Thought about [O III] and Fe II (should post to shareflow soon).
Investigated SDSS-III spectra. Vive le French Participation Group! Their qso value-added catalog saved me days of work.
Submitted WLQ GN proposal.
Prepared talk on WLQs/PHL 1811 analogs for tomorrow.
Thursday, March 31, 2011
Tuesday, March 29, 2011
Back
Have been:
* finalizing post-referee resubmission of SEB paper with Rafiee.
* converting WLQ Hbeta-spectra proposal to MgII with Ohad Shemmer et al.
* finalizing post-referee resubmission of PHL 1811 analog paper with Wu, Brandt, Richards, Shemmer, Gibson. Much discussion and figure-tweaking.
* brief email discussions with Chajet and Rogerson.
* reading a few papers to post to ShareFlow soon.
* finalizing post-referee resubmission of SEB paper with Rafiee.
* converting WLQ Hbeta-spectra proposal to MgII with Ohad Shemmer et al.
* finalizing post-referee resubmission of PHL 1811 analog paper with Wu, Brandt, Richards, Shemmer, Gibson. Much discussion and figure-tweaking.
* brief email discussions with Chajet and Rogerson.
* reading a few papers to post to ShareFlow soon.
Friday, March 25, 2011
Terse
Reading about ICA.
Skype w/Rafiee.
Chat w/Hewett.
Revised PHL 1811 analog / WLQ unification figure. Much discussion ensued.
Skype w/Rafiee.
Chat w/Hewett.
Revised PHL 1811 analog / WLQ unification figure. Much discussion ensued.
Thursday, March 24, 2011
Figures
Shareflow postings on BAL & BLR X-ray observations.
Tweaking of PHL 1811 draft, per suggestions by Rob Gibson.
Draft PHL 1811 / WLQ unification figure.
Reading up on Mean-Field ICA. [Wrote it in my blog, now I have to do it.]
Tweaking of PHL 1811 draft, per suggestions by Rob Gibson.
Draft PHL 1811 / WLQ unification figure.
Reading up on Mean-Field ICA. [Wrote it in my blog, now I have to do it.]
Spring
Tuesday:
Skype w/Rogerson, working on revised contour plot of allowed parameter
space regions for Chen & Tinker model.
Finished (I think) incorporating recent conical-emission-region refinements
into MATLAB disk wind code. Email w/Chajet about that and FWHM comparisons.
Wednesday:
X-ray posting on shareflow, and leafed through a few other papers not worth
posting about.
Revised NATS1740 mini-calendar text, and consideration of new textbook edition.
Quasar club skype: part 2 of Netzer et al. 2008.
Skype w/Rafiee, discussion of SEB paper.
Shareflow postings on emission-line FWHM correlations with radio properties.
Skype w/Rogerson, working on revised contour plot of allowed parameter
space regions for Chen & Tinker model.
Finished (I think) incorporating recent conical-emission-region refinements
into MATLAB disk wind code. Email w/Chajet about that and FWHM comparisons.
Wednesday:
X-ray posting on shareflow, and leafed through a few other papers not worth
posting about.
Revised NATS1740 mini-calendar text, and consideration of new textbook edition.
Quasar club skype: part 2 of Netzer et al. 2008.
Skype w/Rafiee, discussion of SEB paper.
Shareflow postings on emission-line FWHM correlations with radio properties.
Monday, March 21, 2011
Potpourri
Skype with Laura Chajet: beginning to incorporate recent refinements into code, and to set up framework for comparison of observed dispersion of emission line widths with disk wind model predictions for same.
Reading about Independent Component Analysis.
Comments on PHL 1811 analog draft.
Comments on plots on results of MIPS observations of FeLoBALs.
Predicted X-ray weakness of 6 weak-lined quasars based on optical/UV spectra. Watch this space to learn how well I did....
Reading about Independent Component Analysis.
Comments on PHL 1811 analog draft.
Comments on plots on results of MIPS observations of FeLoBALs.
Predicted X-ray weakness of 6 weak-lined quasars based on optical/UV spectra. Watch this space to learn how well I did....
