masa masiva. halo de materia oscura exótica. [39] [40]

Según un análisis de 2020 de los datos producidos por la nave espacial Gaia, parecería posible explicar al menos la curva de rotación de la Vía Láctea sin requerir materia oscura si en lugar de una aproximación newtoniana se adoptara todo el conjunto de ecuaciones de la relatividad general. [41]

En marzo de 2021, Gerson Otto Ludwig publicó un modelo basado en la relatividad general que explica las curvas de rotación de galaxias con gravitoelectromagnetismo. [42]

## ¿Es posible calcular el centro de masa del universo visible? - Astronomía

EL MISTERIO DE LA MASA DESAPARECIDA

[159] Falta la mayor parte de la masa del universo. ¿O está simplemente escondido en alguna forma exótica, aún indetectable? Nadie está seguro de cuál. Sin embargo, una cosa es segura. El problema de la masa faltante ha llegado al punto en que es más que un problema. Es una vergüenza, un obstáculo para comprender cosas como la estructura de las galaxias, la evolución de los cúmulos de galaxias y el destino final del universo.

Se trata de la situación en la que se encuentran los astrofísicos hoy. No tratando de comprender el movimiento de los planetas alrededor del Sol (la teoría funciona bien allí), sino tratando de comprender los movimientos de las estrellas y el gas en las regiones exteriores de las galaxias, o de las galaxias y el gas en los cúmulos de galaxias.

En los últimos años, los astrónomos han medido minuciosamente la velocidad a la que las estrellas y las nubes de gas en las partes externas de las galaxias espirales orbitan el centro de masa de esas galaxias. Las fotografías ópticas muestran que las galaxias espirales son elegantes molinetes de miles de millones de estrellas, con la luz cayendo de manera constante desde las regiones centrales hacia las externas. Dado que la luz es producida por estrellas, naturalmente esperamos que la materia y su campo de fuerza gravitacional asociado muestren una concentración similar. De ello se deduce, entonces, que la velocidad de rotación de las estrellas y el gas debería disminuir a medida que uno se mueve de las regiones internas a las externas de las galaxias.

Para sorpresa y consternación de los astrónomos, esto no es lo que se observa. As radio and optical observations have extended the velocity measurements for the stars and gas to the outer regions of spiral galaxies, they have found that the stars and gas clouds are moving at the same speed as the ones closer in! A substantial part of the mass of the galaxy is not concentrated toward the center of the galaxy but must be [ 160 ] distributed in some dark, unseen halo surrounding the visible galaxy. The outer regions of galaxies, faint and inconspicuous on a photograph, may actually contain most of the matter. In the words of astronomers Margaret and Geoffrey Burbidge, it appears that "the tail wags the dog."

Just how large is this unseen halo? Why can't it be seen? No one knows the answer to either question. What is known is that the problem involves more than a few isolated galaxies. Most of the spiral galaxies in which the rotation pattern has been studied in detail, including our own Milky Way Galaxy, show evidence for an extensive halo of dark matter.

Nor is the problem confined to spiral galaxies. Perhaps the most spectacular evidence for a halo of dark matter around a galaxy comes from the giant spherically shaped galaxy, M87. X-ray observations show that M87 is enveloped in a cloud of hot, X-ray emitting gas nearly a million light years across. If this hot gas is not confined somehow, it will expand. In about 100 million years, it would disperse. Although this may seem like a long time, it is only 1 percent of the total lifetime of the galaxy. To account for the gas cloud as it is now observed, there are three possibilities: (1) some force is confining the gas to the galaxy (2) the gas is being continuously replenished or (3) we are observing the galaxy at a special time in its history, before the gas has had time to disperse. The third alternative is possible but improbable. The second not only requires an exorbitant amount of energy but also implies that the hot cloud should be spread out over a much larger volume of space than is observed. That leaves the first alternative, confinement by a force. The confining force could either be gravity or the pressure of an even hotter gas outside the M87 halo. Observations from the HEAOs rule out this latter possibility. That leaves gravity.

This is an important result. It means that X-ray observations can be used to measure the gravitational forces around galaxies. From the distribution of the X-ray brightness of the gas cloud, one can estimate the distribution of the gas in space. From that distribution, the mass needed for gravitational confinement can be estimated. Observations with HEAO 2 imply the presence of a halo of dark matter containing the mass of 30 trillion suns! This is several hundred times the mass observed in the disk of large spiral galaxies such as ours and the Andromeda Galaxy and about 30 times larger than the previous estimates of the mass of M87.