Thursday, March 17, 2011
Wednesday, Thursday
* e-mail discussion with Chajet finalizing accounting for a conical (not disklike) emission region in our disk wind modelling
* final comments on resubmitted Rafiee & Hall DR3 BH mass catalog paper, and on coding for rerunning DR7 BH masses
* inspection of Plotkin et al 2010ab weak-lined quasars, pulling out a few more redshifts along the way; a fair number of them show properties consistent with unification with PHL 1811 analogs
* thinking about BAL quasar continuum reconstruction
* final comments on resubmitted Rafiee & Hall DR3 BH mass catalog paper, and on coding for rerunning DR7 BH masses
* inspection of Plotkin et al 2010ab weak-lined quasars, pulling out a few more redshifts along the way; a fair number of them show properties consistent with unification with PHL 1811 analogs
* thinking about BAL quasar continuum reconstruction
Wednesday, March 16, 2011
Midweek in Review
Spent time over weekend and Monday/Tuesday investigating PCA fits and mass estimates for DR7 quasars. Rafiee is now running PCA fitting with revised error calculation.
Also thought a fair bit about simultaneous reconstruction & dereddening of quasar spectra.
Skypes with Chajet and Rafiee on Monday.
Tuesday: Finished reading, and sending email to, Jon Trump on his recent paper. Also spend more time thinking about PHL 1811 analogs, and inspecting candidate analogs/WLQs from Plotkin et al. 2010ab.
Also thought a fair bit about simultaneous reconstruction & dereddening of quasar spectra.
Skypes with Chajet and Rafiee on Monday.
Tuesday: Finished reading, and sending email to, Jon Trump on his recent paper. Also spend more time thinking about PHL 1811 analogs, and inspecting candidate analogs/WLQs from Plotkin et al. 2010ab.
Monday, March 14, 2011
Testing, Testing
Over the weekend I finished some investigations of X-ray objects from the forthcoming paper by Gordon's student. Nice relationship between alpha_ox and CIV blueshift turned up.
Testing some wikidot functionality here:
[[math]]
\beta i \tau\ epsilon = \mu \eta
[[/math]]
Didn't think it would work, but worth a try.
Testing some wikidot functionality here:
[[math]]
\beta i \tau\ epsilon = \mu \eta
[[/math]]
Didn't think it would work, but worth a try.
Friday, March 11, 2011
Week in Review
Wednesday: Thought of another minor correction for disk wind emission. Helped out with PHL 1811 analog proposal for Chandra.
Thursday/Friday: Read draft DR3+DR7 MBH+PCA catalog paper. Rafiee pointed out a number of extra spectra he had run PCA fitting on. Examination of them revealed 16 good spectra (but no new objects) which I added to master list of SDSS quasar spectra. Skype w/Rafiee; he will refit objects with bad FeII fits with a different starting normalization.
Also spent time looking at SDSS objects w/X-ray data, & potential targets for such. C IV absorption distorts their EW-bshift locations, but doesn't get rid of all objects with weak but unblueshifted CIV. Using Shen et al. 2011 blueshifts (relative to MgII) and EWs doesn't either, although the EWs seem less affected by absorption.
Thursday/Friday: Read draft DR3+DR7 MBH+PCA catalog paper. Rafiee pointed out a number of extra spectra he had run PCA fitting on. Examination of them revealed 16 good spectra (but no new objects) which I added to master list of SDSS quasar spectra. Skype w/Rafiee; he will refit objects with bad FeII fits with a different starting normalization.
Also spent time looking at SDSS objects w/X-ray data, & potential targets for such. C IV absorption distorts their EW-bshift locations, but doesn't get rid of all objects with weak but unblueshifted CIV. Using Shen et al. 2011 blueshifts (relative to MgII) and EWs doesn't either, although the EWs seem less affected by absorption.
If A Planet Died, Would We Notice?
Would the impact of a planet on its host star yield a noticeable brightening if it happened to occur on the side of the star facing you?
First, can a planet impact its host star? Yes, if it is solid and more than twice as dense as the star. So only the cores, not the gaseous envelopes, of hot Jupiters are likely to impact their host stars (the envelopes will be tidally stripped first). If the planet is molten then some or all if it might be tidally stripped before impact. But as long as the stripped material stays high density it should produce the same luminosity from shocked gas on the star's surface, just more spread out over time, as the tidally stripped material will be spread out before and behind the planet in its orbit.