The same principles can be used to measure the gravitational field on a much larger scale. X-ray observations of clusters of galaxies show that the mass needed to confine the hot gas observed in clusters of galaxies is about 5 or 10 times greater than the mass that can be detected in these clusters through observation in any wavelength band, from radio through X-ray. This is in agreement with optical observations. They show that the motions of galaxies orbiting around the center of mass of the cluster can be understood only if the gravitational field is much stronger than would be deduced from the amount of detectable matter. That is, they imply that about 80 to 90 percent of the mass of the cluster has escaped detection.

Coma Cluster. This rich cluster of galaxies in the constellation Coma Berenices contains thousands of galaxies. Studies of the motions of the galaxies indicate that they are held together by their mutual gravitational attraction. The amount of mass present as visible matter, however, falls far short of the amount needed for gravitational stability. (Kits Peak Observatory photo)

On an even larger scale, studies of the motion of the Local Group of galaxies that includes our Milky Way Galaxy indicate that we are part of a supercluster of galaxies. An analysis of the motion of the Local Group suggests that a large amount of hidden matter is necessary to provide the gravitational force needed to keep the supercluster from flying apart. The amount of missing mass is about 10 times the amount of visible mass.

In summary then, radio, optical, and X-ray observations of galaxies, clusters of galaxies, and superclusters of galaxies indicate that 80 to 90 percent of the matter is either missing or hidden from view. If this ratio holds throughout the universe, then our ideas as to the ultimate fate of the universe may be profoundly affected. In a large measure, the fate of the universe is determined by the mass density of the universe, that is, the amount of mass in a unit volume. If the mass density is larger than a certain critical value, the expansion of the universe that began with the initial "big bang" will not continue forever but will slow down, and the universe will collapse. The endpoint of such a collapse is unknown. The universe could collapse forever into a universe-sized black hole, or it could go through an unending cycle of expansion, collapse, and reexpansion. On the other hand, if the mass density is too low, the universe will expand forever it will be "open." Current estimates indicate that the mass density of the universe falls short of the critical density by a factor of 10 or more, implying that the [ 162 ] universe will expand forever. However, if the mass density is 10 times greater than it appears to be, as suggested by the missing mass mystery, then the universe may be closed after all. Seen in this light, the hidden mass problem becomes a very big problem indeed.

What is the answer to the problem? Is something wrong with our understanding of gravity? Is there some additional force that comes into play over these very large scales, a force that is missing from our calculations of the orbits or of the confinement of hot gas? Or is the universe full of dark matter that has escaped detection? Although attempts have been made to modify gravitational theory in the required way, most of the effort has been concentrated into ways that the matter could be hidden from view.

Astronomers have searched long and hard for this matter. They have used radio, infrared, optical, ultraviolet, and X-ray telescopes to scan the outer regions of galaxies and the intergalactic spaces for enough cool gas, hot gas, or dust. They have found some of each, but not enough to solve the problem of the missing mass.

A large population of white dwarfs, neutron stars, or black holes could remain hidden from the view of optical telescopes, but they would have to be 50 to 100 times more abundant on the outer edges of galaxies than in the regions of our galaxy that have been carefully observed so far. No plausible explanation as to why this should be has been advanced. Furthermore, if the population of collapsed stars were in fact 50 or more times larger in the outer regions, we might expect to find far more X-ray sources in the outer regions of galaxies than are observed. In addition, heavy elements ejected from these stars prior to their collapse should be 50 or more times more abundant in the outer regions of galaxies than in the inner regions. This is just the opposite of what is observed. Thus collapsed stars are unlikely candidates to explain the missing mass.

Another durable suggestion has been that a major part of the missing mass in galaxies and clusters of galaxies is made up of very low mass stars. These stars, which would have masses of only a few percent that of the Sun, are red, brown, and black dwarf stars. These stars are very dim because of their small size and low surface temperature. The red dwarfs, which have a mass of 10 to 50 percent that of the Sun, are known to be very common in the solar neighborhood. Of the 90 nearest stars to the Sun that have been classified, 62 of them are red dwarfs. Red dwarf stars produce intense radio, optical, and X-ray flares. This property should make it possible for advanced X-ray telescopes, working in concert with the Space Telescope, to attack the question as to whether 90 percent of the matter on the edges of galaxies is in the form of red dwarf stars.

Brown and black dwarfs are a much more difficult proposition. These objects, which are essentially freely wandering Jupiter-like objects, are so dim that it may be impossible to ever detect them. Although there are no sound theoretical reasons for believing that they exist in the required [ 163 ] numbers, it is possible that such objects were produced in large numbers by the star formation process in globular clusters long ago, when galaxies were just beginning to form. The black and brown dwarfs may then have diffused out of their star clusters and formed very large halos around galaxies. Because of their low luminosities, they would be extremely difficult to detect, even if there were quadrillions of them around every galaxy.

One argument against the missing mass being in the form of normal matter of any type comes from cosmologic considerations. According to the big-bang model, the deuterium (heavy hydrogen) that is observed to exist in interstellar space was created about three minutes after the "beginning" in a billion degree broth of neutrons, protons, photons, and neutrinos. But if the broth were too thick, that is, if the mass density were too high, the deuterium would have all been processed into helium. The greater the mass density, the greater the fusion of deuterium nuclei into helium nuclei, and the less deuterium remains. By observing the amount of deuterium in interstellar space, we can get an idea as to the mass density of normal matter in the universe. The observations suggest that the mass density of normal matter is at most 10 percent of the value needed to turn around the present expansion.

This result lends support to yet another hypothesis for the missing mass, namely, that it is in the form of neutrinos. Neutrinos are elusive subatomic particles that are produced in certain nuclear reactions. Nuclear reactions of the type that produce neutrinos are thought to have been so common in the early universe that many cosmologists have believed for some time that we are literally awash in a sea of neutrinos.

Until recently, however, it did not seem to matter much, because neutrinos were thought to be particles with some energy but no mass, in the same way that photons have energy but no mass. Since it was thought that the energy of the neutrinos was by now quite low, the great abundance of neutrinos was of no practical consequence, or so it seemed.

Then a recent experiment suggested that the neutrino might have a very small mass. The mass of an individual neutrino might be very small, 100 million times smaller than that of a hydrogen atom. Yet, because there are so many neutrinos in the universe, their combined mass could dominate the universe! Thus, the solution to astronomy's greatest riddles, that of the missing mass, might have been found, not by studying distant galaxies, but in a series of experiments right here on Earth.

Serious questions about the neutrino hypothesis must still be answered. For one thing, further experiments have clouded the issue as to whether neutrinos really have mass, and if so how much. There is also a problem in understanding how it is possible for matter to form into galaxy-sized clumps in a universe dominated by fast-moving neutrinos. An analysis of this question suggests that clumps the size of superclusters would form first and that galaxies and clusters of galaxies would condense from these clumps. Yet the [ 164 ] HEAO observations of clusters of galaxies indicate that just the opposite happened. The neutrino hypothesis also suggests that the fraction of missing mass around galaxies should be much less than in clusters of galaxies. This is apparently not observed. These problems have led some astrophysicists to postulate that the existence of yet another particle, the gravitino, is responsible for the missing mass. Gravitinos would have been formed in the very early universe, less than about one millionth of a second after the expansion began, when the temperature was around 100 billion degrees. These particles, which are expected to be more massive than neutrinos, would condense into galaxy-sized clumps. The theory therefore predicts that the fraction of missing mass around galaxies is about the same as in clusters of galaxies. This is what the data now available suggest-a point in favor of the gravitino hypothesis. However, the data are sparse, and no one believes that the final answer is in. More data and calculations are needed.

Thus, the plot thickens, and the number of suspects multiplies in the mystery of the missing mass. And why not? That's the way a good mystery should read, and this is one of the best around.

## 36. Have computers discovered the biblical ‘long days’?

The report that computers have discovered the biblical ‘long days’ continues to be told but is unfounded. It is challenged here because false ideas should never be used to “support” Scripture. Furthermore, the computer story appears to raise modern science to a level of certainty that it does not possess.

As printed in tracts and magazines, the story describes a problem that scientists faced in the space program. Apparently a missing day turned up in the computer positions for the sun and moon over the past centuries. These celestial bodies were not quite where they belonged! The key to the problem was then found in the Old Testament. Mathematical corrections seemed to be needed for the “long days” of Joshua and Hezekiah ( Josh. 10:13 , 2 Kings 20:11 ). These events, when inserted into the computer, made everything turn out exactly right. Although this apparent verification of Scripture makes a very interesting story, computers are not this smart! The only way to determine a change in the sun’s or moon’s location is to know their exact positions prior to the change, but there is no such reference point available. We do not know exactly where the created sun and moon were first placed in the sky. Even eclipse records do not prove useful in solving the problem.