A way to estimate the impact luminosity is to take a spherical planet of a certain density and radius R_p, give it in a Keplerian azimuthal velocity at the photosphere of a star of radius R_s and temperature T_eff, and some radial velocity. Treating the stellar photosphere as a uniform-density slab of gas, work out the post-shock temperature of the obliquely shocked gas and the timescale t for the planet to move its own diameter into the star as its azimuthal velocity slows. (I am assuming that the tau=1 distance in the stellar atmosphere is << R_p). The radiating area of the shocked gas is roughly A=2*R_p*v_phi*t (for v_phi*t < R_s), and the fractional luminosity increase from the shock-heated gas is dL=[A/(pi*R_s^2)]*[(T_shock^4/T_eff^4)-1]. Taking a maximal case of A=2*R_p*R_s, dL~(R_p/R_s)*(T_shock^4/T_eff^4) where I've assumed T_shock >> T_eff. For Earth, R_p/R_s=0.01, so the effect can be large in principle. Even if you scale back and assume A ~ R_p^2, the dependence on the fourth power of the temperature means it might be a big flash.
Next step: refine the analysis. Suppose that the planet has sunk beyond sight by the time it has lost a fraction X of its original momentum (assuming v_phi >> v_rad, then it has slowed from v_phi to (1-X)v_phi). After that time t an energy (M_p/2)*(Xv_phi)^2 has been converted into heat. Thermal energy E_th deposited by planet is 3/2 n V k_B (T_shock-T_eff) where n is pre-shock density at stellar surface and V is volume swept out by planet before it is too deep in the Sun to be seen (I am taking this to be the point at which the planet's center is at R=R_s-R_p): V = 1/2 \pi R_p^2 v_phi(1-X/2) t, so E_th = 3(1-X/2)/4 n \pi R_p^2 v_phi t k_B (T_shock-T_eff).
Equating the lost kinetic energy E_k to the gained thermal energy,
T_shock-T_eff = M_p X^2 v_phi^2 * 2 / (1-X/2)*2 n \pi R_p^2 v_phi t k_B, or roughly
T_shock-T_eff = M_p X^2 v_phi / \pi k_B n R_p^2 t, which is ~4x low for X~1.
For a Keplerian orbit at the stellar surface, v_phi=sqrt(GM_s/R_s). In that case:
T_shock-T_eff \propto M_p M_s^1/2 X^2 / R_s^1/2 R_p^2 n t.
The timescale for shocked gas to radiatively cool from T_shock to T_eff is the ratio of the deposited thermal energy to the radiative flux (~ A \sigma_SB T_shock^4):
t_cool \propto (\pi/2) n R_p^2 v_phi t k_B dT / 2 R_p v_phi t \sigma_SB T_shock^4
t_cool \propto (\pi/4) n R_p k_B dT / \sigma_SB T_shock^4 \propto R_p/T_shock^3 for T_shock >> T_eff. Ignoring conduction overestimates the length of the luminous phase. The conduction timescale depends on T_shock-T_eff, so conduction will hasten the initial dropoff in luminosity but yield a longer tail at slightly elevated luminosity.
So with E_k \propto M_p X^2 M_s / R_s (assume a Keplerian v_phi) and
t_cool \propto R_p^7 R_s^3/2 n^3 t^3 / M_p^3 M_s^3/2 X^6, the peak luminosity will be roughly E_k/t_cool, or L_peak \propto M_p^4 v_phi^5/2 X^8 / R_p^7 n^3 t^3. The more massive the planet, the brighter the flash. The faster the planet is orbiting on impact, the brighter the flash. The more momentum is dumped before the planet sinks beyond sight, the brighter the flash. The smaller the planet (at fixed mass), the brighter the flash (the same momentum is dumped into a smaller volume of the star). The shorter the timescale over which momentum/energy is transferred, the brighter the flash. (For "brighter" above read "more luminous".)