Can we not conclude that the long day of Joshua occurred exactly as described? And also that the backward motion of the sun in Hezekiah’s time was a literal sign of God ’s power? Computers are neither needed nor able to prove these Old Testament events scientifically.

## 28.4 The Challenge of Dark Matter

So far this chapter has focused almost entirely on matter that radiates electromagnetic energy—stars, planets, gas, and dust. But, as we have pointed out in several earlier chapters (especially The Milky Way Galaxy), it is now clear that galaxies contain large amounts of dark matter as well. There is much more dark matter , in fact, than matter we can see—which means it would be foolish to ignore the effect of this unseen material in our theories about the structure of the universe. (As many a ship captain in the polar seas found out too late, the part of the iceberg visible above the ocean’s surface was not necessarily the only part he needed to pay attention to.) Dark matter turns out to be extremely important in determining the evolution of galaxies and of the universe as a whole.

The idea that much of the universe is filled with dark matter may seem like a bizarre concept, but we can cite a historical example of “dark matter” much closer to home. In the mid-nineteenth century, measurements showed that the planet Uranus did not follow exactly the orbit predicted from Newton’s laws if one added up the gravitational forces of all the known objects in the solar system. Some people worried that Newton’s laws may simply not work so far out in our solar system. But the more straightforward interpretation was to attribute Uranus’ orbital deviations to the gravitational effects of a new planet that had not yet been seen. Calculations showed where that planet had to be, and Neptune was discovered just about in the predicted location.

In the same way, astronomers now routinely determine the location and amount of dark matter in galaxies by measuring its gravitational effects on objects we can see. And, by measuring the way that galaxies move in clusters, scientists have discovered that dark matter is also distributed among the galaxies in the clusters. Since the environment surrounding a galaxy is important in its development, dark matter must play a central role in galaxy evolution as well. Indeed, it appears that dark matter makes up most of the matter in the universe. But what es dark matter? What is it made of? We’ll look next at the search for dark matter and the quest to determine its nature.

### Dark Matter in the Local Neighborhood

Is there dark matter in our own solar system? Astronomers have examined the orbits of the known planets and of spacecraft as they journey to the outer planets and beyond. No deviations have been found from the orbits predicted on the basis of the masses of objects already discovered in our solar system and the theory of gravity. We therefore conclude that there is no evidence that there are large amounts of dark matter nearby.

Astronomers have also looked for evidence of dark matter in the region of the Milky Way Galaxy that lies within a few hundred light-years of the Sun. In this vicinity, most of the stars are restricted to a thin disk. It is possible to calculate how much mass the disk must contain in order to keep the stars from wandering far above or below it. The total matter that must be in the disk is less than twice the amount of luminous matter. This means that no more than half of the mass in the region near the Sun can be dark matter.

### Dark Matter in and around Galaxies

In contrast to our local neighborhood near the Sun and solar system, there is (as we saw in The Milky Way Galaxy) ample evidence strongly suggesting that about 90% of the mass in the entire galaxy is in the form of a halo of dark matter. In other words, there is apparently about nine times more dark matter than visible matter. Astronomers have found some stars in the outer regions of the Milky Way beyond its bright disk, and these stars are revolving very rapidly around its center. The mass contained in all the stars and all the interstellar matter we can detect in the galaxy does not exert enough gravitational force to explain how those fast-moving stars remain in their orbits and do not fly away. Only by having large amounts of unseen matter could the galaxy be holding on to those fast-moving outer stars. The same result is found for other spiral galaxies as well.

Figure 28.23 is an example of the kinds of observations astronomers are making, for the Triangulum galaxy, a member of our Local Group. The observed rotation of spiral galaxies like Andromeda is usually seen in plots, known as rotation curves, that show velocity versus distance from the galaxy center. Such plots suggest that the dark matter is found in a large halo surrounding the luminous parts of each galaxy. The radius of the halos around the Milky Way and Andromeda may be as large as 300,000 light-years, much larger than the visible size of these galaxies.

### Dark Matter in Clusters of Galaxies

Galaxies in clusters also move around: they orbit the cluster’s center of mass. It is not possible for us to follow a galaxy around its entire orbit because that typically takes about a billion years. It is possible, however, to measure the velocities with which galaxies in a cluster are moving, and then estimate what the total mass in the cluster must be to keep the individual galaxies from flying out of the cluster. The observations indicate that the mass of the galaxies alone cannot keep the cluster together—some other gravity must again be present. The total amount of dark matter in clusters exceeds by more than ten times the luminous mass contained within the galaxies themselves, indicating that dark matter exists between galaxies as well as inside them.

There is another approach we can take to measuring the amount of dark matter in clusters of galaxies. As we saw, the universe is expanding, but this expansion is not perfectly uniform, thanks to the interfering hand of gravity. Suppose, for example, that a galaxy lies outside but relatively close to a rich cluster of galaxies. The gravitational force of the cluster will tug on that neighboring galaxy and slow down the rate at which it moves away from the cluster due to the expansion of the universe.

Consider the Local Group of galaxies, lying on the outskirts of the Virgo Supercluster. The mass concentrated at the center of the Virgo Cluster exerts a gravitational force on the Local Group. As a result, the Local Group is moving away from the center of the Virgo Cluster at a velocity a few hundred kilometers per second slower than the Hubble law predicts. By measuring such deviations from a smooth expansion, astronomers can estimate the total amount of mass contained in large clusters.

There are two other very useful methods for measuring the amount of dark matter in galaxy clusters, and both of them have produced results in general agreement with the method of measuring galaxy velocities: gravitational lensing and X-ray emission. Let’s take a look at both.

As Albert Einstein showed in his theory of general relativity, the presence of mass bends the surrounding fabric of spacetime. Light follows those bends, so very massive objects can bend light significantly. You saw examples of this in the Astronomy Basics feature box Gravitational Lensing in the previous section. Visible galaxies are not the only possible gravitational lenses. Dark matter can also reveal its presence by producing this effect. Figure 28.24 shows a galaxy cluster that is acting like a gravitational lens the streaks and arcs you see on the picture are lensed images of more distant galaxies. Gravitational lensing is well enough understood that astronomers can use the many ovals and arcs seen in this image to calculate detailed maps of how much matter there is in the cluster and how that mass is distributed. The result from studies of many such gravitational lens clusters shows that, like individual galaxies, galaxy clusters contain more than ten times as much dark matter as luminous matter.

The third method astronomers use to detect and measure dark matter in galaxy clusters is to image them in the light of X-rays. When the first sensitive X-ray telescopes were launched into orbit around Earth in the 1970s and trained on massive galaxy clusters, it was quickly discovered that the clusters emit copious X-ray radiation (see Figure 28.25). Most stars do not emit much X-ray radiation, and neither does most of the gas or dust between the stars inside galaxies. What could be emitting the X-rays seen from virtually all massive galaxy clusters?

It turns out that just as galaxies have gas distributed between their stars, clusters of galaxies have gas distributed between their galaxies. The particles in these huge reservoirs of gas are not just sitting still rather, they are constantly moving, zooming around under the influence of the cluster’s immense gravity like mini planets around a giant sun. As they move and bump against each other, the gas heats up hotter and hotter until, at temperatures as high as 100 million K, it shines brightly at X-ray wavelengths. The more mass the cluster has, the faster the motions, the hotter the gas, and the brighter the X-rays. Astronomers calculate that the mass present to induce those motions must be about ten times the mass they can see in the clusters, including all the galaxies and all the gas. Once again, this is evidence that the galaxy clusters are seen to be dominated by dark matter.

### Mass-to-Light Ratio

We described the use of the mass-to-light ratio to characterize the matter in galaxies or clusters of galaxies in Properties of Galaxies. For systems containing mostly old stars, the mass-to-light ratio is typically 10 to 20, where mass and light are measured in units of the Sun’s mass and luminosity. A mass-to-light ratio of 100 or more is a signal that a substantial amount of dark matter is present. Table 28.1 summarizes the results of measurements of mass-to-light ratios for various classes of objects. Very large mass-to-light ratios are found for all systems of galaxy size and larger, indicating that dark matter is present in all these types of objects. This is why we say that dark matter apparently makes up most of the total mass of the universe.

Type of Object Mass-to-Light Ratio
sol 1
Matter in vicinity of Sun 2
Mass in Milky Way within 80,000 light-years of the center 10
Small groups of galaxies 50–150
Rich clusters of galaxies 250–300

The clustering of galaxies can be used to derive the total amount of mass in a given region of space, while visible radiation is a good indicator of where the luminous mass is. Studies show that the dark matter and luminous matter are very closely associated. The dark matter halos do extend beyond the luminous boundaries of the galaxies that they surround. However, where there are large clusters of galaxies, you will also find large amounts of dark matter. Voids in the galaxy distribution are also voids in the distribution of dark matter.