The only remaining free parameters are t and X. We need two equations involving them to eliminate them; the first is momentum conservation. The planet's initial momentum equals the total momentum of planet plus stellar gas at the point where the planet disappears from sight (the stellar gas is pushed aside, but immediately after impact has velocity ~v_phi): M_p v_phi = (M_p + mu_s n V) X v_phi
where mu_s is the mean mass per particle in the star's atmosphere and the star's rotational velocity is ignored. This becomes a quadratic equation for X which involves t: M_p = (M_p + mu_s n \pi R_p^2 \sqrt{GM_s/R_s} (1-X/2) t / 2) X.
The second equation comes from approximating the planet's trajectory as an elliptical orbit with apoapsis at R_s and velocity v_ap=(1-X/2)sqrt(GM_s/R_s) at that apoapsis. Those two parameters determine the eccentricity e:
v_ap=\sqrt{(1-e)GM_s/R_s} so (1-X/2)^2 = (1-e). Approximate t as twice the time for an object in such an elliptical orbit to move from R=R_s to R=R_s-R_p.
Given an initial guess for X, that time can be computed from equal areas in equal times + equations for the arc length and circumference of an ellipse of known e and apoapsis.
Once t is found, it can be plugged into the quadratic to yield a new value for X. The process can be iterated until (hopefully) it converges.
Knowing t and X should give you the absolute values and scalings of t_cool and L_peak, dependent only on R_p, M_p, R_s, M_s, n, mu_s, T_eff. One can also find the peak magnitude increase from -2.5*log10[(A/\piR_s^2)(T_shock/T_eff)^4]. However, some of those dependences will be non-analytic, subsumed in the estimation of t. (Complicated analytic approximations for the arc length and circumference of ellipses do exist, so complicated analytic approximations for t_cool and L_peak could be given. But my estimation of L_peak=E_th/t_cool is rather crude, so before giving complicated expressions I would improve the existing analysis. E.g. by allowing for non-negligible radial velocity [elliptical orbit from the start].)
L_peak will also have an inclination angle correction: the shocked gas will emit isotropically, but its projected area will depend on its location on the side of the stellar surface facing you. If the planet/stellar atmosphere density contrast is large enough that the length of the strip of the star's surface affected by the planet is >~ R_p, the inclination correction will get complicated.
[Possibly to be continued at some point when/if I feel like working out the numbers for an Earth analogue impacting a G2V star.]
First, can a planet impact its host star? Yes, if it is solid and more than twice as dense as the star. So only the cores, not the gaseous envelopes, of hot Jupiters are likely to impact their host stars (the envelopes will be tidally stripped first). If the planet is molten then some or all if it might be tidally stripped before impact. But as long as the stripped material stays high density it should produce the same luminosity from shocked gas on the star's surface, just more spread out over time, as the tidally stripped material will be spread out before and behind the planet in its orbit.
A way to estimate the impact luminosity is to take a spherical planet of a certain density and radius R_p, give it in a Keplerian azimuthal velocity at the photosphere of a star of radius R_s and temperature T_eff, and some radial velocity. Treating the stellar photosphere as a uniform-density slab of gas, work out the post-shock temperature of the obliquely shocked gas and the timescale t for the planet to move its own diameter into the star as its azimuthal velocity slows. (I am assuming that the tau=1 distance in the stellar atmosphere is << R_p). The radiating area of the shocked gas is roughly A=2*R_p*v_phi*t (for v_phi*t < R_s), and the fractional luminosity increase from the shock-heated gas is dL=[A/(pi*R_s^2)]*[(T_shock^4/T_eff^4)-1]. Taking a maximal case of A=2*R_p*R_s, dL~(R_p/R_s)*(T_shock^4/T_eff^4) where I've assumed T_shock >> T_eff. For Earth, R_p/R_s=0.01, so the effect can be large in principle. Even if you scale back and assume A ~ R_p^2, the dependence on the fourth power of the temperature means it might be a big flash.
Next step: refine the analysis. Suppose that the planet has sunk beyond sight by the time it has lost a fraction X of its original momentum (assuming v_phi >> v_rad, then it has slowed from v_phi to (1-X)v_phi). After that time t an energy (M_p/2)*(Xv_phi)^2 has been converted into heat. Thermal energy E_th deposited by planet is 3/2 n V k_B (T_shock-T_eff) where n is pre-shock density at stellar surface and V is volume swept out by planet before it is too deep in the Sun to be seen (I am taking this to be the point at which the planet's center is at R=R_s-R_p): V = 1/2 \pi R_p^2 v_phi(1-X/2) t, so E_th = 3(1-X/2)/4 n \pi R_p^2 v_phi t k_B (T_shock-T_eff).