### What Is the Dark Matter?

How do we go about figuring out what the dark matter consists of? The technique we might use depends on its composition. Let’s consider the possibility that some of the dark matter is made up of normal particles: protons, neutrons, and electrons. Suppose these particles were assembled into black holes, brown dwarfs, or white dwarfs. If the black holes had no accretion disks, they would be invisible to us. White and brown dwarfs do emit some radiation but have such low luminosities that they cannot be seen at distances greater than a few thousand light-years.

We can, however, look for such compact objects because they can act as gravitational lens es. (See the Astronomy Basics feature box Gravitational Lensing.) Suppose the dark matter in the halo of the Milky Way were made up of black holes, brown dwarfs, and white dwarfs. These objects have been whimsically dubbed MACHOs (MAssive Compact Halo Objects). If an invisible MACHO passes directly between a distant star and Earth, it acts as a gravitational lens, focusing the light from the distant star. This causes the star to appear to brighten over a time interval of a few hours to several days before returning to its normal brightness. Since we can’t predict when any given star might brighten this way, we have to monitor huge numbers of stars to catch one in the act. There are not enough astronomers to keep monitoring so many stars, but today’s automated telescopes and computer systems can do it for us.

Research teams making observations of millions of stars in the nearby galaxy called the Large Magellanic Cloud have reported several examples of the type of brightening expected if MACHOs are present in the halo of the Milky Way (Figure 28.26). However, there are not enough MACHOs in the halo of the Milky Way to account for the mass of the dark matter in the halo.

This result, along with a variety of other experiments, leads us to conclude that the types of matter we are familiar with can make up only a tiny portion of the dark matter. Another possibility is that dark matter is composed of some new type of particle—one that researchers are now trying to detect in laboratories here on Earth (see The Big Bang).

The kinds of dark matter particles that astronomers and physicists have proposed generally fall into two main categories: hot and cold dark matter. The terms hot y cold don’t refer to true temperatures, but rather to the average velocities of the particles, analogous to how we might think of particles of air moving in your room right now. In a cold room, the air particles move more slowly on average than in a warm room.

In the early universe, if dark matter particles easily moved fast and far compared to the lumps and bumps of ordinary matter that eventually became galaxies and larger structures, we call those particles hot dark matter . In that case, smaller lumps and bumps would be smeared out by the particle motions, meaning fewer small galaxies would get made.

On the other hand, if the dark matter particles moved slowly and covered only small distances compared to the sizes of the lumps in the early universe, we call that cold dark matter . Their slow speeds and energy would mean that even the smaller lumps of ordinary matter would survive to grow into small galaxies. By looking at when galaxies formed and how they evolve, we can use observations to distinguish between the two kinds of dark matter. So far, observations seem most consistent with models based on cold dark matter.

Solving the dark matter problem is one of the biggest challenges facing astronomers. After all, we can hardly understand the evolution of galaxies and the long-term history of the universe without understanding what its most massive component is made of. For example, we need to know just what role dark matter played in starting the higher-density “seeds” that led to the formation of galaxies. And since many galaxies have large halos made of dark matter, how does this affect their interactions with one another and the shapes and types of galaxies that their collisions create?

Astronomers armed with various theories are working hard to produce models of galaxy structure and evolution that take dark matter into account in just the right way. Even though we don’t know what the dark matter is, we do have some clues about how it affected the formation of the very first galaxies. As we will see in The Big Bang, careful measurements of the microwave radiation left over after the Big Bang have allowed astronomers to set very tight limits on the actual sizes of those early seeds that led to the formation of the large galaxies that we see in today’s universe. Astronomers have also measured the relative numbers and distances between galaxies and clusters of different sizes in the universe today. So far, most of the evidence seems to weigh heavily in favor of cold dark matter, and most current models of galaxy and large-scale structure formation use cold dark matter as their main ingredient.

As if the presence of dark matter —a mysterious substance that exerts gravity and outweighs all the known stars and galaxies in the universe but does not emit or absorb light—were not enough, there is an even more baffling and equally important constituent of the universe that has only recently been discovered: we have called it dark energy in parallel with dark matter. We will say more about it and explore its effects on the evolution of the universe in The Big Bang. For now, we can complete our inventory of the contents of the universe by noting that it appears that the entire universe contains some mysterious energy that pushes spacetime apart, taking galaxies and the larger structures made of galaxies along with it. Observations show that dark energy becomes more and more important relative to gravity as the universe ages. As a result, the expansion of the universe is accelerating, and this acceleration seems to be happening mostly since the universe was about half its current age.

What we see when we peer out into the universe—the light from trillions of stars in hundreds of billions of galaxies wrapped in intricate veils of gas and dust—is therefore actually only a sprinkling of icing on top of the cake: as we will see in The Big Bang, when we look outside galaxies and clusters of galaxies at the universe as a whole, astronomers find that for every gram of luminous normal matter, such as protons, neutrons, electrons, and atoms in the universe, there are about 4 grams of nonluminous normal matter, mainly intergalactic hydrogen and helium. There are about 27 grams of dark matter, and the energy equivalent (remember Einstein’s famous mi = mc 2 ) of about 68 grams of dark energy. Dark matter, and (as we will see) even more so dark energy, are dramatic demonstrations of what we have tried to emphasize throughout this book: science is always a “progress report,” and we often encounter areas where we have more questions than answers.

Let’s next put together all these clues to trace the life history of galaxies and large-scale structure in the universe. What follows is the current consensus, but research in this field is moving rapidly, and some of these ideas will probably be modified as new observations are made.

## Is it Possible to Calculate The Centre of Mass of the Visible Universe? - Astronomía

Key points: Evidence for dark matter ideas for what it is Evidence for Dark Energy

The rotation of our galaxy and many others have been measured using Doppler shifts of the 21cm (radio) line of hydrogen (from The Essential Cosmic Perspective, Bennett et al.)

 If the mass followed the "normal" matter -- stars and gas -- the rotation speed would drop like the "Keplerian motion" line, like for the planets. Then their speeds would be as we derived when we were discussing Kepler's Laws. This relation assumes essentially all the mass is in the central object (the sun for the planetary system). Instead, the rotation curve is nearly flat with increasing radius. Evidently there are huge amounts of unseen "dark" matter in the outer parts of the galaxy that add gravitational field beyond that just from the center, causing the stars and gas to orbit faster. (Figures from The Essential Cosmic Perspective, by Bennett et al.)
 Like the Milky Way, virtually all galaxies have flat rotation curves to well beyond where they have many stars, indicating that they are all surrounded by large halos of dark matter. (From The Essential Cosmic Perspective, by Bennett et al.)

When we account carefully for the mass in stars in a galaxy, it turns out to be much less than the mass we measure from Newton's laws! In addition, there appears to be mass we can't see outside the region occupied by the stars. As much of 90% of galaxies may be in some form of unseen mass.

We have no good idea of what galaxies are mostly made!! Is there some basic particle of physics that we don't know about that accounts for the unseen mass? This is evidently the dark matter we know played such a central role in shaping the Universe, but all we know about local examples is from galaxy rotation curves. A good link for further information is at http://www.eclipse.net/

To left: from Supernova Cosmology Project, Knop et al., Lawrence Berkeley National Laboratory, http://supernova.lbl.gov/

Thus, the distance measurements using Type 1 supernovae indicate that the expansion of the Universe is getting faster.

Brian Schmidt at the Nobel Prize ceremony

It is humbling, perhaps even humiliating, that we know almost nothing about 96% of what is "out there"!!

What eventually happens depends on the behavior of the dark energy with time, and since we don't know what it is we certainly don't know how it is going to behave billions of years from now. (from http://www.scholarpedia.org/article/Dark_energy)

Test your understanding before going on

Galaxy quilt, by Paula van der Zwaan, from http://members.lycos.nl/hollandquilt/id211.htm

In the 18th Century, Thomas Wright proposed that theUniverse was filled with groupings of stars like the Milky Way, dehttp://homepage.mac/com/kvmagruder/bcp/milky/shape.htm

hypertext G. H. Rieke

## Binary Stars

Stars do not form in isolation. When clumps of gas in a GMC begin to collapse, the clumps usually fragment into smaller clumps, each of which forms a star. After the formation process ends, many stars wind up gravitationally bound to one or more partner stars. The fraction of stars that are found in multiple star systems is actually a difficult measurement to make, but the fractions are likely higher than you might expect. For massive stars, we think a large fraction may be in multiple systems—for Sun-like stars it may be about half of all stars, and for low mass stars, less than half.

For example, take some famous bright stars in the sky: Albireo (we saw an image of Albireo in Lesson 4) appears in a telescope to be a pair of stars. The brightest star in the winter sky, Sirius, also has a companion (an X-ray image of the Sirius pair is available at Astronomy Picture of the Day). Also, there is a star in the handle of the Big Dipper known as Mizar, which can be resolved into a double star, too.