Equating the lost kinetic energy E_k to the gained thermal energy,
T_shock-T_eff = M_p X^2 v_phi^2 * 2 / (1-X/2)*2 n \pi R_p^2 v_phi t k_B, or roughly
T_shock-T_eff = M_p X^2 v_phi / \pi k_B n R_p^2 t, which is ~4x low for X~1.
For a Keplerian orbit at the stellar surface, v_phi=sqrt(GM_s/R_s). In that case:
T_shock-T_eff \propto M_p M_s^1/2 X^2 / R_s^1/2 R_p^2 n t.
The timescale for shocked gas to radiatively cool from T_shock to T_eff is the ratio of the deposited thermal energy to the radiative flux (~ A \sigma_SB T_shock^4):
t_cool \propto (\pi/2) n R_p^2 v_phi t k_B dT / 2 R_p v_phi t \sigma_SB T_shock^4
t_cool \propto (\pi/4) n R_p k_B dT / \sigma_SB T_shock^4 \propto R_p/T_shock^3 for T_shock >> T_eff. Ignoring conduction overestimates the length of the luminous phase. The conduction timescale depends on T_shock-T_eff, so conduction will hasten the initial dropoff in luminosity but yield a longer tail at slightly elevated luminosity.
So with E_k \propto M_p X^2 M_s / R_s (assume a Keplerian v_phi) and
t_cool \propto R_p^7 R_s^3/2 n^3 t^3 / M_p^3 M_s^3/2 X^6, the peak luminosity will be roughly E_k/t_cool, or L_peak \propto M_p^4 v_phi^5/2 X^8 / R_p^7 n^3 t^3. The more massive the planet, the brighter the flash. The faster the planet is orbiting on impact, the brighter the flash. The more momentum is dumped before the planet sinks beyond sight, the brighter the flash. The smaller the planet (at fixed mass), the brighter the flash (the same momentum is dumped into a smaller volume of the star). The shorter the timescale over which momentum/energy is transferred, the brighter the flash. (For "brighter" above read "more luminous".)
The only remaining free parameters are t and X. We need two equations involving them to eliminate them; the first is momentum conservation. The planet's initial momentum equals the total momentum of planet plus stellar gas at the point where the planet disappears from sight (the stellar gas is pushed aside, but immediately after impact has velocity ~v_phi): M_p v_phi = (M_p + mu_s n V) X v_phi
where mu_s is the mean mass per particle in the star's atmosphere and the star's rotational velocity is ignored. This becomes a quadratic equation for X which involves t: M_p = (M_p + mu_s n \pi R_p^2 \sqrt{GM_s/R_s} (1-X/2) t / 2) X.
The second equation comes from approximating the planet's trajectory as an elliptical orbit with apoapsis at R_s and velocity v_ap=(1-X/2)sqrt(GM_s/R_s) at that apoapsis. Those two parameters determine the eccentricity e:
v_ap=\sqrt{(1-e)GM_s/R_s} so (1-X/2)^2 = (1-e). Approximate t as twice the time for an object in such an elliptical orbit to move from R=R_s to R=R_s-R_p.
Given an initial guess for X, that time can be computed from equal areas in equal times + equations for the arc length and circumference of an ellipse of known e and apoapsis.
Once t is found, it can be plugged into the quadratic to yield a new value for X. The process can be iterated until (hopefully) it converges.
Knowing t and X should give you the absolute values and scalings of t_cool and L_peak, dependent only on R_p, M_p, R_s, M_s, n, mu_s, T_eff. One can also find the peak magnitude increase from -2.5*log10[(A/\piR_s^2)(T_shock/T_eff)^4]. However, some of those dependences will be non-analytic, subsumed in the estimation of t. (Complicated analytic approximations for the arc length and circumference of ellipses do exist, so complicated analytic approximations for t_cool and L_peak could be given. But my estimation of L_peak=E_th/t_cool is rather crude, so before giving complicated expressions I would improve the existing analysis. E.g. by allowing for non-negligible radial velocity [elliptical orbit from the start].)