#### Try this with Starry Night!

There are a number of "visual binary" stars that you can observe with small telescopes or with Starry Night. Using the "find" feature on Starry Night, search for the stars listed below. You may have to vary the date and time so they are visible at night. Once you have them centered in your field of view, use the zoom feature to zoom in to see how they would appear magnified through a telescope. Also, read the descriptions that pop up when you mouse over them.

1. Mizar & Alcor (be sure to zoom in even further on Mizar)
2. Albireo
3. Algieba (gamma Leonis)
4. Castor
5. Epsilon Lyrae (to find this in Starry Night, go first to Vega, and Epsilon Lyrae is one of the bright stars in Lyra near Vega)

Stars classified as visual binaries are rare examples of stars that are close enough to the Earth that in images we can directly observe that they have a companion. In most cases, however, stars are so far away and their companions are so close that images taken by even the most powerful telescopes in the world cannot tell if there is one star or two present. However, we have observational methods to determine if a star is in a binary system even if an image appears to show only one point of light. Three of these techniques are:

Spectroscopy: Recall that stars were originally separated into different spectral types by their spectral lines. Occasionally, the spectrum of what appears to be a single star will contain absorption lines from two different spectral types (e.g., G and K), indicating that this is really a binary star system, not a single star. Just like the planets in our Solar System orbit the center of mass of the Solar System, the two stars in a binary star system will orbit the common center of mass of the binary system as shown in this animation (:21):

As demonstrated in the animation, we can also occasionally observe the motion of the stars in a binary star system by observing periodic changes in their spectral lines. This is explained in a bit more detail in the spectroscopic binary movie at an Ohio State astronomy course website. (Once you click on the link, you will see three links at the top of the new window. You can click on any of the links because they all show the same animation. They are just different file formats.)

Binary stars are very useful tools in the study of the properties of stars. In the previous lesson, we discussed that we can measure a star's luminosity, distance, and velocity, but we did not discuss any methods for measuring the mass or radius of a star. You might be curious how those properties correlate with the other properties we did discuss, like luminosity, for example. Our knowledge of the masses and radii of stars comes mostly from the study of stars in binary systems. For example, we can use Kepler's third law to derive the masses of the stars in a binary system. Recall that when two objects orbit each other the following equation applies:

If we measure the separation between the objects (a) and the period of their orbit (P), we can calculate their masses. Unfortunately, depending on the type of binary (e.g., spectroscopic, eclipsing, astrometric), we are often unable to directly measure its orbital properties unambiguously. Since the inclination angle of a binary star's orbit with our line of sight (that is, is it edge-on, face-on, or somewhere in between?) is often unknown or only able to be estimated, in many cases what you measure is not the mass of the star, but the mass times sin (i) where i is the inclination angle of the orbit. Thus, you get a limit on the mass, but not the true value. If you have a spectroscopic binary that is also eclipsing, you can measure the velocities, period, separation, and inclination angle, because you know that the orbital plane has to be edge-on or nearly edge-on for us to witness eclipses from Earth. Thus, it is these systems that really help us measure stellar masses quite accurately.

Eclipsing binaries also provide us with a tool for measuring the radius of a star. In the following animation (:29), you can watch the binary stars orbit their center of mass several times.

In the next animation (:33), the inclination of the orbit with respect to the viewer (you) has been set to 85 degrees, and the orbital eccentricity has been set to 0.0.

Note the stars' orientation to each other at the beginning of the deep eclipse and at the end of the deep eclipse.

### ¿Querer aprender más?

In the interests of time and space, I am skipping the details of making the calculations of stellar mass and stellar radii using binary systems, but you can read about these topics in more detail in the online astronomy textbook Astronomy Notes:

## How do barycenters help us find other planets?

If a star has planets, the star orbits around a barycenter that is not at its very center. This causes the star to look like it’s wobbling.

As seen from above, a large planet and a star orbit their shared center of mass, or barycenter.

As seen from the side, a large planet and a star orbit their shared center of mass, or barycenter. The slightly off-center barycenter is what makes the star appear to wobble back and forth.

Planets around other stars—called exoplanets—are very hard to see directly. They are hidden by the bright glare of the stars they orbit. Detecting a star's wobble is one way to find out if there are planets orbiting it. By studying barycenters—and using several other techniques—astronomers have detected many planets around other stars!