L_peak will also have an inclination angle correction: the shocked gas will emit isotropically, but its projected area will depend on its location on the side of the stellar surface facing you. If the planet/stellar atmosphere density contrast is large enough that the length of the strip of the star's surface affected by the planet is >~ R_p, the inclination correction will get complicated.
[Possibly to be continued at some point when/if I feel like working out the numbers for an Earth analogue impacting a G2V star.]
Craters on Neutron Stars
Productive tea this morning! Productive in the sense of coming up with lots of interesting questions I don't have time to answer.
Spurred by Shri Kulkarni's colloquium on the Palomar Transient Factory yesterday, I wondered if anyone has estimated the signature of a 'death spiral' of a hot Jupiter/Neptune/(super-)Earth into its parent star. Apparently it is one idea for explaining luminous red novae: a hot Jupiter entering a giant star's atmosphere might heat up the atmosphere and create an artificial supergiant. Cool, and we know there are white dwarfs with metal in their atmospheres from disrupted asteroids. So could you detect an asteroid impact on a white dwarf? How about a neutron star? In fact, white dwarfs are fluid/gaseous, but neutron stars have a stiff equation of state... so could you get craters on neutron stars?
Spurred by Shri Kulkarni's colloquium on the Palomar Transient Factory yesterday, I wondered if anyone has estimated the signature of a 'death spiral' of a hot Jupiter/Neptune/(super-)Earth into its parent star. Apparently it is one idea for explaining luminous red novae: a hot Jupiter entering a giant star's atmosphere might heat up the atmosphere and create an artificial supergiant. Cool, and we know there are white dwarfs with metal in their atmospheres from disrupted asteroids. So could you detect an asteroid impact on a white dwarf? How about a neutron star? In fact, white dwarfs are fluid/gaseous, but neutron stars have a stiff equation of state... so could you get craters on neutron stars?
Tuesday, March 8, 2011
Sitting and Thinking
Friday: Looked for PHL 1811 analogs without C IV blueshifts; hard to find! Skyped with Rafiee.
Monday: Skyped with Chajet, discussion of Fine et al. style study of the dispersion in CIV linewidths due to inclination. Looked at spectra of some quasars with X-ray data but without C IV absorption. Started thinking about echo mapping of disk winds.
Tuesday: Responded to email about BAL variability at last. Skyped with Rogerson; proper weighting & treatment of paired-sightline MgII EW measurements appears ready to go. Thought more about echo mapping of disk winds and along the way thought of a minor correction we should make to our disk wind emission calculations. Nice to have the time to sit and think and follow where the thoughts go.
Monday: Skyped with Chajet, discussion of Fine et al. style study of the dispersion in CIV linewidths due to inclination. Looked at spectra of some quasars with X-ray data but without C IV absorption. Started thinking about echo mapping of disk winds.
Tuesday: Responded to email about BAL variability at last. Skyped with Rogerson; proper weighting & treatment of paired-sightline MgII EW measurements appears ready to go. Thought more about echo mapping of disk winds and along the way thought of a minor correction we should make to our disk wind emission calculations. Nice to have the time to sit and think and follow where the thoughts go.
Thursday, March 3, 2011
The Title Goes Here
Finished review of Rafiee & Hall revised BH mass catalog paper. Finished second-pass look at PHL 1811 analog candidates & their blueshifts and absorption line properties. More going through literature. Bounced an email I shouldn't have. Looking at spectra of weak-lined, low-blueshift quasars.
Wednesday, March 2, 2011
It seemed like I did more than this today
Skype with Rogerson, Rafiee today. Quasar club. Computed blueshifts for new PHL 1811 analog candidates, and catalogued absorption redshifts. Emailed Richards about possible Chandra proposal. Began review of revised BH mass catalog paper.
Unification, Part II
Tuesday was mostly spent writing up comments on the referee's response to the PHL 1811 analogs paper, including outlining my idea for unifying them with the broader population of weak-lined quasars. Also thought and commented a bit about the X-ray C IV followup paper of Richards et al.
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